Finite Group Databasebeta

← #33293020

Subgroups — #33293020

Order 18688.

2432 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989179C211yesmaximal, characteristic, complemented
2C2×#17989096C211yesmaximal, characteristic, complemented
3#22618224C211yesmaximal, characteristic, complemented
4#22618219C211yesmaximal, characteristic, complemented
5#22616632C211yesmaximal, characteristic, complemented
6#22616617C211yesmaximal, characteristic, complemented
7#22616587C211yesmaximal, characteristic, complemented
8#22616572C211yesmaximal, characteristic, complemented
9#22616542C211yesmaximal, characteristic, complemented
10#22616503C211yesmaximal, characteristic, complemented
11#22616493C211yesmaximal, characteristic, complemented
12#22616320C211yesmaximal, characteristic, complemented
13#22616302C211yesmaximal, characteristic, complemented
14#22616295C211yesmaximal, characteristic, complemented
15#22616281C211yesmaximal, characteristic, complemented
16#22616278C211yesmaximal, characteristic, complemented
17#22616269C211yesmaximal, characteristic, complemented
18#22616269C211yesmaximal, characteristic, complemented
19#22616254C211yesmaximal, characteristic, complemented
20#22616251C211yesmaximal, characteristic, complemented
21#22615851C211yesmaximal, characteristic, complemented
22#22615772C211yesmaximal, characteristic, complemented
23#22615623C211yesmaximal, characteristic, complemented
24#22615558C211yesmaximal, characteristic, complemented
25#22615522C211yesmaximal, characteristic, complemented
26#22615518C211yesmaximal, characteristic, complemented
27#22615280C211yesmaximal, characteristic, complemented
28#22615131C211yesmaximal, characteristic, complemented
29#22613277C211yesmaximal, characteristic, complemented
30#22613268C211yesmaximal, characteristic, complemented
31C73×#2319C211yesmaximal, characteristic, complemented
32C22×#11924028C2211yescharacteristic
33C23×C4×D73C2211yescharacteristic
34#17989179—28no—
35C2×#14556585C2211yescharacteristic, complemented
36C2×#14556584C2211yescharacteristic
37C2×#14556583C2211yescharacteristic, complemented
38C2×#14556581C2211yescharacteristic, complemented
39#17989096—28no—
40C2×#14556576C2211yescharacteristic
41C2×#14556575C2211yescharacteristic
42C2×#14556575C2211yescharacteristic
43C2×#14556575C2211yescharacteristic, complemented
44C2×#14556575C2211yescharacteristic, complemented
45C2×#14556574C2211yescharacteristic
46C2×#14556573C2211yescharacteristic
47C2×#14556573C2211yescharacteristic
48C2×#14556572C2211yescharacteristic
49C2×#14556571C2211yescharacteristic
50C2×#14556571C2211yescharacteristic
51C2×#14556571C2211yescharacteristic, complemented
52C2×#14556570C2211yescharacteristic
53C2×#14556569C2211yescharacteristic
54C2×#14556569C2211yescharacteristic, complemented
55C2×#14556568C2211yescharacteristic
56C2×#14556568C2211yescharacteristic, complemented
57C2×#14556566C2211yescharacteristic
58C2×#14556564C2211yescharacteristic
59C2×#14556563C2211yescharacteristic
60C2×#14556563C2211yescharacteristic
61C2×#14556561C2211yescharacteristic
62C2×#14556561C2211yescharacteristic
63C2×#14556559C2211yescharacteristic
64C2×C4×D292C2211yescharacteristic
65C2×C4×C22⋊D73C2211yescharacteristic
66C2×C4×C22⋊D73C2211yescharacteristic
67C2×C4×C22⋊D73C2211yescharacteristic, complemented
68C2×#14556548C2211yescharacteristic
69C22×#11924007C2211yescharacteristic, complemented
70#17988527C2211yescharacteristic, complemented
71#17988524C2211yescharacteristic
72#17988519C2211yescharacteristic, complemented
73#17988519C2211yescharacteristic, complemented
74#17988519C2211yescharacteristic, complemented
75#17988517C2211yescharacteristic, complemented
76#17988517C2211yescharacteristic, complemented
77#17988517C2211yescharacteristic, complemented
78#17988517C2211yescharacteristic, complemented
79#17988514C2211yescharacteristic
80#17988514C2211yescharacteristic, complemented
81#17988514C2211yescharacteristic, complemented
82#17988512C2211yescharacteristic
83#17988512C2211yescharacteristic
84#17988512C2211yescharacteristic
85#17988512C2211yescharacteristic, complemented
86#17988509C2211yescharacteristic
87#17988509C2211yescharacteristic
88#17988509C2211yescharacteristic
89#17988509C2211yescharacteristic
90#17988509C2211yescharacteristic
91#17988509C2211yescharacteristic, complemented
92#17988509C2211yescharacteristic, complemented
93#17988509C2211yescharacteristic, complemented
94#17988509C2211yescharacteristic, complemented
95#17988509C2211yescharacteristic, complemented
96#17988508C2211yescharacteristic, complemented
97#17988508C2211yescharacteristic, complemented
98#17988508C2211yescharacteristic, complemented
99#17988505C2211yescharacteristic
100#17988505C2211yescharacteristic
101#17988505C2211yescharacteristic
102#17988504C2211yescharacteristic
103#17988504C2211yescharacteristic, complemented
104#17988503C2211yescharacteristic
105#17988503C2211yescharacteristic
106#17988503C2211yescharacteristic
107#17988503C2211yescharacteristic
108#17988503C2211yescharacteristic
109#17988503C2211yescharacteristic
110#17988503C2211yescharacteristic, complemented
111#17988503C2211yescharacteristic, complemented
112#17988500C2211yescharacteristic, complemented
113#17988497C2211yescharacteristic
114#17988496C2211yescharacteristic
115#17988496C2211yescharacteristic
116#17988496C2211yescharacteristic
117#17988496C2211yescharacteristic, complemented
118#17988492C2211yescharacteristic, complemented
119#17988489C2211yescharacteristic
120#17988489C2211yescharacteristic
121#17988489C2211yescharacteristic
122#17988489C2211yescharacteristic
123#17988489C2211yescharacteristic, complemented
124#17988488C2211yescharacteristic
125#17988485C2211yescharacteristic, complemented
126#17988485C2211yescharacteristic, complemented
127#17988485C2211yescharacteristic, complemented
128#17988479C2211yescharacteristic
129#17988479C2211yescharacteristic, complemented
130#17988478C2211yescharacteristic
131#17988478C2211yescharacteristic
132#17988478C2211yescharacteristic
133#17988478C2211yescharacteristic
134#17988478C2211yescharacteristic, complemented
135#17988478C2211yescharacteristic, complemented
136#17988472C2211yescharacteristic, complemented
137#17988472C2211yescharacteristic, complemented
138#17988472C2211yescharacteristic, complemented
139#17988472C2211yescharacteristic, complemented
140#17988465C2211yescharacteristic
141#17988465C2211yescharacteristic
142#17988465C2211yescharacteristic
143#17988465C2211yescharacteristic
144#17988465C2211yescharacteristic
145#17988465C2211yescharacteristic, complemented
146#17988464C2211yescharacteristic
147#17988464C2211yescharacteristic
148#17988464C2211yescharacteristic
149#17988464C2211yescharacteristic, complemented
150#17988462C2211yescharacteristic
151#17988462C2211yescharacteristic
152#17988462C2211yescharacteristic, complemented
153#17988462C2211yescharacteristic, complemented
154#17988461C2211yescharacteristic
155#17988461C2211yescharacteristic
156#17988461C2211yescharacteristic
157#17988461C2211yescharacteristic
158#17988461C2211yescharacteristic
159#17988461C2211yescharacteristic
160#17988461C2211yescharacteristic
161#17988461C2211yescharacteristic
162#17988461C2211yescharacteristic, complemented
163#17988461C2211yescharacteristic, complemented
164#17988461C2211yescharacteristic, complemented
165#17988461C2211yescharacteristic, complemented
166#17988457C2211yescharacteristic, complemented
167#17988453C2211yescharacteristic, complemented
168#17988448C2211yescharacteristic
169#17988444C2211yescharacteristic
170#17988444C2211yescharacteristic
171#17988442C2211yescharacteristic
172#17988442C2211yescharacteristic
173#17988442C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175#390×C73C2211yescharacteristic
176#390×C73C2211yescharacteristic
177#389×C73C2211yescharacteristic, complemented
178#389×C73C2211yescharacteristic, complemented
179#388×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic, complemented
182#388×C73C2211yescharacteristic, complemented
183#381×C73C2211yescharacteristic
184#381×C73C2211yescharacteristic, complemented
185#380×C73C2211yescharacteristic
186#380×C73C2211yescharacteristic, complemented
187C4×C4⋊C4×C73C2211yescharacteristic, complemented
188#376×C73C2211yescharacteristic, complemented
189C24×D73C2311yescharacteristic
190C2×#11924028—24no—
191C2×#11924028—42no—
192C2×#11924028—42no—
193C22×Dic146C2311yescharacteristic
194C22×Dic146C2311yescharacteristic
195C22×D292C2311yescharacteristic
196C22×D292C2311yescharacteristic
197C22×D292C2311yescharacteristic
198C22×D292C2311yescharacteristic
199C22×D292C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C22×C22⋊D73C2311yescharacteristic
204C22×C22⋊D73C2311yescharacteristic
205C22×C22⋊D73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C23×Dic73C2311yescharacteristic
208C23×Dic73C2311yescharacteristic
209C22×C4×D73—24no—
210C22×C4×D73—42no—
211C22×C4×D73—42no—
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214C22×C4×D73C2311yescharacteristic
215C22×C4×D73C2311yescharacteristic
216C22×C4×D73C2311yescharacteristic
217C22×C4×D73C2311yescharacteristic
218#14556585—24no—
219#14556584—24no—
220#14556583—24no—
221#14556581—24no—
222#14556576—24no—
223#14556575—24no—
224#14556575—42no—
225#14556575—42no—
226#14556575—42no—
227#14556574—24no—
228#14556573—24no—
229#14556573—24no—
230#14556572—24no—
231#14556571—42no—
232#14556571—42no—
233#14556571—42no—
234#14556570—24no—
235#14556569—24no—
236#14556569—24no—
237#14556568—24no—
238#14556568—24no—
239#14556566—42no—
240#14556564—24no—
241#14556563—24no—
242#14556563—24no—
243#14556561—24no—
244#14556561—42no—
245#14556559—24no—
246C4×D292—24no—
247C4×C22⋊D73—24no—
248C4×C22⋊D73—24no—
249C4×C22⋊D73—24no—
250#14556548—24no—
251C2×C4⋊Dic73C2311yescharacteristic
252C2×C4⋊Dic73C2311yescharacteristic
253C2×C4⋊Dic73C2311yescharacteristic
254C2×C4⋊Dic73C2311yescharacteristic
255C2×C4⋊Dic73C2311yescharacteristic
256C2×C4⋊Dic73C2311yescharacteristic
257C2×C4⋊Dic73C2311yescharacteristic
258C2×C4⋊Dic73C2311yescharacteristic
259C2×C4⋊Dic73C2311yescharacteristic
260C2×C4⋊Dic73C2311yescharacteristic
261C2×C4⋊Dic73C2311yescharacteristic
262C2×C4⋊Dic73C2311yescharacteristic
263C2×C4⋊Dic73C2311yescharacteristic
264C2×C4⋊Dic73C2311yescharacteristic
265C2×C4⋊Dic73C2311yescharacteristic
266C2×C4⋊Dic73C2311yescharacteristic
267C2×C4⋊Dic73C2311yescharacteristic
268C2×#11924007—24no—
269C2×#11924007C2311yescharacteristic
270C2×#11924007C2311yescharacteristic
271C2×#11924007C2311yescharacteristic
272C2×#11924007C2311yescharacteristic
273C2×#11924007C2311yescharacteristic
274C2×#11924007C2311yescharacteristic
275C2×#11924007C2311yescharacteristic
276C2×#11924007C2311yescharacteristic
277C2×#11924007C2311yescharacteristic
278C2×#11924007C2311yescharacteristic
279C2×#11924007C2311yescharacteristic
280C2×#11924007C2311yescharacteristic
281C2×#11924007C2311yescharacteristic
282C2×#11924007C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×C22⋊Dic73C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×#11924005C2311yescharacteristic
302C2×#11924005C2311yescharacteristic
303C2×#11924005C2311yescharacteristic
304C2×#11924005C2311yescharacteristic
305C2×#11924005C2311yescharacteristic
306C2×#11924005C2311yescharacteristic
307C2×#11924005C2311yescharacteristic
308C2×#11924005C2311yescharacteristic
309C2×#11924005C2311yescharacteristic
310C2×#11924005C2311yescharacteristic
311C2×#11924005C2311yescharacteristic
312C2×#11924005C2311yescharacteristic
313C2×#11924005C2311yescharacteristic
314C2×#11924005C2311yescharacteristic
315C2×#11924005C2311yescharacteristic
316C2×#11924005C2311yescharacteristic
317C2×#11924005C2311yescharacteristic
318C2×#11924005C2311yescharacteristic
319C2×#11924005C2311yescharacteristic
320C2×#11924005C2311yescharacteristic
321C2×#11924005C2311yescharacteristic
322C2×#11924005C2311yescharacteristic
323C2×#11924005C2311yescharacteristic
324C2×#11924005C2311yescharacteristic
325C2×C4×Dic73C2311yescharacteristic
326C2×C4×Dic73C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348#14556498C2311yescharacteristic
349C22×D4×C73C2311yescharacteristic
350C23×C4×C73C2311yescharacteristic
351C23×C4×C73C2311yescharacteristic
352C4×D4×C73D418yescomplemented
353C2×C4⋊C4×C73C2311yescharacteristic
354C2×C4⋊C4×C73C2311yescharacteristic
355C2×C4⋊C4×C73C2311yescharacteristic
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C4⋊C4×C73C2311yescharacteristic
358C2×C4⋊C4×C73C2311yescharacteristic
359C2×C4⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C22⋊C4×C73C2311yescharacteristic
370C2×C42×C73C2311yescharacteristic
371C2×C42×C73C2311yescharacteristic
372C2×C42×C73C2311yescharacteristic
373C2×C42×C73C2311yescharacteristic
374C2×C42×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376#95×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385C23×D73—22no—
386C23×D73—22no—
387C23×D73—22no—
388C23×D73—41no—
389C23×D73—41no—
390C23×D73—41no—
391C23×D73—41no—
392C23×D73C2411yescharacteristic
393C23×D73C2411yescharacteristic
394C23×D73C2411yescharacteristic
395C23×D73C2411yescharacteristic
396#11924028—416no—
397C2×Dic146—22no—
398C2×Dic146—22no—
399C2×Dic146—22no—
400C2×Dic146—41no—
401C2×Dic146—41no—
402C2×Dic146—41no—
403C2×D292—22no—
404C2×D292—22no—
405C2×D292—22no—
406C2×D292—22no—
407C2×D292—22no—
408C2×D292—22no—
409C2×D292—41no—
410C2×D292—41no—
411C2×D292—41no—
412C2×D292—41no—
413C2×D292—41no—
414C2×D292—41no—
415C2×D292—41no—
416C2×D292—41no—
417C2×D292—41no—
418C2×C22⋊D73—22no—
419C2×C22⋊D73—22no—
420C2×C22⋊D73—22no—
421C2×C22⋊D73—22no—
422C2×C22⋊D73—22no—
423C2×C22⋊D73—22no—
424C2×C22⋊D73—22no—
425C2×C22⋊D73—22no—
426C2×C22⋊D73—22no—
427C2×C22⋊D73—41no—
428C2×C22⋊D73—41no—
429C2×C22⋊D73—41no—
430C2×C22⋊D73—41no—
431C2×C22⋊D73—41no—
432C2×C22⋊D73—41no—
433C2×C22⋊D73—41no—
434C2×C22⋊D73—41no—
435C2×C22⋊D73—41no—
436C22×Dic73—22no—
437C22×Dic73—22no—
438C22×Dic73—22no—
439C22×Dic73—22no—
440C22×Dic73—41no—
441C22×Dic73—41no—
442C22×Dic73—41no—
443C22×Dic73—41no—
444C22×Dic73—41no—
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C22×Dic73C2411yescharacteristic
451C22×Dic73C2411yescharacteristic
452C22×Dic73C2411yescharacteristic
453C22×Dic73C2411yescharacteristic
454C22×Dic73C2411yescharacteristic
455C22×Dic73C2411yescharacteristic
456C22×Dic73C2411yescharacteristic
457C2×C4×D73—22no—
458C2×C4×D73—22no—
459C2×C4×D73—22no—
460C2×C4×D73—22no—
461C2×C4×D73—22no—
462C2×C4×D73—22no—
463C2×C4×D73—22no—
464C2×C4×D73—22no—
465C2×C4×D73—22no—
466C2×C4×D73—22no—
467C2×C4×D73—416no—
468C2×C4×D73—41no—
469C2×C4×D73—41no—
470C2×C4×D73—41no—
471C2×C4×D73—41no—
472C2×C4×D73—41no—
473C2×C4×D73—41no—
474C2×C4×D73—41no—
475C2×C4×D73—41no—
476C4⋊Dic73—22no—
477C4⋊Dic73—22no—
478C4⋊Dic73—22no—
479C4⋊Dic73—22no—
480C4⋊Dic73—22no—
481C4⋊Dic73—22no—
482C4⋊Dic73—22no—
483C4⋊Dic73—41no—
484C4⋊Dic73—41no—
485C4⋊Dic73—41no—
486C4⋊Dic73—41no—
487C4⋊Dic73—41no—
488C4⋊Dic73—41no—
489C4⋊Dic73—41no—
490C4⋊Dic73—41no—
491C4⋊Dic73—41no—
492C4⋊Dic73—41no—
493#11924007—22no—
494#11924007—22no—
495#11924007—22no—
496#11924007—22no—
497#11924007—22no—
498#11924007—22no—
499#11924007—22no—
500#11924007—22no—
501#11924007—22no—
502#11924007—22no—
503#11924007—22no—
504#11924007—22no—
505#11924007—22no—
506#11924007—22no—
507C22⋊Dic73—22no—
508C22⋊Dic73—22no—
509C22⋊Dic73—22no—
510C22⋊Dic73—22no—
511C22⋊Dic73—22no—
512C22⋊Dic73—22no—
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—22no—
522#11924005—22no—
523#11924005—22no—
524#11924005—22no—
525#11924005—22no—
526#11924005—22no—
527#11924005—22no—
528#11924005—41no—
529#11924005—41no—
530#11924005—41no—
531#11924005—41no—
532#11924005—41no—
533#11924005—41no—
534#11924005—41no—
535#11924005—41no—
536#11924005—41no—
537#11924005—41no—
538#11924005—41no—
539#11924005—41no—
540#11924005—41no—
541#11924005—41no—
542#11924005—41no—
543#11924005—41no—
544#11924005—41no—
545#11924005—41no—
546#11924005—41no—
547#11924005—41no—
548#11924005—41no—
549C4×Dic73—22no—
550C4×Dic73—22no—
551C24×C73C2411yescharacteristic
552C24×C73C2411yescharacteristic
553C2×D4×C73—41no—
554C2×D4×C73—41no—
555C2×D4×C73C2×D414yes—
556C22×C4×C73—41no—
557C22×C4×C73—41no—
558C22×C4×C73—41no—
559C22×C4×C73—41no—
560C22×C4×C73C2×D414yes—
561C22×C4×C73C2×D414yes—
562C22×C4×C73C2411yescharacteristic
563C22×C4×C73C2411yescharacteristic
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C22×C4×C73C2411yescharacteristic
571C22×C4×C73C2411yescharacteristic
572C22×C4×C73C2411yescharacteristic
573C22×C4×C73C2411yescharacteristic
574C22×C4×C73C2411yescharacteristic
575C4⋊C4×C73—41no—
576C4⋊C4×C73—41no—
577C4⋊C4×C73—41no—
578C4⋊C4×C73—41no—
579C4⋊C4×C73—41no—
580C4⋊C4×C73—41no—
581C4⋊C4×C73C2×D414yes—
582C22⋊C4×C73—41no—
583C22⋊C4×C73—41no—
584C22⋊C4×C73—41no—
585C22⋊C4×C73—41no—
586C22⋊C4×C73—41no—
587C22⋊C4×C73—41no—
588C22⋊C4×C73—41no—
589C22⋊C4×C73—41no—
590C22⋊C4×C73C2×D414yes—
591C22⋊C4×C73C2×D414yes—
592C42×C73—41no—
593C42×C73—41no—
594C42×C73—41no—
595C42×C73—41no—
596C42×C73C2×D414yes—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73—21no—
603C23×C73—21no—
604C23×C73—21no—
605C23×C73—21no—
606C23×C73—21no—
607C23×C73—21no—
608C23×C73—21no—
609C23×C73C22×D412yes—
610C23×C73C22×D412yes—
611C23×C73C2511yescharacteristic
612C22×D73—21no—
613C22×D73—21no—
614C22×D73—21no—
615C22×D73—21no—
616C22×D73—21no—
617C22×D73—21no—
618C22×D73—21no—
619C22×D73—21no—
620C22×D73—21no—
621C22×D73—21no—
622C22×D73—21no—
623C22×D73—21no—
624C22×D73—21no—
625C22×D73—21no—
626C22×D73—21no—
627C22×D73—21no—
628C22×D73—21no—
629C22×D73—21no—
630C22×D73—21no—
631C22×D73—21no—
632C22×D73—21no—
633C22×D73—21no—
634C22×D73—21no—
635C22×D73—21no—
636C22×D73—21no—
637C22×D73—21no—
638C22×D73—44no—
639C22×D73—44no—
640C22×D73—44no—
641C22×D73—44no—
642C22×D73—44no—
643C22×D73—44no—
644C22×D73—44no—
645C22×D73H(5,𝔽2)12yes—
646C22×D732−1+412yes—
647D4×C73—44no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—44no—
683C2×C4×C73—44no—
684C2×C4×C73C22×D412yes—
685C2×C4×C73C22×D412yes—
686C2×C4×C73C22×D412yes—
687C2×C4×C73C22×D412yes—
688C2×C4×C73C22×D412yes—
689C22⋊D73—44no—
690C22⋊D73—44no—
691C22⋊D73—44no—
692C22⋊D73—44no—
693C22⋊D73—44no—
694C22⋊D73—82no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—21no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—44no—
731C2×Dic73—44no—
732C2×Dic73—82no—
733C2×Dic73H(5,𝔽2)12yes—
734D292—44no—
735D292—44no—
736D292—82no—
737D292—82no—
738D292—82no—
739C4×D73—28no—
740C4×D73—44no—
741C4×D73—44no—
742C4×D73—44no—
743C4×D73—44no—
744C4×D73—82no—
745Dic146—44no—
746Dic146—82no—
747C22×C73—22no—
748C22×C73—22no—
749C22×C73—22no—
750C22×C73—22no—
751C22×C73—22no—
752C22×C73—22no—
753C22×C73—41no—
754C22×C73—41no—
755C22×C73—41no—
756C22×C73—41no—
757C22×C73—41no—
758C22×C73—41no—
759C22×C73—41no—
760C22×C73—41no—
761C22×C73C23×D411yescharacteristic
762C22×C73C2×H(5,𝔽2)11yescharacteristic
763C22×C73C2×H(5,𝔽2)11yescharacteristic
764C22×C73C2×2−1+411yescharacteristic
765C22×C73#58511yescharacteristic
766C22×C73#58511yescharacteristic
767C22×C73#58511yescharacteristic
768C2×D73—22no—
769C2×D73—22no—
770C2×D73—22no—
771C2×D73—22no—
772C2×D73—22no—
773C2×D73—22no—
774C2×D73—416no—
775C2×D73—41no—
776C2×D73—41no—
777C2×D73—41no—
778C2×D73—41no—
779C2×D73—41no—
780C2×D73—41no—
781C2×D73—41no—
782C2×D73—41no—
783C2×D73—41no—
784C2×D73—41no—
785C2×D73—41no—
786C2×D73—41no—
787C2×D73—41no—
788C2×D73—41no—
789C2×D73—41no—
790C2×D73—41no—
791C2×D73—41no—
792C2×D73—41no—
793C2×D73—41no—
794C2×D73—41no—
795C2×D73—41no—
796C2×D73—41no—
797C4×C73—22no—
798C4×C73—22no—
799C4×C73—22no—
800C4×C73—22no—
801C4×C73—22no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807C4×C73—41no—
808C4×C73—41no—
809C4×C73—41no—
810Dic73—22no—
811Dic73—41no—
812Dic73—41no—
813Dic73—41no—
814Dic73—41no—
815Dic73—41no—
816Dic73—41no—
817Dic73—41no—
818Dic73—41no—
819Dic73—41no—
820Dic73—41no—
821Dic73—41no—
822#36723—731nomaximal, Sylow
823C2×C73—42no—
824C2×C73—42no—
825C2×C73#344911yescharacteristic
826C2×C73#348411yescharacteristic
827C2×C73#348911yescharacteristic
828C2×C73#353311yescharacteristic
829C2×C73#353511yescharacteristic
830C2×C73#353911yescharacteristic
831C2×C73#354111yescharacteristic
832D73—42no—
833D73—42no—
834D73—81no—
835D73—81no—
836C2×#539—731no—
837C2×#525—731no—
838#2849—731no—
839#2848—731no—
840#2707—731no—
841#2706—731no—
842#2704—731no—
843#2703—731no—
844#2701—731no—
845#2698—731no—
846#2697—731no—
847#2685—731no—
848#2683—731no—
849#2682—731no—
850#2681—731no—
851#2681—731no—
852#2680—731no—
853#2680—731no—
854#2678—731no—
855#2678—731no—
856#2638—731no—
857#2630—731no—
858#2611—731no—
859#2603—731no—
860#2601—731no—
861#2600—731no—
862#2579—731no—
863#2566—731no—
864#2407—731no—
865#2406—731no—
866#2319D7311yescharacteristic, complemented
867C73#3672311yescharacteristic, complemented, Sylow
868C22×#41—731no—
869C24×C4—731no—
870#539—1468no—
871C2×#126—731no—
872C2×#126—731no—
873C2×#125—731no—
874C2×#125—731no—
875#525—1468no—
876C2×#123—731no—
877C2×#123—731no—
878C2×#123—731no—
879C2×#123—731no—
880C2×#123—731no—
881C2×#123—731no—
882C2×#123—731no—
883C2×#123—731no—
884C2×#123—731no—
885C2×C22⋊Q8—731no—
886C2×C22⋊Q8—731no—
887C2×C22⋊Q8—731no—
888C2×C22⋊Q8—731no—
889C2×C22⋊Q8—731no—
890C2×C22⋊Q8—731no—
891C2×C22⋊Q8—731no—
892C2×C22⋊Q8—731no—
893C2×#121—731no—
894C2×#121—731no—
895C2×#121—731no—
896C2×#121—731no—
897C2×#120—731no—
898C2×#120—731no—
899C2×#120—731no—
900C2×C4×D4—731no—
901C2×C4×D4—731no—
902C2×C4×D4—731no—
903C2×C4×D4—731no—
904C2×C4×D4C2×D7311yescharacteristic
905C2×#117—731no—
906C22×C4⋊C4—731no—
907#400—731no—
908#399—731no—
909#398—731no—
910#398—731no—
911#398—731no—
912#398—731no—
913#398—731no—
914#398—731no—
915#398—731no—
916#397—731no—
917#397—731no—
918#397—731no—
919#397—731no—
920#397—731no—
921#397—731no—
922#397—731no—
923#396—731no—
924#396—731no—
925#396—731no—
926#396—731no—
927#396—731no—
928#396—731no—
929#396—731no—
930#396—731no—
931#396—731no—
932#396—731no—
933#395—731no—
934#395—731no—
935#395—731no—
936#394—731no—
937#394—731no—
938#394—731no—
939#394—731no—
940#394—731no—
941#394—731no—
942#394—731no—
943#394—731no—
944#394—731no—
945#394—731no—
946#394—731no—
947#394—731no—
948#394—731no—
949#393—731no—
950#392—731no—
951#392—731no—
952#392—731no—
953#392—731no—
954#392—731no—
955#391—731no—
956#390—731no—
957#390—731no—
958#390—731no—
959#390—731no—
960#390—731no—
961#390—731no—
962#390C2×D7311yescharacteristic
963#390C2×D7311yescharacteristic
964#389—731no—
965#389—731no—
966#389—731no—
967#389C2×D7311yescharacteristic, complemented
968#389C2×D7311yescharacteristic, complemented
969#388—731no—
970#388—731no—
971#388—731no—
972#388—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388C2×D7311yescharacteristic
978#388C2×D7311yescharacteristic
979#388C2×D7311yescharacteristic, complemented
980#388C2×D7311yescharacteristic, complemented
981#387—731no—
982#387—731no—
983#387—731no—
984#387—731no—
985#386—731no—
986#386—731no—
987#386—731no—
988#386—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#385—731no—
996#385—731no—
997#385—731no—
998#385—731no—
999#385—731no—
1000#385—731no—
1001#385—731no—
1002#385—731no—
1003#385—731no—
1004#385—731no—
1005#385—731no—
1006#385—731no—
1007#385—731no—
1008#385—731no—
1009#385—731no—
1010#385—731no—
1011#384—731no—
1012#382—731no—
1013#381—731no—
1014#381C2×D7311yescharacteristic
1015#381C2×D7311yescharacteristic, complemented
1016#380—731no—
1017#380—731no—
1018#380C2×D7311yescharacteristic
1019#380C2×D7311yescharacteristic, complemented
1020#379—731no—
1021#379—731no—
1022#379—731no—
1023C4×C4⋊C4C2×D7311yescharacteristic, complemented
1024#376C2×D7311yescharacteristic, complemented
1025C25—731no—
1026C2×#41—2922no—
1027C2×#41—2922no—
1028C2×#41—1464no—
1029C22×Q8—731no—
1030C22×Q8—731no—
1031C22×D4—731no—
1032C22×D4—731no—
1033C22×D4—731no—
1034C22×D4—731no—
1035C22×D4—731no—
1036C22×D4—731no—
1037C22×D4—731no—
1038C22×D4—731no—
1039C22×D4—731no—
1040C22×D4—731no—
1041C22×D4—731no—
1042C22×D4C22×D7311yescharacteristic
1043C23×C4—2922no—
1044C23×C4—2922no—
1045C23×C4—731no—
1046C23×C4—731no—
1047C23×C4—731no—
1048C23×C4—731no—
1049C23×C4—731no—
1050C23×C4—731no—
1051C23×C4—731no—
1052C23×C4—731no—
1053C23×C4—731no—
1054C23×C4—1464no—
1055C23×C4C22×D7311yescharacteristic
1056C23×C4C22×D7311yescharacteristic
1057#126—1464no—
1058#126—1464no—
1059#125—1464no—
1060#125—1464no—
1061#123—2922no—
1062#123—2922no—
1063#123—2922no—
1064#123—1464no—
1065#123—1464no—
1066#123—1464no—
1067#123—1464no—
1068#123—1464no—
1069#123—1464no—
1070C22⋊Q8—2922no—
1071C22⋊Q8—2922no—
1072C22⋊Q8—2922no—
1073C22⋊Q8—1464no—
1074C22⋊Q8—1464no—
1075C22⋊Q8—1464no—
1076C22⋊Q8—1464no—
1077C22⋊Q8—1464no—
1078#121—2922no—
1079#121—1464no—
1080#121—1464no—
1081#121—1464no—
1082#120—2922no—
1083#120—1464no—
1084#120—1464no—
1085C4×D4—1464no—
1086C4×D4—1464no—
1087C4×D4—1464no—
1088C4×D4—1464no—
1089C4×D4D29218yescomplemented
1090#117—1464no—
1091C2×C4⋊C4—731no—
1092C2×C4⋊C4—731no—
1093C2×C4⋊C4—731no—
1094C2×C4⋊C4—731no—
1095C2×C4⋊C4—731no—
1096C2×C4⋊C4—731no—
1097C2×C4⋊C4—731no—
1098C2×C4⋊C4—731no—
1099C2×C4⋊C4—731no—
1100C2×C4⋊C4—731no—
1101C2×C4⋊C4—731no—
1102C2×C4⋊C4—731no—
1103C2×C4⋊C4—731no—
1104C2×C4⋊C4—731no—
1105C2×C4⋊C4—731no—
1106C2×C4⋊C4—731no—
1107C2×C4⋊C4—731no—
1108C2×C4⋊C4—731no—
1109C2×C4⋊C4—731no—
1110C2×C4⋊C4—731no—
1111C2×C4⋊C4—731no—
1112C2×C4⋊C4—731no—
1113C2×C4⋊C4—731no—
1114C2×C4⋊C4—731no—
1115C2×C4⋊C4—731no—
1116C2×C4⋊C4—731no—
1117C2×C4⋊C4—731no—
1118C2×C4⋊C4—731no—
1119C2×C4⋊C4—731no—
1120C2×C4⋊C4—731no—
1121C2×C4⋊C4—731no—
1122C2×C4⋊C4—1464no—
1123C2×C4⋊C4C22×D7311yescharacteristic
1124C2×C4⋊C4C22×D7311yescharacteristic
1125C2×C4⋊C4C22×D7311yescharacteristic
1126C2×C4⋊C4C22×D7311yescharacteristic
1127C2×C4⋊C4C22×D7311yescharacteristic
1128C2×C4⋊C4C22×D7311yescharacteristic
1129C2×C4⋊C4C22×D7311yescharacteristic
1130C2×C22⋊C4—731no—
1131C2×C22⋊C4—731no—
1132C2×C22⋊C4—731no—
1133C2×C22⋊C4—731no—
1134C2×C22⋊C4—731no—
1135C2×C22⋊C4—731no—
1136C2×C22⋊C4—731no—
1137C2×C22⋊C4—731no—
1138C2×C22⋊C4—731no—
1139C2×C22⋊C4—731no—
1140C2×C22⋊C4—731no—
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4—731no—
1171C2×C22⋊C4—731no—
1172C2×C22⋊C4C22×D7311yescharacteristic
1173C2×C22⋊C4C22×D7311yescharacteristic
1174C2×C22⋊C4C22×D7311yescharacteristic
1175C2×C22⋊C4C22×D7311yescharacteristic
1176C2×C22⋊C4C22×D7311yescharacteristic
1177C2×C22⋊C4C22×D7311yescharacteristic
1178C2×C22⋊C4C22×D7311yescharacteristic
1179C2×C22⋊C4C22×D7311yescharacteristic
1180C2×C22⋊C4C22×D7311yescharacteristic
1181C2×C22⋊C4C22×D7311yescharacteristic
1182C2×C42—731no—
1183C2×C42—731no—
1184C2×C42C22×D7311yescharacteristic
1185C2×C42C22×D7311yescharacteristic
1186C2×C42C22×D7311yescharacteristic
1187C2×C42C22×D7311yescharacteristic
1188C2×C42C22×D7311yescharacteristic
1189#95—731no—
1190#95—731no—
1191#95—731no—
1192#95—731no—
1193#95—731no—
1194#95—731no—
1195#95—731no—
1196#95—731no—
1197#95—731no—
1198#95—731no—
1199#95—731no—
1200#95—731no—
1201#95—731no—
1202#95—731no—
1203#95—731no—
1204#95—731no—
1205#95—731no—
1206#95—731no—
1207#95—731no—
1208#95—731no—
1209#95—731no—
1210#95—731no—
1211#95C22×D7311yescharacteristic
1212#95C22×D7311yescharacteristic
1213#95C22×D7311yescharacteristic
1214#95C22×D7311yescharacteristic
1215#95C22×D7311yescharacteristic
1216#95C22×D7311yescharacteristic
1217#95C22×D7311yescharacteristic
1218#95C22×D7311yescharacteristic
1219#95C22×D7311yescharacteristic
1220#95C22×D7311yescharacteristic
1221C24—2921no—
1222C24—2921no—
1223C24—2921no—
1224C24—2921no—
1225C24—731no—
1226C24—731no—
1227C24—731no—
1228C24—731no—
1229C24—1462no—
1230C24—1462no—
1231C24—1462no—
1232C24C23×D7311yescharacteristic
1233C24C23×D7311yescharacteristic
1234#41—29216no—
1235C2×Q8—2921no—
1236C2×Q8—2921no—
1237C2×Q8—2921no—
1238C2×Q8—1462no—
1239C2×Q8—1462no—
1240C2×Q8—1462no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—2921no—
1244C2×D4—2921no—
1245C2×D4—2921no—
1246C2×D4—2921no—
1247C2×D4—2921no—
1248C2×D4—2921no—
1249C2×D4—2921no—
1250C2×D4—2921no—
1251C2×D4—2921no—
1252C2×D4—2921no—
1253C2×D4—2921no—
1254C2×D4—2921no—
1255C2×D4—2921no—
1256C2×D4—2921no—
1257C2×D4—2921no—
1258C2×D4—2921no—
1259C2×D4—2921no—
1260C2×D4—2921no—
1261C2×D4—1462no—
1262C2×D4—1462no—
1263C2×D4—1462no—
1264C2×D4—1462no—
1265C2×D4—1462no—
1266C2×D4—1462no—
1267C2×D4—1462no—
1268C2×D4—1462no—
1269C2×D4—1462no—
1270C2×D4—1462no—
1271C2×D4—1462no—
1272C2×D4—1462no—
1273C2×D4—1462no—
1274C2×D4—1462no—
1275C2×D4—1462no—
1276C2×D4C2×D29214yes—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—2921no—
1282C22×C4—2921no—
1283C22×C4—2921no—
1284C22×C4—2921no—
1285C22×C4—2921no—
1286C22×C4—2921no—
1287C22×C4—2921no—
1288C22×C4—2921no—
1289C22×C4—29216no—
1290C22×C4—2921no—
1291C22×C4—2921no—
1292C22×C4—2921no—
1293C22×C4—2921no—
1294C22×C4—2921no—
1295C22×C4—731no—
1296C22×C4—731no—
1297C22×C4—731no—
1298C22×C4—731no—
1299C22×C4—731no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—731no—
1304C22×C4—731no—
1305C22×C4—731no—
1306C22×C4—731no—
1307C22×C4—1462no—
1308C22×C4—1462no—
1309C22×C4—1462no—
1310C22×C4—1462no—
1311C22×C4—1462no—
1312C22×C4—1462no—
1313C22×C4—1462no—
1314C22×C4—1462no—
1315C22×C4—1462no—
1316C22×C4—1462no—
1317C22×C4—1462no—
1318C22×C4—1462no—
1319C22×C4—1462no—
1320C22×C4—1462no—
1321C22×C4C2×D29214yes—
1322C22×C4C2×D29214yes—
1323C22×C4C23×D7311yescharacteristic
1324C22×C4C23×D7311yescharacteristic
1325C22×C4C23×D7311yescharacteristic
1326C22×C4C23×D7311yescharacteristic
1327C22×C4C23×D7311yescharacteristic
1328C22×C4C23×D7311yescharacteristic
1329C22×C4C23×D7311yescharacteristic
1330C22×C4C23×D7311yescharacteristic
1331C22×C4C23×D7311yescharacteristic
1332C22×C4C23×D7311yescharacteristic
1333C22×C4C23×D7311yescharacteristic
1334C22×C4C23×D7311yescharacteristic
1335C22×C4C23×D7311yescharacteristic
1336C4⋊C4—41no—
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—2921no—
1343C4⋊C4—2921no—
1344C4⋊C4—2921no—
1345C4⋊C4—2921no—
1346C4⋊C4—2921no—
1347C4⋊C4—2921no—
1348C4⋊C4—2921no—
1349C4⋊C4—2921no—
1350C4⋊C4—2921no—
1351C4⋊C4—2921no—
1352C4⋊C4—1462no—
1353C4⋊C4—1462no—
1354C4⋊C4—1462no—
1355C4⋊C4—1462no—
1356C4⋊C4—1462no—
1357C4⋊C4—1462no—
1358C4⋊C4—1462no—
1359C4⋊C4—1462no—
1360C4⋊C4—1462no—
1361C4⋊C4—1462no—
1362C4⋊C4—1462no—
1363C4⋊C4—1462no—
1364C4⋊C4—1462no—
1365C4⋊C4—1462no—
1366C4⋊C4—1462no—
1367C4⋊C4—1462no—
1368C4⋊C4—1462no—
1369C4⋊C4—1462no—
1370C4⋊C4—1462no—
1371C4⋊C4—1462no—
1372C4⋊C4—1462no—
1373C4⋊C4C2×D29214yes—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—2921no—
1383C22⋊C4—2921no—
1384C22⋊C4—2921no—
1385C22⋊C4—2921no—
1386C22⋊C4—2921no—
1387C22⋊C4—2921no—
1388C22⋊C4—2921no—
1389C22⋊C4—2921no—
1390C22⋊C4—2921no—
1391C22⋊C4—2921no—
1392C22⋊C4—2921no—
1393C22⋊C4—2921no—
1394C22⋊C4—2921no—
1395C22⋊C4—2921no—
1396C22⋊C4—2921no—
1397C22⋊C4—2921no—
1398C22⋊C4—2921no—
1399C22⋊C4—2921no—
1400C22⋊C4—2921no—
1401C22⋊C4—2921no—
1402C22⋊C4—2921no—
1403C22⋊C4—1462no—
1404C22⋊C4—1462no—
1405C22⋊C4—1462no—
1406C22⋊C4—1462no—
1407C22⋊C4—1462no—
1408C22⋊C4—1462no—
1409C22⋊C4—1462no—
1410C22⋊C4—1462no—
1411C22⋊C4—1462no—
1412C22⋊C4—1462no—
1413C22⋊C4—1462no—
1414C22⋊C4—1462no—
1415C22⋊C4—1462no—
1416C22⋊C4—1462no—
1417C22⋊C4—1462no—
1418C22⋊C4—1462no—
1419C22⋊C4—1462no—
1420C22⋊C4—1462no—
1421C22⋊C4—1462no—
1422C22⋊C4—1462no—
1423C22⋊C4—1462no—
1424C22⋊C4C2×D29214yes—
1425C22⋊C4C2×D29214yes—
1426C42—41no—
1427C42—41no—
1428C42—41no—
1429C42—41no—
1430C42—1462no—
1431C42—1462no—
1432C42C2×D29214yes—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—2924no—
1446C23—2924no—
1447C23—2924no—
1448C23—2924no—
1449C23—2924no—
1450C23—2924no—
1451C23—2924no—
1452C23—732no—
1453C23—732no—
1454C23—1461no—
1455C23—1461no—
1456C23—1461no—
1457C23—1461no—
1458C23—1461no—
1459C23—1461no—
1460C23—1461no—
1461C23—1461no—
1462C23—1461no—
1463C23—1461no—
1464C23—1461no—
1465C23—1461no—
1466C23—1461no—
1467C23—1461no—
1468C23—1461no—
1469C23—1461no—
1470C23—1461no—
1471C23—1461no—
1472C23—1461no—
1473C23—1461no—
1474C23—1461no—
1475C23—1461no—
1476C23—1461no—
1477C23—1461no—
1478C23—1461no—
1479C23—1461no—
1480C23C22×D29212yes—
1481C23C22×D29212yes—
1482C23C24×D7311yescharacteristic
1483Q8—2924no—
1484Q8—5842no—
1485D4—44no—
1486D4—2924no—
1487D4—2924no—
1488D4—2924no—
1489D4—2924no—
1490D4—2924no—
1491D4—2924no—
1492D4—2924no—
1493D4—5842no—
1494D4—5842no—
1495D4—5842no—
1496D4—5842no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—44no—
1532C2×C4—44no—
1533C2×C4—2924no—
1534C2×C4—2924no—
1535C2×C4—2924no—
1536C2×C4—2924no—
1537C2×C4—2924no—
1538C2×C4—2924no—
1539C2×C4—5842no—
1540C2×C4—5842no—
1541C2×C4—732no—
1542C2×C4—1468no—
1543C2×C4—1461no—
1544C2×C4—1461no—
1545C2×C4—1461no—
1546C2×C4—1461no—
1547C2×C4—1461no—
1548C2×C4—1461no—
1549C2×C4—1461no—
1550C2×C4—1461no—
1551C2×C4—1461no—
1552C2×C4—1461no—
1553C2×C4—1461no—
1554C2×C4—1461no—
1555C2×C4—1461no—
1556C2×C4—1461no—
1557C2×C4—1461no—
1558C2×C4—1461no—
1559C2×C4—1461no—
1560C2×C4—1461no—
1561C2×C4—1461no—
1562C2×C4—1461no—
1563C2×C4—1461no—
1564C2×C4—1461no—
1565C2×C4—1461no—
1566C2×C4—1461no—
1567C2×C4—1461no—
1568C2×C4—1461no—
1569C2×C4—1461no—
1570C2×C4—1461no—
1571C2×C4—1461no—
1572C2×C4—1461no—
1573C2×C4—1461no—
1574C2×C4—1461no—
1575C2×C4—1461no—
1576C2×C4—1461no—
1577C2×C4—1461no—
1578C2×C4C22×D29212yes—
1579C2×C4C22×D29212yes—
1580C2×C4C22×D29212yes—
1581C2×C4C22×D29212yes—
1582C2×C4C22×D29212yes—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—29216no—
1598C22—2921no—
1599C22—2921no—
1600C22—2921no—
1601C22—2921no—
1602C22—2921no—
1603C22—2921no—
1604C22—2921no—
1605C22—2921no—
1606C22—2921no—
1607C22—2921no—
1608C22—2921no—
1609C22—2921no—
1610C22—2921no—
1611C22—2921no—
1612C22—2921no—
1613C22—2921no—
1614C22—2921no—
1615C22—2921no—
1616C22—2921no—
1617C22—2921no—
1618C22—2921no—
1619C22—2921no—
1620C22—1462no—
1621C22—1462no—
1622C22—1462no—
1623C22—1462no—
1624C22—1462no—
1625C22—1462no—
1626C22C23×D29211yescharacteristic
1627C22H(5,𝔽2)×D7311yescharacteristic
1628C22H(5,𝔽2)×D7311yescharacteristic
1629C222−1+4×D7311yescharacteristic
1630C22#1798942211yescharacteristic
1631C22#1798942311yescharacteristic
1632C22#1798942311yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—22no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—2921no—
1647C4—2921no—
1648C4—2921no—
1649C4—2921no—
1650C4—2921no—
1651C4—2921no—
1652C4—2921no—
1653C4—2921no—
1654C4—2921no—
1655C4—2921no—
1656C4—2921no—
1657C4—1462no—
1658C2—42no—
1659C2—42no—
1660C2—2922no—
1661C2—2922no—
1662C2—5841no—
1663C2—5841no—
1664C2#2262326411yescharacteristic
1665C2#2262356711yescharacteristic
1666C2#2262361211yescharacteristic
1667C2#2262409111yescharacteristic
1668C2#2262413311yescharacteristic
1669C2#2262418311yescharacteristic
1670C2#2262421511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2319C2
hypercenter#2319D73
hypocenterC73#36723
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2319

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989179C2semidirect
2. C2×#17989096C2semidirect
3. #22618224C2semidirect
4. #22618219C2semidirect
5. #22616632C2semidirect
6. #22616617C2semidirect
7. #22616587C2semidirect
8. #22616572C2semidirect
9. #22616542C2semidirect
10. #22616503C2semidirect
11. #22616493C2semidirect
12. #22616320C2semidirect
13. #22616302C2semidirect
14. #22616295C2semidirect
15. #22616281C2semidirect
16. #22616278C2semidirect
17. #22616269C2semidirect
18. #22616269C2semidirect
19. #22616254C2semidirect
20. #22616251C2semidirect
21. #22615851C2semidirect
22. #22615772C2semidirect
23. #22615623C2semidirect
24. #22615558C2semidirect
25. #22615522C2semidirect
26. #22615518C2semidirect
27. #22615280C2semidirect
28. #22615131C2semidirect
29. #22613277C2semidirect
30. #22613268C2semidirect
31. C73×#2319C2semidirect
35. C2×#14556585C22semidirect
37. C2×#14556583C22semidirect
38. C2×#14556581C22semidirect
43. C2×#14556575C22semidirect
44. C2×#14556575C22semidirect
51. C2×#14556571C22semidirect
54. C2×#14556569C22semidirect
56. C2×#14556568C22semidirect
67. C2×C4×C22⋊D73C22semidirect
69. C22×#11924007C22semidirect
70. #17988527C22semidirect
72. #17988519C22semidirect
73. #17988519C22semidirect
74. #17988519C22semidirect
75. #17988517C22semidirect
76. #17988517C22semidirect
77. #17988517C22semidirect
78. #17988517C22semidirect
80. #17988514C22semidirect
81. #17988514C22semidirect
85. #17988512C22semidirect
91. #17988509C22semidirect
92. #17988509C22semidirect
93. #17988509C22semidirect
94. #17988509C22semidirect
95. #17988509C22semidirect
96. #17988508C22semidirect
97. #17988508C22semidirect
98. #17988508C22semidirect
103. #17988504C22semidirect
110. #17988503C22semidirect
111. #17988503C22semidirect
112. #17988500C22semidirect
117. #17988496C22semidirect
118. #17988492C22semidirect
123. #17988489C22semidirect
125. #17988485C22semidirect
126. #17988485C22semidirect
127. #17988485C22semidirect
129. #17988479C22semidirect
134. #17988478C22semidirect
135. #17988478C22semidirect
136. #17988472C22semidirect
137. #17988472C22semidirect
138. #17988472C22semidirect
139. #17988472C22semidirect
145. #17988465C22semidirect
149. #17988464C22semidirect
152. #17988462C22semidirect
153. #17988462C22semidirect
162. #17988461C22semidirect
163. #17988461C22semidirect
164. #17988461C22semidirect
165. #17988461C22semidirect
166. #17988457C22semidirect
167. #17988453C22semidirect
177. #389×C73C22semidirect
178. #389×C73C22semidirect
181. #388×C73C22semidirect
182. #388×C73C22semidirect
184. #381×C73C22semidirect
186. #380×C73C22semidirect
187. C4×C4⋊C4×C73C22semidirect
188. #376×C73C22semidirect
352. C4×D4×C73D4semidirect
866. #2319D73semidirect
867. C73#36723semidirect
967. #389C2×D73semidirect
968. #389C2×D73semidirect
979. #388C2×D73semidirect
980. #388C2×D73semidirect
1015. #381C2×D73semidirect
1019. #380C2×D73semidirect
1023. C4×C4⋊C4C2×D73semidirect
1024. #376C2×D73semidirect
1089. C4×D4D292semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891792
C2×#179890962
#226182242
#226182192
#226166322
#226166172
#226165872
#226165722
#226165422
#226165032
#226164932
#226163202
#226163022
#226162952
#226162812
#226162782
#226162692
#226162542
#226162512
#226158512
#226157722
#226156232
#226155582
#226155222
#226155182
#226152802
#226151312
#226132772
#226132682
C73×#23192
#3672373