Finite Group Databasebeta

← #33258987

Subgroups — #33258987

Order 18688.

2404 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989185C211yesmaximal, characteristic, complemented
2C2×#17989176C211yesmaximal, characteristic, complemented
3#22618300C211yesmaximal, characteristic, complemented
4#22618299C211yesmaximal, characteristic, complemented
5#22618258C211yesmaximal, characteristic, complemented
6#22618233C211yesmaximal, characteristic, complemented
7#22616089C211yesmaximal, characteristic, complemented
8#22616084C211yesmaximal, characteristic, complemented
9#22616069C211yesmaximal, characteristic, complemented
10#22616064C211yesmaximal, characteristic, complemented
11#22615073C211yesmaximal, characteristic, complemented
12#22615066C211yesmaximal, characteristic, complemented
13#22615043C211yesmaximal, characteristic, complemented
14#22615036C211yesmaximal, characteristic, complemented
15#22614938C211yesmaximal, characteristic, complemented
16#22614892C211yesmaximal, characteristic, complemented
17#22614858C211yesmaximal, characteristic, complemented
18#22614822C211yesmaximal, characteristic, complemented
19#22614628C211yesmaximal, characteristic, complemented
20#22614254C211yesmaximal, characteristic, complemented
21#22614061C211yesmaximal, characteristic, complemented
22#22613939C211yesmaximal, characteristic, complemented
23#22613898C211yesmaximal, characteristic, complemented
24#22613489C211yesmaximal, characteristic, complemented
25#22613472C211yesmaximal, characteristic, complemented
26#22612604C211yesmaximal, characteristic, complemented
27#22612593C211yesmaximal, characteristic, complemented
28C4×#14556566C211yesmaximal, characteristic, complemented
29#388×D73C211yesmaximal, characteristic, complemented
30C4×#14556553C211yesmaximal, characteristic, complemented
31C73×#2519C211yesmaximal, characteristic, complemented
32#17989185—28no—
33#17989176—28no—
34C2×#14556586C2211yescharacteristic
35C2×#14556586C2211yescharacteristic, complemented
36C2×#14556585C2211yescharacteristic, complemented
37C2×#14556581C2211yescharacteristic, complemented
38C2×#14556579C2211yescharacteristic
39C2×#14556579C2211yescharacteristic
40C2×#14556577C2211yescharacteristic
41C2×#14556576C2211yescharacteristic
42C2×#14556576C2211yescharacteristic
43C2×#14556576C2211yescharacteristic
44C2×#14556576C2211yescharacteristic
45C2×#14556576C2211yescharacteristic, complemented
46C2×#14556576C2211yescharacteristic, complemented
47C2×#14556573C2211yescharacteristic
48C2×#14556571C2211yescharacteristic, complemented
49C2×#14556569C2211yescharacteristic
50C2×#14556569C2211yescharacteristic
51C2×#14556569C2211yescharacteristic, complemented
52C2×#14556566C2211yescharacteristic
53C2×#14556566C2211yescharacteristic
54C2×#14556566C2211yescharacteristic
55C2×#14556566C2211yescharacteristic
56C2×#14556564C2211yescharacteristic
57C2×#14556564C2211yescharacteristic
58C2×#14556561C2211yescharacteristic
59C2×#14556561C2211yescharacteristic
60C2×#14556561C2211yescharacteristic
61C2×C4×D292C2211yescharacteristic
62C2×C4×D292C2211yescharacteristic
63C2×C4×D292C2211yescharacteristic
64C2×C4×D292C2211yescharacteristic, complemented
65C2×#14556553C2211yescharacteristic
66C2×#14556553C2211yescharacteristic
67C2×C4⋊C4×D73C2211yescharacteristic
68C2×C22⋊C4×D73C2211yescharacteristic
69C2×C22⋊C4×D73C2211yescharacteristic
70C2×C22⋊C4×D73C2211yescharacteristic
71C2×C42×D73C2211yescharacteristic
72C2×C42×D73C2211yescharacteristic, complemented
73#17988528C2211yescharacteristic, complemented
74#17988525C2211yescharacteristic, complemented
75#17988522C2211yescharacteristic
76#17988521C2211yescharacteristic, complemented
77#17988520C2211yescharacteristic, complemented
78#17988516C2211yescharacteristic
79#17988513C2211yescharacteristic, complemented
80#17988513C2211yescharacteristic, complemented
81#17988513C2211yescharacteristic, complemented
82#17988509C2211yescharacteristic
83#17988509C2211yescharacteristic
84#17988509C2211yescharacteristic, complemented
85#17988508C2211yescharacteristic, complemented
86#17988507C2211yescharacteristic, complemented
87#17988504C2211yescharacteristic
88#17988504C2211yescharacteristic
89#17988504C2211yescharacteristic, complemented
90#17988504C2211yescharacteristic, complemented
91#17988503C2211yescharacteristic
92#17988503C2211yescharacteristic
93#17988503C2211yescharacteristic
94#17988502C2211yescharacteristic
95#17988500C2211yescharacteristic, complemented
96#17988499C2211yescharacteristic
97#17988497C2211yescharacteristic
98#17988497C2211yescharacteristic
99#17988497C2211yescharacteristic, complemented
100#17988496C2211yescharacteristic
101#17988492C2211yescharacteristic, complemented
102#17988491C2211yescharacteristic, complemented
103#17988491C2211yescharacteristic, complemented
104#17988489C2211yescharacteristic
105#17988488C2211yescharacteristic
106#17988488C2211yescharacteristic
107#17988488C2211yescharacteristic
108#17988488C2211yescharacteristic, complemented
109#17988487C2211yescharacteristic
110#17988487C2211yescharacteristic
111#17988487C2211yescharacteristic
112#17988487C2211yescharacteristic
113#17988486C2211yescharacteristic, complemented
114#17988486C2211yescharacteristic, complemented
115#17988484C2211yescharacteristic, complemented
116#17988483C2211yescharacteristic, complemented
117#17988482C2211yescharacteristic, complemented
118#17988481C2211yescharacteristic
119#17988481C2211yescharacteristic
120#17988480C2211yescharacteristic
121#17988480C2211yescharacteristic
122#17988479C2211yescharacteristic
123#17988479C2211yescharacteristic
124#17988479C2211yescharacteristic, complemented
125#17988479C2211yescharacteristic, complemented
126#17988479C2211yescharacteristic, complemented
127#17988478C2211yescharacteristic
128#17988478C2211yescharacteristic
129#17988478C2211yescharacteristic, complemented
130#17988478C2211yescharacteristic, complemented
131#17988477C2211yescharacteristic
132#17988477C2211yescharacteristic
133#17988477C2211yescharacteristic, complemented
134#17988477C2211yescharacteristic, complemented
135#17988476C2211yescharacteristic
136#17988476C2211yescharacteristic
137#17988476C2211yescharacteristic, complemented
138#17988476C2211yescharacteristic, complemented
139#17988475C2211yescharacteristic
140#17988471C2211yescharacteristic, complemented
141#17988465C2211yescharacteristic
142#17988465C2211yescharacteristic
143#17988465C2211yescharacteristic
144#17988465C2211yescharacteristic
145#17988465C2211yescharacteristic
146#17988465C2211yescharacteristic
147#17988465C2211yescharacteristic
148#17988465C2211yescharacteristic, complemented
149#17988465C2211yescharacteristic, complemented
150#17988465C2211yescharacteristic, complemented
151#17988463C2211yescharacteristic
152#17988463C2211yescharacteristic
153#17988461C2211yescharacteristic
154#17988461C2211yescharacteristic, complemented
155#17988458C2211yescharacteristic
156#17988458C2211yescharacteristic, complemented
157#17988449C2211yescharacteristic
158#17988446C2211yescharacteristic, complemented
159#17988444C2211yescharacteristic
160#17988442C2211yescharacteristic
161C4⋊C4×Dic73C2211yescharacteristic, complemented
162C4⋊C4×Dic73C2211yescharacteristic, complemented
163C4×#11924005C2211yescharacteristic
164C4×#11924005C2211yescharacteristic, complemented
165C4×#11924005C2211yescharacteristic, complemented
166C4×#11924005C2211yescharacteristic, complemented
167#17988434C2211yescharacteristic
168#17988434C2211yescharacteristic
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic
173C42×Dic73C2211yescharacteristic, complemented
174C2×#126×C73C2211yescharacteristic
175C2×#125×C73C2211yescharacteristic, complemented
176#399×C73C2211yescharacteristic
177#398×C73C2211yescharacteristic, complemented
178#398×C73C2211yescharacteristic, complemented
179#396×C73C2211yescharacteristic
180#389×C73C2211yescharacteristic, complemented
181#388×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic
184#388×C73C2211yescharacteristic
185#387×C73C2211yescharacteristic, complemented
186#382×C73C2211yescharacteristic, complemented
187C4×C4⋊C4×C73C2211yescharacteristic, complemented
188C4×C4⋊C4×C73C2211yescharacteristic, complemented
189C24×D73C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×Dic146C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×D292C2311yescharacteristic
194C22×D292C2311yescharacteristic
195C22×D292C2311yescharacteristic
196C22×D292C2311yescharacteristic
197C22×D292C2311yescharacteristic
198C22×D292C2311yescharacteristic
199C22×D292C2311yescharacteristic
200C22×D292C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C22×C22⋊D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214C22×C4×D73C2311yescharacteristic
215#14556586—24no—
216#14556586—24no—
217#14556585—24no—
218#14556581—24no—
219#14556579—24no—
220#14556579—42no—
221#14556577—24no—
222#14556576—24no—
223#14556576—24no—
224#14556576—24no—
225#14556576—24no—
226#14556576—24no—
227#14556576—24no—
228#14556573—24no—
229#14556571—24no—
230#14556569—24no—
231#14556569—24no—
232#14556569—24no—
233#14556566—24no—
234#14556566—24no—
235#14556566—24no—
236#14556566—24no—
237#14556564—24no—
238#14556564—42no—
239#14556561—24no—
240#14556561—24no—
241#14556561—24no—
242C4×D292—24no—
243C4×D292—24no—
244C4×D292—24no—
245C4×D292—42no—
246#14556553—24no—
247#14556553D418yescomplemented
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×C4⋊Dic73C2311yescharacteristic
253C2×C4⋊Dic73C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C4⋊C4×D73—24no—
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
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
311C22⋊C4×D73—24no—
312C22⋊C4×D73—24no—
313C22⋊C4×D73—42no—
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322C2×C4×Dic73C2311yescharacteristic
323C2×C4×Dic73C2311yescharacteristic
324C42×D73—42no—
325C42×D73—42no—
326#14556498C2311yescharacteristic
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#126×C73—24no—
349#125×C73—24no—
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
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×C4⋊C4×C73C2311yescharacteristic
361C2×C4⋊C4×C73C2311yescharacteristic
362C2×C4⋊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
396C23×D73C2411yescharacteristic
397C2×Dic146—22no—
398C2×Dic146—22no—
399C2×Dic146—41no—
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—22no—
410C2×D292—22no—
411C2×D292—22no—
412C2×D292—22no—
413C2×D292—22no—
414C2×D292—22no—
415C2×D292—22no—
416C2×D292—22no—
417C2×D292—41no—
418C2×D292—41no—
419C2×D292—41no—
420C2×D292—41no—
421C2×D292—41no—
422C2×D292—41no—
423C2×D292—41no—
424C2×D292—41no—
425C2×D292—41no—
426C2×D292—41no—
427C2×D292—41no—
428C2×D292—41no—
429C2×D292C2×D414yes—
430C2×C22⋊D73—22no—
431C2×C22⋊D73—22no—
432C2×C22⋊D73—22no—
433C2×C22⋊D73—41no—
434C2×C22⋊D73—41no—
435C2×C22⋊D73—41no—
436C2×C22⋊D73—41no—
437C2×C22⋊D73—41no—
438C2×C22⋊D73—41no—
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—22no—
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—22no—
458C2×C4×D73—22no—
459C2×C4×D73—22no—
460C2×C4×D73—22no—
461C2×C4×D73—22no—
462C2×C4×D73—41no—
463C2×C4×D73—41no—
464C2×C4×D73—41no—
465C2×C4×D73—41no—
466C2×C4×D73—41no—
467C2×C4×D73—41no—
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—
476C2×C4×D73—41no—
477C2×C4×D73—41no—
478C2×C4×D73—41no—
479C2×C4×D73—41no—
480C2×C4×D73C2×D414yes—
481C2×C4×D73C2×D414yes—
482C2×C4×D73#4114yes—
483C4⋊Dic73—22no—
484C4⋊Dic73—22no—
485C4⋊Dic73—22no—
486C4⋊Dic73—22no—
487C4⋊Dic73—41no—
488C4⋊Dic73—41no—
489#11924007—22no—
490#11924007—22no—
491#11924007—22no—
492#11924007—22no—
493#11924007—22no—
494#11924007—22no—
495#11924007—22no—
496#11924007—22no—
497#11924007—22no—
498#11924007—41no—
499#11924007—41no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—41no—
503C22⋊Dic73—41no—
504#11924005—22no—
505#11924005—22no—
506#11924005—22no—
507#11924005—22no—
508#11924005—22no—
509#11924005—22no—
510#11924005—22no—
511#11924005—22no—
512#11924005—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—22no—
529#11924005—22no—
530#11924005—22no—
531#11924005—22no—
532#11924005—22no—
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#11924005C2×D414yes—
543#11924005C2×D414yes—
544#11924005#4114yes—
545C4×Dic73—22no—
546C4×Dic73—22no—
547C4×Dic73—41no—
548C4×Dic73—41no—
549C4×Dic73—41no—
550C4×Dic73—41no—
551C4×Dic73—41no—
552C4×Dic73—41no—
553C4×Dic73—41no—
554C4×Dic73C2×D414yes—
555C24×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C22×C4×C73C2411yescharacteristic
559C22×C4×C73C2411yescharacteristic
560C22×C4×C73C2411yescharacteristic
561C22×C4×C73C2411yescharacteristic
562C22×C4×C73C2411yescharacteristic
563C22×C4×C73C2411yescharacteristic
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C4⋊C4×C73—22no—
571C4⋊C4×C73—22no—
572C4⋊C4×C73—22no—
573C4⋊C4×C73—22no—
574C4⋊C4×C73—22no—
575C4⋊C4×C73—22no—
576C4⋊C4×C73—22no—
577C4⋊C4×C73—22no—
578C4⋊C4×C73—22no—
579C4⋊C4×C73—22no—
580C4⋊C4×C73—41no—
581C4⋊C4×C73—41no—
582C4⋊C4×C73C2×D414yes—
583C22⋊C4×C73—22no—
584C22⋊C4×C73—22no—
585C22⋊C4×C73—22no—
586C22⋊C4×C73—22no—
587C22⋊C4×C73—22no—
588C22⋊C4×C73—22no—
589C22⋊C4×C73—41no—
590C42×C73—22no—
591C42×C73—22no—
592C42×C73—22no—
593C42×C73—22no—
594C42×C73—22no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73C2511yescharacteristic
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—21no—
611C22×D73—21no—
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—44no—
635C22×D73—44no—
636C22×D73—44no—
637C22×D73—82no—
638C22×D73—82no—
639C22×D73—82no—
640C22×D73—82no—
641C22×D73C22×D412yes—
642C22×D73C22×D412yes—
643C22×D73C2×#4112yes—
644C22×D73C2×#4112yes—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
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×C73C22×D412yes—
682C2×C4×C73C22×D412yes—
683C2×C4×C73C22×D412yes—
684C2×C4×C73C2×#4112yes—
685C2×C4×C73C2×#4112yes—
686C2×C4×C73H(5,𝔽2)12yes—
687C22⋊D73—82no—
688C22⋊D73—82no—
689C22⋊D73—82no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
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×Dic73C22×D412yes—
720C2×Dic73C22×D412yes—
721C2×Dic73C2×#4112yes—
722C2×Dic73C2×#4112yes—
723D292—28no—
724D292—44no—
725D292—44no—
726D292—44no—
727D292—82no—
728D292—82no—
729D292—82no—
730D292—82no—
731D292—82no—
732C4×D73—44no—
733C4×D73—44no—
734C4×D73—44no—
735C4×D73—44no—
736C4×D73—44no—
737C4×D73—44no—
738C4×D73—44no—
739C4×D73—82no—
740C4×D73—82no—
741C4×D73—82no—
742C4×D73—82no—
743Dic146—82no—
744Dic146—82no—
745C22×C73—41no—
746C22×C73—41no—
747C22×C73—41no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73—41no—
751C22×C73—41no—
752C22×C73C23×D411yescharacteristic
753C22×C73C22×#4111yescharacteristic
754C22×C73C22×#4111yescharacteristic
755C22×C73C2×H(5,𝔽2)11yescharacteristic
756C22×C73#58511yescharacteristic
757C22×C73#58511yescharacteristic
758C22×C73#58511yescharacteristic
759C2×D73—22no—
760C2×D73—22no—
761C2×D73—22no—
762C2×D73—22no—
763C2×D73—22no—
764C2×D73—22no—
765C2×D73—22no—
766C2×D73—22no—
767C2×D73—22no—
768C2×D73—41no—
769C2×D73—41no—
770C2×D73—41no—
771C2×D73—41no—
772C2×D73—41no—
773C2×D73—41no—
774C2×D73—41no—
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—88no—
794C2×D73#53214yes—
795C4×C73—22no—
796C4×C73—22no—
797C4×C73—22no—
798C4×C73—22no—
799C4×C73—22no—
800C4×C73—22no—
801C4×C73—41no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807C4×C73—41no—
808C4×C73—41no—
809Dic73—22no—
810Dic73—22no—
811Dic73—22no—
812Dic73—22no—
813Dic73—41no—
814Dic73—41no—
815Dic73—41no—
816Dic73—41no—
817Dic73—41no—
818Dic73—41no—
819Dic73—41no—
820#35009—731nomaximal, Sylow
821C2×C73—81no—
822C2×C73C2×#53211yescharacteristic
823C2×C73#345511yescharacteristic
824C2×C73#345911yescharacteristic
825C2×C73#349611yescharacteristic
826C2×C73#350011yescharacteristic
827C2×C73#351311yescharacteristic
828C2×C73#352111yescharacteristic
829D73—24no—
830D73—42no—
831D73—81no—
832D73—81no—
833D73—81no—
834C2×#539—731no—
835C2×#538—731no—
836#2861—731no—
837#2860—731no—
838#2854—731no—
839#2850—731no—
840#2664—731no—
841#2663—731no—
842#2662—731no—
843#2661—731no—
844#2560—731no—
845#2559—731no—
846#2558—731no—
847#2557—731no—
848#2549—731no—
849#2543—731no—
850#2539—731no—
851#2534—731no—
852#2521—731no—
853#2519D7311yescharacteristic, complemented
854#2488—731no—
855#2472—731no—
856#2464—731no—
857#2461—731no—
858#2425—731no—
859#2424—731no—
860#2322—731no—
861#2321—731no—
862C4×#121—731no—
863C2×#388—731no—
864C42×D4—731no—
865C73#3500911yescharacteristic, complemented, Sylow
866#539—1468no—
867#538—1468no—
868C2×#126—731no—
869C2×#126—731no—
870C2×#126—731no—
871C2×#126C2×D7311yescharacteristic
872C2×#125—731no—
873C2×#125C2×D7311yescharacteristic, complemented
874C2×#124—731no—
875C2×#124—731no—
876C2×#124—731no—
877C2×#123—731no—
878C2×#123—731no—
879C2×#123—731no—
880C2×#123—731no—
881C2×#123—731no—
882C2×#123—731no—
883C2×#123—731no—
884C2×C22⋊Q8—731no—
885C2×C22⋊Q8—731no—
886C2×C22⋊Q8—731no—
887C2×C22⋊Q8—731no—
888C2×#121—731no—
889C2×#121—731no—
890C2×#121—731no—
891C2×#121—731no—
892C2×#121—731no—
893C2×#121—731no—
894C2×#120—731no—
895C2×#120—731no—
896C2×#120—731no—
897C2×C4×D4—731no—
898C2×C4×D4—731no—
899C2×C4×D4—731no—
900C2×C4×D4—731no—
901C2×C4×D4—731no—
902C2×C4×D4—731no—
903C22×C4⋊C4—731no—
904C22×C22⋊C4—731no—
905C22×C22⋊C4—731no—
906C22×C22⋊C4—731no—
907C22×C42—731no—
908C22×C42—731no—
909#400—731no—
910#400—731no—
911#399—731no—
912#399C2×D7311yescharacteristic
913#398—731no—
914#398—731no—
915#398C2×D7311yescharacteristic, complemented
916#398C2×D7311yescharacteristic, complemented
917#397—731no—
918#397—731no—
919#397—731no—
920#397—731no—
921#396—731no—
922#396—731no—
923#396—731no—
924#396C2×D7311yescharacteristic
925#395—731no—
926#395—731no—
927#394—731no—
928#394—731no—
929#394—731no—
930#394—731no—
931#394—731no—
932#394—731no—
933#394—731no—
934#394—731no—
935#393—731no—
936#393—731no—
937#392—731no—
938#392—731no—
939#392—731no—
940#392—731no—
941#391—731no—
942#391—731no—
943#391—731no—
944#390—731no—
945#390—731no—
946#390—731no—
947#390—731no—
948#390—731no—
949#390—731no—
950#390—731no—
951#390—731no—
952#390—731no—
953#389—731no—
954#389—731no—
955#389—731no—
956#389—731no—
957#389—731no—
958#389C2×D7311yescharacteristic, complemented
959#388—731no—
960#388—731no—
961#388—731no—
962#388—731no—
963#388—731no—
964#388—731no—
965#388—731no—
966#388—731no—
967#388—731no—
968#388—731no—
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#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388C2×D7311yescharacteristic
982#388C2×D7311yescharacteristic
983#388C2×D7311yescharacteristic
984#388C2×D7311yescharacteristic
985#387—731no—
986#387C2×D7311yescharacteristic, complemented
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#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#385—731no—
1000#385—731no—
1001#385—731no—
1002#385—731no—
1003#382C2×D7311yescharacteristic, complemented
1004#381—731no—
1005#380—731no—
1006#380—731no—
1007#379—731no—
1008C4×C4⋊C4—731no—
1009C4×C4⋊C4—731no—
1010C4×C4⋊C4C2×D7311yescharacteristic, complemented
1011C4×C4⋊C4C2×D7311yescharacteristic, complemented
1012C4×C22⋊C4—731no—
1013C4×C22⋊C4—731no—
1014C4×C22⋊C4—731no—
1015C4×C22⋊C4—731no—
1016C4×C22⋊C4—731no—
1017C4×C22⋊C4—731no—
1018C4×C22⋊C4—731no—
1019C4×C22⋊C4—731no—
1020C2×#95—731no—
1021C2×#95—731no—
1022C43—731no—
1023C25—731no—
1024C22×Q8—731no—
1025C22×Q8—731no—
1026C22×D4—731no—
1027C22×D4—731no—
1028C22×D4—731no—
1029C22×D4—731no—
1030C22×D4—731no—
1031C22×D4—731no—
1032C22×D4—731no—
1033C22×D4—731no—
1034C22×D4—731no—
1035C22×D4—731no—
1036C22×D4—731no—
1037C22×D4—731no—
1038C23×C4—731no—
1039C23×C4—731no—
1040C23×C4—731no—
1041C23×C4—731no—
1042C23×C4—731no—
1043C23×C4—731no—
1044C23×C4—731no—
1045C23×C4—731no—
1046C23×C4—731no—
1047C23×C4—731no—
1048C23×C4—731no—
1049#126—24no—
1050#126—1464no—
1051#126—1464no—
1052#126—1464no—
1053#125—24no—
1054#125—1464no—
1055#124—2922no—
1056#124—1464no—
1057#124—1464no—
1058#123—1464no—
1059#123—1464no—
1060#123—1464no—
1061#123—1464no—
1062#123—1464no—
1063#123—1464no—
1064#123—1464no—
1065C22⋊Q8—1464no—
1066C22⋊Q8—1464no—
1067C22⋊Q8—1464no—
1068C22⋊Q8—1464no—
1069#121—2922no—
1070#121—1464no—
1071#121—1464no—
1072#121—1464no—
1073#121—1464no—
1074#121—1464no—
1075#120—1464no—
1076#120—1464no—
1077#120—1464no—
1078C4×D4—2922no—
1079C4×D4—738no—
1080C4×D4—1464no—
1081C4×D4—1464no—
1082C4×D4—1464no—
1083C4×D4—1464no—
1084C2×C4⋊C4—731no—
1085C2×C4⋊C4—731no—
1086C2×C4⋊C4—731no—
1087C2×C4⋊C4—731no—
1088C2×C4⋊C4—731no—
1089C2×C4⋊C4—731no—
1090C2×C4⋊C4—731no—
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—1464no—
1102C2×C4⋊C4C22×D7311yescharacteristic
1103C2×C4⋊C4C22×D7311yescharacteristic
1104C2×C4⋊C4C22×D7311yescharacteristic
1105C2×C4⋊C4C22×D7311yescharacteristic
1106C2×C4⋊C4C22×D7311yescharacteristic
1107C2×C4⋊C4C22×D7311yescharacteristic
1108C2×C4⋊C4C22×D7311yescharacteristic
1109C2×C4⋊C4C22×D7311yescharacteristic
1110C2×C4⋊C4C22×D7311yescharacteristic
1111C2×C4⋊C4C22×D7311yescharacteristic
1112C2×C4⋊C4C22×D7311yescharacteristic
1113C2×C4⋊C4C22×D7311yescharacteristic
1114C2×C4⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4—2922no—
1116C2×C22⋊C4—731no—
1117C2×C22⋊C4—731no—
1118C2×C22⋊C4—731no—
1119C2×C22⋊C4—731no—
1120C2×C22⋊C4—731no—
1121C2×C22⋊C4—731no—
1122C2×C22⋊C4—731no—
1123C2×C22⋊C4—731no—
1124C2×C22⋊C4—731no—
1125C2×C22⋊C4—731no—
1126C2×C22⋊C4—731no—
1127C2×C22⋊C4—731no—
1128C2×C22⋊C4—731no—
1129C2×C22⋊C4—731no—
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—1464no—
1162C2×C22⋊C4—1464no—
1163C2×C22⋊C4C22×D7311yescharacteristic
1164C2×C22⋊C4C22×D7311yescharacteristic
1165C2×C22⋊C4C22×D7311yescharacteristic
1166C2×C22⋊C4C22×D7311yescharacteristic
1167C2×C22⋊C4C22×D7311yescharacteristic
1168C2×C22⋊C4C22×D7311yescharacteristic
1169C2×C22⋊C4C22×D7311yescharacteristic
1170C2×C42—2922no—
1171C2×C42—2922no—
1172C2×C42—731no—
1173C2×C42—731no—
1174C2×C42—731no—
1175C2×C42—731no—
1176C2×C42—731no—
1177C2×C42—731no—
1178C2×C42—731no—
1179C2×C42—731no—
1180C2×C42—731no—
1181C2×C42—731no—
1182C2×C42C22×D7311yescharacteristic
1183C2×C42C22×D7311yescharacteristic
1184C2×C42C22×D7311yescharacteristic
1185C2×C42C22×D7311yescharacteristic
1186C2×C42C22×D7311yescharacteristic
1187#95—731no—
1188#95—731no—
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#95C22×D7311yescharacteristic
1210#95C22×D7311yescharacteristic
1211#95C22×D7311yescharacteristic
1212#95C22×D7311yescharacteristic
1213#95C22×D7311yescharacteristic
1214#95C22×D7311yescharacteristic
1215#95C22×D7311yescharacteristic
1216#95C22×D7311yescharacteristic
1217#95C22×D7311yescharacteristic
1218#95C22×D7311yescharacteristic
1219C24—2921no—
1220C24—2921no—
1221C24—2921no—
1222C24—2921no—
1223C24—731no—
1224C24—731no—
1225C24—731no—
1226C24—731no—
1227C24—731no—
1228C24—1462no—
1229C24—1462no—
1230C24—1462no—
1231C24C23×D7311yescharacteristic
1232C2×Q8—2921no—
1233C2×Q8—2921no—
1234C2×Q8—2921no—
1235C2×Q8—2921no—
1236C2×Q8—1462no—
1237C2×Q8—1462no—
1238C2×D4—2921no—
1239C2×D4—2921no—
1240C2×D4—2921no—
1241C2×D4—2921no—
1242C2×D4—2921no—
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—734no—
1257C2×D4—1462no—
1258C2×D4—1462no—
1259C2×D4—1462no—
1260C2×D4—1462no—
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—
1274C22×C4—2921no—
1275C22×C4—2921no—
1276C22×C4—2921no—
1277C22×C4—2921no—
1278C22×C4—2921no—
1279C22×C4—2921no—
1280C22×C4—2921no—
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—2921no—
1290C22×C4—2921no—
1291C22×C4—2921no—
1292C22×C4—734no—
1293C22×C4—734no—
1294C22×C4—734no—
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—1462no—
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×C4C23×D7311yescharacteristic
1319C22×C4C23×D7311yescharacteristic
1320C22×C4C23×D7311yescharacteristic
1321C22×C4C23×D7311yescharacteristic
1322C22×C4C23×D7311yescharacteristic
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
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—2921no—
1345C4⋊C4—2921no—
1346C4⋊C4—2921no—
1347C4⋊C4—2921no—
1348C4⋊C4—1462no—
1349C4⋊C4—1462no—
1350C4⋊C4—1462no—
1351C4⋊C4—1462no—
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⋊C4D4×D7314yes—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—41no—
1369C22⋊C4—2921no—
1370C22⋊C4—2921no—
1371C22⋊C4—2921no—
1372C22⋊C4—2921no—
1373C22⋊C4—2921no—
1374C22⋊C4—2921no—
1375C22⋊C4—2921no—
1376C22⋊C4—2921no—
1377C22⋊C4—2921no—
1378C22⋊C4—2921no—
1379C22⋊C4—2921no—
1380C22⋊C4—734no—
1381C22⋊C4—734no—
1382C22⋊C4—734no—
1383C22⋊C4—1462no—
1384C22⋊C4—1462no—
1385C22⋊C4—1462no—
1386C22⋊C4—1462no—
1387C22⋊C4—1462no—
1388C22⋊C4—1462no—
1389C22⋊C4—1462no—
1390C22⋊C4—1462no—
1391C22⋊C4—1462no—
1392C22⋊C4—1462no—
1393C22⋊C4—1462no—
1394C22⋊C4—1462no—
1395C22⋊C4—1462no—
1396C22⋊C4—1462no—
1397C22⋊C4—1462no—
1398C22⋊C4—1462no—
1399C22⋊C4—1462no—
1400C22⋊C4—1462no—
1401C22⋊C4—1462no—
1402C22⋊C4—1462no—
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—
1414C42—22no—
1415C42—22no—
1416C42—22no—
1417C42—22no—
1418C42—22no—
1419C42—2921no—
1420C42—2921no—
1421C42—2921no—
1422C42—2921no—
1423C42—2921no—
1424C42—2921no—
1425C42—2921no—
1426C42—734no—
1427C42—1462no—
1428C42—1462no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—2924no—
1437C23—2924no—
1438C23—2924no—
1439C23—5842no—
1440C23—5842no—
1441C23—5842no—
1442C23—5842no—
1443C23—732no—
1444C23—732no—
1445C23—732no—
1446C23—732no—
1447C23—1461no—
1448C23—1461no—
1449C23—1461no—
1450C23—1461no—
1451C23—1461no—
1452C23—1461no—
1453C23—1461no—
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—
1478C23C24×D7311yescharacteristic
1479Q8—5842no—
1480Q8—5842no—
1481D4—2924no—
1482D4—2924no—
1483D4—2924no—
1484D4—5842no—
1485D4—5842no—
1486D4—5842no—
1487D4—5842no—
1488D4—5842no—
1489D4—5842no—
1490D4—5842no—
1491D4—5842no—
1492D4—1468no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
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—2924no—
1530C2×C4—2924no—
1531C2×C4—2924no—
1532C2×C4—2924no—
1533C2×C4—2924no—
1534C2×C4—2924no—
1535C2×C4—2924no—
1536C2×C4—5842no—
1537C2×C4—5842no—
1538C2×C4—5842no—
1539C2×C4—5842no—
1540C2×C4—732no—
1541C2×C4—732no—
1542C2×C4—732no—
1543C2×C4—732no—
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×C4C2×D4×D7312yes—
1574C2×C4C2×D4×D7312yes—
1575C2×C4C2×D4×D7312yes—
1576C2×C4#41×D7312yes—
1577C2×C4#41×D7312yes—
1578C2×C4#1455663712yes—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—2921no—
1587C22—2921no—
1588C22—2921no—
1589C22—2921no—
1590C22—2921no—
1591C22—2921no—
1592C22—2921no—
1593C22—2921no—
1594C22—2921no—
1595C22—2921no—
1596C22—2921no—
1597C22—2921no—
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—5848no—
1612C22—734no—
1613C22—1462no—
1614C22—1462no—
1615C22—1462no—
1616C22—1462no—
1617C22—1462no—
1618C22—1462no—
1619C22—1462no—
1620C22—1462no—
1621C22—1462no—
1622C22C22×D4×D7311yescharacteristic
1623C22C2×#41×D7311yescharacteristic
1624C22C2×#41×D7311yescharacteristic
1625C22C2×#1455663711yescharacteristic
1626C22#1798942311yescharacteristic
1627C22#1798942411yescharacteristic
1628C22#1798942411yescharacteristic
1629C4—22no—
1630C4—22no—
1631C4—22no—
1632C4—22no—
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—2921no—
1644C4—2921no—
1645C4—2921no—
1646C4—2921no—
1647C4—2921no—
1648C4—2921no—
1649C4—2921no—
1650C4—1462no—
1651C4—1462no—
1652C4—1462no—
1653C4—1462no—
1654C2—81no—
1655C2—2922no—
1656C2—5841no—
1657C2—5841no—
1658C2—5841no—
1659C2—1464no—
1660C2#532×D7311yescharacteristic
1661C2#2262332211yescharacteristic
1662C2#2262334111yescharacteristic
1663C2#2262368911yescharacteristic
1664C2#2262372211yescharacteristic
1665C2#2262387611yescharacteristic
1666C2#2262398611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2519C2
hypercenter#2519D73
hypocenterC73#35009
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2519

Complements

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

NH ≅ G/Ntype
1. C2×#17989185C2semidirect
2. C2×#17989176C2semidirect
3. #22618300C2semidirect
4. #22618299C2semidirect
5. #22618258C2semidirect
6. #22618233C2semidirect
7. #22616089C2semidirect
8. #22616084C2semidirect
9. #22616069C2semidirect
10. #22616064C2semidirect
11. #22615073C2semidirect
12. #22615066C2semidirect
13. #22615043C2semidirect
14. #22615036C2semidirect
15. #22614938C2semidirect
16. #22614892C2semidirect
17. #22614858C2semidirect
18. #22614822C2semidirect
19. #22614628C2semidirect
20. #22614254C2semidirect
21. #22614061C2semidirect
22. #22613939C2semidirect
23. #22613898C2semidirect
24. #22613489C2semidirect
25. #22613472C2semidirect
26. #22612604C2semidirect
27. #22612593C2semidirect
28. C4×#14556566C2semidirect
29. #388×D73C2semidirect
30. C4×#14556553C2semidirect
31. C73×#2519C2semidirect
35. C2×#14556586C22semidirect
36. C2×#14556585C22semidirect
37. C2×#14556581C22semidirect
45. C2×#14556576C22semidirect
46. C2×#14556576C22semidirect
48. C2×#14556571C22semidirect
51. C2×#14556569C22semidirect
64. C2×C4×D292C22semidirect
72. C2×C42×D73C22semidirect
73. #17988528C22semidirect
74. #17988525C22semidirect
76. #17988521C22semidirect
77. #17988520C22semidirect
79. #17988513C22semidirect
80. #17988513C22semidirect
81. #17988513C22semidirect
84. #17988509C22semidirect
85. #17988508C22semidirect
86. #17988507C22semidirect
89. #17988504C22semidirect
90. #17988504C22semidirect
95. #17988500C22semidirect
99. #17988497C22semidirect
101. #17988492C22semidirect
102. #17988491C22semidirect
103. #17988491C22semidirect
108. #17988488C22semidirect
113. #17988486C22semidirect
114. #17988486C22semidirect
115. #17988484C22semidirect
116. #17988483C22semidirect
117. #17988482C22semidirect
124. #17988479C22semidirect
125. #17988479C22semidirect
126. #17988479C22semidirect
129. #17988478C22semidirect
130. #17988478C22semidirect
133. #17988477C22semidirect
134. #17988477C22semidirect
137. #17988476C22semidirect
138. #17988476C22semidirect
140. #17988471C22semidirect
148. #17988465C22semidirect
149. #17988465C22semidirect
150. #17988465C22semidirect
154. #17988461C22semidirect
156. #17988458C22semidirect
158. #17988446C22semidirect
161. C4⋊C4×Dic73C22semidirect
162. C4⋊C4×Dic73C22semidirect
164. C4×#11924005C22semidirect
165. C4×#11924005C22semidirect
166. C4×#11924005C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
173. C42×Dic73C22semidirect
175. C2×#125×C73C22semidirect
177. #398×C73C22semidirect
178. #398×C73C22semidirect
180. #389×C73C22semidirect
185. #387×C73C22semidirect
186. #382×C73C22semidirect
187. C4×C4⋊C4×C73C22semidirect
188. C4×C4⋊C4×C73C22semidirect
247. #14556553D4semidirect
853. #2519D73semidirect
865. C73#35009semidirect
873. C2×#125C2×D73semidirect
915. #398C2×D73semidirect
916. #398C2×D73semidirect
958. #389C2×D73semidirect
986. #387C2×D73semidirect
1003. #382C2×D73semidirect
1010. C4×C4⋊C4C2×D73semidirect
1011. C4×C4⋊C4C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891852
C2×#179891762
#226183002
#226182992
#226182582
#226182332
#226160892
#226160842
#226160692
#226160642
#226150732
#226150662
#226150432
#226150362
#226149382
#226148922
#226148582
#226148222
#226146282
#226142542
#226140612
#226139392
#226138982
#226134892
#226134722
#226126042
#226125932
C4×#145565662
#388×D732
C4×#145565532
C73×#25192
#3500973