Finite Group Databasebeta

← #33293019

Subgroups — #33293019

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×#17989181C211yesmaximal, characteristic, complemented
2C2×#17989097C211yesmaximal, characteristic, complemented
3#22618222C211yesmaximal, characteristic, complemented
4#22618219C211yesmaximal, characteristic, complemented
5#22616636C211yesmaximal, characteristic, complemented
6#22616613C211yesmaximal, characteristic, complemented
7#22616589C211yesmaximal, characteristic, complemented
8#22616547C211yesmaximal, characteristic, complemented
9#22616504C211yesmaximal, characteristic, complemented
10#22616495C211yesmaximal, characteristic, complemented
11#22616317C211yesmaximal, characteristic, complemented
12#22616304C211yesmaximal, characteristic, complemented
13#22616298C211yesmaximal, characteristic, complemented
14#22616282C211yesmaximal, characteristic, complemented
15#22616277C211yesmaximal, characteristic, complemented
16#22616269C211yesmaximal, characteristic, complemented
17#22616269C211yesmaximal, characteristic, complemented
18#22616249C211yesmaximal, characteristic, complemented
19#22616249C211yesmaximal, characteristic, complemented
20#22615853C211yesmaximal, characteristic, complemented
21#22615775C211yesmaximal, characteristic, complemented
22#22615632C211yesmaximal, characteristic, complemented
23#22615551C211yesmaximal, characteristic, complemented
24#22615535C211yesmaximal, characteristic, complemented
25#22615512C211yesmaximal, characteristic, complemented
26#22615275C211yesmaximal, characteristic, complemented
27#22615133C211yesmaximal, characteristic, complemented
28#22613269C211yesmaximal, characteristic, complemented
29#22613265C211yesmaximal, characteristic, complemented
30#22612572C211yesmaximal, characteristic, complemented
31C73×#2703C211yesmaximal, characteristic, complemented
32C22×#11924027C2211yescharacteristic
33C23×C4×D73C2211yescharacteristic
34#17989181—28no—
35C2×#14556586C2211yescharacteristic
36C2×#14556584C2211yescharacteristic, complemented
37C2×#14556582C2211yescharacteristic, complemented
38C2×#14556581C2211yescharacteristic, complemented
39#17989097—28no—
40C2×#14556575C2211yescharacteristic
41C2×#14556575C2211yescharacteristic
42C2×#14556574C2211yescharacteristic
43C2×#14556573C2211yescharacteristic
44C2×#14556573C2211yescharacteristic
45C2×#14556573C2211yescharacteristic
46C2×#14556573C2211yescharacteristic
47C2×#14556572C2211yescharacteristic, complemented
48C2×#14556571C2211yescharacteristic
49C2×#14556571C2211yescharacteristic
50C2×#14556571C2211yescharacteristic
51C2×#14556570C2211yescharacteristic
52C2×#14556570C2211yescharacteristic
53C2×#14556568C2211yescharacteristic, complemented
54C2×#14556568C2211yescharacteristic, complemented
55C2×#14556568C2211yescharacteristic, complemented
56C2×#14556563C2211yescharacteristic
57C2×#14556563C2211yescharacteristic
58C2×#14556562C2211yescharacteristic
59C2×#14556559C2211yescharacteristic
60C2×#14556559C2211yescharacteristic
61C2×#14556559C2211yescharacteristic
62C2×D4×Dic73C2211yescharacteristic
63C2×D4×Dic73C2211yescharacteristic
64C2×D4×Dic73C2211yescharacteristic, complemented
65C2×#14556551C2211yescharacteristic
66C2×#14556551C2211yescharacteristic
67C2×#14556549C2211yescharacteristic
68C22×C4⋊Dic73C2211yescharacteristic, complemented
69#17988522C2211yescharacteristic
70#17988521C2211yescharacteristic, complemented
71#17988519C2211yescharacteristic, complemented
72#17988519C2211yescharacteristic, complemented
73#17988519C2211yescharacteristic, complemented
74#17988518C2211yescharacteristic, complemented
75#17988517C2211yescharacteristic, complemented
76#17988517C2211yescharacteristic, complemented
77#17988516C2211yescharacteristic
78#17988514C2211yescharacteristic
79#17988514C2211yescharacteristic
80#17988514C2211yescharacteristic
81#17988512C2211yescharacteristic, complemented
82#17988512C2211yescharacteristic, complemented
83#17988511C2211yescharacteristic
84#17988510C2211yescharacteristic
85#17988510C2211yescharacteristic
86#17988510C2211yescharacteristic
87#17988510C2211yescharacteristic
88#17988510C2211yescharacteristic, complemented
89#17988510C2211yescharacteristic, complemented
90#17988510C2211yescharacteristic, complemented
91#17988510C2211yescharacteristic, complemented
92#17988510C2211yescharacteristic, complemented
93#17988508C2211yescharacteristic, complemented
94#17988508C2211yescharacteristic, complemented
95#17988508C2211yescharacteristic, complemented
96#17988503C2211yescharacteristic
97#17988503C2211yescharacteristic
98#17988503C2211yescharacteristic
99#17988503C2211yescharacteristic
100#17988502C2211yescharacteristic
101#17988502C2211yescharacteristic
102#17988502C2211yescharacteristic
103#17988502C2211yescharacteristic
104#17988501C2211yescharacteristic
105#17988501C2211yescharacteristic
106#17988501C2211yescharacteristic, complemented
107#17988501C2211yescharacteristic, complemented
108#17988499C2211yescharacteristic, complemented
109#17988495C2211yescharacteristic
110#17988495C2211yescharacteristic
111#17988491C2211yescharacteristic, complemented
112#17988490C2211yescharacteristic
113#17988490C2211yescharacteristic
114#17988490C2211yescharacteristic, complemented
115#17988487C2211yescharacteristic
116#17988487C2211yescharacteristic
117#17988487C2211yescharacteristic
118#17988487C2211yescharacteristic
119#17988484C2211yescharacteristic, complemented
120#17988484C2211yescharacteristic, complemented
121#17988484C2211yescharacteristic, complemented
122#17988482C2211yescharacteristic, complemented
123#17988482C2211yescharacteristic, complemented
124#17988481C2211yescharacteristic
125#17988481C2211yescharacteristic, complemented
126#17988480C2211yescharacteristic, complemented
127#17988478C2211yescharacteristic
128#17988478C2211yescharacteristic
129#17988476C2211yescharacteristic
130#17988476C2211yescharacteristic
131#17988476C2211yescharacteristic
132#17988475C2211yescharacteristic
133#17988475C2211yescharacteristic, complemented
134#17988474C2211yescharacteristic, complemented
135#17988474C2211yescharacteristic, complemented
136#17988474C2211yescharacteristic, complemented
137#17988474C2211yescharacteristic, complemented
138#17988467C2211yescharacteristic
139#17988467C2211yescharacteristic
140#17988467C2211yescharacteristic
141#17988467C2211yescharacteristic, complemented
142#17988466C2211yescharacteristic
143#17988463C2211yescharacteristic
144#17988463C2211yescharacteristic
145#17988462C2211yescharacteristic
146#17988462C2211yescharacteristic
147#17988462C2211yescharacteristic
148#17988462C2211yescharacteristic, complemented
149#17988462C2211yescharacteristic, complemented
150#17988462C2211yescharacteristic, complemented
151#17988462C2211yescharacteristic, complemented
152#17988462C2211yescharacteristic, complemented
153#17988461C2211yescharacteristic
154#17988461C2211yescharacteristic
155#17988461C2211yescharacteristic
156#17988461C2211yescharacteristic
157#17988461C2211yescharacteristic
158#17988461C2211yescharacteristic
159#17988460C2211yescharacteristic
160#17988460C2211yescharacteristic, complemented
161#17988457C2211yescharacteristic, complemented
162#17988452C2211yescharacteristic, complemented
163#17988449C2211yescharacteristic
164#17988449C2211yescharacteristic
165#17988448C2211yescharacteristic, complemented
166#17988445C2211yescharacteristic, complemented
167#17988444C2211yescharacteristic
168#17988444C2211yescharacteristic
169#17988442C2211yescharacteristic
170#17988442C2211yescharacteristic
171#17988442C2211yescharacteristic
172C4×#11924007C2211yescharacteristic, complemented
173#17988432C2211yescharacteristic, complemented
174C2×#123×C73C2211yescharacteristic, complemented
175C2×#121×C73C2211yescharacteristic
176#400×C73C2211yescharacteristic, complemented
177#397×C73C2211yescharacteristic, complemented
178#394×C73C2211yescharacteristic, complemented
179#392×C73C2211yescharacteristic
180#392×C73C2211yescharacteristic
181#392×C73C2211yescharacteristic, complemented
182#390×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic, complemented
184#388×C73C2211yescharacteristic, complemented
185#386×C73C2211yescharacteristic
186#386×C73C2211yescharacteristic
187#386×C73C2211yescharacteristic, complemented
188#380×C73C2211yescharacteristic
189C24×D73C2311yescharacteristic
190C2×#11924027—24no—
191C2×#11924027—42no—
192C2×#11924027—42no—
193C22×Dic146C2311yescharacteristic
194C22×Dic146C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C22×C4×D73—24no—
207C22×C4×D73—42no—
208C22×C4×D73—42no—
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213#14556586—24no—
214#14556584—24no—
215#14556582—24no—
216#14556581—24no—
217#14556575—24no—
218#14556575—42no—
219#14556574—24no—
220#14556573—24no—
221#14556573—24no—
222#14556573—24no—
223#14556573—42no—
224#14556572—42no—
225#14556571—24no—
226#14556571—24no—
227#14556571—42no—
228#14556570—24no—
229#14556570—42no—
230#14556568—24no—
231#14556568—24no—
232#14556568—42no—
233#14556563—24no—
234#14556563—42no—
235#14556562—24no—
236#14556559—24no—
237#14556559—24no—
238#14556559—42no—
239D4×Dic73—24no—
240D4×Dic73—24no—
241D4×Dic73—24no—
242#14556551—24no—
243#14556551D418yescomplemented
244#14556549—24no—
245C2×C4⋊Dic73—24no—
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
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×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×#11924007C2311yescharacteristic
268C2×#11924007C2311yescharacteristic
269C2×#11924007C2311yescharacteristic
270C2×#11924007C2311yescharacteristic
271C2×#11924007C2311yescharacteristic
272C2×#11924007C2311yescharacteristic
273C2×#11924007C2311yescharacteristic
274C2×#11924007C2311yescharacteristic
275C2×#11924007C2311yescharacteristic
276C2×#11924007C2311yescharacteristic
277C2×#11924007C2311yescharacteristic
278C2×#11924007C2311yescharacteristic
279C2×#11924007C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×C22⋊Dic73C2311yescharacteristic
289C2×C22⋊Dic73C2311yescharacteristic
290C2×C22⋊Dic73C2311yescharacteristic
291C2×C22⋊Dic73C2311yescharacteristic
292C2×C22⋊Dic73C2311yescharacteristic
293C2×C22⋊Dic73C2311yescharacteristic
294C2×C22⋊Dic73C2311yescharacteristic
295C2×C22⋊Dic73C2311yescharacteristic
296C2×C22⋊Dic73C2311yescharacteristic
297C2×C22⋊Dic73C2311yescharacteristic
298C2×C22⋊Dic73C2311yescharacteristic
299C2×C22⋊Dic73C2311yescharacteristic
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×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322C2×C4×Dic73C2311yescharacteristic
323C2×C4×Dic73C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
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
348C22×D4×C73C2311yescharacteristic
349C22×D4×C73C2311yescharacteristic
350C22×D4×C73C2311yescharacteristic
351C22×D4×C73C2311yescharacteristic
352C22×D4×C73C2311yescharacteristic
353C22×D4×C73C2311yescharacteristic
354C23×C4×C73C2311yescharacteristic
355C23×C4×C73C2311yescharacteristic
356#123×C73—24no—
357#121×C73—24no—
358C2×C4⋊C4×C73C2311yescharacteristic
359C2×C4⋊C4×C73C2311yescharacteristic
360C2×C4⋊C4×C73C2311yescharacteristic
361C2×C4⋊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×C22⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73C2311yescharacteristic
372C2×C22⋊C4×C73C2311yescharacteristic
373C2×C22⋊C4×C73C2311yescharacteristic
374C2×C22⋊C4×C73C2311yescharacteristic
375C2×C22⋊C4×C73C2311yescharacteristic
376C2×C42×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
394#11924027—416no—
395C2×Dic146—22no—
396C2×Dic146—22no—
397C2×Dic146—22no—
398C2×Dic146—41no—
399C2×Dic146—41no—
400C2×Dic146—41no—
401C2×C22⋊D73—22no—
402C2×C22⋊D73—22no—
403C2×C22⋊D73—22no—
404C2×C22⋊D73—22no—
405C2×C22⋊D73—22no—
406C2×C22⋊D73—22no—
407C2×C22⋊D73—22no—
408C2×C22⋊D73—41no—
409C2×C22⋊D73—41no—
410C2×C22⋊D73—41no—
411C2×C22⋊D73—41no—
412C2×C22⋊D73—41no—
413C2×C22⋊D73—41no—
414C2×C22⋊D73—41no—
415C2×C22⋊D73—41no—
416C2×C22⋊D73—41no—
417C2×C22⋊D73—41no—
418C2×C22⋊D73C2×D414yes—
419C22×Dic73—22no—
420C22×Dic73—22no—
421C22×Dic73—22no—
422C22×Dic73—22no—
423C22×Dic73—41no—
424C22×Dic73—41no—
425C22×Dic73—41no—
426C22×Dic73—41no—
427C22×Dic73—41no—
428C22×Dic73—41no—
429C22×Dic73—41no—
430C22×Dic73—41no—
431C22×Dic73—41no—
432C22×Dic73—41no—
433C22×Dic73C2×D414yes—
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C2×C4×D73—22no—
449C2×C4×D73—22no—
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—22no—
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—416no—
456C2×C4×D73—41no—
457C2×C4×D73—41no—
458C2×C4×D73—41no—
459C2×C4×D73—41no—
460C2×C4×D73C2×D414yes—
461C4⋊Dic73—22no—
462C4⋊Dic73—22no—
463C4⋊Dic73—22no—
464C4⋊Dic73—22no—
465C4⋊Dic73—22no—
466C4⋊Dic73—22no—
467C4⋊Dic73—22no—
468C4⋊Dic73—22no—
469C4⋊Dic73—22no—
470C4⋊Dic73—41no—
471C4⋊Dic73—41no—
472C4⋊Dic73—41no—
473C4⋊Dic73—41no—
474C4⋊Dic73—41no—
475C4⋊Dic73—41no—
476C4⋊Dic73—41no—
477#11924007—22no—
478#11924007—22no—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007—22no—
486#11924007—41no—
487#11924007—41no—
488#11924007—41no—
489#11924007—41no—
490#11924007—41no—
491#11924007—41no—
492#11924007—41no—
493#11924007—41no—
494#11924007C2×D414yes—
495C22⋊Dic73—22no—
496C22⋊Dic73—22no—
497C22⋊Dic73—22no—
498C22⋊Dic73—22no—
499C22⋊Dic73—22no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—22no—
503C22⋊Dic73—41no—
504C22⋊Dic73—41no—
505C22⋊Dic73—41no—
506C22⋊Dic73—41no—
507C22⋊Dic73—41no—
508C22⋊Dic73—41no—
509C22⋊Dic73—41no—
510C22⋊Dic73—41no—
511C22⋊Dic73—41no—
512C22⋊Dic73—41no—
513C22⋊Dic73—41no—
514C22⋊Dic73—41no—
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—41no—
525#11924005—41no—
526#11924005—41no—
527#11924005—41no—
528#11924005—41no—
529#11924005—41no—
530#11924005—41no—
531#11924005—41no—
532#11924005C2×D414yes—
533C4×Dic73—22no—
534C4×Dic73—22no—
535C4×Dic73—41no—
536C4×Dic73—41no—
537C4×Dic73—41no—
538C4×Dic73C2×D414yes—
539C24×C73C2411yescharacteristic
540C24×C73C2411yescharacteristic
541C24×C73C2411yescharacteristic
542C24×C73C2411yescharacteristic
543C2×D4×C73—22no—
544C2×D4×C73—22no—
545C2×D4×C73—22no—
546C2×D4×C73—22no—
547C2×D4×C73—22no—
548C2×D4×C73—22no—
549C2×D4×C73—22no—
550C2×D4×C73—22no—
551C2×D4×C73—41no—
552C2×D4×C73—41no—
553C2×D4×C73—41no—
554C2×D4×C73—41no—
555C2×D4×C73—41no—
556C2×D4×C73—41no—
557C2×D4×C73—41no—
558C2×D4×C73—41no—
559C2×D4×C73—41no—
560C2×D4×C73—41no—
561C22×C4×C73—22no—
562C22×C4×C73—22no—
563C22×C4×C73—22no—
564C22×C4×C73—41no—
565C22×C4×C73—41no—
566C22×C4×C73—41no—
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C22×C4×C73C2411yescharacteristic
571C22×C4×C73C2411yescharacteristic
572C22×C4×C73C2411yescharacteristic
573C22×C4×C73C2411yescharacteristic
574C22×C4×C73C2411yescharacteristic
575C22×C4×C73C2411yescharacteristic
576C22×C4×C73C2411yescharacteristic
577C22×C4×C73C2411yescharacteristic
578C4⋊C4×C73—22no—
579C4⋊C4×C73—22no—
580C4⋊C4×C73—22no—
581C4⋊C4×C73—41no—
582C22⋊C4×C73—22no—
583C22⋊C4×C73—22no—
584C22⋊C4×C73—22no—
585C22⋊C4×C73—22no—
586C22⋊C4×C73—41no—
587C22⋊C4×C73—41no—
588C22⋊C4×C73—41no—
589C22⋊C4×C73—41no—
590C22⋊C4×C73—41no—
591C22⋊C4×C73—41no—
592C22⋊C4×C73—41no—
593C22⋊C4×C73—41no—
594C22⋊C4×C73—41no—
595C22⋊C4×C73C2×D414yes—
596C42×C73—41no—
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×C73—21no—
610C23×C73—21no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—21no—
621C23×C73—21no—
622C23×C73—21no—
623C23×C73C22×D412yes—
624C23×C732−1+412yes—
625C23×C73C2511yescharacteristic
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×D73C22×D412yes—
646C22×D73H(5,𝔽2)12yes—
647D4×C73—44no—
648D4×C73—44no—
649D4×C73—44no—
650D4×C73—44no—
651D4×C73—82no—
652D4×C73—82no—
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—21no—
683C2×C4×C73—44no—
684C2×C4×C73—44no—
685C2×C4×C73C22×D412yes—
686C2×C4×C73C22×D412yes—
687C2×C4×C73H(5,𝔽2)12yes—
688C22⋊D73—44no—
689C22⋊D73—44no—
690C22⋊D73—44no—
691C22⋊D73—44no—
692C22⋊D73—82no—
693C22⋊D73—82no—
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×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—21no—
731C2×Dic73—21no—
732C2×Dic73—21no—
733C2×Dic73—44no—
734C2×Dic73—44no—
735C2×Dic73—44no—
736C2×Dic73—82no—
737C2×Dic73—82no—
738C2×Dic73C22×D412yes—
739C2×Dic73C22×D412yes—
740C2×Dic73C22×D412yes—
741C4×D73—28no—
742C4×D73—44no—
743C4×D73—44no—
744C4×D73—44no—
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×C73—41no—
762C22×C73—41no—
763C22×C73—41no—
764C22×C73—41no—
765C22×C73—41no—
766C22×C73—41no—
767C22×C73—41no—
768C22×C73—41no—
769C22×C73—41no—
770C22×C73—41no—
771C22×C73—41no—
772C22×C73—41no—
773C22×C73—41no—
774C22×C73—41no—
775C22×C73C23×D411yescharacteristic
776C22×C73C2×H(5,𝔽2)11yescharacteristic
777C22×C73C2×H(5,𝔽2)11yescharacteristic
778C22×C73C2×2−1+411yescharacteristic
779C22×C73#58511yescharacteristic
780C22×C73#58511yescharacteristic
781C22×C73#58511yescharacteristic
782C2×D73—22no—
783C2×D73—22no—
784C2×D73—22no—
785C2×D73—22no—
786C2×D73—22no—
787C2×D73—22no—
788C2×D73—416no—
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—41no—
801C4×C73—41no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807C4×C73—41no—
808Dic73—22no—
809Dic73—22no—
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—81no—
826C2×C73—81no—
827C2×C73#344911yescharacteristic
828C2×C73#348411yescharacteristic
829C2×C73#348911yescharacteristic
830C2×C73#353311yescharacteristic
831C2×C73#353511yescharacteristic
832C2×C73#353911yescharacteristic
833C2×C73#354111yescharacteristic
834D73—42no—
835D73—42no—
836C2×#539—731no—
837C2×#525—731no—
838#2849—731no—
839#2848—731no—
840#2707—731no—
841#2706—731no—
842#2704—731no—
843#2703D7311yescharacteristic, complemented
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#2319—731no—
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×#123C2×D7311yescharacteristic, complemented
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×#121C2×D7311yescharacteristic
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×D4—731no—
905C2×#117—731no—
906C22×C4⋊C4—731no—
907#400C2×D7311yescharacteristic, complemented
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#397C2×D7311yescharacteristic, complemented
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#394C2×D7311yescharacteristic, complemented
949#393—731no—
950#392—731no—
951#392—731no—
952#392C2×D7311yescharacteristic
953#392C2×D7311yescharacteristic
954#392C2×D7311yescharacteristic, complemented
955#391—731no—
956#390—731no—
957#390—731no—
958#390—731no—
959#390—731no—
960#390—731no—
961#390—731no—
962#390—731no—
963#390C2×D7311yescharacteristic
964#389—731no—
965#389—731no—
966#389—731no—
967#389—731no—
968#389—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#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#386C2×D7311yescharacteristic
993#386C2×D7311yescharacteristic
994#386C2×D7311yescharacteristic, complemented
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#381—731no—
1015#381—731no—
1016#380—731no—
1017#380—731no—
1018#380—731no—
1019#380C2×D7311yescharacteristic
1020#379—731no—
1021#379—731no—
1022#379—731no—
1023C4×C4⋊C4—731no—
1024#376—731no—
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×D4C22×D7311yescharacteristic
1038C22×D4C22×D7311yescharacteristic
1039C22×D4C22×D7311yescharacteristic
1040C22×D4C22×D7311yescharacteristic
1041C22×D4C22×D7311yescharacteristic
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—24no—
1062#123—2922no—
1063#123—2922no—
1064#123—2922no—
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—24no—
1079#121—2922no—
1080#121—1464no—
1081#121—1464no—
1082#120—2922no—
1083#120—1464no—
1084#120—1464no—
1085C4×D4—738no—
1086C4×D4—1464no—
1087C4×D4—1464no—
1088C4×D4—1464no—
1089C4×D4—1464no—
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—731no—
1123C2×C4⋊C4—731no—
1124C2×C4⋊C4—731no—
1125C2×C4⋊C4—1464no—
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⋊C4C22×D7311yescharacteristic
1169C2×C22⋊C4C22×D7311yescharacteristic
1170C2×C22⋊C4C22×D7311yescharacteristic
1171C2×C22⋊C4C22×D7311yescharacteristic
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×C42—731no—
1185C2×C42—731no—
1186C2×C42—731no—
1187C2×C42—731no—
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#95—731no—
1212#95—731no—
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—1462no—
1228C24—1462no—
1229C24—1462no—
1230C24C23×D7311yescharacteristic
1231C24C23×D7311yescharacteristic
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—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—2921no—
1260C2×D4—2921no—
1261C2×D4—2921no—
1262C2×D4—2921no—
1263C2×D4—2921no—
1264C2×D4—2921no—
1265C2×D4—2921no—
1266C2×D4—2921no—
1267C2×D4—2921no—
1268C2×D4—2921no—
1269C2×D4—734no—
1270C2×D4—1462no—
1271C2×D4—1462no—
1272C2×D4—1462no—
1273C2×D4—1462no—
1274C2×D4—1462no—
1275C2×D4—1462no—
1276C2×D4—1462no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—41no—
1283C22×C4—2921no—
1284C22×C4—2921no—
1285C22×C4—2921no—
1286C22×C4—2921no—
1287C22×C4—29216no—
1288C22×C4—2921no—
1289C22×C4—2921no—
1290C22×C4—2921no—
1291C22×C4—2921no—
1292C22×C4—2921no—
1293C22×C4—2921no—
1294C22×C4—2921no—
1295C22×C4—2921no—
1296C22×C4—2921no—
1297C22×C4—2921no—
1298C22×C4—734no—
1299C22×C4—734no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—731no—
1304C22×C4—731no—
1305C22×C4—731no—
1306C22×C4—731no—
1307C22×C4—731no—
1308C22×C4—731no—
1309C22×C4—731no—
1310C22×C4—731no—
1311C22×C4—731no—
1312C22×C4—731no—
1313C22×C4—731no—
1314C22×C4—1462no—
1315C22×C4—1462no—
1316C22×C4—1462no—
1317C22×C4—1462no—
1318C22×C4—1462no—
1319C22×C4—1462no—
1320C22×C4—1462no—
1321C22×C4—1462no—
1322C22×C4—1462no—
1323C22×C4—1462no—
1324C22×C4—1462no—
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—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—41no—
1340C4⋊C4—2921no—
1341C4⋊C4—2921no—
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—2921no—
1353C4⋊C4—2921no—
1354C4⋊C4—2921no—
1355C4⋊C4—734no—
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⋊C4—1462no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
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—2921no—
1404C22⋊C4—2921no—
1405C22⋊C4—2921no—
1406C22⋊C4—2921no—
1407C22⋊C4—734no—
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⋊C4—1462no—
1425C22⋊C4D4×D7314yes—
1426C42—41no—
1427C42—2921no—
1428C42—2921no—
1429C42—2921no—
1430C42—734no—
1431C42—1462no—
1432C42—1462no—
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—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—2924no—
1460C23—2924no—
1461C23—2924no—
1462C23—2924no—
1463C23—2924no—
1464C23—2924no—
1465C23—2924no—
1466C23—732no—
1467C23—732no—
1468C23—1461no—
1469C23—1461no—
1470C23—1461no—
1471C23—1461no—
1472C23—1461no—
1473C23—1461no—
1474C23—1461no—
1475C23—1461no—
1476C23—1461no—
1477C23—1461no—
1478C23—1461no—
1479C23—1461no—
1480C23C2×D4×D7312yes—
1481C23#1455663812yes—
1482C23C24×D7311yescharacteristic
1483Q8—2924no—
1484Q8—5842no—
1485D4—44no—
1486D4—44no—
1487D4—44no—
1488D4—44no—
1489D4—82no—
1490D4—82no—
1491D4—2924no—
1492D4—2924no—
1493D4—2924no—
1494D4—2924no—
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—44no—
1528C2×C4—44no—
1529C2×C4—2924no—
1530C2×C4—2924no—
1531C2×C4—2924no—
1532C2×C4—2924no—
1533C2×C4—2924no—
1534C2×C4—2924no—
1535C2×C4—5842no—
1536C2×C4—5842no—
1537C2×C4—732no—
1538C2×C4—732no—
1539C2×C4—732no—
1540C2×C4—1468no—
1541C2×C4—1461no—
1542C2×C4—1461no—
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×C4—1461no—
1579C2×C4—1461no—
1580C2×C4C2×D4×D7312yes—
1581C2×C4C2×D4×D7312yes—
1582C2×C4#1455663712yes—
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—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—29216no—
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—
1626C22C22×D4×D7311yescharacteristic
1627C22H(5,𝔽2)×D7311yescharacteristic
1628C22C2×#1455663711yescharacteristic
1629C22C2×#1455663811yescharacteristic
1630C22#1798942211yescharacteristic
1631C22#1798942211yescharacteristic
1632C22#1798942211yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—2921no—
1645C4—2921no—
1646C4—2921no—
1647C4—2921no—
1648C4—2921no—
1649C4—2921no—
1650C4—2921no—
1651C4—2921no—
1652C4—2921no—
1653C4—2921no—
1654C4—2921no—
1655C4—1462no—
1656C4—1462no—
1657C4—1462no—
1658C2—42no—
1659C2—42no—
1660C2—81no—
1661C2—81no—
1662C2—2922no—
1663C2—2922no—
1664C2#2262326211yescharacteristic
1665C2#2262356111yescharacteristic
1666C2#2262360211yescharacteristic
1667C2#2262410011yescharacteristic
1668C2#2262412911yescharacteristic
1669C2#2262419011yescharacteristic
1670C2#2262421811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2703C2
hypercenter#2703D73
hypocenterC73#36723
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2703

Complements

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

NH ≅ G/Ntype
1. C2×#17989181C2semidirect
2. C2×#17989097C2semidirect
3. #22618222C2semidirect
4. #22618219C2semidirect
5. #22616636C2semidirect
6. #22616613C2semidirect
7. #22616589C2semidirect
8. #22616547C2semidirect
9. #22616504C2semidirect
10. #22616495C2semidirect
11. #22616317C2semidirect
12. #22616304C2semidirect
13. #22616298C2semidirect
14. #22616282C2semidirect
15. #22616277C2semidirect
16. #22616269C2semidirect
17. #22616269C2semidirect
18. #22616249C2semidirect
19. #22616249C2semidirect
20. #22615853C2semidirect
21. #22615775C2semidirect
22. #22615632C2semidirect
23. #22615551C2semidirect
24. #22615535C2semidirect
25. #22615512C2semidirect
26. #22615275C2semidirect
27. #22615133C2semidirect
28. #22613269C2semidirect
29. #22613265C2semidirect
30. #22612572C2semidirect
31. C73×#2703C2semidirect
36. C2×#14556584C22semidirect
37. C2×#14556582C22semidirect
38. C2×#14556581C22semidirect
47. C2×#14556572C22semidirect
53. C2×#14556568C22semidirect
54. C2×#14556568C22semidirect
55. C2×#14556568C22semidirect
64. C2×D4×Dic73C22semidirect
68. C22×C4⋊Dic73C22semidirect
70. #17988521C22semidirect
71. #17988519C22semidirect
72. #17988519C22semidirect
73. #17988519C22semidirect
74. #17988518C22semidirect
75. #17988517C22semidirect
76. #17988517C22semidirect
81. #17988512C22semidirect
82. #17988512C22semidirect
88. #17988510C22semidirect
89. #17988510C22semidirect
90. #17988510C22semidirect
91. #17988510C22semidirect
92. #17988510C22semidirect
93. #17988508C22semidirect
94. #17988508C22semidirect
95. #17988508C22semidirect
106. #17988501C22semidirect
107. #17988501C22semidirect
108. #17988499C22semidirect
111. #17988491C22semidirect
114. #17988490C22semidirect
119. #17988484C22semidirect
120. #17988484C22semidirect
121. #17988484C22semidirect
122. #17988482C22semidirect
123. #17988482C22semidirect
125. #17988481C22semidirect
126. #17988480C22semidirect
133. #17988475C22semidirect
134. #17988474C22semidirect
135. #17988474C22semidirect
136. #17988474C22semidirect
137. #17988474C22semidirect
141. #17988467C22semidirect
148. #17988462C22semidirect
149. #17988462C22semidirect
150. #17988462C22semidirect
151. #17988462C22semidirect
152. #17988462C22semidirect
160. #17988460C22semidirect
161. #17988457C22semidirect
162. #17988452C22semidirect
165. #17988448C22semidirect
166. #17988445C22semidirect
172. C4×#11924007C22semidirect
173. #17988432C22semidirect
174. C2×#123×C73C22semidirect
176. #400×C73C22semidirect
177. #397×C73C22semidirect
178. #394×C73C22semidirect
181. #392×C73C22semidirect
183. #388×C73C22semidirect
184. #388×C73C22semidirect
187. #386×C73C22semidirect
243. #14556551D4semidirect
843. #2703D73semidirect
867. C73#36723semidirect
884. C2×#123C2×D73semidirect
907. #400C2×D73semidirect
922. #397C2×D73semidirect
948. #394C2×D73semidirect
954. #392C2×D73semidirect
979. #388C2×D73semidirect
980. #388C2×D73semidirect
994. #386C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891812
C2×#179890972
#226182222
#226182192
#226166362
#226166132
#226165892
#226165472
#226165042
#226164952
#226163172
#226163042
#226162982
#226162822
#226162772
#226162692
#226162492
#226158532
#226157752
#226156322
#226155512
#226155352
#226155122
#226152752
#226151332
#226132692
#226132652
#226125722
C73×#27032
#3672373