Finite Group Databasebeta

← #33954473

Subgroups — #33954473

Order 18688.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623321C211yesmaximal, characteristic, complemented
2#22620208C214yesmaximal, complemented
3#22620193C214yesmaximal, complemented
4#22620145C214yesmaximal, complemented
5#22620130C214yesmaximal, complemented
6#22619854C212yesmaximal, complemented
7#22619736C211yesmaximal, characteristic, complemented
8#22619728C211yesmaximal, characteristic, complemented
9#22619403C211yesmaximal, characteristic, complemented
10#22619395C211yesmaximal, characteristic, complemented
11#22619173C212yesmaximal, complemented
12C4×#14556622C212yesmaximal, complemented
13C4×#14556617C212yesmaximal, complemented
14#22618569C211yesmaximal, characteristic, complemented
15C2×#520×C73C211yesmaximal, characteristic, complemented
16C2×#14556622C2212yes—
17C2×#14556617C2212yes—
18#17989208C2212yescomplemented
19#17989208C2212yescomplemented
20#17989199C2212yescomplemented
21#17989192C2212yescomplemented
22#17989184—21no—
23#17989184—21no—
24#17989175—21no—
25#17989175—21no—
26#17989144C2211yescharacteristic
27#17989137C2211yescharacteristic
28#17989115—22no—
29#17989115—22no—
30#17989098C2212yes—
31C4×#11924028C2212yes—
32#17988922C2214yescomplemented
33#17988917C2214yescomplemented
34#17988905C2214yescomplemented
35#17988900C2214yescomplemented
36#17988894C2214yescomplemented
37#17988887C2214yescomplemented
38#17988882C2212yescomplemented
39#17988877C2212yescomplemented
40#17988872C2212yescomplemented
41#17988867C2212yescomplemented
42#17988809C2214yescomplemented
43#17988802C2214yescomplemented
44#17988797C2212yescomplemented
45#17988792C2212yescomplemented
46#17988787C2212yescomplemented
47#17988782C2212yescomplemented
48#17988749C2214yes—
49#17988749C2214yes—
50#17988732C2214yes—
51#17988732C2214yes—
52#17988697C2214yescomplemented
53#17988692C2214yescomplemented
54#17988687C2214yescomplemented
55#17988685C2214yescomplemented
56C4×#11924018C2214yescomplemented
57C4×#11924015C2214yescomplemented
58C4×#11924016C2214yescomplemented
59C4×#11924013C2214yescomplemented
60#17988648C2214yescomplemented
61#17988648C2214yescomplemented
62#17988627C2212yes—
63#17988627C2212yes—
64#17988611C2211yescharacteristic
65#17988611C2211yescharacteristic
66#17988596C2212yes—
67#17988592C2212yes—
68#17988586C2212yes—
69#17988586C2212yes—
70#17988551C2212yes—
71C4×#11924012C2212yes—
72C22×#41×C73C2211yescharacteristic
73#520×C73—22no—
74#520×C73—22no—
75#520×C73C2214yes—
76#520×C73C2214yes—
77C2×C4×Q8×C73C2211yescharacteristic
78C2×C4×Q8×C73C2211yescharacteristic
79C2×C4×D4×C73—21no—
80C2×C4×D4×C73—21no—
81C2×C4×D4×C73C2211yescharacteristic
82C2×C4×D4×C73C2211yescharacteristic
83C2×#117×C73—21no—
84C2×#117×C73C2211yescharacteristic
85C22×C4⋊C4×C73—21no—
86C22×C4⋊C4×C73C2211yescharacteristic
87C2×#11924028C2312yes—
88#14556622—28no—
89#14556617—28no—
90C2×#11924018C2314yes—
91C2×#11924016C2314yes—
92C2×#11924015C2314yes—
93C2×#11924013C2314yes—
94C2×#11924012C2312yes—
95C2×#11924012C2312yes—
96#14556591C2311yescharacteristic
97#14556591C2311yescharacteristic
98#14556591C2311yescharacteristic
99#14556588C2311yescharacteristic
100#14556586—22no—
101#14556586—22no—
102#14556584—22no—
103#14556584—22no—
104#14556583C2312yes—
105#14556581—22no—
106#14556581—22no—
107#14556579C2312yes—
108#14556577—22no—
109#14556577—22no—
110#14556576—22no—
111#14556576—22no—
112#14556574—22no—
113#14556573—22no—
114#14556573—22no—
115#14556570—21no—
116#14556570—21no—
117#14556570C2312yes—
118#14556570C2312yes—
119#14556569—22no—
120#14556569—22no—
121#14556565—21no—
122#14556565—21no—
123#14556565C2312yes—
124#14556565C2312yes—
125#14556564—22no—
126#14556564—22no—
127#14556560—22no—
128C4×Dic146—21no—
129C4×Dic146—21no—
130C4×Dic146C2312yes—
131C4×Dic146C2312yes—
132C4×D292—21no—
133C4×D292—21no—
134C4×D292C2312yes—
135C4×D292C2312yes—
136C4×C22⋊D73—22no—
137C4×C22⋊D73—22no—
138C4×C22⋊D73—22no—
139C4×C22⋊D73—22no—
140#14556550C2312yes—
141#14556548—22no—
142C42×D73—22no—
143#14556524C2314yes—
144#14556524C2314yes—
145#14556522C2314yes—
146#14556522C2314yes—
147C4⋊#10596831C2312yes—
148C4⋊#10596831C2312yes—
149C4⋊#10596831C2312yes—
150C4⋊#10596831C2312yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556514C2314yes—
154#14556514C2314yes—
155#14556512C2314yes—
156#14556512C2314yes—
157#14556511C2314yes—
158#14556511C2314yes—
159C22⋊#10596831C2314yes—
160C22⋊#10596831C2314yes—
161#14556502C2314yes—
162C4×#10596831C2314yes—
163C2×#41×C73—24no—
164C2×#41×C73—24no—
165C2×#41×C73—22no—
166C2×#41×C73C2314yes—
167C22×Q8×C73C2311yescharacteristic
168C22×D4×C73—21no—
169C22×D4×C73C2311yescharacteristic
170C23×C4×C73—21no—
171C23×C4×C73—21no—
172C23×C4×C73—21no—
173C23×C4×C73—21no—
174C23×C4×C73C2311yescharacteristic
175C4×Q8×C73—22no—
176C4×Q8×C73—21no—
177C4×Q8×C73—21no—
178C4×Q8×C73C2312yes—
179C4×Q8×C73C2312yes—
180C4×Q8×C73C2314yes—
181C4×D4×C73—24no—
182C4×D4×C73—24no—
183C4×D4×C73—24no—
184C4×D4×C73—24no—
185C4×D4×C73—22no—
186C4×D4×C73—21no—
187C4×D4×C73—21no—
188C4×D4×C73C2312yes—
189C4×D4×C73C2312yes—
190C4×D4×C73C2314yes—
191#117×C73—24no—
192#117×C73—24no—
193#117×C73D412yes—
194#117×C73D412yes—
195#117×C73C2312yes—
196#117×C73C2312yes—
197C2×C4⋊C4×C73—21no—
198C2×C4⋊C4×C73—21no—
199C2×C4⋊C4×C73—21no—
200C2×C4⋊C4×C73—22no—
201C2×C4⋊C4×C73—24no—
202C2×C4⋊C4×C73—24no—
203C2×C4⋊C4×C73D411yescharacteristic
204C2×C4⋊C4×C73D411yescharacteristic
205C2×C4⋊C4×C73C2311yescharacteristic
206C2×C4⋊C4×C73C2311yescharacteristic
207C2×C4⋊C4×C73C2314yes—
208C2×C22⋊C4×C73—21no—
209C2×C22⋊C4×C73—21no—
210C2×C22⋊C4×C73D411yescharacteristic
211C2×C22⋊C4×C73D411yescharacteristic
212C2×C42×C73—21no—
213C2×C42×C73—21no—
214C2×C42×C73C2311yescharacteristic
215C2×C42×C73C2311yescharacteristic
216#11924028—24no—
217#11924028—24no—
218C2×Dic146—21no—
219C2×Dic146—21no—
220C2×Dic146C2412yes—
221C2×D292—21no—
222C2×D292—21no—
223C2×D292C2412yes—
224C2×C22⋊D73—22no—
225C2×C22⋊D73—22no—
226C2×C22⋊D73—22no—
227C2×C4×D73—22no—
228C2×C4×D73—22no—
229C2×C4×D73—22no—
230#11924018—28no—
231#11924016—28no—
232#11924015—28no—
233#11924013—28no—
234#11924012—24no—
235#11924012—24no—
236C2×#10596831C2414yes—
237C2×#10596831C2414yes—
238C4⋊Dic73—21no—
239C4⋊Dic73—21no—
240C4⋊Dic73—21no—
241C4⋊Dic73—21no—
242C4⋊Dic73C2412yes—
243C4⋊Dic73C2412yes—
244#11924007—22no—
245#11924007—22no—
246#11924007—22no—
247#11924007—22no—
248#11924007—22no—
249#11924007—22no—
250C22⋊Dic73—22no—
251C22⋊Dic73—22no—
252C22⋊Dic73—22no—
253#11924005—22no—
254#11924005—22no—
255#11924005—22no—
256#11924005—22no—
257#11924005—22no—
258#11924005—22no—
259C4×Dic73—22no—
260C4×Dic73—22no—
261C4×Dic73—22no—
262C24×C73—21no—
263C24×C73C2×D411yescharacteristic
264#41×C73—216no—
265#41×C73—28no—
266#41×C73—28no—
267C2×Q8×C73—21no—
268C2×Q8×C73—22no—
269C2×Q8×C73#4114yes—
270C2×Q8×C73C2412yes—
271C2×D4×C73—28no—
272C2×D4×C73—24no—
273C2×D4×C73—21no—
274C2×D4×C73—22no—
275C2×D4×C73#4114yes—
276C2×D4×C73C2412yes—
277C22×C4×C73—28no—
278C22×C4×C73—21no—
279C22×C4×C73—24no—
280C22×C4×C73—22no—
281C22×C4×C73—22no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—24no—
285C22×C4×C73—24no—
286C22×C4×C73—22no—
287C22×C4×C73—22no—
288C22×C4×C73—82no—
289C22×C4×C73—82no—
290C22×C4×C73—82no—
291C22×C4×C73C2×D411yescharacteristic
292C22×C4×C73C2×D412yes—
293C22×C4×C73C2×D411yescharacteristic
294C22×C4×C73C2×D411yescharacteristic
295C22×C4×C73C2×D411yescharacteristic
296C22×C4×C73C2×D411yescharacteristic
297C22×C4×C73C2412yes—
298C22×C4×C73C2411yescharacteristic
299C4⋊C4×C73—24no—
300C4⋊C4×C73—24no—
301C4⋊C4×C73—22no—
302C4⋊C4×C73—22no—
303C4⋊C4×C73—21no—
304C4⋊C4×C73—21no—
305C4⋊C4×C73C2×D412yes—
306C4⋊C4×C73C2×D412yes—
307C4⋊C4×C73C2×D412yes—
308C4⋊C4×C73C2×D412yes—
309C4⋊C4×C73C2412yes—
310C4⋊C4×C73C2412yes—
311C22⋊C4×C73—24no—
312C22⋊C4×C73—22no—
313C22⋊C4×C73—22no—
314C22⋊C4×C73C2×D412yes—
315C22⋊C4×C73C2×D412yes—
316C22⋊C4×C73C2×D412yes—
317C22⋊C4×C73C2×D412yes—
318C42×C73—24no—
319C42×C73—22no—
320C42×C73—22no—
321C42×C73C2×D412yes—
322C42×C73C2×D411yescharacteristic
323C42×C73C2×D411yescharacteristic
324C42×C73C2412yes—
325C42×C73C2411yescharacteristic
326C42×C73C2411yescharacteristic
327C23×C73—22no—
328C23×C73—24no—
329C23×C73—22no—
330C23×C73—41no—
331C23×C73—41no—
332C23×C73—42no—
333C23×C73—42no—
334C23×C73C22×D412yes—
335C23×C73C22×D411yescharacteristic
336C22×D73—22no—
337Q8×C73—24no—
338Q8×C73—22no—
339Q8×C73C2×#4114yes—
340D4×C73—216no—
341D4×C73—24no—
342D4×C73—22no—
343D4×C73C2×#4114yes—
344C2×C4×C73—216no—
345C2×C4×C73—22no—
346C2×C4×C73—24no—
347C2×C4×C73—22no—
348C2×C4×C73—24no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—42no—
358C2×C4×C73—42no—
359C2×C4×C73—82no—
360C2×C4×C73—84no—
361C2×C4×C73—82no—
362C2×C4×C73—84no—
363C2×C4×C73C22×D412yes—
364C2×C4×C73C22×D411yescharacteristic
365C2×C4×C73C22×D411yescharacteristic
366C2×C4×C73C22×D412yes—
367C2×C4×C73C22×D411yescharacteristic
368C2×C4×C73C22×D411yescharacteristic
369C2×C4×C73C22×D412yes—
370C2×C4×C73C22×D411yescharacteristic
371C2×C4×C73C2×#4112yes—
372C2×C4×C73C2×#4112yes—
373C2×C4×C73C2511yescharacteristic
374C22⋊D73—44no—
375C22⋊D73—82no—
376C22⋊D73—82no—
377C2×Dic73—22no—
378C2×Dic73—22no—
379C2×Dic73—22no—
380D292—22no—
381D292—22no—
382D292—81no—
383D292—81no—
384C4×D73—44no—
385C4×D73—82no—
386C4×D73—82no—
387Dic146—22no—
388Dic146—22no—
389Dic146—81no—
390Dic146—81no—
391#10596831—24no—
392#10596831—24no—
393C22×C73—21no—
394C22×C73—21no—
395C22×C73—22no—
396C22×C73—22no—
397C22×C73—22no—
398C22×C73—24no—
399C22×C73—44no—
400C22×C73—48no—
401C22×C73—42no—
402C22×C73—42no—
403C22×C73#52512yes—
404C22×C73C23×D411yescharacteristic
405C2×D73—42no—
406C2×D73—42no—
407C2×D73—42no—
408C4×C73—21no—
409C4×C73—22no—
410C4×C73—21no—
411C4×C73—21no—
412C4×C73—22no—
413C4×C73—21no—
414C4×C73—22no—
415C4×C73—24no—
416C4×C73—42no—
417C4×C73—42no—
418C4×C73#52512yes—
419C4×C73C22×#4111yescharacteristic
420C4×C73C22×#4111yescharacteristic
421Dic73—42no—
422Dic73—42no—
423Dic73—42no—
424#60565—731nomaximal, Sylow
425C2×C73—22no—
426C2×C73—42no—
427C2×C73—44no—
428C2×C73C2×#52511yescharacteristic
429C2×C73#358511yescharacteristic
430C2×C73#358611yescharacteristic
431D73—82no—
432#3455—731no—
433C2×#520D7311yescharacteristic, complemented
434#3125—734no—
435#3124—734no—
436#3120—734no—
437#3119—734no—
438#3092—732no—
439#3078—731no—
440#3077—731no—
441#3037—731no—
442#3036—731no—
443#3005—732no—
444C4×#137—732no—
445C4×AGL(1,ℤ/8)—732no—
446#2921—731no—
447C73#6056511yescharacteristic, complemented, Sylow
448C22×#41C2×D7311yescharacteristic
449C2×#137—732no—
450C2×AGL(1,ℤ/8)—732no—
451#542—732no—
452#542—732no—
453#541—732no—
454#540—732no—
455#539—1461no—
456#539—1461no—
457#538—1461no—
458#538—1461no—
459#533—731no—
460#532—731no—
461#529—1462no—
462#529—1462no—
463#525—732no—
464#520—22no—
465#520—22no—
466#520C2×D7314yes—
467#520C2×D7314yes—
468C4×#41—732no—
469C2×C4×Q8C2×D7311yescharacteristic
470C2×C4×Q8C2×D7311yescharacteristic
471C2×C4×D4—21no—
472C2×C4×D4—21no—
473C2×C4×D4C2×D7311yescharacteristic
474C2×C4×D4C2×D7311yescharacteristic
475C2×#117—21no—
476C2×#117C2×D7311yescharacteristic
477C22×C4⋊C4—21no—
478C22×C4⋊C4C2×D7311yescharacteristic
479#484—734no—
480#483—734no—
481#481—734no—
482#480—734no—
483#479—734no—
484#478—734no—
485#477—732no—
486#476—732no—
487#475—732no—
488#474—732no—
489#464—734no—
490#463—734no—
491#462—732no—
492#461—732no—
493#460—732no—
494#459—732no—
495#452—734no—
496#452—734no—
497#449—734no—
498#449—734no—
499#442—734no—
500#441—734no—
501#440—734no—
502#440—734no—
503C4×Q16—734no—
504C4×SD16—734no—
505C4×SD16—734no—
506C4×D8—734no—
507#433—734no—
508#433—734no—
509#428—732no—
510#428—732no—
511#423—731no—
512#423—731no—
513#419—732no—
514#418—732no—
515#417—732no—
516#417—732no—
517#407—732no—
518C4×M16—732no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—732no—
523C2×#41C22×D7314yes—
524C22×Q8C22×D7311yescharacteristic
525C22×D4—21no—
526C22×D4C22×D7311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D7311yescharacteristic
532#137—1468no—
533AGL(1,ℤ/8)—1468no—
534C2×Q16—734no—
535C2×SD16—734no—
536C2×SD16—734no—
537C2×D8—734no—
538C2×M16—732no—
539C2×M16—732no—
540C4⋊Q8—731no—
541C4⋊Q8—731no—
542C4⋊Q8—731no—
543#127—731no—
544#126—1462no—
545#126—1462no—
546#126—1462no—
547#126—1462no—
548#125—732no—
549#125—1462no—
550#125—1462no—
551#124—732no—
552#124—1462no—
553#124—1462no—
554#123—1462no—
555#123—1462no—
556#123—1462no—
557#123—1462no—
558#123—1462no—
559C22⋊Q8—732no—
560C22⋊Q8—732no—
561C22⋊Q8—1461no—
562C22⋊Q8—1461no—
563C22⋊Q8—1462no—
564C22⋊Q8—1462no—
565#121—732no—
566#121—732no—
567#121—1461no—
568#121—1461no—
569#121—1462no—
570#121—1462no—
571#120—1462no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—732no—
576C4×Q8—732no—
577C4×Q8—1461no—
578C4×Q8—1461no—
579C4×Q8C22×D7314yes—
580C4×Q8C22×D7312yes—
581C4×Q8C22×D7312yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—732no—
590C4×D4—732no—
591C4×D4—1462no—
592C4×D4—1462no—
593C4×D4—1462no—
594C4×D4—1462no—
595C4×D4—1461no—
596C4×D4—1461no—
597C4×D4C22×D7314yes—
598C4×D4C22×D7312yes—
599C4×D4C22×D7312yes—
600#117—24no—
601#117—24no—
602#117—732no—
603#117—1462no—
604#117C22⋊D7312yes—
605#117C22⋊D7312yes—
606#117C22×D7312yes—
607#117C22×D7312yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D7311yescharacteristic
615C2×C4⋊C4C22⋊D7311yescharacteristic
616C2×C4⋊C4C22×D7311yescharacteristic
617C2×C4⋊C4C22×D7311yescharacteristic
618C2×C4⋊C4C22×D7314yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D7311yescharacteristic
622C2×C22⋊C4C22⋊D7311yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—1462no—
626C2×C42C22×D7311yescharacteristic
627C2×C42C22×D7311yescharacteristic
628#107—734no—
629#107—734no—
630#106—734no—
631#106—734no—
632C4⋊C8—732no—
633C4⋊C8—732no—
634C4⋊C8—732no—
635C4⋊C8—732no—
636#103—734no—
637#103—734no—
638#103—734no—
639#103—734no—
640#102—734no—
641#102—734no—
642#102—734no—
643#102—734no—
644C22⋊C8—734no—
645C22⋊C8—734no—
646#97—734no—
647C4×C8—734no—
648C24—21no—
649C24C2×C22⋊D7311yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—1464no—
654#41—1464no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—732no—
658C2×Q8—1461no—
659C2×Q8—1461no—
660C2×Q8#1192402814yes—
661C2×Q8C23×D7312yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—732no—
667C2×D4—1462no—
668C2×D4—1462no—
669C2×D4—1462no—
670C2×D4—1461no—
671C2×D4—1461no—
672C2×D4#1192402814yes—
673C2×D4C23×D7312yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—1462no—
689C22×C4—1462no—
690C22×C4—1462no—
691C22×C4C2×C22⋊D7311yescharacteristic
692C22×C4C2×C22⋊D7312yes—
693C22×C4C2×C22⋊D7311yescharacteristic
694C22×C4C2×C22⋊D7311yescharacteristic
695C22×C4C2×C22⋊D7311yescharacteristic
696C22×C4C2×C22⋊D7311yescharacteristic
697C22×C4C23×D7312yes—
698C22×C4C23×D7311yescharacteristic
699Q16—1468no—
700SD16—1468no—
701SD16—1468no—
702D8—1468no—
703M16—1464no—
704M16—1464no—
705C2×C8—734no—
706C2×C8—734no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—732no—
714C4⋊C4—732no—
715C4⋊C4—1462no—
716C4⋊C4—1462no—
717C4⋊C4—1462no—
718C4⋊C4—1462no—
719C4⋊C4—1462no—
720C4⋊C4—1462no—
721C4⋊C4—1461no—
722C4⋊C4—1461no—
723C4⋊C4—1461no—
724C4⋊C4—1461no—
725C4⋊C4C2×C22⋊D7312yes—
726C4⋊C4C2×C22⋊D7312yes—
727C4⋊C4C2×C22⋊D7312yes—
728C4⋊C4C2×C22⋊D7312yes—
729C4⋊C4C23×D7312yes—
730C4⋊C4C23×D7312yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—1462no—
735C22⋊C4—1462no—
736C22⋊C4—1462no—
737C22⋊C4—1462no—
738C22⋊C4—1462no—
739C22⋊C4—1462no—
740C22⋊C4—1462no—
741C22⋊C4—1462no—
742C22⋊C4—1462no—
743C22⋊C4C2×C22⋊D7312yes—
744C22⋊C4C2×C22⋊D7312yes—
745C22⋊C4C2×C22⋊D7312yes—
746C22⋊C4C2×C22⋊D7312yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—1462no—
751C42—1462no—
752C42—1462no—
753C42C2×C22⋊D7312yes—
754C42C2×C22⋊D7311yescharacteristic
755C42C2×C22⋊D7311yescharacteristic
756C42C23×D7312yes—
757C42C23×D7311yescharacteristic
758C42C23×D7311yescharacteristic
759C23—22no—
760C23—22no—
761C23—24no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—1462no—
767C23C22×C22⋊D7312yes—
768C23C22×C22⋊D7311yescharacteristic
769Q8—22no—
770Q8—24no—
771Q8—5841no—
772Q8—5841no—
773Q8—1462no—
774Q8—1462no—
775Q8C2×#1192402814yes—
776D4—216no—
777D4—22no—
778D4—24no—
779D4—2924no—
780D4—5841no—
781D4—5841no—
782D4—5842no—
783D4—5842no—
784D4—1462no—
785D4—1462no—
786D4C2×#1192402814yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—2924no—
807C2×C4—5842no—
808C2×C4—5842no—
809C2×C4—1462no—
810C2×C4—1462no—
811C2×C4—1462no—
812C2×C4C22×C22⋊D7312yes—
813C2×C4C22×C22⋊D7311yescharacteristic
814C2×C4C22×C22⋊D7311yescharacteristic
815C2×C4C22×C22⋊D7312yes—
816C2×C4C22×C22⋊D7311yescharacteristic
817C2×C4C22×C22⋊D7311yescharacteristic
818C2×C4C22×C22⋊D7312yes—
819C2×C4C22×C22⋊D7311yescharacteristic
820C2×C4C2×#1192402812yes—
821C2×C4C2×#1192402812yes—
822C2×C4C24×D7311yescharacteristic
823C8—1464no—
824C8—1464no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—2922no—
836C22—2922no—
837C22—2922no—
838C22#1798909812yes—
839C22C23×C22⋊D7311yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—2922no—
851C4—2922no—
852C4—2922no—
853C4#1798909812yes—
854C4C22×#1192402811yescharacteristic
855C4C22×#1192402811yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—5842no—
860C2C2×#1798909811yescharacteristic
861C2#2262471111yescharacteristic
862C2#2262471811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#520×C73C2
socleC22×C73C23×D4
hypercenterC2×#520D73
hypocenterC73#60565
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22623321C2semidirect
2. #22620208C2semidirect
3. #22620193C2semidirect
4. #22620145C2semidirect
5. #22620130C2semidirect
6. #22619854C2semidirect
7. #22619736C2semidirect
8. #22619728C2semidirect
9. #22619403C2semidirect
10. #22619395C2semidirect
11. #22619173C2semidirect
12. C4×#14556622C2semidirect
13. C4×#14556617C2semidirect
14. #22618569C2semidirect
15. C2×#520×C73C2semidirect
18. #17989208C22semidirect
19. #17989208C22semidirect
20. #17989199C22semidirect
21. #17989192C22semidirect
32. #17988922C22semidirect
33. #17988917C22semidirect
34. #17988905C22semidirect
35. #17988900C22semidirect
36. #17988894C22semidirect
37. #17988887C22semidirect
38. #17988882C22semidirect
39. #17988877C22semidirect
40. #17988872C22semidirect
41. #17988867C22semidirect
42. #17988809C22semidirect
43. #17988802C22semidirect
44. #17988797C22semidirect
45. #17988792C22semidirect
46. #17988787C22semidirect
47. #17988782C22semidirect
52. #17988697C22semidirect
53. #17988692C22semidirect
54. #17988687C22semidirect
55. #17988685C22semidirect
56. C4×#11924018C22semidirect
57. C4×#11924015C22semidirect
58. C4×#11924016C22semidirect
59. C4×#11924013C22semidirect
60. #17988648C22semidirect
61. #17988648C22semidirect
433. C2×#520D73semidirect
447. C73#60565semidirect

Maximal subgroups

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

subgroupindex
#226233212
#226202082
#226201932
#226201452
#226201302
#226198542
#226197362
#226197282
#226194032
#226193952
#226191732
C4×#145566222
C4×#145566172
#226185692
C2×#520×C732
#6056573