Finite Group Databasebeta

← #33950673

Subgroups — #33950673

Order 18688.

1914 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623498C211yesmaximal, characteristic
2#22618950C212yesmaximal, complemented
3#22618934C212yesmaximal, complemented
4#22618934C214yesmaximal, complemented
5#22618915C214yesmaximal, complemented
6#22618905C212yesmaximal, complemented
7#22618896C212yesmaximal, complemented
8#22618880C211yesmaximal, characteristic, complemented
9#22618666C211yesmaximal, characteristic, complemented
10#22618655C212yesmaximal, complemented
11#22618636C212yesmaximal, complemented
12C2×#17988666C211yesmaximal, characteristic, complemented
13#22618599C211yesmaximal, characteristic, complemented
14#22618588C212yesmaximal, complemented
15C4×#14556597C211yesmaximal, characteristic, complemented
16#22618347C212yesmaximal, complemented
17C73×#2960C211yesmaximal, characteristic, complemented
18C2×#14556597C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20C22×#11924011C2212yes—
21C2×M16×D73C2212yes—
22#17989311C411yescharacteristic
23#17989303C411yescharacteristic
24#17989298C411yescharacteristic
25#17989290C412yes—
26#17989279C412yes—
27#17989275C412yes—
28#17989264C414yes—
29#17989240C411yescharacteristic
30#17989228C412yes—
31#17989124C2212yes—
32#17989124C2214yes—
33#17989099C2212yes—
34C4×#11924029C2212yes—
35C4×#11924028C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37#117×D73C2212yes—
38#17988718C2212yescomplemented
39#17988718C2214yescomplemented
40Q8×#10596831C2212yescomplemented
41#17988666C2211yescharacteristic
42#17988666C2211yescharacteristic
43#17988666C2212yes—
44#17988666C2211yescharacteristic
45#17988666C2212yes—
46#17988666C2211yescharacteristic
47#17988666C2214yescomplemented
48#17988666C2214yescomplemented
49#17988664C2212yes—
50#17988664C2214yescomplemented
51#17988660C2214yescomplemented
52#17988660C2214yescomplemented
53#17988657C2214yes—
54#17988657C2214yescomplemented
55#17988657C2214yescomplemented
56#17988652C2212yes—
57#17988652C2214yescomplemented
58#17988647C2214yescomplemented
59#17988647C2214yescomplemented
60#17988647C2214yescomplemented
61#17988643C2212yescomplemented
62#17988643C2214yescomplemented
63#17988639C2214yescomplemented
64#17988639C2212yescomplemented
65#17988614C2212yes—
66C2×C4⋊#10596831C2211yescharacteristic
67#17988555C2212yes—
68#17988550C2212yes—
69C2×#14556503C2212yes—
70#17988545C2212yes—
71#17988544C2214yescomplemented
72#17988543C2212yes—
73#17988542C2211yescharacteristic
74#17988542C2211yescharacteristic
75#17988541C2212yescomplemented
76#17988541C2214yescomplemented
77#17988541C2212yescomplemented
78C4×#11924012C2211yescharacteristic
79#17988539C2214yescomplemented
80C4×#11924011C2214yescomplemented
81C4×#11924011C2212yescomplemented
82C4×C8×D73C2212yescomplemented
83#533×C73C2211yescharacteristic
84#446×C73C2212yescomplemented
85#446×C73C2212yescomplemented
86C8×Q8×C73C2212yescomplemented
87C8×Q8×C73C2212yescomplemented
88#424×C73C2212yes—
89#423×C73C2211yescharacteristic
90#405×C73C2212yes—
91C2×C4×C8×C73C2211yescharacteristic
92C2×#11924029C2×C412yes—
93C2×#11924028C2311yescharacteristic
94C22×D292C2×C411yescharacteristic
95C22×C4×D73C2312yes—
96#14556597—24no—
97#14556597—24no—
98C2×#11924012C2311yescharacteristic
99C2×#11924012C2311yescharacteristic
100C2×#11924011—28no—
101C2×#11924011C2314yes—
102C2×#11924011C2312yes—
103C2×#11924011C2312yes—
104C2×#11924011C2312yes—
105C2×#11924011C2312yes—
106C2×#11924011C2312yes—
107C2×#11924011C2312yes—
108M16×D73—28no—
109C22×#10596831C2312yes—
110C2×C8×D73C2314yes—
111C2×C8×D73C2312yes—
112C2×C8×D73C2312yes—
113#14556586C2×C414yes—
114#14556586C2×C414yes—
115#14556586C2×C414yes—
116#14556582C2×C414yes—
117#14556582C2×C412yes—
118#14556580C2×C412yes—
119#14556580C2×C414yes—
120#14556576C2×C414yes—
121#14556576C2×C414yes—
122#14556576C2×C414yes—
123#14556575C2×C414yes—
124#14556571C2×C412yes—
125#14556571C2×C412yes—
126#14556567C2×C412yes—
127#14556567C2×C414yes—
128#14556566C2×C414yes—
129#14556566C2×C412yes—
130#14556566C2×C412yes—
131#14556566C2×C412yes—
132#14556561C2×C414yes—
133Q8×Dic73C2×C412yes—
134C4×Dic146C2×C411yescharacteristic
135C4×Dic146C2×C411yescharacteristic
136C4×D292C2×C411yescharacteristic
137C4×D292C2×C411yescharacteristic
138C4×D292C2×C412yes—
139C4×D292C2×C411yescharacteristic
140C4×D292C2×C411yescharacteristic
141C4×D292C2311yescharacteristic
142C4×D292C2314yes—
143C4×D292C2312yes—
144C4×D292C2314yes—
145C4×D292C2311yescharacteristic
146#14556553C2×C412yes—
147#14556553C2×C414yes—
148C4×C22⋊D73C2×C412yes—
149C4×C22⋊D73C2×C412yes—
150#14556550C2311yescharacteristic
151#14556549C2×C414yes—
152#14556549C2×C412yes—
153#14556549C2×C412yes—
154#14556549C2×C412yes—
155#14556548C2314yes—
156#14556548C2312yes—
157#14556547C2×C414yes—
158C2×C4⋊Dic73C2×C411yescharacteristic
159C4⋊C4×D73C2×C412yes—
160C4⋊C4×D73C2×C412yes—
161C2×#11924005C2×C412yes—
162C22⋊C4×D73C2×C414yes—
163C42×D73C2314yes—
164C42×D73C2312yes—
165C4⋊#10596831C2311yescharacteristic
166C4⋊#10596831C2311yescharacteristic
167C4⋊#10596831C2312yes—
168C4⋊#10596831C2314yes—
169C4⋊#10596831C2314yes—
170#14556503C2312yes—
171#14556503C2314yes—
172#14556503C2314yes—
173#14556503C2312yes—
174#14556503C2314yes—
175#14556503C2314yes—
176#14556503C2312yes—
177#14556503C2312yes—
178#14556502C2312yes—
179#14556502C2314yes—
180#14556501C2312yes—
181#14556501C2314yes—
182#14556501C2312yes—
183C4×#10596831C2312yes—
184C4×#10596831C2314yes—
185C8×Dic73C2312yes—
186C8×Dic73C2314yes—
187C8×Dic73C2312yes—
188C2×M16×C73C2312yes—
189C22×C8×C73C2311yescharacteristic
190C22×C8×C73C2311yescharacteristic
191C4⋊Q8×C73C2×C411yescharacteristic
192C4⋊Q8×C73C2×C411yescharacteristic
193#125×C73C2×C412yes—
194C22⋊Q8×C73C2×C412yes—
195C22⋊Q8×C73C2×C412yes—
196C4×Q8×C73C2312yes—
197C4×Q8×C73C2312yes—
198#117×C73C2312yes—
199C2×C42×C73C2311yescharacteristic
200C4⋊C8×C73C2312yes—
201C4⋊C8×C73C2314yes—
202C4⋊C8×C73C2314yes—
203C4⋊C8×C73C2312yes—
204#97×C73C2314yes—
205C4×C8×C73C2311yescharacteristic
206C4×C8×C73C2311yescharacteristic
207C4×C8×C73C2311yescharacteristic
208C4×C8×C73C2311yescharacteristic
209C4×C8×C73C2314yes—
210C23×D73C22×C412yes—
211#11924029—44no—
212#11924028—22no—
213#11924028—22no—
214C2×Dic146C22×C411yescharacteristic
215C2×D292—42no—
216C2×D292C22×C411yescharacteristic
217C2×D292C22×C411yescharacteristic
218C2×D292C22×C411yescharacteristic
219C2×D292C22×C414yes—
220C2×D292C22×C412yes—
221C2×D292C22×C414yes—
222C2×C22⋊D73C22×C412yes—
223C22×Dic73C22×C412yes—
224C2×C4×D73—24no—
225C2×C4×D73—24no—
226C2×C4×D73C22×C412yes—
227C2×C4×D73C22×C412yes—
228C2×C4×D73C22×C412yes—
229C2×C4×D73C22×C414yes—
230C2×C4×D73C22×C414yes—
231C2×C4×D73C22×C412yes—
232C2×C4×D73C2412yes—
233C2×C4×D73C2412yes—
234C2×C4×D73C2412yes—
235#11924012—22no—
236#11924012#4114yescomplemented
237#11924011—24no—
238#11924011—24no—
239#11924011—24no—
240#11924011—24no—
241#11924011—24no—
242#11924011—28no—
243#11924011—24no—
244C2×#10596831—24no—
245C2×#10596831C2412yes—
246C2×#10596831C2412yes—
247C2×#10596831C2412yes—
248C2×#10596831C2412yes—
249C8×D73—24no—
250C8×D73—28no—
251C8×D73—24no—
252C4⋊Dic73C22×C411yescharacteristic
253C4⋊Dic73C22×C411yescharacteristic
254C4⋊Dic73C22×C411yescharacteristic
255C4⋊Dic73C22×C411yescharacteristic
256C4⋊Dic73C22×C412yes—
257C4⋊Dic73C22×C414yes—
258C4⋊Dic73C22×C414yes—
259#11924007C22×C414yes—
260#11924007C22×C414yes—
261#11924007C22×C412yes—
262#11924007C22×C412yes—
263C22⋊Dic73C22×C412yes—
264#11924005C22×C414yes—
265#11924005C22×C414yes—
266#11924005C22×C412yes—
267#11924005C22×C412yes—
268#11924005C22×C412yes—
269#11924005C22×C412yes—
270#11924005C22×C412yes—
271#11924005C22×C412yes—
272#11924005C22×C414yes—
273#11924005C22×C414yes—
274#11924005C22×C414yes—
275#11924005C22×C414yes—
276C4×Dic73C22×C414yes—
277C4×Dic73C22×C414yes—
278C4×Dic73C22×C412yes—
279C4×Dic73C22×C412yes—
280C4×Dic73C2412yes—
281C2×Q8×C73C22×C412yes—
282C2×Q8×C73C22×C412yes—
283C22×C4×C73C22×C411yescharacteristic
284C22×C4×C73C22×C411yescharacteristic
285C22×C4×C73C2411yescharacteristic
286M16×C73—24no—
287C2×C8×C73—22no—
288C2×C8×C73#4114yescomplemented
289C2×C8×C73C2411yescharacteristic
290C2×C8×C73C2411yescharacteristic
291C2×C8×C73C2414yes—
292C2×C8×C73C2411yescharacteristic
293C2×C8×C73C2411yescharacteristic
294C4⋊C4×C73C22×C412yes—
295C4⋊C4×C73C22×C412yes—
296C4⋊C4×C73C22×C414yes—
297C4⋊C4×C73C22×C414yes—
298C4⋊C4×C73C22×C412yes—
299C4⋊C4×C73C22×C412yes—
300C22⋊C4×C73C22×C414yes—
301C42×C73C22×C411yescharacteristic
302C42×C73C22×C411yescharacteristic
303C42×C73C2411yescharacteristic
304C42×C73C2411yescharacteristic
305C42×C73C2414yes—
306C23×C73C23×C411yescharacteristic
307C22×D73—24no—
308C22×D73—42no—
309C22×D73—42no—
310C22×D73C23×C412yes—
311C22×D73C23×C412yes—
312C22×D73C23×C412yes—
313Q8×C73—24no—
314Q8×C73—42no—
315C2×C4×C73—22no—
316C2×C4×C73—41no—
317C2×C4×C73C23×C411yescharacteristic
318C2×C4×C73C23×C411yescharacteristic
319C2×C4×C73C23×C411yescharacteristic
320C2×C4×C73C23×C414yes—
321C2×C4×C73C23×C414yes—
322C2×C4×C73C23×C411yescharacteristic
323C2×C4×C73C23×C411yescharacteristic
324C2×C4×C73C2×#4112yes—
325C2×C4×C73C2×#4112yes—
326C2×C4×C73C2511yescharacteristic
327C22⋊D73—24no—
328C2×Dic73—24no—
329C2×Dic73C23×C412yes—
330C2×Dic73C23×C412yes—
331C2×Dic73C23×C412yes—
332C2×Dic73C23×C412yes—
333C2×Dic73C23×C412yes—
334D292—22no—
335D292—22no—
336D292—22no—
337D292—42no—
338D292—44no—
339D292—44no—
340C4×D73—24no—
341C4×D73—24no—
342C4×D73—24no—
343C4×D73—22no—
344C4×D73—22no—
345C4×D73—22no—
346C4×D73—22no—
347C4×D73—22no—
348C4×D73—22no—
349C4×D73—42no—
350C4×D73—44no—
351C4×D73—44no—
352Dic146—22no—
353C8×C73—21no—
354C8×C73—21no—
355C8×C73—24no—
356C8×C73C2×#4112yes—
357C8×C73C2×#4112yes—
358#10596831—22no—
359#10596831—22no—
360#10596831—22no—
361#10596831C2×#4114yes—
362C22×C73—21no—
363C22×C73—21no—
364C22×C73C4×#4112yes—
365C22×C73C24×C411yescharacteristic
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—84no—
376C4×C73—24no—
377C4×C73—21no—
378C4×C73—21no—
379C4×C73—24no—
380C4×C73—21no—
381C4×C73C4×#4112yes—
382C4×C73#56812yes—
383C4×C73C22×#4111yescharacteristic
384C4×C73C22×#4111yescharacteristic
385Dic73—22no—
386Dic73—22no—
387Dic73—22no—
388Dic73—22no—
389Dic73—22no—
390#60217—731nomaximal, Sylow
391C2×C73—22no—
392C2×C73C2×C4×#4111yescharacteristic
393C2×C73C2×#56811yescharacteristic
394C2×C73#357311yescharacteristic
395D73—42no—
396D73—42no—
397D73—42no—
398#3475—731no—
399#2971—732no—
400#2969—732no—
401#2969—734no—
402#2967—734no—
403#2966—732no—
404#2965—732no—
405#2962—731no—
406#2960D7311yescharacteristic, complemented
407D4×M16—731no—
408#2933—732no—
409#2930—732no—
410C2×#436—731no—
411#2925—731no—
412#2924—732no—
413C4×#131—731no—
414#2873—732no—
415C73#6021711yescharacteristic, complemented, Sylow
416C2×#131—731no—
417C2×#131—731no—
418C22×M16—732no—
419C22×M16—732no—
420#556—731no—
421#555—731no—
422#554—731no—
423#553—732no—
424#552—732no—
425#552—732no—
426#551—734no—
427#547—731no—
428#546—732no—
429#533C2×D7311yescharacteristic
430#529—732no—
431#529—734no—
432#525—732no—
433C4×#41—732no—
434C4×#41—731no—
435C2×C4×D4—731no—
436C2×#117—732no—
437#446—732no—
438#446—734no—
439#446C2×D7312yescomplemented
440#446C2×D7312yescomplemented
441C8×Q8—732no—
442C8×Q8C2×D7312yescomplemented
443C8×Q8C2×D7312yescomplemented
444#436—732no—
445#436—734no—
446#436—731no—
447#436—731no—
448#436—732no—
449#436—731no—
450#436—732no—
451#436—731no—
452#436—734no—
453#436—734no—
454#435—734no—
455#435—734no—
456#435—734no—
457#435—734no—
458#435—734no—
459C8×D4—732no—
460C8×D4—734no—
461#433—734no—
462#433—734no—
463#433—734no—
464#432—734no—
465#432—732no—
466#431—734no—
467#431—732no—
468#424—732no—
469#424C2×D7312yes—
470#423C2×D7311yescharacteristic
471C2×C4⋊C8—731no—
472#408—732no—
473#407—732no—
474C2×C22⋊C8—732no—
475#405—732no—
476#405—731no—
477#405—731no—
478#405—732no—
479#405—734no—
480#405—734no—
481#405—732no—
482#405—732no—
483#405C2×D7312yes—
484C4×M16—731no—
485C4×M16—734no—
486C4×M16—734no—
487C4×M16—732no—
488C2×C4×C8—732no—
489C2×C4×C8C2×D7311yescharacteristic
490C2×#41—732no—
491C2×#41—731no—
492C22×D4—731no—
493C23×C4—732no—
494#131—1464no—
495#131—1464no—
496C2×M16—731no—
497C2×M16—731no—
498C2×M16—734no—
499C2×M16—732no—
500C2×M16—732no—
501C2×M16—732no—
502C2×M16—732no—
503C2×M16—732no—
504C2×M16—732no—
505C2×M16—1468no—
506C2×M16—1468no—
507C2×M16C22×D7312yes—
508C22×C8—732no—
509C22×C8—734no—
510C22×C8—732no—
511C22×C8—732no—
512C22×C8C22×D7311yescharacteristic
513C22×C8C22×D7311yescharacteristic
514C4⋊Q8C4×D7311yescharacteristic
515C4⋊Q8C4×D7311yescharacteristic
516#126—734no—
517#126—734no—
518#126—734no—
519#125—734no—
520#125—732no—
521#125C4×D7312yes—
522#124—732no—
523#124—734no—
524#123—734no—
525#123—734no—
526#123—734no—
527#123—734no—
528C22⋊Q8—732no—
529C22⋊Q8—734no—
530C22⋊Q8—732no—
531C22⋊Q8—732no—
532C22⋊Q8C4×D7312yes—
533C22⋊Q8C4×D7312yes—
534#121—732no—
535#121—732no—
536#121—734no—
537#121—732no—
538#120—734no—
539C4×Q8—732no—
540C4×Q8—731no—
541C4×Q8—731no—
542C4×Q8C22×D7312yes—
543C4×Q8C22×D7312yes—
544C4×D4—732no—
545C4×D4—732no—
546C4×D4—732no—
547C4×D4—734no—
548C4×D4—731no—
549C4×D4—732no—
550C4×D4—731no—
551C4×D4—731no—
552C4×D4—731no—
553C4×D4—731no—
554C4×D4—731no—
555C4×D4—732no—
556C4×D4—734no—
557C4×D4—734no—
558#117—731no—
559#117—732no—
560#117—732no—
561#117—734no—
562#117—732no—
563#117—734no—
564#117—734no—
565#117—732no—
566#117C22×D7312yes—
567C2×C4⋊C4—731no—
568C2×C4⋊C4—732no—
569C2×C4⋊C4—732no—
570C2×C22⋊C4—732no—
571C2×C22⋊C4—734no—
572C2×C42—734no—
573C2×C42—732no—
574C2×C42C22×D7311yescharacteristic
575C4⋊C8—731no—
576C4⋊C8—731no—
577C4⋊C8—732no—
578C4⋊C8—734no—
579C4⋊C8—734no—
580C4⋊C8C22×D7312yes—
581C4⋊C8C22×D7312yes—
582C4⋊C8C22×D7314yes—
583C4⋊C8C22×D7314yes—
584C22⋊C8—732no—
585C22⋊C8—732no—
586C22⋊C8—732no—
587C22⋊C8—732no—
588C22⋊C8—734no—
589C22⋊C8—734no—
590C22⋊C8—734no—
591C22⋊C8—734no—
592#97—732no—
593#97—734no—
594#97—732no—
595#97—734no—
596#97—732no—
597#97C22×D7314yes—
598C4×C8—732no—
599C4×C8—732no—
600C4×C8—734no—
601C4×C8—732no—
602C4×C8—734no—
603C4×C8C22×D7311yescharacteristic
604C4×C8C22×D7311yescharacteristic
605C4×C8C22×D7311yescharacteristic
606C4×C8C22×D7311yescharacteristic
607C4×C8C22×D7314yes—
608C24—732no—
609#41—2924no—
610#41—1462no—
611#41—1462no—
612C2×Q8—731no—
613C2×Q8C2×C4×D7312yes—
614C2×Q8C2×C4×D7312yes—
615C2×D4—2922no—
616C2×D4—732no—
617C2×D4—734no—
618C2×D4—732no—
619C2×D4—734no—
620C2×D4—731no—
621C2×D4—731no—
622C2×D4—731no—
623C22×C4—734no—
624C22×C4—734no—
625C22×C4—732no—
626C22×C4—732no—
627C22×C4—732no—
628C22×C4—732no—
629C22×C4—732no—
630C22×C4—732no—
631C22×C4—732no—
632C22×C4—732no—
633C22×C4—1464no—
634C22×C4—1464no—
635C22×C4C2×C4×D7311yescharacteristic
636C22×C4C2×C4×D7311yescharacteristic
637C22×C4C23×D7311yescharacteristic
638M16—24no—
639M16—734no—
640M16—1468no—
641M16—1464no—
642M16—1462no—
643M16—1464no—
644M16—1464no—
645M16—1464no—
646M16—1464no—
647M16—1464no—
648C2×C8—22no—
649C2×C8—732no—
650C2×C8—732no—
651C2×C8—732no—
652C2×C8—732no—
653C2×C8—1468no—
654C2×C8—1464no—
655C2×C8—1464no—
656C2×C8—1464no—
657C2×C8#1192402914yescomplemented
658C2×C8C23×D7311yescharacteristic
659C2×C8C23×D7314yes—
660C2×C8C23×D7311yescharacteristic
661C2×C8C23×D7311yescharacteristic
662C2×C8C23×D7311yescharacteristic
663C4⋊C4—734no—
664C4⋊C4—734no—
665C4⋊C4—732no—
666C4⋊C4—732no—
667C4⋊C4—731no—
668C4⋊C4—731no—
669C4⋊C4—731no—
670C4⋊C4—731no—
671C4⋊C4—732no—
672C4⋊C4—734no—
673C4⋊C4—734no—
674C4⋊C4C2×C4×D7312yes—
675C4⋊C4C2×C4×D7312yes—
676C4⋊C4C2×C4×D7312yes—
677C4⋊C4C2×C4×D7314yes—
678C4⋊C4C2×C4×D7314yes—
679C4⋊C4C2×C4×D7312yes—
680C22⋊C4—732no—
681C22⋊C4—732no—
682C22⋊C4—734no—
683C22⋊C4—734no—
684C22⋊C4—732no—
685C22⋊C4—732no—
686C22⋊C4—732no—
687C22⋊C4—734no—
688C22⋊C4—732no—
689C22⋊C4—734no—
690C22⋊C4—732no—
691C22⋊C4—734no—
692C22⋊C4—734no—
693C22⋊C4C2×C4×D7314yes—
694C42—734no—
695C42—734no—
696C42—732no—
697C42—732no—
698C42—732no—
699C42C2×C4×D7311yescharacteristic
700C42C2×C4×D7311yescharacteristic
701C42C23×D7311yescharacteristic
702C42C23×D7314yes—
703C42C23×D7311yescharacteristic
704C23—2922no—
705C23—2922no—
706C23—732no—
707C23—732no—
708C23—732no—
709C23—1464no—
710C23C22×C4×D7311yescharacteristic
711Q8—24no—
712Q8—42no—
713Q8—1462no—
714D4—2922no—
715D4—2924no—
716D4—2924no—
717D4—1464no—
718D4—1462no—
719D4—1462no—
720D4—1462no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—2924no—
724C2×C4—2922no—
725C2×C4—2924no—
726C2×C4—732no—
727C2×C4—732no—
728C2×C4—732no—
729C2×C4—732no—
730C2×C4—732no—
731C2×C4—1464no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1464no—
739C2×C4—1464no—
740C2×C4—1464no—
741C2×C4C22×C4×D7311yescharacteristic
742C2×C4C22×C4×D7314yes—
743C2×C4C22×C4×D7314yes—
744C2×C4C22×C4×D7311yescharacteristic
745C2×C4C22×C4×D7311yescharacteristic
746C2×C4C22×C4×D7311yescharacteristic
747C2×C4C22×C4×D7311yescharacteristic
748C2×C4#41×D7312yes—
749C2×C4C2×#1192402912yes—
750C2×C4C24×D7311yescharacteristic
751C8—21no—
752C8—21no—
753C8—24no—
754C8—734no—
755C8—1462no—
756C8—1462no—
757C8—1462no—
758C8C2×#1192402912yes—
759C8C2×#1192402912yes—
760C22—21no—
761C22—21no—
762C22—5844no—
763C22—1462no—
764C22—1462no—
765C22—1462no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22—1462no—
771C22—1462no—
772C22C4×#1192402912yes—
773C22C23×C4×D7311yescharacteristic
774C4—21no—
775C4—24no—
776C4—21no—
777C4—21no—
778C4—24no—
779C4—1462no—
780C4—1462no—
781C4—1462no—
782C4—1462no—
783C4—1462no—
784C4C4×#1192402912yes—
785C4#1798935212yes—
786C4C2×#41×D7311yescharacteristic
787C4C22×#1192402911yescharacteristic
788C2—22no—
789C2—2922no—
790C2—2922no—
791C2—2922no—
792C2C2×C4×#1192402911yescharacteristic
793C2C2×#1798935211yescharacteristic
794C2#2262464211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2960C2
prime radical#22623498C2
cosocleC2×C4×C73C25
hypercenter#2960D73
hypocenterC73#60217
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2960

Complements

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

NH ≅ G/Ntype
2. #22618950C2semidirect
3. #22618934C2semidirect
4. #22618934C2semidirect
5. #22618915C2semidirect
6. #22618905C2semidirect
7. #22618896C2semidirect
8. #22618880C2semidirect
9. #22618666C2semidirect
10. #22618655C2semidirect
11. #22618636C2semidirect
12. C2×#17988666C2semidirect
13. #22618599C2semidirect
14. #22618588C2semidirect
15. C4×#14556597C2semidirect
16. #22618347C2semidirect
17. C73×#2960C2semidirect
38. #17988718C22semidirect
39. #17988718C22semidirect
40. Q8×#10596831C22semidirect
47. #17988666C22semidirect
48. #17988666C22semidirect
50. #17988664C22semidirect
51. #17988660C22semidirect
52. #17988660C22semidirect
54. #17988657C22semidirect
55. #17988657C22semidirect
57. #17988652C22semidirect
58. #17988647C22semidirect
59. #17988647C22semidirect
60. #17988647C22semidirect
61. #17988643C22semidirect
62. #17988643C22semidirect
63. #17988639C22semidirect
64. #17988639C22semidirect
71. #17988544C22semidirect
75. #17988541C22semidirect
76. #17988541C22semidirect
77. #17988541C22semidirect
79. #17988539C22semidirect
80. C4×#11924011C22semidirect
81. C4×#11924011C22semidirect
82. C4×C8×D73C22semidirect
84. #446×C73C22semidirect
85. #446×C73C22semidirect
86. C8×Q8×C73C22semidirect
87. C8×Q8×C73C22semidirect
236. #11924012#41semidirect
288. C2×C8×C73#41semidirect
406. #2960D73semidirect
415. C73#60217semidirect
439. #446C2×D73semidirect
440. #446C2×D73semidirect
442. C8×Q8C2×D73semidirect
443. C8×Q8C2×D73semidirect
657. C2×C8#11924029semidirect

Maximal subgroups

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

subgroupindex
#226234982
#226189502
#226189342
#226189152
#226189052
#226188962
#226188802
#226186662
#226186552
#226186362
C2×#179886662
#226185992
#226185882
C4×#145565972
#226183472
C73×#29602
#6021773