Finite Group Databasebeta

← #33950488

Subgroups — #33950488

Order 18688.

2050 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#22623223C211yesmaximal, characteristic
2#22618901C214yesmaximal, complemented
3#22618899C214yesmaximal, complemented
4#22618891C214yesmaximal, complemented
5C8×#11924027C214yesmaximal, complemented
6#22618864C211yesmaximal, characteristic, complemented
7#22618863C211yesmaximal, characteristic, complemented
8#22618641C211yesmaximal, characteristic, complemented
9#22618639C211yesmaximal, characteristic, complemented
10#22618626C211yesmaximal, characteristic, complemented
11#22618625C211yesmaximal, characteristic, complemented
12#22618621C211yesmaximal, characteristic, complemented
13#22618574C211yesmaximal, characteristic, complemented
14#22618571C211yesmaximal, characteristic, complemented
15#22618560C211yesmaximal, characteristic, complemented
16#22618353C211yesmaximal, characteristic, complemented
17#131×Dic73C211yesmaximal, characteristic, complemented
18C22×C8×Dic73C211yesmaximal, characteristic, complemented
19C73×#2929C211yesmaximal, characteristic, complemented
20C2×#14556599C2211yescharacteristic
21C2×#14556598C2211yescharacteristic
22C2×#14556597C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24#17989140C2211yescharacteristic
25#17989139C412yes—
26#17989133C2211yescharacteristic
27#17989132C412yes—
28#17989123C412yes—
29#17989118C412yes—
30#17989117C2214yes—
31#17989114C414yes—
32#17989098C2211yescharacteristic
33#17989093C414yes—
34#41×Dic73C2211yescharacteristic
35#17989055C2211yescharacteristic
36C4×#11924027C2214yes—
37C22×C4×Dic73C2211yescharacteristic
38#17988716C2214yescomplemented
39#17988715C2214yescomplemented
40C8×Dic146C2214yescomplemented
41#17988711C2214yescomplemented
42#17988663C2214yescomplemented
43#17988662C2214yescomplemented
44#17988659C2214yes—
45#17988658C2214yes—
46#17988655C2214yes—
47D4×#10596831C2214yes—
48C8×C22⋊D73C2214yes—
49C8×C22⋊D73C2214yescomplemented
50#17988650C2214yes—
51#17988650C2214yescomplemented
52#17988647C2214yescomplemented
53#17988645C2214yescomplemented
54#17988641C2214yes—
55#17988639C2214yescomplemented
56#17988637C2214yes—
57#17988637C2214yescomplemented
58#17988615C2211yescharacteristic
59#17988614C2211yescharacteristic
60#17988613C2211yescharacteristic
61#17988610C2211yescharacteristic
62#17988610C2211yescharacteristic
63#17988555C2211yescharacteristic
64#17988554C2211yescharacteristic
65#17988553C2211yescharacteristic
66#17988551C2211yescharacteristic
67#17988545C2211yescharacteristic
68#17988545C2212yescomplemented
69#17988544C2212yescomplemented
70#17988543C2211yescharacteristic
71#17988542C2211yescharacteristic
72#17988542C2212yescomplemented
73#17988541C2212yescomplemented
74#17988539C2212yescomplemented
75M16×Dic73C2211yescharacteristic
76M16×Dic73C2211yescharacteristic
77M16×Dic73C2212yescomplemented
78C2×C8×Dic73C2212yes—
79C2×C8×Dic73C2212yes—
80C2×C8×Dic73C2211yescharacteristic
81C2×C8×Dic73C2211yescharacteristic
82C2×C8×Dic73C2212yes—
83C2×C8×Dic73C2212yes—
84C2×C8×Dic73C2211yescharacteristic
85C2×C8×Dic73C2211yescharacteristic
86C2×C8×Dic73C2212yescomplemented
87C4×C8×D73C2212yescomplemented
88C2×#131×C73C2211yescharacteristic
89C23×C8×C73C2211yescharacteristic
90#525×C73C2211yescharacteristic
91#435×C73C2214yes—
92C8×D4×C73C2214yes—
93#424×C73C2211yescharacteristic
94#408×C73C2211yescharacteristic
95#407×C73C2211yescharacteristic
96#405×C73C2211yescharacteristic
97C2×#11924028C2311yescharacteristic
98C2×#11924027C2×C414yes—
99C23×Dic73C2×C412yes—
100#14556599—24no—
101#14556598—24no—
102#14556597—24no—
103C2×#11924012C2311yescharacteristic
104C2×#11924012C2311yescharacteristic
105C2×#11924012C2312yes—
106C2×#11924011C2312yes—
107C2×#11924011C2312yes—
108C22×#10596831—24no—
109C22×#10596831C2311yescharacteristic
110C22×#10596831C2312yes—
111C22×#10596831C2312yes—
112C22×#10596831C2312yes—
113C22×#10596831C2311yescharacteristic
114C2×C8×D73C2312yes—
115C2×C8×D73C2312yes—
116#14556590C2×C412yes—
117#14556589C2×C411yescharacteristic
118#14556587C2×C411yescharacteristic
119#14556586C2×C414yes—
120#14556584C2×C414yes—
121#14556582C2×C412yes—
122#14556581C2×C414yes—
123#14556580C2×C411yescharacteristic
124#14556578C2×C411yescharacteristic
125#14556577C2×C414yes—
126#14556575C2×C414yes—
127#14556574C2×C412yes—
128#14556572C2×C414yes—
129#14556570C2×C412yes—
130#14556568C2×C414yes—
131#14556568C2×C414yes—
132#14556565C2×C412yes—
133#14556563C2×C414yes—
134#14556563C2×C414yes—
135#14556560C2×C412yes—
136Q8×Dic73C2×C412yes—
137C4×Dic146C2314yes—
138#14556556C2×C414yes—
139#14556556C2×C412yes—
140D4×Dic73C2×C412yes—
141D4×Dic73C2×C414yes—
142D4×Dic73C2×C414yes—
143#14556553C2×C412yes—
144C4×C22⋊D73C2314yes—
145C4×C22⋊D73C2314yes—
146#14556551C2×C414yes—
147#14556551C2×C414yes—
148#14556551C2×C414yes—
149#14556550C2311yescharacteristic
150#14556550C2312yes—
151#14556549C2×C414yes—
152#14556548C2312yes—
153#14556547C2×C414yes—
154#14556547C2×C414yes—
155C2×C4×Dic73C2×C412yes—
156C2×C4×Dic73C2×C412yes—
157C2×C4×Dic73C2×C412yes—
158C2×C4×Dic73C2311yescharacteristic
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2312yes—
161C2×C4×Dic73C2312yes—
162C2×C4×Dic73C2311yescharacteristic
163C42×D73C2312yes—
164C4⋊#10596831C2314yes—
165#14556520C2314yes—
166#14556520C2314yes—
167#14556520C2314yes—
168#14556520C2314yes—
169C22⋊#10596831C2314yes—
170C22⋊#10596831C2314yes—
171#14556503C2314yes—
172#14556503C2314yes—
173#14556502C2312yes—
174#14556501C2312yes—
175#14556501C2312yes—
176#14556501C2312yes—
177#14556501C2312yes—
178C4×#10596831C2312yes—
179C8×Dic73C2312yes—
180C8×Dic73C2312yes—
181C8×Dic73C2312yes—
182C8×Dic73C2312yes—
183C8×Dic73C2312yes—
184C8×Dic73C2312yes—
185C8×Dic73C2312yes—
186C8×Dic73C2312yes—
187C8×Dic73C2312yes—
188C8×Dic73C2312yes—
189C8×Dic73C2311yescharacteristic
190C8×Dic73C2311yescharacteristic
191C8×Dic73C2311yescharacteristic
192C8×Dic73C2311yescharacteristic
193C2×#41×C73C2311yescharacteristic
194C23×C4×C73C2311yescharacteristic
195#131×C73—24no—
196C2×M16×C73C2311yescharacteristic
197C2×M16×C73C2311yescharacteristic
198C2×M16×C73C2312yes—
199C22×C8×C73—24no—
200C22×C8×C73C2311yescharacteristic
201C22×C8×C73C2312yes—
202C22×C8×C73C2312yes—
203C22×C8×C73C2312yes—
204C22×C8×C73C2311yescharacteristic
205#123×C73C2×C412yes—
206C22⋊Q8×C73C2×C412yes—
207#121×C73C2×C412yes—
208#120×C73C2×C412yes—
209C4×D4×C73C2314yes—
210#117×C73C2311yescharacteristic
211C4⋊C8×C73C2314yes—
212C22⋊C8×C73C2314yes—
213C22⋊C8×C73C2314yes—
214#97×C73C2312yes—
215C4×C8×C73C2312yes—
216#11924028—22no—
217#11924028—22no—
218#11924027—216no—
219C2×Dic146C22×C411yescharacteristic
220C2×Dic146C22×C414yes—
221C2×D292C22×C411yescharacteristic
222C2×C22⋊D73C22×C412yes—
223C2×C22⋊D73C22×C414yes—
224C2×C22⋊D73C22×C414yes—
225C22×Dic73—28no—
226C22×Dic73C22×C412yes—
227C22×Dic73C22×C412yes—
228C22×Dic73C22×C412yes—
229C22×Dic73C22×C412yes—
230C22×Dic73C22×C412yes—
231C22×Dic73C22×C414yes—
232C22×Dic73C22×C412yes—
233C2×C4×D73C22×C414yes—
234C2×C4×D73C2412yes—
235#11924012—22no—
236#11924012—22no—
237#11924012—24no—
238#11924011—24no—
239#11924011—24no—
240C2×#10596831—22no—
241C2×#10596831—24no—
242C2×#10596831—24no—
243C2×#10596831—24no—
244C2×#10596831#4114yescomplemented
245C2×#10596831C2412yes—
246C2×#10596831C2412yes—
247C2×#10596831C2412yes—
248C2×#10596831C2411yescharacteristic
249C2×#10596831C2411yescharacteristic
250C8×D73—24no—
251C8×D73—24no—
252C4⋊Dic73C22×C414yes—
253C4⋊Dic73C22×C412yes—
254C4⋊Dic73C22×C414yes—
255#11924007C22×C414yes—
256#11924007C22×C414yes—
257#11924007C22×C414yes—
258#11924007C22×C414yes—
259#11924007C22×C414yes—
260C22⋊Dic73C22×C414yes—
261C22⋊Dic73C22×C414yes—
262C22⋊Dic73C22×C412yes—
263C22⋊Dic73C22×C414yes—
264#11924005C22×C414yes—
265#11924005C22×C414yes—
266#11924005C22×C414yes—
267C4×Dic73C22×C414yes—
268C4×Dic73C22×C412yes—
269C4×Dic73C22×C412yes—
270C4×Dic73C22×C412yes—
271C4×Dic73C22×C412yes—
272C4×Dic73C22×C411yescharacteristic
273C4×Dic73C22×C412yes—
274C4×Dic73C22×C411yescharacteristic
275C4×Dic73C22×C414yes—
276C4×Dic73C2411yescharacteristic
277C4×Dic73C2411yescharacteristic
278C4×Dic73C2412yes—
279C4×Dic73C2412yes—
280C24×C73C22×C411yescharacteristic
281#41×C73—22no—
282#41×C73—22no—
283C2×Q8×C73C22×C411yescharacteristic
284C2×D4×C73C22×C414yes—
285C2×D4×C73C22×C412yes—
286C2×D4×C73C22×C411yescharacteristic
287C22×C4×C73—22no—
288C22×C4×C73—22no—
289C22×C4×C73C22×C412yes—
290C22×C4×C73C22×C411yescharacteristic
291C22×C4×C73C2412yes—
292C22×C4×C73C2412yes—
293C22×C4×C73C2411yescharacteristic
294M16×C73—22no—
295M16×C73—22no—
296M16×C73—24no—
297C2×C8×C73—22no—
298C2×C8×C73—24no—
299C2×C8×C73—24no—
300C2×C8×C73—24no—
301C2×C8×C73#4114yescomplemented
302C2×C8×C73C2412yes—
303C2×C8×C73C2412yes—
304C2×C8×C73C2412yes—
305C2×C8×C73C2411yescharacteristic
306C2×C8×C73C2411yescharacteristic
307C4⋊C4×C73C22×C412yes—
308C4⋊C4×C73C22×C414yes—
309C22⋊C4×C73C22×C412yes—
310C22⋊C4×C73C22×C414yes—
311C22⋊C4×C73C22×C414yes—
312C42×C73C2412yes—
313C23×C73—22no—
314C23×C73—24no—
315C23×C73C23×C412yes—
316C23×C73C23×C411yescharacteristic
317C23×C73C23×C412yes—
318C22×D73C23×C412yes—
319Q8×C73—22no—
320D4×C73—24no—
321D4×C73—28no—
322D4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—24no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73C23×C414yes—
330C2×C4×C73C23×C412yes—
331C2×C4×C73C23×C412yes—
332C2×C4×C73C23×C411yescharacteristic
333C2×C4×C73C2×#4112yes—
334C2×C4×C73C2×#4112yes—
335C2×C4×C73C2511yescharacteristic
336C22⋊D73—24no—
337C22⋊D73—28no—
338C22⋊D73—28no—
339C2×Dic73—24no—
340C2×Dic73—24no—
341C2×Dic73—24no—
342C2×Dic73—24no—
343C2×Dic73—24no—
344C2×Dic73—28no—
345C2×Dic73#13118yescomplemented
346C2×Dic73C23×C412yes—
347C2×Dic73C23×C412yes—
348C2×Dic73C23×C412yes—
349C2×Dic73C23×C414yes—
350C2×Dic73C23×C412yes—
351C2×Dic73C23×C412yes—
352D292—22no—
353C4×D73—22no—
354C4×D73—22no—
355C4×D73—28no—
356Dic146—22no—
357Dic146—28no—
358C8×C73—22no—
359C8×C73—22no—
360C8×C73—22no—
361C8×C73C2×#4112yes—
362C8×C73C2×#4112yes—
363#10596831—22no—
364#10596831—22no—
365#10596831—22no—
366#10596831C2×#4112yes—
367#10596831C2×#4112yes—
368C22×C73—28no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—22no—
373C22×C73—24no—
374C22×C73C4×#4112yes—
375C22×C73C2×#13114yes—
376C22×C73C24×C411yescharacteristic
377C2×D73—22no—
378C2×D73—24no—
379C4×C73—22no—
380C4×C73—22no—
381C4×C73—24no—
382C4×C73C4×#4112yes—
383C4×C73C22×#4111yescharacteristic
384C4×C73C22×#4111yescharacteristic
385Dic73—22no—
386Dic73—24no—
387Dic73—22no—
388Dic73—22no—
389Dic73C2×#13114yes—
390Dic73C2×#13114yes—
391#60204—731nomaximal, Sylow
392C2×C73—22no—
393C2×C73—24no—
394C2×C73—42no—
395C2×C73C2×C4×#4111yescharacteristic
396C2×C73C22×#13112yes—
397D73—42no—
398#3444—731no—
399#2966—734no—
400#2966—734no—
401#2965—734no—
402C8×#41—734no—
403#2960—731no—
404#2960—731no—
405#2931—731no—
406#2931—731no—
407#2929—731no—
408#2929—731no—
409#2929—731no—
410#2929D7311yescharacteristic, complemented
411#2922—731no—
412#2922—731no—
413#2920—731no—
414C4×#131—731no—
415C4×#131—731no—
416C22×C4×C8—731no—
417C73#6020411yescharacteristic, complemented, Sylow
418C2×#131—731no—
419C2×#131—731no—
420C2×#131—731no—
421C2×#131C2×D7311yescharacteristic
422C23×C8—731no—
423C23×C8C2×D7311yescharacteristic
424#533—732no—
425#533—731no—
426#532—731no—
427#532—732no—
428#529—734no—
429#529—732no—
430#529—732no—
431#529—734no—
432#525—731no—
433#525—734no—
434#525C2×D7311yescharacteristic
435C4×#41—731no—
436C4×#41—734no—
437C4×#41—731no—
438C22×C42—731no—
439#446—734no—
440#446—734no—
441C8×Q8—734no—
442C8×Q8—734no—
443#436—734no—
444#436—734no—
445#435—734no—
446#435—734no—
447#435—734no—
448#435C2×D7314yes—
449C8×D4—734no—
450C8×D4—734no—
451C8×D4—734no—
452C8×D4—734no—
453C8×D4—734no—
454C8×D4C2×D7314yes—
455#433—734no—
456#433—734no—
457#432—734no—
458#431—734no—
459#431—734no—
460#431—734no—
461#424—731no—
462#424—731no—
463#424—731no—
464#424C2×D7311yescharacteristic
465#423—731no—
466#423—731no—
467#408—731no—
468#408—731no—
469#408—731no—
470#408C2×D7311yescharacteristic
471#407—731no—
472#407C2×D7311yescharacteristic
473#405—731no—
474#405—732no—
475#405—731no—
476#405—732no—
477#405—731no—
478#405—732no—
479#405—732no—
480#405C2×D7311yescharacteristic
481C4×M16—731no—
482C4×M16—731no—
483C4×M16—732no—
484C4×M16—732no—
485C2×C4×C8—731no—
486C2×C4×C8—731no—
487C2×C4×C8—731no—
488C2×C4×C8—731no—
489C2×C4×C8—732no—
490C2×C4×C8—732no—
491C2×C4×C8—732no—
492C2×C4×C8—732no—
493C2×C4×C8—732no—
494C2×C4×C8—732no—
495C2×#41—734no—
496C2×#41—731no—
497C2×#41C22×D7311yescharacteristic
498C23×C4—732no—
499C23×C4C22×D7311yescharacteristic
500#131—24no—
501#131—1464no—
502#131—1464no—
503#131—1464no—
504C2×M16—731no—
505C2×M16—731no—
506C2×M16—732no—
507C2×M16—732no—
508C2×M16—732no—
509C2×M16C22×D7311yescharacteristic
510C2×M16C22×D7311yescharacteristic
511C2×M16C22×D7312yes—
512C22×C8—24no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—732no—
516C22×C8—732no—
517C22×C8—732no—
518C22×C8—732no—
519C22×C8—732no—
520C22×C8—1464no—
521C22×C8C22×D7311yescharacteristic
522C22×C8C22×D7312yes—
523C22×C8C22×D7312yes—
524C22×C8C22×D7312yes—
525C22×C8C22×D7311yescharacteristic
526C4⋊Q8—731no—
527C4⋊Q8—732no—
528#127—731no—
529#126—734no—
530#126—734no—
531#125—734no—
532#125—732no—
533#124—731no—
534#124—731no—
535#124—734no—
536#123—734no—
537#123—732no—
538#123—734no—
539#123C4×D7312yes—
540C22⋊Q8—732no—
541C22⋊Q8—734no—
542C22⋊Q8—734no—
543C22⋊Q8C4×D7312yes—
544#121—734no—
545#121—734no—
546#121—732no—
547#121C4×D7312yes—
548#120—732no—
549#120C4×D7312yes—
550C4×Q8—732no—
551C4×Q8—734no—
552C4×Q8—732no—
553C4×Q8—734no—
554C4×D4—734no—
555C4×D4—734no—
556C4×D4—732no—
557C4×D4—734no—
558C4×D4—734no—
559C4×D4—732no—
560C4×D4—734no—
561C4×D4—734no—
562C4×D4—734no—
563C4×D4C22×D7314yes—
564#117—731no—
565#117—732no—
566#117—734no—
567#117—734no—
568#117—734no—
569#117—732no—
570#117C22×D7311yescharacteristic
571C2×C42—732no—
572C2×C42—732no—
573C2×C42—732no—
574C2×C42—732no—
575C2×C42—731no—
576C2×C42—732no—
577C2×C42—732no—
578C2×C42—731no—
579C2×C42—732no—
580C4⋊C8—734no—
581C4⋊C8—734no—
582C4⋊C8—734no—
583C4⋊C8—734no—
584C4⋊C8—734no—
585C4⋊C8C22×D7314yes—
586C22⋊C8—734no—
587C22⋊C8—734no—
588C22⋊C8—734no—
589C22⋊C8—734no—
590C22⋊C8C22×D7314yes—
591C22⋊C8C22×D7314yes—
592#97—732no—
593#97—732no—
594#97—732no—
595#97—732no—
596#97—732no—
597#97C22×D7312yes—
598C4×C8—731no—
599C4×C8—731no—
600C4×C8—732no—
601C4×C8—732no—
602C4×C8—732no—
603C4×C8—732no—
604C4×C8—732no—
605C4×C8—732no—
606C4×C8—732no—
607C4×C8—732no—
608C4×C8—731no—
609C4×C8—731no—
610C4×C8—732no—
611C4×C8—732no—
612C4×C8—732no—
613C4×C8C22×D7312yes—
614C24C2×C4×D7311yescharacteristic
615#41—22no—
616#41—22no—
617#41—14616no—
618#41—1462no—
619#41—1462no—
620C2×Q8—734no—
621C2×Q8—731no—
622C2×Q8C2×C4×D7311yescharacteristic
623C2×D4—732no—
624C2×D4—734no—
625C2×D4—734no—
626C2×D4—731no—
627C2×D4C2×C4×D7312yes—
628C2×D4C2×C4×D7311yescharacteristic
629C2×D4C2×C4×D7314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—732no—
633C22×C4—732no—
634C22×C4—732no—
635C22×C4—732no—
636C22×C4—732no—
637C22×C4—732no—
638C22×C4—734no—
639C22×C4—734no—
640C22×C4—732no—
641C22×C4—1468no—
642C22×C4C2×C4×D7312yes—
643C22×C4C2×C4×D7311yescharacteristic
644C22×C4C23×D7312yes—
645C22×C4C23×D7312yes—
646C22×C4C23×D7311yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—1464no—
651M16—1464no—
652M16—1462no—
653M16—1462no—
654M16—1464no—
655C2×C8—22no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—734no—
660C2×C8—731no—
661C2×C8—731no—
662C2×C8—732no—
663C2×C8—732no—
664C2×C8—732no—
665C2×C8—1464no—
666C2×C8—1464no—
667C2×C8—1464no—
668C2×C8—1464no—
669C2×C8—1462no—
670C2×C8—1464no—
671C2×C8#1192402714yescomplemented
672C2×C8C23×D7312yes—
673C2×C8C23×D7312yes—
674C2×C8C23×D7312yes—
675C2×C8C23×D7311yescharacteristic
676C2×C8C23×D7311yescharacteristic
677C4⋊C4—734no—
678C4⋊C4—734no—
679C4⋊C4—734no—
680C4⋊C4—734no—
681C4⋊C4—734no—
682C4⋊C4—732no—
683C4⋊C4—734no—
684C4⋊C4—734no—
685C4⋊C4C2×C4×D7314yes—
686C4⋊C4C2×C4×D7312yes—
687C22⋊C4—732no—
688C22⋊C4—734no—
689C22⋊C4—734no—
690C22⋊C4—734no—
691C22⋊C4—734no—
692C22⋊C4—734no—
693C22⋊C4—734no—
694C22⋊C4C2×C4×D7314yes—
695C22⋊C4C2×C4×D7314yes—
696C22⋊C4C2×C4×D7312yes—
697C42—732no—
698C42—732no—
699C42—732no—
700C42—732no—
701C42—731no—
702C42—732no—
703C42—731no—
704C42—734no—
705C42—734no—
706C42—731no—
707C42—731no—
708C42—732no—
709C42—732no—
710C42C23×D7312yes—
711C23—22no—
712C23—24no—
713C23—732no—
714C23C22×C4×D7312yes—
715C23C22×C4×D7311yescharacteristic
716C23C22×C4×D7312yes—
717Q8—22no—
718Q8—1468no—
719Q8—1462no—
720D4—24no—
721D4—28no—
722D4—22no—
723D4—1468no—
724D4—1464no—
725D4—1468no—
726D4—1462no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—732no—
734C2×C4—732no—
735C2×C4—738no—
736C2×C4—732no—
737C2×C4—732no—
738C2×C4—734no—
739C2×C4—732no—
740C2×C4—1468no—
741C2×C4—1464no—
742C2×C4—1464no—
743C2×C4—1464no—
744C2×C4—1464no—
745C2×C4—1468no—
746C2×C4—1464no—
747C2×C4—1462no—
748C2×C4—1462no—
749C2×C4C22×C4×D7312yes—
750C2×C4C22×C4×D7312yes—
751C2×C4C22×C4×D7314yes—
752C2×C4C22×C4×D7311yescharacteristic
753C2×C4#41×D7312yes—
754C2×C4C2×#1192402712yes—
755C2×C4C24×D7311yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—732no—
760C8—732no—
761C8—1462no—
762C8—1462no—
763C8—1462no—
764C8C2×#1192402712yes—
765C8C2×#1192402712yes—
766C22—28no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—1464no—
773C22—1462no—
774C22C4×#1192402712yes—
775C22#131×D7314yes—
776C22C23×C4×D7311yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—734no—
781C4—734no—
782C4—1462no—
783C4—1462no—
784C4—1464no—
785C4—1462no—
786C4C4×#1192402712yes—
787C4C2×#41×D7311yescharacteristic
788C4C22×#1192402711yescharacteristic
789C2—22no—
790C2—24no—
791C2—42no—
792C2—2922no—
793C2C2×C4×#1192402711yescharacteristic
794C2C2×#131×D7312yes—
subgroupG/H
centerC2×C8C23×D73
commutator, socleC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC73×#2929C2
prime radical#22623223C2
cosocleC2×C4×C73C25
hypercenter#2929D73
hypocenterC73#60204
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #22618901C2semidirect
3. #22618899C2semidirect
4. #22618891C2semidirect
5. C8×#11924027C2semidirect
6. #22618864C2semidirect
7. #22618863C2semidirect
8. #22618641C2semidirect
9. #22618639C2semidirect
10. #22618626C2semidirect
11. #22618625C2semidirect
12. #22618621C2semidirect
13. #22618574C2semidirect
14. #22618571C2semidirect
15. #22618560C2semidirect
16. #22618353C2semidirect
17. #131×Dic73C2semidirect
18. C22×C8×Dic73C2semidirect
19. C73×#2929C2semidirect
38. #17988716C22semidirect
39. #17988715C22semidirect
40. C8×Dic146C22semidirect
41. #17988711C22semidirect
42. #17988663C22semidirect
43. #17988662C22semidirect
49. C8×C22⋊D73C22semidirect
51. #17988650C22semidirect
52. #17988647C22semidirect
53. #17988645C22semidirect
55. #17988639C22semidirect
57. #17988637C22semidirect
68. #17988545C22semidirect
69. #17988544C22semidirect
72. #17988542C22semidirect
73. #17988541C22semidirect
74. #17988539C22semidirect
77. M16×Dic73C22semidirect
86. C2×C8×Dic73C22semidirect
87. C4×C8×D73C22semidirect
244. C2×#10596831#41semidirect
301. C2×C8×C73#41semidirect
345. C2×Dic73#131semidirect
410. #2929D73semidirect
417. C73#60204semidirect
671. C2×C8#11924027semidirect

Maximal subgroups

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

subgroupindex
#226232232
#226189012
#226188992
#226188912
C8×#119240272
#226188642
#226188632
#226186412
#226186392
#226186262
#226186252
#226186212
#226185742
#226185712
#226185602
#226183532
#131×Dic732
C22×C8×Dic732
C73×#29292
#6020473