Finite Group Databasebeta

← #33950665

Subgroups — #33950665

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#22623495C211yesmaximal, characteristic
2#22618948C212yesmaximal, complemented
3#22618933C214yesmaximal, complemented
4#22618929C212yesmaximal, complemented
5#22618914C214yesmaximal, complemented
6#22618900C212yesmaximal, complemented
7#22618892C212yesmaximal, complemented
8#22618874C211yesmaximal, characteristic, complemented
9#22618861C211yesmaximal, characteristic, complemented
10#22618666C211yesmaximal, characteristic, complemented
11#22618661C212yesmaximal, complemented
12#22618637C212yesmaximal, complemented
13C2×#17988664C211yesmaximal, characteristic, complemented
14#22618586C212yesmaximal, complemented
15C4×#14556598C211yesmaximal, characteristic, complemented
16#22618347C212yesmaximal, complemented
17C73×#2925C211yesmaximal, characteristic, complemented
18C2×#14556598C2211yescharacteristic
19C2×#14556598C2211yescharacteristic
20C22×#11924011C2212yes—
21C2×M16×D73C2212yes—
22#17989310C411yescharacteristic
23#17989302C411yescharacteristic
24#17989297C411yescharacteristic
25#17989287C412yes—
26#17989278C412yes—
27#17989277C412yes—
28#17989266C414yes—
29#17989242C411yescharacteristic
30#17989233C412yes—
31#17989144C2211yescharacteristic
32#17989121C2212yes—
33#17989115C2214yes—
34#17989094C2212yes—
35C4×#11924028C2212yes—
36C2×C4×D292C2211yescharacteristic
37#117×D73C2212yes—
38#17988716C2214yescomplemented
39#17988714C2212yescomplemented
40#17988714C2212yescomplemented
41#17988714C2212yescomplemented
42#17988711C2212yescomplemented
43#17988711C2212yescomplemented
44#17988711C2212yescomplemented
45#17988664C2211yescharacteristic
46#17988664C2212yes—
47#17988664C2211yescharacteristic
48#17988664C2212yes—
49#17988664C2211yescharacteristic
50#17988664C2212yes—
51#17988664C2211yescharacteristic
52#17988662C2214yescomplemented
53#17988662C2214yescomplemented
54#17988662C2214yescomplemented
55#17988661C2214yescomplemented
56#17988657C2214yes—
57#17988655C2214yescomplemented
58#17988655C2214yescomplemented
59#17988655C2214yescomplemented
60#17988652C2212yes—
61#17988650C2214yescomplemented
62#17988649C2214yescomplemented
63#17988646C2214yescomplemented
64#17988642C2214yescomplemented
65#17988638C2214yescomplemented
66#17988615C2212yes—
67#17988613C2212yes—
68#17988550C2212yes—
69C2×#14556503C2212yes—
70#17988545C2212yes—
71#17988544C2214yescomplemented
72#17988543C2211yescharacteristic
73#17988543C2211yescharacteristic
74#17988543C2212yescomplemented
75#17988543C2212yescomplemented
76#17988542C2212yes—
77#17988541C2214yescomplemented
78C4×#11924012C2211yescharacteristic
79C4×#11924012C2212yescomplemented
80#17988539C2214yescomplemented
81C4×#11924011C2214yescomplemented
82C2×C4×#10596831C2211yescharacteristic
83C2×C4×#10596831C2212yescomplemented
84C4×#41×C73C2211yescharacteristic
85#433×C73C2214yescomplemented
86#432×C73C2212yescomplemented
87#431×C73C2212yescomplemented
88#423×C73C2211yescharacteristic
89C2×C4⋊C8×C73C2211yescharacteristic
90#408×C73C2212yes—
91#405×C73C2212yes—
92C2×#11924028C2×C412yes—
93C22×D292C2×C411yescharacteristic
94C22×C4×D73C2312yes—
95#14556598—24no—
96#14556598—24no—
97C2×#11924012C2311yescharacteristic
98C2×#11924012C2312yes—
99C2×#11924012C2312yes—
100C2×#11924012C2311yescharacteristic
101C2×#11924011—28no—
102C2×#11924011C2312yes—
103C2×#11924011C2312yes—
104C2×#11924011C2314yes—
105C2×#11924011C2312yes—
106C2×#11924011C2312yes—
107M16×D73—28no—
108C22×#10596831C2311yescharacteristic
109C22×#10596831C2312yes—
110C22×#10596831C2312yes—
111C22×#10596831C2311yescharacteristic
112C2×C8×D73C2314yes—
113#14556591C2×C411yescharacteristic
114#14556591C2×C411yescharacteristic
115#14556586C2×C414yes—
116#14556585C2×C414yes—
117#14556584C2×C414yes—
118#14556583C2×C412yes—
119#14556583C2×C412yes—
120#14556581C2×C414yes—
121#14556579C2×C412yes—
122#14556577C2×C414yes—
123#14556576C2×C414yes—
124#14556574C2×C414yes—
125#14556573C2×C414yes—
126#14556572C2×C414yes—
127#14556570C2×C412yes—
128#14556570C2×C412yes—
129#14556570C2×C412yes—
130#14556569C2×C414yes—
131#14556567C2×C412yes—
132#14556567C2×C412yes—
133#14556565C2×C412yes—
134#14556564C2×C414yes—
135#14556562C2×C412yes—
136#14556562C2×C412yes—
137#14556559C2×C414yes—
138C4×Dic146C2×C412yes—
139C4×Dic146C2312yes—
140C4×Dic146C2312yes—
141C4×D292C2×C412yes—
142C4×D292C2×C411yescharacteristic
143C4×D292C2×C412yes—
144C4×D292C2×C411yescharacteristic
145C4×D292C2311yescharacteristic
146C4×D292C2312yes—
147C4×D292C2311yescharacteristic
148C4×C22⋊D73C2×C414yes—
149C4×C22⋊D73C2314yes—
150C4×C22⋊D73C2314yes—
151#14556550C2×C412yes—
152#14556550C2312yes—
153#14556549C2×C412yes—
154#14556549C2×C412yes—
155#14556548C2×C414yes—
156#14556548C2314yes—
157#14556547C2×C414yes—
158C2×C4⋊Dic73C2×C411yescharacteristic
159C4⋊C4×D73C2×C412yes—
160C4⋊C4×D73C2×C412yes—
161C2×#11924005C2×C412yes—
162C22⋊C4×D73C2×C414yes—
163C42×D73C2314yes—
164#14556520C2314yes—
165#14556520C2314yes—
166#14556520C2314yes—
167#14556520C2314yes—
168#14556503C2312yes—
169#14556503C2314yes—
170#14556503C2312yes—
171#14556503C2312yes—
172#14556503C2314yes—
173#14556503C2312yes—
174#14556502C2312yes—
175#14556502C2312yes—
176#14556502C2312yes—
177#14556501C2314yes—
178#14556501C2314yes—
179C4×#10596831C2312yes—
180C4×#10596831C2312yes—
181C4×#10596831C2311yescharacteristic
182C4×#10596831C2311yescharacteristic
183C4×#10596831C2311yescharacteristic
184C4×#10596831C2311yescharacteristic
185C4×#10596831C2312yes—
186C8×Dic73C2314yes—
187C8×Dic73C2314yes—
188C2×#41×C73C2311yescharacteristic
189C2×M16×C73C2312yes—
190C22×C8×C73C2312yes—
191C4×Q8×C73C2×C411yescharacteristic
192C4×Q8×C73C2×C411yescharacteristic
193C4×D4×C73C2×C412yes—
194C4×D4×C73C2×C411yescharacteristic
195C4×D4×C73C2×C412yes—
196C4×D4×C73C2×C411yescharacteristic
197#117×C73C2311yescharacteristic
198#117×C73C2312yes—
199C2×C42×C73C2312yes—
200C2×C42×C73C2311yescharacteristic
201C4⋊C8×C73C2312yes—
202C4⋊C8×C73C2311yescharacteristic
203C4⋊C8×C73C2311yescharacteristic
204C4⋊C8×C73C2312yes—
205C4⋊C8×C73C2312yes—
206C22⋊C8×C73C2314yes—
207C22⋊C8×C73C2314yes—
208#97×C73C2314yes—
209C4×C8×C73C2314yes—
210C23×D73C22×C412yes—
211#11924028—44no—
212C2×Dic146C22×C412yes—
213C2×Dic146C22×C412yes—
214C2×D292—42no—
215C2×D292C22×C411yescharacteristic
216C2×D292C22×C411yescharacteristic
217C2×D292C22×C412yes—
218C2×C22⋊D73C22×C414yes—
219C2×C22⋊D73C22×C414yes—
220C22×Dic73C22×C412yes—
221C2×C4×D73—24no—
222C2×C4×D73—24no—
223C2×C4×D73C22×C412yes—
224C2×C4×D73C22×C412yes—
225C2×C4×D73C22×C414yes—
226C2×C4×D73C22×C414yes—
227C2×C4×D73C2412yes—
228C2×C4×D73C2412yes—
229#11924012—22no—
230#11924012—24no—
231#11924012—24no—
232#11924012#4114yescomplemented
233#11924011—28no—
234#11924011—24no—
235#11924011—24no—
236#11924011—24no—
237#11924011—24no—
238C2×#10596831—22no—
239C2×#10596831—24no—
240C2×#10596831—24no—
241C2×#10596831#4114yescomplemented
242C2×#10596831C2411yescharacteristic
243C2×#10596831C2412yes—
244C2×#10596831C2411yescharacteristic
245C2×#10596831C2411yescharacteristic
246C2×#10596831C2412yes—
247C2×#10596831C2411yescharacteristic
248C8×D73—28no—
249C4⋊Dic73C22×C412yes—
250C4⋊Dic73C22×C412yes—
251C4⋊Dic73C22×C411yescharacteristic
252C4⋊Dic73C22×C411yescharacteristic
253C4⋊Dic73C22×C412yes—
254C4⋊Dic73C22×C412yes—
255C4⋊Dic73C22×C412yes—
256#11924007C22×C414yes—
257#11924007C22×C414yes—
258#11924007C22×C414yes—
259#11924007C22×C414yes—
260#11924007C22×C414yes—
261#11924007C22×C414yes—
262C22⋊Dic73C22×C414yes—
263C22⋊Dic73C22×C414yes—
264C22⋊Dic73C22×C414yes—
265#11924005C22×C414yes—
266#11924005C22×C414yes—
267#11924005C22×C412yes—
268#11924005C22×C412yes—
269#11924005C22×C412yes—
270#11924005C22×C412yes—
271#11924005C22×C414yes—
272#11924005C22×C414yes—
273C4×Dic73C22×C414yes—
274C4×Dic73C22×C414yes—
275C4×Dic73C2414yes—
276#41×C73—22no—
277#41×C73—22no—
278C2×Q8×C73C22×C411yescharacteristic
279C2×D4×C73C22×C412yes—
280C2×D4×C73C22×C411yescharacteristic
281C22×C4×C73C22×C411yescharacteristic
282C22×C4×C73C22×C412yes—
283C22×C4×C73C22×C411yescharacteristic
284C22×C4×C73C22×C412yes—
285C22×C4×C73C2412yes—
286C22×C4×C73C2411yescharacteristic
287M16×C73—24no—
288C2×C8×C73—24no—
289C2×C8×C73C2412yes—
290C2×C8×C73C2414yes—
291C2×C8×C73C2412yes—
292C4⋊C4×C73C22×C411yescharacteristic
293C4⋊C4×C73C22×C411yescharacteristic
294C4⋊C4×C73C22×C412yes—
295C4⋊C4×C73C22×C412yes—
296C22⋊C4×C73C22×C412yes—
297C22⋊C4×C73C22×C412yes—
298C22⋊C4×C73C22×C412yes—
299C42×C73C22×C412yes—
300C42×C73C22×C411yescharacteristic
301C42×C73C22×C411yescharacteristic
302C42×C73C22×C412yes—
303C42×C73C2412yes—
304C42×C73C2411yescharacteristic
305C42×C73C2411yescharacteristic
306C23×C73C23×C412yes—
307C23×C73C23×C411yescharacteristic
308C22×D73—24no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73C23×C412yes—
312C22×D73C23×C412yes—
313Q8×C73—22no—
314D4×C73—24no—
315D4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—24no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—41no—
321C2×C4×C73—42no—
322C2×C4×C73C23×C411yescharacteristic
323C2×C4×C73C23×C412yes—
324C2×C4×C73C23×C412yes—
325C2×C4×C73C23×C412yes—
326C2×C4×C73C23×C411yescharacteristic
327C2×C4×C73C23×C411yescharacteristic
328C2×C4×C73C23×C411yescharacteristic
329C2×C4×C73C23×C411yescharacteristic
330C2×C4×C73C2×#4112yes—
331C2×C4×C73C2×#4112yes—
332C2×C4×C73C2511yescharacteristic
333C22⋊D73—44no—
334C22⋊D73—44no—
335C2×Dic73—24no—
336C2×Dic73C23×C412yes—
337C2×Dic73C23×C414yes—
338C2×Dic73C23×C414yes—
339C2×Dic73C23×C412yes—
340D292—22no—
341D292—22no—
342D292—42no—
343C4×D73—24no—
344C4×D73—24no—
345C4×D73—22no—
346C4×D73—22no—
347C4×D73—22no—
348C4×D73—22no—
349C4×D73—44no—
350C4×D73—44no—
351Dic146—24no—
352Dic146—42no—
353C8×C73—22no—
354C8×C73—22no—
355C8×C73—24no—
356#10596831—21no—
357#10596831—21no—
358#10596831—22no—
359#10596831C2×#4114yes—
360#10596831C2×#4112yes—
361#10596831C2×#4112yes—
362C22×C73—21no—
363C22×C73—21no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73C4×#4112yes—
368C22×C73C24×C411yescharacteristic
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—84no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—21no—
379C4×C73—21no—
380C4×C73—22no—
381C4×C73—21no—
382C4×C73C4×#4112yes—
383C4×C73#56812yes—
384C4×C73C22×#4111yescharacteristic
385C4×C73C22×#4111yescharacteristic
386Dic73—22no—
387Dic73—22no—
388Dic73—24no—
389Dic73—24no—
390#60217—731nomaximal, Sylow
391C2×C73—22no—
392C2×C73—42no—
393C2×C73C2×C4×#4111yescharacteristic
394C2×C73C2×#56811yescharacteristic
395C2×C73#357311yescharacteristic
396D73—42no—
397D73—42no—
398#3475—731no—
399#2971—732no—
400#2969—734no—
401#2969—732no—
402#2967—734no—
403#2966—732no—
404#2965—732no—
405#2962—731no—
406#2960—731no—
407D4×M16—731no—
408#2933—732no—
409#2930—732no—
410C2×#436—731no—
411#2925D7311yescharacteristic, complemented
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#533—731no—
430#529—734no—
431#529—732no—
432#525—732no—
433C4×#41—732no—
434C4×#41C2×D7311yescharacteristic
435C2×C4×D4—731no—
436C2×#117—732no—
437#446—732no—
438#446—732no—
439#446—732no—
440#446—734no—
441C8×Q8—732no—
442C8×Q8—732no—
443C8×Q8—732no—
444#436—731no—
445#436—731no—
446#436—732no—
447#436—731no—
448#436—732no—
449#436—731no—
450#436—732no—
451#436—734no—
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#433C2×D7314yescomplemented
464#432—734no—
465#432C2×D7312yescomplemented
466#431—734no—
467#431C2×D7312yescomplemented
468#424—732no—
469#424—732no—
470#423C2×D7311yescharacteristic
471C2×C4⋊C8C2×D7311yescharacteristic
472#408C2×D7312yes—
473#407—732no—
474C2×C22⋊C8—732no—
475#405—732no—
476#405—732no—
477#405—731no—
478#405—731no—
479#405—732no—
480#405—732no—
481#405—734no—
482#405—734no—
483#405C2×D7312yes—
484C4×M16—731no—
485C4×M16—732no—
486C4×M16—734no—
487C4×M16—734no—
488C2×C4×C8—731no—
489C2×C4×C8—732no—
490C2×#41—732no—
491C2×#41C22×D7311yescharacteristic
492C22×D4—731no—
493C23×C4—732no—
494#131—1464no—
495#131—1464no—
496C2×M16—731no—
497C2×M16—731no—
498C2×M16—732no—
499C2×M16—732no—
500C2×M16—734no—
501C2×M16—732no—
502C2×M16—732no—
503C2×M16—732no—
504C2×M16—732no—
505C2×M16—1468no—
506C2×M16—1468no—
507C2×M16C22×D7312yes—
508C22×C8—731no—
509C22×C8—731no—
510C22×C8—732no—
511C22×C8—732no—
512C22×C8—734no—
513C22×C8C22×D7312yes—
514C4⋊Q8—731no—
515C4⋊Q8—731no—
516#126—734no—
517#126—734no—
518#126—734no—
519#125—734no—
520#125—732no—
521#125—732no—
522#124—734no—
523#124—732no—
524#123—734no—
525#123—734no—
526#123—734no—
527#123—734no—
528C22⋊Q8—732no—
529C22⋊Q8—732no—
530C22⋊Q8—732no—
531C22⋊Q8—732no—
532C22⋊Q8—732no—
533C22⋊Q8—734no—
534#121—732no—
535#121—732no—
536#121—732no—
537#121—734no—
538#120—734no—
539C4×Q8—732no—
540C4×Q8—732no—
541C4×Q8—732no—
542C4×Q8C4×D7311yescharacteristic
543C4×Q8C4×D7311yescharacteristic
544C4×D4—734no—
545C4×D4—734no—
546C4×D4—734no—
547C4×D4—731no—
548C4×D4—732no—
549C4×D4—731no—
550C4×D4—732no—
551C4×D4—731no—
552C4×D4—731no—
553C4×D4—732no—
554C4×D4C4×D7312yes—
555C4×D4C4×D7311yescharacteristic
556C4×D4C4×D7312yes—
557C4×D4C4×D7311yescharacteristic
558#117—732no—
559#117—732no—
560#117—732no—
561#117—732no—
562#117—734no—
563#117—734no—
564#117—734no—
565#117C22×D7311yescharacteristic
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×C42C22×D7311yescharacteristic
574C2×C42C22×D7312yes—
575C4⋊C8—734no—
576C4⋊C8—734no—
577C4⋊C8—734no—
578C4⋊C8—734no—
579C4⋊C8C22×D7311yescharacteristic
580C4⋊C8C22×D7311yescharacteristic
581C4⋊C8C22×D7312yes—
582C4⋊C8C22×D7312yes—
583C4⋊C8C22×D7312yes—
584C22⋊C8—732no—
585C22⋊C8—732no—
586C22⋊C8—732no—
587C22⋊C8—732no—
588C22⋊C8—734no—
589C22⋊C8—734no—
590C22⋊C8C22×D7314yes—
591C22⋊C8C22×D7314yes—
592#97—734no—
593#97—734no—
594#97—732no—
595#97—732no—
596#97—732no—
597#97C22×D7314yes—
598C4×C8—734no—
599C4×C8—734no—
600C4×C8—731no—
601C4×C8—732no—
602C4×C8—732no—
603C4×C8—731no—
604C4×C8—732no—
605C4×C8—731no—
606C4×C8—731no—
607C4×C8C22×D7314yes—
608C24—732no—
609#41—22no—
610#41—22no—
611#41—2924no—
612C2×Q8—732no—
613C2×Q8—732no—
614C2×Q8C2×C4×D7311yescharacteristic
615C2×D4—2922no—
616C2×D4—734no—
617C2×D4—734no—
618C2×D4—732no—
619C2×D4—731no—
620C2×D4—731no—
621C2×D4C2×C4×D7312yes—
622C2×D4C2×C4×D7311yescharacteristic
623C22×C4—734no—
624C22×C4—734no—
625C22×C4—732no—
626C22×C4—732no—
627C22×C4—732no—
628C22×C4—732no—
629C22×C4—732no—
630C22×C4—1464no—
631C22×C4—1464no—
632C22×C4C2×C4×D7311yescharacteristic
633C22×C4C2×C4×D7312yes—
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×C4×D7312yes—
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638M16—24no—
639M16—734no—
640M16—1464no—
641M16—1464no—
642M16—1464no—
643M16—1464no—
644M16—1468no—
645M16—1464no—
646M16—1464no—
647M16—1462no—
648C2×C8—24no—
649C2×C8—734no—
650C2×C8—731no—
651C2×C8—731no—
652C2×C8—732no—
653C2×C8—731no—
654C2×C8—732no—
655C2×C8—731no—
656C2×C8—1468no—
657C2×C8—1464no—
658C2×C8—1464no—
659C2×C8—1462no—
660C2×C8C23×D7312yes—
661C2×C8C23×D7314yes—
662C2×C8C23×D7312yes—
663C4⋊C4—734no—
664C4⋊C4—734no—
665C4⋊C4—734no—
666C4⋊C4—734no—
667C4⋊C4—734no—
668C4⋊C4—734no—
669C4⋊C4—731no—
670C4⋊C4—732no—
671C4⋊C4—732no—
672C4⋊C4—731no—
673C4⋊C4—732no—
674C4⋊C4—732no—
675C4⋊C4—732no—
676C4⋊C4C2×C4×D7311yescharacteristic
677C4⋊C4C2×C4×D7311yescharacteristic
678C4⋊C4C2×C4×D7312yes—
679C4⋊C4C2×C4×D7312yes—
680C22⋊C4—734no—
681C22⋊C4—734no—
682C22⋊C4—734no—
683C22⋊C4—732no—
684C22⋊C4—734no—
685C22⋊C4—734no—
686C22⋊C4—732no—
687C22⋊C4—732no—
688C22⋊C4—732no—
689C22⋊C4—734no—
690C22⋊C4—734no—
691C22⋊C4C2×C4×D7312yes—
692C22⋊C4C2×C4×D7312yes—
693C22⋊C4C2×C4×D7312yes—
694C42—734no—
695C42—734no—
696C42—734no—
697C42C2×C4×D7312yes—
698C42C2×C4×D7311yescharacteristic
699C42C2×C4×D7311yescharacteristic
700C42C2×C4×D7312yes—
701C42C23×D7311yescharacteristic
702C42C23×D7312yes—
703C42C23×D7311yescharacteristic
704C23—2922no—
705C23—2922no—
706C23—732no—
707C23—732no—
708C23—1464no—
709C23C22×C4×D7312yes—
710C23C22×C4×D7311yescharacteristic
711Q8—22no—
712Q8—2922no—
713Q8—1464no—
714D4—24no—
715D4—22no—
716D4—2922no—
717D4—2924no—
718D4—2924no—
719D4—1462no—
720D4—1462no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—2924no—
728C2×C4—2924no—
729C2×C4—732no—
730C2×C4—734no—
731C2×C4—734no—
732C2×C4—732no—
733C2×C4—1464no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1464no—
739C2×C4—1464no—
740C2×C4C22×C4×D7312yes—
741C2×C4C22×C4×D7312yes—
742C2×C4C22×C4×D7311yescharacteristic
743C2×C4C22×C4×D7312yes—
744C2×C4C22×C4×D7311yescharacteristic
745C2×C4C22×C4×D7311yescharacteristic
746C2×C4C22×C4×D7311yescharacteristic
747C2×C4C22×C4×D7311yescharacteristic
748C2×C4#41×D7312yes—
749C2×C4#41×D7312yes—
750C2×C4C24×D7311yescharacteristic
751C8—22no—
752C8—22no—
753C8—24no—
754C8—732no—
755C8—732no—
756C8—734no—
757C8—1461no—
758C8—1462no—
759C8—1461no—
760C22—21no—
761C22—21no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—5844no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22—1462no—
771C22—1462no—
772C22#1798905512yes—
773C22C23×C4×D7311yescharacteristic
774C4—22no—
775C4—21no—
776C4—21no—
777C4—22no—
778C4—21no—
779C4—22no—
780C4—1464no—
781C4—1464no—
782C4—1462no—
783C4—1462no—
784C4#1798905512yes—
785C4#1798935212yes—
786C4C2×#41×D7311yescharacteristic
787C4C2×#41×D7311yescharacteristic
788C2—22no—
789C2—42no—
790C2—2922no—
791C2—2922no—
792C2C2×#1798905511yescharacteristic
793C2C2×#1798935211yescharacteristic
794C2#2262464411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2925C2
prime radical#22623495C2
cosocleC2×C4×C73C25
hypercenter#2925D73
hypocenterC73#60217
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #22618948C2semidirect
3. #22618933C2semidirect
4. #22618929C2semidirect
5. #22618914C2semidirect
6. #22618900C2semidirect
7. #22618892C2semidirect
8. #22618874C2semidirect
9. #22618861C2semidirect
10. #22618666C2semidirect
11. #22618661C2semidirect
12. #22618637C2semidirect
13. C2×#17988664C2semidirect
14. #22618586C2semidirect
15. C4×#14556598C2semidirect
16. #22618347C2semidirect
17. C73×#2925C2semidirect
38. #17988716C22semidirect
39. #17988714C22semidirect
40. #17988714C22semidirect
41. #17988714C22semidirect
42. #17988711C22semidirect
43. #17988711C22semidirect
44. #17988711C22semidirect
52. #17988662C22semidirect
53. #17988662C22semidirect
54. #17988662C22semidirect
55. #17988661C22semidirect
57. #17988655C22semidirect
58. #17988655C22semidirect
59. #17988655C22semidirect
61. #17988650C22semidirect
62. #17988649C22semidirect
63. #17988646C22semidirect
64. #17988642C22semidirect
65. #17988638C22semidirect
71. #17988544C22semidirect
74. #17988543C22semidirect
75. #17988543C22semidirect
77. #17988541C22semidirect
79. C4×#11924012C22semidirect
80. #17988539C22semidirect
81. C4×#11924011C22semidirect
83. C2×C4×#10596831C22semidirect
85. #433×C73C22semidirect
86. #432×C73C22semidirect
87. #431×C73C22semidirect
232. #11924012#41semidirect
241. C2×#10596831#41semidirect
411. #2925D73semidirect
415. C73#60217semidirect
463. #433C2×D73semidirect
465. #432C2×D73semidirect
467. #431C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226234952
#226189482
#226189332
#226189292
#226189142
#226189002
#226188922
#226188742
#226188612
#226186662
#226186612
#226186372
C2×#179886642
#226185862
C4×#145565982
#226183472
C73×#29252
#6021773