Finite Group Databasebeta

← #33093838

Subgroups — #33093838

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619721C211yesmaximal, characteristic
2#22618871C211yesmaximal, characteristic, complemented
3#22618356C211yesmaximal, characteristic
4#22610874C211yesmaximal, characteristic, complemented
5#22610707C211yesmaximal, characteristic, complemented
6#22610531C211yesmaximal, characteristic, complemented
7#22610531C211yesmaximal, characteristic, complemented
8#22610209C211yesmaximal, characteristic
9#22610209C211yesmaximal, characteristic
10#22609952C211yesmaximal, characteristic
11#22609815C211yesmaximal, characteristic, complemented
12#22609810C211yesmaximal, characteristic, complemented
13#22609775C211yesmaximal, characteristic
14#22609768C211yesmaximal, characteristic
15C73×#1771C211yesmaximal, characteristic, complemented
16C2×#14556597C2211yescharacteristic
17C2×#14556597C2211yescharacteristic
18#17989144C2211yescharacteristic
19C4×#11924028C2211yescharacteristic
20#17988895C411yescharacteristic, complemented
21#17988895C411yescharacteristic, complemented
22#17988888C411yescharacteristic, complemented
23#17988888C411yescharacteristic, complemented
24#17988883C411yescharacteristic, complemented
25#17988878C411yescharacteristic, complemented
26#17988873C411yescharacteristic, complemented
27#17988868C411yescharacteristic, complemented
28#17988715—21no—
29#17988715—21no—
30#17988715—21no—
31#17988715—21no—
32C2×#14556527C2211yescharacteristic
33C2×#14556527C2211yescharacteristic
34#17988625C2211yescharacteristic
35#17988625C2211yescharacteristic
36#17988613C2211yescharacteristic
37#17988613C2211yescharacteristic
38#17988611C2211yescharacteristic
39C2×#14556519C2211yescharacteristic
40C2×#14556519C2211yescharacteristic
41#17988584C2211yescharacteristic
42#17988584C2211yescharacteristic
43#17988544—21no—
44#17988544—21no—
45#17988542C2211yescharacteristic
46#17988542C2211yescharacteristic
47#17988542C2211yescharacteristic
48#17988542C2211yescharacteristic
49C4×#11924012C2211yescharacteristic
50#17988539—21no—
51#97×D73—21no—
52#17988352C2211yescharacteristic
53#17988352C2211yescharacteristic
54#17988347C2211yescharacteristic
55#17988347C2211yescharacteristic
56#17988347C2211yescharacteristic
57#17988347C2211yescharacteristic
58#17988347C2211yescharacteristic
59#17988347C2211yescharacteristic
60C2×C4⋊C8×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63C2×C4×C8×C73C2211yescharacteristic
64C4×C4⋊C4×C73C2211yescharacteristic
65#336×C73C2211yescharacteristic
66#336×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68#14556597—22no—
69#14556597—22no—
70#14556597—22no—
71#14556597Q814yescomplemented
72C2×#11924012C2311yescharacteristic
73C2×#11924012C2311yescharacteristic
74C2×#11924012C2311yescharacteristic
75C2×#11924012C2311yescharacteristic
76C2×#11924011—21no—
77C2×#11924011—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80#14556591C2×C411yescharacteristic
81#14556591C2×C411yescharacteristic
82#14556583C2×C411yescharacteristic
83#14556583C2×C411yescharacteristic
84#14556570—21no—
85#14556570—21no—
86C4×Dic146—21no—
87C4×Dic146—21no—
88C4×Dic146C2×C411yescharacteristic
89C4×Dic146C2×C411yescharacteristic
90C4×D292C2×C411yescharacteristic
91C4×D292C2×C411yescharacteristic
92C4×C22⋊D73—21no—
93C4×C22⋊D73—21no—
94#14556550C2311yescharacteristic
95#14556550C2311yescharacteristic
96#14556550C2311yescharacteristic
97#14556548—21no—
98C42×D73—21no—
99#14556527—22no—
100#14556527—22no—
101#14556525C2×C411yescharacteristic
102#14556525C2×C411yescharacteristic
103#14556525C2×C411yescharacteristic
104#14556525C2×C411yescharacteristic
105#14556523C2×C411yescharacteristic
106#14556523C2×C411yescharacteristic
107#14556523C2×C411yescharacteristic
108#14556523C2×C411yescharacteristic
109C4⋊#10596831—21no—
110C4⋊#10596831—21no—
111#14556520—21no—
112#14556520—21no—
113#14556520—21no—
114#14556520—21no—
115#14556519—22no—
116#14556519—22no—
117#14556516C2×C411yescharacteristic
118#14556516C2×C411yescharacteristic
119#14556516C2×C411yescharacteristic
120#14556516C2×C411yescharacteristic
121#14556513C2×C411yescharacteristic
122#14556513C2×C411yescharacteristic
123#14556513C2×C411yescharacteristic
124#14556513C2×C411yescharacteristic
125#14556502—21no—
126#14556501—21no—
127#14556501—21no—
128#14556501—21no—
129#14556501—21no—
130C4×#10596831—21no—
131C8×Dic73—21no—
132C8×Dic73—21no—
133C8×Dic73—21no—
134C8×Dic73—21no—
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C2×C4⋊C4×C73—21no—
140C2×C42×C73C2311yescharacteristic
141C2×C42×C73C2311yescharacteristic
142C2×C42×C73C2311yescharacteristic
143C4⋊C8×C73C2×C411yescharacteristic
144C4⋊C8×C73C2×C411yescharacteristic
145C4⋊C8×C73C2×C411yescharacteristic
146C4⋊C8×C73C2×C411yescharacteristic
147#97×C73—22no—
148#97×C73D411yescharacteristic
149#97×C73D411yescharacteristic
150#97×C73D411yescharacteristic
151#97×C73D411yescharacteristic
152C4×C8×C73—22no—
153#95×C73—21no—
154#11924028—21no—
155#11924028—21no—
156#11924028C2×Q812yes—
157#11924028#4112yes—
158C2×Dic146—21no—
159C2×Dic146—21no—
160C2×Dic146C22×C411yescharacteristic
161C2×D292C22×C411yescharacteristic
162C2×C22⋊D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166#11924012—21no—
167#11924012—21no—
168#11924012—21no—
169#11924012—21no—
170#11924012—21no—
171#11924012—21no—
172#11924012C2×Q812yes—
173#11924012#4112yes—
174#11924011—24no—
175#11924011—24no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C8×D73—24no—
181C8×D73—24no—
182C4⋊Dic73—21no—
183C4⋊Dic73—21no—
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188C4⋊Dic73C22×C411yescharacteristic
189C4⋊Dic73C22×C411yescharacteristic
190#11924007—21no—
191#11924007—21no—
192#11924007—21no—
193#11924007—21no—
194#11924007—21no—
195#11924007—21no—
196C22⋊Dic73—21no—
197C22⋊Dic73—21no—
198C22⋊Dic73—21no—
199#11924005—21no—
200#11924005—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—21no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73#4111yescharacteristic
209C22×C4×C73#4111yescharacteristic
210C22×C4×C73C2411yescharacteristic
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73C22×C411yescharacteristic
218C2×C8×C73C22×C411yescharacteristic
219C2×C8×C73C22×C411yescharacteristic
220C2×C8×C73C22×C411yescharacteristic
221C2×C8×C73C2×D411yescharacteristic
222C2×C8×C73C2×D411yescharacteristic
223C2×C8×C73C2×D411yescharacteristic
224C2×C8×C73C2×D411yescharacteristic
225C2×C8×C73C2×Q812yes—
226C2×C8×C73#4112yes—
227C4⋊C4×C73—42no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73C22×C411yescharacteristic
233C42×C73C22×C411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C42×C73C2×D411yescharacteristic
236C23×C73C2×#4111yescharacteristic
237C22×D73—21no—
238C2×C4×C73—22no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73C4×D411yescharacteristic
247C2×C4×C73C4×D411yescharacteristic
248C2×C4×C73C4×D411yescharacteristic
249C2×C4×C73C4×D411yescharacteristic
250C2×C4×C73C23×C411yescharacteristic
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C22×Q811yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C22⋊D73—22no—
257C22⋊D73—22no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265D292—21no—
266D292C4×Q812yes—
267C4×D73—22no—
268C4×D73—22no—
269C4×D73—81no—
270C4×D73—81no—
271Dic146—21no—
272Dic146—81no—
273Dic146—81no—
274Dic146C4×Q812yes—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—21no—
278C8×C73—21no—
279C8×C73—21no—
280C8×C73—21no—
281C8×C73C22⋊Q812yes—
282C8×C73C22⋊Q812yes—
283#10596831—22no—
284#10596831—22no—
285#10596831—41no—
286#10596831—41no—
287C22×C73—21no—
288C22×C73—21no—
289C22×C73C2×C4×D411yescharacteristic
290C22×C73#52911yescharacteristic
291C22×C73#53311yescharacteristic
292C2×D73—22no—
293C2×D73—41no—
294C2×D73—41no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—42no—
300C4×C73—81no—
301C4×C73C2×C4×Q811yescharacteristic
302C4×C73C4×#4111yescharacteristic
303C4×C73C2×C22⋊Q811yescharacteristic
304C4×C73#52511yescharacteristic
305Dic73—22no—
306Dic73—41no—
307Dic73—41no—
308Dic73—41no—
309Dic73—41no—
310Dic73—41no—
311Dic73—41no—
312#21629—731nomaximal, Sylow
313C2×C73—21no—
314C2×C73—21no—
315C2×C73C4×C22⋊Q811yescharacteristic
316C2×C73#295611yescharacteristic
317C2×C73#295711yescharacteristic
318D73—42no—
319#3076—731no—
320#2961—731no—
321#2875—731no—
322#1986—731no—
323#1950—731no—
324#1922—731no—
325#1922—731no—
326#1866—731no—
327#1866—731no—
328#1806—731no—
329#1773—731no—
330#1772—731no—
331#1771D7311yescharacteristic, complemented
332#1765—731no—
333#1764—731no—
334C73#2162911yescharacteristic, complemented, Sylow
335C2×#131—731no—
336C2×#131—731no—
337#533—731no—
338C4×#41—731no—
339#479—731no—
340#479—731no—
341#478—731no—
342#478—731no—
343#477—731no—
344#476—731no—
345#475—731no—
346#474—731no—
347#446—1461no—
348#446—1461no—
349#446—1461no—
350#446—1461no—
351C2×#108—731no—
352C2×#108—731no—
353#427—731no—
354#427—731no—
355#424—731no—
356#424—731no—
357#423—731no—
358C2×C4⋊C8C2×D7311yescharacteristic
359C2×#104—731no—
360C2×#104—731no—
361#416—731no—
362#416—731no—
363#405—731no—
364#405—731no—
365#405—731no—
366#405—731no—
367#405—1461no—
368#405—1461no—
369C4×M16—731no—
370C4×M16—1461no—
371C2×#97—1461no—
372C2×#97C2×D7311yescharacteristic
373C2×#97C2×D7311yescharacteristic
374C2×C4×C8C2×D7311yescharacteristic
375C4×C4⋊C4C2×D7311yescharacteristic
376#341—731no—
377#341—731no—
378#339—731no—
379#339—731no—
380#339—731no—
381#339—731no—
382#339—731no—
383#339—731no—
384#336C2×D7311yescharacteristic
385#336C2×D7311yescharacteristic
386C2×#41—731no—
387#131—734no—
388#131—1462no—
389#131—1462no—
390#131—1462no—
391C2×M16—731no—
392C2×M16—731no—
393C2×M16—731no—
394C2×M16—731no—
395C2×M16—1461no—
396C2×M16—1461no—
397C22×C8—1461no—
398C22×C8—1461no—
399C22×C8C22×D7311yescharacteristic
400C22×C8C22×D7311yescharacteristic
401C22×C8C22×D7311yescharacteristic
402C22×C8C22×D7311yescharacteristic
403C4⋊Q8—731no—
404C4⋊Q8—731no—
405#125—731no—
406#125—731no—
407C22⋊Q8—1461no—
408C22⋊Q8—1461no—
409C4×Q8—731no—
410C4×Q8—731no—
411C4×Q8—1461no—
412C4×Q8—1461no—
413C4×D4—731no—
414C4×D4—731no—
415C4×D4—1461no—
416C4×D4—1461no—
417#117—731no—
418#117—731no—
419#117—731no—
420#117—1461no—
421C2×C4⋊C4—21no—
422C2×C42—1461no—
423C2×C42C22×D7311yescharacteristic
424C2×C42C22×D7311yescharacteristic
425C2×C42C22×D7311yescharacteristic
426#108—1462no—
427#108—1462no—
428#107—731no—
429#107—731no—
430#107—731no—
431#107—731no—
432#106—731no—
433#106—731no—
434#106—731no—
435#106—731no—
436C4⋊C8—1461no—
437C4⋊C8—1461no—
438C4⋊C8—1461no—
439C4⋊C8—1461no—
440C4⋊C8—1461no—
441C4⋊C8—1461no—
442C4⋊C8C4×D7311yescharacteristic
443C4⋊C8C4×D7311yescharacteristic
444C4⋊C8C4×D7311yescharacteristic
445C4⋊C8C4×D7311yescharacteristic
446#104—1462no—
447#104—1462no—
448#103—731no—
449#103—731no—
450#103—731no—
451#103—731no—
452#102—731no—
453#102—731no—
454#102—731no—
455#102—731no—
456#97—22no—
457#97—1461no—
458#97—1461no—
459#97—1461no—
460#97—1461no—
461#97—1461no—
462#97D29211yescharacteristic
463#97D29211yescharacteristic
464#97D29211yescharacteristic
465#97D29211yescharacteristic
466C4×C8—22no—
467C4×C8—1461no—
468C4×C8—1461no—
469C4×C8—1461no—
470C4×C8—1461no—
471C4×C8—1461no—
472#95—21no—
473#41—732no—
474#41—732no—
475#41—1461no—
476#41—1461no—
477C2×Q8—731no—
478C2×Q8—1461no—
479C2×Q8—1461no—
480C2×D4—731no—
481C2×D4—1461no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4#1192402811yescharacteristic
488C22×C4#1192402811yescharacteristic
489C22×C4C23×D7311yescharacteristic
490M16—732no—
491M16—732no—
492M16—1464no—
493M16—1461no—
494M16—1461no—
495M16—1461no—
496M16—1461no—
497M16—1461no—
498M16—1461no—
499M16—1464no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—1464no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1464no—
512C2×C8C2×C4×D7311yescharacteristic
513C2×C8C2×C4×D7311yescharacteristic
514C2×C8C2×C4×D7311yescharacteristic
515C2×C8C2×C4×D7311yescharacteristic
516C2×C8C2×D29211yescharacteristic
517C2×C8C2×D29211yescharacteristic
518C2×C8C2×D29211yescharacteristic
519C2×C8C2×D29211yescharacteristic
520C2×C8Q8×D7312yes—
521C2×C8#1192402712yes—
522C4⋊C4—42no—
523C4⋊C4—731no—
524C4⋊C4—731no—
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—731no—
528C4⋊C4—731no—
529C4⋊C4—1461no—
530C4⋊C4—1461no—
531C4⋊C4—1461no—
532C4⋊C4—1461no—
533C4⋊C4—1461no—
534C4⋊C4—1461no—
535C4⋊C4—1461no—
536C4⋊C4—1461no—
537C22⋊C4—1461no—
538C22⋊C4—1461no—
539C22⋊C4—1461no—
540C22⋊C4—1461no—
541C22⋊C4—1461no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42C2×C4×D7311yescharacteristic
552C42C2×C4×D7311yescharacteristic
553C42C2×D29211yescharacteristic
554C42C2×D29211yescharacteristic
555C23—1461no—
556C23C2×#1192402811yescharacteristic
557Q8—5841no—
558Q8—5841no—
559Q8—732no—
560Q8—1461no—
561D4—732no—
562D4—1462no—
563D4—1462no—
564D4—1461no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—5841no—
574C2×C4—5841no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1462no—
583C2×C4—1462no—
584C2×C4C4×D29211yescharacteristic
585C2×C4C4×D29211yescharacteristic
586C2×C4C4×D29211yescharacteristic
587C2×C4C4×D29211yescharacteristic
588C2×C4C22×C4×D7311yescharacteristic
589C2×C4C22×D29211yescharacteristic
590C2×C4C2×Q8×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4C2×#1192402711yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—2921no—
601C8—2921no—
602C8—1462no—
603C8—1462no—
604C8#1455657112yes—
605C8#1455657112yes—
606C22—21no—
607C22—21no—
608C22—2921no—
609C22—2921no—
610C22—1462no—
611C22C2×C4×D29211yescharacteristic
612C22#1798911911yescharacteristic
613C22#1798914111yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—81no—
620C4—2921no—
621C4—2921no—
622C4—2921no—
623C4—2921no—
624C4—2921no—
625C4—2921no—
626C4—1462no—
627C4C4×Q8×D7311yescharacteristic
628C4C4×#1192402711yescharacteristic
629C4C2×#1455657111yescharacteristic
630C4#1798909911yescharacteristic
631C2—21no—
632C2—21no—
633C2—2922no—
634C2C4×#1455657111yescharacteristic
635C2#2261884211yescharacteristic
636C2#2261884911yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1771C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#1771D73
hypocenterC73#21629
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #22618871C2semidirect
4. #22610874C2semidirect
5. #22610707C2semidirect
6. #22610531C2semidirect
7. #22610531C2semidirect
11. #22609815C2semidirect
12. #22609810C2semidirect
15. C73×#1771C2semidirect
20. #17988895C4semidirect
21. #17988895C4semidirect
22. #17988888C4semidirect
23. #17988888C4semidirect
24. #17988883C4semidirect
25. #17988878C4semidirect
26. #17988873C4semidirect
27. #17988868C4semidirect
71. #14556597Q8semidirect
331. #1771D73semidirect
334. C73#21629semidirect

Maximal subgroups

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

subgroupindex
#226197212
#226188712
#226183562
#226108742
#226107072
#226105312
#226102092
#226099522
#226098152
#226098102
#226097752
#226097682
C73×#17712
#2162973