Finite Group Databasebeta

← #33093836

Subgroups — #33093836

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#22619719C211yesmaximal, characteristic
2#22618871C211yesmaximal, characteristic, complemented
3#22610875C211yesmaximal, characteristic, complemented
4#22610706C211yesmaximal, characteristic, complemented
5#22610530C211yesmaximal, characteristic, complemented
6#22610530C211yesmaximal, characteristic, complemented
7#22610206C211yesmaximal, characteristic
8#22610206C211yesmaximal, characteristic
9#22609951C211yesmaximal, characteristic
10#22609816C211yesmaximal, characteristic, complemented
11#22609811C211yesmaximal, characteristic, complemented
12#22609803C211yesmaximal, characteristic, complemented
13#22609773C211yesmaximal, characteristic
14#22609766C211yesmaximal, characteristic
15C73×#2875C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988894C411yescharacteristic, complemented
18#17988894C411yescharacteristic, complemented
19#17988887C411yescharacteristic, complemented
20#17988887C411yescharacteristic, complemented
21#17988882C411yescharacteristic, complemented
22#17988877C411yescharacteristic, complemented
23#17988872C411yescharacteristic, complemented
24#17988867C411yescharacteristic, complemented
25#17988715—21no—
26#17988715—21no—
27#17988715—21no—
28#17988715—21no—
29C2×#14556526C2211yescharacteristic
30C2×#14556526C2211yescharacteristic
31#17988623C2211yescharacteristic
32#17988623C2211yescharacteristic
33#17988613C2211yescharacteristic
34#17988613C2211yescharacteristic
35#17988611C2211yescharacteristic
36C2×C4⋊#10596831C2211yescharacteristic
37C2×#14556518C2211yescharacteristic
38C2×#14556518C2211yescharacteristic
39#17988583C2211yescharacteristic
40#17988583C2211yescharacteristic
41#17988542C2211yescharacteristic
42#17988542C2211yescharacteristic
43C2×#14556501C2211yescharacteristic
44C2×C8×Dic73C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46#17988351C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988348C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988348C2211yescharacteristic
51#17988348C2211yescharacteristic
52#17988346C2211yescharacteristic
53#17988346C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C2×#131×C73C2211yescharacteristic
57C2×#131×C73C2211yescharacteristic
58C4×#41×C73C2211yescharacteristic
59#405×C73—21no—
60#405×C73—21no—
61#405×C73C2211yescharacteristic
62#405×C73C2211yescharacteristic
63C4×M16×C73—21no—
64C4×M16×C73C2211yescharacteristic
65C2×#97×C73—21no—
66C2×#97×C73C2211yescharacteristic
67C2×#11924012C2311yescharacteristic
68C2×#11924012C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556591C2×C411yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556583C2×C411yescharacteristic
74#14556583C2×C411yescharacteristic
75#14556570—21no—
76#14556570—21no—
77C4×Dic146—21no—
78C4×Dic146—21no—
79#14556550C2311yescharacteristic
80#14556550C2311yescharacteristic
81C2×C4⋊Dic73—21no—
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84#14556526—22no—
85#14556526—22no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556524C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91#14556522C2×C411yescharacteristic
92#14556522C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94C4⋊#10596831—21no—
95C4⋊#10596831—21no—
96C4⋊#10596831C2×C411yescharacteristic
97C4⋊#10596831C2×C411yescharacteristic
98C4⋊#10596831C2×C411yescharacteristic
99C4⋊#10596831C2×C411yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556518—22no—
105#14556518—22no—
106#14556515C2×C411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113#14556512C2×C411yescharacteristic
114#14556501—21no—
115#14556501—21no—
116#14556501—22no—
117C8×Dic73—21no—
118C8×Dic73—21no—
119C8×Dic73—22no—
120#14556498—21no—
121C2×#41×C73C2311yescharacteristic
122#131×C73—22no—
123#131×C73—22no—
124#131×C73—22no—
125#131×C73Q814yescomplemented
126C2×M16×C73—21no—
127C2×M16×C73—21no—
128C2×M16×C73C2311yescharacteristic
129C2×M16×C73C2311yescharacteristic
130C22×C8×C73—21no—
131C22×C8×C73—21no—
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C4×Q8×C73C2×C411yescharacteristic
135C4×Q8×C73C2×C411yescharacteristic
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73C2×C411yescharacteristic
139C4×D4×C73C2×C411yescharacteristic
140#117×C73—21no—
141#117×C73C2311yescharacteristic
142C2×C42×C73—21no—
143C2×C42×C73C2311yescharacteristic
144#97×C73—21no—
145#97×C73—21no—
146#97×C73—21no—
147#97×C73D411yescharacteristic
148#97×C73D411yescharacteristic
149#97×C73D411yescharacteristic
150#97×C73D411yescharacteristic
151C4×C8×C73—21no—
152C4×C8×C73—21no—
153C4×C8×C73—21no—
154C2×Dic146—21no—
155C2×Dic146—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158#11924012—21no—
159#11924012—21no—
160#11924012—21no—
161#11924012—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—42no—
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191#41×C73—21no—
192#41×C73—21no—
193#41×C73C2×Q812yes—
194#41×C73#4112yes—
195C2×Q8×C73C22×C411yescharacteristic
196C2×D4×C73—21no—
197C2×D4×C73C22×C411yescharacteristic
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73#4111yescharacteristic
203C22×C4×C73C2411yescharacteristic
204M16×C73—24no—
205M16×C73—21no—
206M16×C73—21no—
207M16×C73—24no—
208M16×C73C2×Q812yes—
209M16×C73#4112yes—
210C2×C8×C73—24no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—24no—
216C2×C8×C73C2×D411yescharacteristic
217C2×C8×C73C2×D411yescharacteristic
218C2×C8×C73C2×D411yescharacteristic
219C2×C8×C73C2×D411yescharacteristic
220C2×C8×C73C2×Q812yes—
221C2×C8×C73#4112yes—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73C22×C411yescharacteristic
225C4⋊C4×C73C22×C411yescharacteristic
226C22⋊C4×C73—21no—
227C22⋊C4×C73—21no—
228C22⋊C4×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73C22×C411yescharacteristic
233C42×C73C22×C411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C42×C73C2×D411yescharacteristic
236C23×C73—21no—
237C23×C73C2×#4111yescharacteristic
238Q8×C73—21no—
239Q8×C73C4×Q812yes—
240D4×C73—22no—
241D4×C73—22no—
242D4×C73—21no—
243D4×C73C4×Q812yes—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—81no—
252C2×C4×C73—81no—
253C2×C4×C73C4×D411yescharacteristic
254C2×C4×C73C4×D411yescharacteristic
255C2×C4×C73C4×D411yescharacteristic
256C2×C4×C73C4×D411yescharacteristic
257C2×C4×C73C23×C411yescharacteristic
258C2×C4×C73C22×D411yescharacteristic
259C2×C4×C73C22×Q811yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C2×C4×C73C2×#4111yescharacteristic
262C2×C4×C73C2×#4111yescharacteristic
263C2×Dic73—22no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273Dic146—81no—
274Dic146—81no—
275C8×C73—22no—
276C8×C73—21no—
277C8×C73—22no—
278C8×C73—21no—
279C8×C73C22⋊Q812yes—
280C8×C73C22⋊Q812yes—
281#10596831—21no—
282#10596831—21no—
283#10596831—21no—
284#10596831—21no—
285#10596831—41no—
286#10596831—41no—
287C22×C73—21no—
288C22×C73—21no—
289C22×C73—22no—
290C22×C73—41no—
291C22×C73—41no—
292C22×C73C2×C4×D411yescharacteristic
293C22×C73#52911yescharacteristic
294C22×C73#53311yescharacteristic
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—22no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73C2×C4×Q811yescharacteristic
303C4×C73C4×#4111yescharacteristic
304C4×C73C2×C22⋊Q811yescharacteristic
305C4×C73#52511yescharacteristic
306Dic73—42no—
307Dic73—41no—
308Dic73—41no—
309Dic73—41no—
310Dic73—41no—
311Dic73—81no—
312#21629—731nomaximal, Sylow
313C2×C73—21no—
314C2×C73—21no—
315C2×C73—42no—
316C2×C73C4×C22⋊Q811yescharacteristic
317C2×C73#295611yescharacteristic
318C2×C73#295711yescharacteristic
319#3076—731no—
320#2961—731no—
321#2875D7311yescharacteristic
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#1771—731no—
332#1765—731no—
333#1764—731no—
334C73#2162911yescharacteristic, complemented, Sylow
335C2×#131C2×D7311yescharacteristic
336C2×#131C2×D7311yescharacteristic
337#533—731no—
338C4×#41C2×D7311yescharacteristic
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⋊C8—731no—
359C2×#104—731no—
360C2×#104—731no—
361#416—731no—
362#416—731no—
363#405—21no—
364#405—21no—
365#405—731no—
366#405—731no—
367#405C2×D7311yescharacteristic
368#405C2×D7311yescharacteristic
369C4×M16—21no—
370C4×M16C2×D7311yescharacteristic
371C2×#97—21no—
372C2×#97—731no—
373C2×#97C2×D7311yescharacteristic
374C2×C4×C8—731no—
375C4×C4⋊C4—731no—
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#336—731no—
385#336—731no—
386C2×#41C22×D7311yescharacteristic
387#131—22no—
388#131—22no—
389#131—22no—
390#131Dic14614yescomplemented
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—731no—
394C2×M16—731no—
395C2×M16C22×D7311yescharacteristic
396C2×M16C22×D7311yescharacteristic
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—731no—
400C22×C8—731no—
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—1461no—
410C4×Q8—1461no—
411C4×Q8C4×D7311yescharacteristic
412C4×Q8C4×D7311yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C4×D7311yescharacteristic
416C4×D4C4×D7311yescharacteristic
417#117—21no—
418#117—731no—
419#117—731no—
420#117C22×D7311yescharacteristic
421C2×C4⋊C4—1461no—
422C2×C42—21no—
423C2×C42—731no—
424C2×C42—731no—
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—731no—
437C4⋊C8—731no—
438C4⋊C8—731no—
439C4⋊C8—731no—
440C4⋊C8—1461no—
441C4⋊C8—1461no—
442C4⋊C8—1461no—
443C4⋊C8—1461no—
444C4⋊C8—1461no—
445C4⋊C8—1461no—
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—21no—
457#97—21no—
458#97—21no—
459#97—1461no—
460#97—1461no—
461#97—1462no—
462#97C22⋊D7311yescharacteristic
463#97C22⋊D7311yescharacteristic
464#97C22⋊D7311yescharacteristic
465#97C22⋊D7311yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—1461no—
470C4×C8—1461no—
471C4×C8—1462no—
472#95—1461no—
473#41—21no—
474#41—21no—
475#41C2×Dic14612yes—
476#41#1192402812yes—
477C2×Q8—1461no—
478C2×Q8—1461no—
479C2×Q8C2×C4×D7311yescharacteristic
480C2×D4—21no—
481C2×D4C2×C4×D7311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4#1192402811yescharacteristic
488C22×C4#1192402811yescharacteristic
489C22×C4C23×D7311yescharacteristic
490M16—24no—
491M16—21no—
492M16—21no—
493M16—24no—
494M16—1461no—
495M16—1461no—
496M16—1461no—
497M16—1461no—
498M16C2×Dic14612yes—
499M16#1192402812yes—
500C2×C8—24no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—24no—
506C2×C8—731no—
507C2×C8—731no—
508C2×C8—731no—
509C2×C8—731no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8C2×C22⋊D7311yescharacteristic
517C2×C8C2×C22⋊D7311yescharacteristic
518C2×C8C2×C22⋊D7311yescharacteristic
519C2×C8C2×C22⋊D7311yescharacteristic
520C2×C8C2×Dic14612yes—
521C2×C8#1192402812yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—2922no—
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⋊C4C2×C4×D7311yescharacteristic
536C4⋊C4C2×C4×D7311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—1461no—
541C22⋊C4—1461no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42C2×C4×D7311yescharacteristic
552C42C2×C4×D7311yescharacteristic
553C42C2×C22⋊D7311yescharacteristic
554C42C2×C22⋊D7311yescharacteristic
555C23—21no—
556C23C2×#1192402811yescharacteristic
557Q8—21no—
558Q8—5841no—
559Q8—5841no—
560Q8C4×Dic14612yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Dic14612yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—1462no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4C4×C22⋊D7311yescharacteristic
585C2×C4C4×C22⋊D7311yescharacteristic
586C2×C4C4×C22⋊D7311yescharacteristic
587C2×C4C4×C22⋊D7311yescharacteristic
588C2×C4C22×C4×D7311yescharacteristic
589C2×C4C22×C22⋊D7311yescharacteristic
590C2×C4C22×Dic14611yescharacteristic
591C2×C4C2×#1192402811yescharacteristic
592C2×C4C2×#1192402811yescharacteristic
593C2×C4C2×#1192402811yescharacteristic
594C8—22no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—2921no—
599C8—2921no—
600C8—1461no—
601C8—1461no—
602C8—1461no—
603C8—1461no—
604C8#1455657012yes—
605C8#1455657012yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×C4×C22⋊D7311yescharacteristic
612C22#1798912111yescharacteristic
613C22#1798914411yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—2922no—
622C4—2921no—
623C4—2921no—
624C4—2921no—
625C4—2921no—
626C4—5841no—
627C4C2×C4×Dic14611yescharacteristic
628C4C4×#1192402811yescharacteristic
629C4C2×#1455657011yescharacteristic
630C4#1798909811yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×#1455657011yescharacteristic
635C2#2261883811yescharacteristic
636C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2875C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C23
cosocleC22×C4×C73C24
hypercenter#2875D73
hypocenterC73#21629
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #22618871C2semidirect
3. #22610875C2semidirect
4. #22610706C2semidirect
5. #22610530C2semidirect
6. #22610530C2semidirect
10. #22609816C2semidirect
11. #22609811C2semidirect
12. #22609803C2semidirect
17. #17988894C4semidirect
18. #17988894C4semidirect
19. #17988887C4semidirect
20. #17988887C4semidirect
21. #17988882C4semidirect
22. #17988877C4semidirect
23. #17988872C4semidirect
24. #17988867C4semidirect
125. #131×C73Q8semidirect
334. C73#21629semidirect
390. #131Dic146semidirect

Maximal subgroups

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

subgroupindex
#226197192
#226188712
#226108752
#226107062
#226105302
#226102062
#226099512
#226098162
#226098112
#226098032
#226097732
#226097662
C73×#28752
#2162973