Finite Group Databasebeta

← #33108071

Subgroups — #33108071

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619719C211yesmaximal, characteristic
2#22618878C211yesmaximal, characteristic, complemented
3#22618499C211yesmaximal, characteristic
4#22610912C211yesmaximal, characteristic, complemented
5#22610706C211yesmaximal, characteristic, complemented
6#22610683C211yesmaximal, characteristic, complemented
7#22610678C211yesmaximal, characteristic, complemented
8#22610533C211yesmaximal, characteristic, complemented
9#22610533C211yesmaximal, characteristic, complemented
10#22610204C211yesmaximal, characteristic
11#22610204C211yesmaximal, characteristic
12#22609788C211yesmaximal, characteristic, complemented
13#22609776C211yesmaximal, characteristic
14#22609769C211yesmaximal, characteristic
15C73×#1759C211yesmaximal, characteristic
16C2×#14556598C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18#17989144C2211yescharacteristic
19#17988894C411yescharacteristic, complemented
20#17988894C411yescharacteristic, complemented
21#17988887C411yescharacteristic, complemented
22#17988887C411yescharacteristic, complemented
23#17988882C411yescharacteristic, complemented
24#17988877C411yescharacteristic, complemented
25#17988872C411yescharacteristic, complemented
26#17988867C411yescharacteristic, complemented
27#17988717—21no—
28#17988715—21no—
29#17988715—21no—
30C8×Dic146—21no—
31C2×#14556526C2211yescharacteristic
32C2×#14556526C2211yescharacteristic
33#17988623C2211yescharacteristic
34#17988623C2211yescharacteristic
35#17988615C2211yescharacteristic
36#17988615C2211yescharacteristic
37#17988614—21no—
38#17988614—21no—
39#17988614C2211yescharacteristic
40#17988614C2211yescharacteristic
41#17988611—21no—
42#17988611C2211yescharacteristic
43C2×C4⋊#10596831—21no—
44C2×C4⋊#10596831C2211yescharacteristic
45C2×C4⋊#10596831C2211yescharacteristic
46#17988583C2211yescharacteristic
47#17988583C2211yescharacteristic
48#17988545C2211yescharacteristic
49#17988545C2211yescharacteristic
50C2×#14556502C2211yescharacteristic
51C2×C4×#10596831C2211yescharacteristic
52#17988351C2211yescharacteristic
53#17988351C2211yescharacteristic
54#17988347C2211yescharacteristic
55#17988347C2211yescharacteristic
56#17988347C2211yescharacteristic
57#17988347C2211yescharacteristic
58#17988342C2211yescharacteristic
59#17988342C2211yescharacteristic
60C4×#41×C73C2211yescharacteristic
61C2×#104×C73C2211yescharacteristic
62C2×#104×C73C2211yescharacteristic
63C4×M16×C73C2211yescharacteristic
64#376×C73C2211yescharacteristic
65#339×C73C2211yescharacteristic
66#339×C73C2211yescharacteristic
67#14556598—22no—
68#14556598—22no—
69#14556598—41no—
70#14556598—41no—
71C2×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924012C2311yescharacteristic
74C2×#11924012C2311yescharacteristic
75C22×#10596831—21no—
76C22×#10596831—21no—
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81#14556591C2×C411yescharacteristic
82#14556591C2×C411yescharacteristic
83#14556583C2×C411yescharacteristic
84#14556583C2×C411yescharacteristic
85#14556570—21no—
86#14556570—21no—
87C4×Dic146—21no—
88C4×Dic146—21no—
89#14556550C2311yescharacteristic
90#14556550C2311yescharacteristic
91#14556526—41no—
92#14556526—41no—
93#14556524C2×C411yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98#14556522C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831—21no—
103C4⋊#10596831—21no—
104C4⋊#10596831—21no—
105C4⋊#10596831—21no—
106C4⋊#10596831—21no—
107C4⋊#10596831C2×C411yescharacteristic
108C4⋊#10596831C2×C411yescharacteristic
109C4⋊#10596831C2×C411yescharacteristic
110C4⋊#10596831C2×C411yescharacteristic
111C4⋊#10596831D411yescharacteristic
112C4⋊#10596831D411yescharacteristic
113C4⋊#10596831D411yescharacteristic
114C4⋊#10596831D411yescharacteristic
115#14556520—21no—
116#14556520—21no—
117#14556520—21no—
118#14556520—21no—
119#14556515C2×C411yescharacteristic
120#14556515C2×C411yescharacteristic
121#14556515C2×C411yescharacteristic
122#14556515C2×C411yescharacteristic
123#14556512C2×C411yescharacteristic
124#14556512C2×C411yescharacteristic
125#14556512C2×C411yescharacteristic
126#14556512C2×C411yescharacteristic
127#14556502—41no—
128#14556501—21no—
129#14556501—21no—
130C4×#10596831—41no—
131C8×Dic73—21no—
132C8×Dic73—21no—
133C2×#41×C73C2311yescharacteristic
134C2×M16×C73C2311yescharacteristic
135C2×M16×C73C2311yescharacteristic
136C4×Q8×C73C2×C411yescharacteristic
137C4×Q8×C73C2×C411yescharacteristic
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73C2×C411yescharacteristic
141C4×D4×C73C2×C411yescharacteristic
142#117×C73—21no—
143#117×C73C2311yescharacteristic
144C2×C42×C73—21no—
145C2×C42×C73C2311yescharacteristic
146C2×C42×C73C2311yescharacteristic
147C2×C42×C73C2311yescharacteristic
148#104×C73—22no—
149#104×C73Q814yescomplemented
150#97×C73—21no—
151C4×C8×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C2×Dic146—21no—
155C2×Dic146—21no—
156#11924012—21no—
157#11924012—21no—
158#11924012—21no—
159#11924012—21no—
160#11924012—42no—
161#11924012—42no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—42no—
173C2×#10596831—42no—
174C2×#10596831C22×C411yescharacteristic
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C22×C411yescharacteristic
177C2×#10596831C22×C411yescharacteristic
178C2×#10596831C2×D411yescharacteristic
179C2×#10596831C2×D411yescharacteristic
180C2×#10596831C2×D411yescharacteristic
181C2×#10596831C2×D411yescharacteristic
182C4⋊Dic73—21no—
183C4⋊Dic73—21no—
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188#11924007—21no—
189#11924007—21no—
190#11924007—21no—
191#11924007—21no—
192C22⋊Dic73—21no—
193C22⋊Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196#41×C73—21no—
197#41×C73—21no—
198#41×C73C2×Q812yes—
199#41×C73#4112yes—
200C2×Q8×C73C22×C411yescharacteristic
201C2×D4×C73—21no—
202C2×D4×C73C22×C411yescharacteristic
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73#4111yescharacteristic
209C22×C4×C73#4111yescharacteristic
210C22×C4×C73C2411yescharacteristic
211M16×C73—21no—
212M16×C73—21no—
213M16×C73—21no—
214M16×C73C2×Q812yes—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73C22×C411yescharacteristic
220C4⋊C4×C73C22×C411yescharacteristic
221C22⋊C4×C73—21no—
222C22⋊C4×C73—21no—
223C22⋊C4×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73C22×C411yescharacteristic
231C42×C73C22×C411yescharacteristic
232C42×C73C2×D411yescharacteristic
233C42×C73C2×D411yescharacteristic
234C42×C73C2×Q812yes—
235C23×C73—21no—
236C23×C73C2×#4111yescharacteristic
237Q8×C73—21no—
238Q8×C73C4×Q812yes—
239D4×C73—22no—
240D4×C73—22no—
241D4×C73—21no—
242D4×C73C4×Q812yes—
243C2×C4×C73—21no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—22no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—42no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—81no—
258C2×C4×C73C4×D411yescharacteristic
259C2×C4×C73C4×D411yescharacteristic
260C2×C4×C73C4×D411yescharacteristic
261C2×C4×C73C4×D411yescharacteristic
262C2×C4×C73C23×C411yescharacteristic
263C2×C4×C73C22×D411yescharacteristic
264C2×C4×C73C22×Q811yescharacteristic
265C2×C4×C73C2×#4111yescharacteristic
266C2×C4×C73H(5,𝔽2)11yescharacteristic
267C2×C4×C732−1+411yescharacteristic
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—21no—
271C2×Dic73—21no—
272Dic146—42no—
273Dic146—81no—
274C8×C73—22no—
275C8×C73—41no—
276#10596831—21no—
277#10596831—21no—
278#10596831—21no—
279#10596831—21no—
280#10596831—21no—
281#10596831—21no—
282#10596831—21no—
283#10596831—21no—
284#10596831—41no—
285#10596831—41no—
286C22×C73—21no—
287C22×C73—21no—
288C22×C73—22no—
289C22×C73—41no—
290C22×C73—41no—
291C22×C73C2×C4×D411yescharacteristic
292C22×C73#55211yescharacteristic
293C22×C73#55411yescharacteristic
294C4×C73—22no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—42no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73—81no—
303C4×C73C2×C4×Q811yescharacteristic
304C4×C73#52011yescharacteristic
305C4×C73#54611yescharacteristic
306C4×C73D4×Q811yescharacteristic
307Dic73—41no—
308Dic73—41no—
309Dic73—41no—
310Dic73—41no—
311#22984—731nomaximal, Sylow
312C2×C73—21no—
313C2×C73—21no—
314C2×C73—42no—
315C2×C73#236011yescharacteristic
316C2×C73#295511yescharacteristic
317C2×C73#295711yescharacteristic
318#3076—731no—
319#2962—731no—
320#2906—731no—
321#1995—731no—
322#1950—731no—
323#1946—731no—
324#1945—731no—
325#1922—731no—
326#1922—731no—
327#1866—731no—
328#1866—731no—
329#1768—731no—
330#1765—731no—
331#1764—731no—
332#1759D7311yescharacteristic
333C73#2298411yescharacteristic, complemented, Sylow
334C2×#131—731no—
335C2×#131—731no—
336#533—731no—
337C4×#41C2×D7311yescharacteristic
338#479—731no—
339#479—731no—
340#478—731no—
341#478—731no—
342#477—731no—
343#476—731no—
344#475—731no—
345#474—731no—
346#446—1461no—
347#446—1461no—
348#446—1461no—
349C8×Q8—1461no—
350C2×#108—731no—
351C2×#108—731no—
352#427—731no—
353#427—731no—
354#424—731no—
355#424—731no—
356#424—731no—
357#424—731no—
358#424—1461no—
359#424—1461no—
360#423—731no—
361#423—1461no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—1461no—
365C2×#104C2×D7311yescharacteristic
366C2×#104C2×D7311yescharacteristic
367#416—731no—
368#416—731no—
369#405—731no—
370#405—731no—
371C4×M16C2×D7311yescharacteristic
372C2×#97—731no—
373C2×C4×C8—731no—
374#376C2×D7311yescharacteristic
375#341—731no—
376#341—731no—
377#339—731no—
378#339—731no—
379#339—731no—
380#339—731no—
381#339C2×D7311yescharacteristic
382#339C2×D7311yescharacteristic
383#336—731no—
384#336—731no—
385C2×#41C22×D7311yescharacteristic
386#131—2921no—
387#131—2921no—
388#131—1462no—
389#131—1462no—
390C2×M16—731no—
391C2×M16—731no—
392C2×M16—1461no—
393C2×M16—1461no—
394C2×M16C22×D7311yescharacteristic
395C2×M16C22×D7311yescharacteristic
396C22×C8—731no—
397C22×C8—731no—
398C22×C8—731no—
399C22×C8—731no—
400C22×C8—1461no—
401C22×C8—1461no—
402C4⋊Q8—731no—
403C4⋊Q8—731no—
404#125—731no—
405#125—731no—
406C22⋊Q8—1461no—
407C22⋊Q8—1461no—
408C4×Q8—1461no—
409C4×Q8—1461no—
410C4×Q8C4×D7311yescharacteristic
411C4×Q8C4×D7311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C4×D7311yescharacteristic
415C4×D4C4×D7311yescharacteristic
416#117—21no—
417#117—731no—
418#117—731no—
419#117C22×D7311yescharacteristic
420C2×C42—21no—
421C2×C42C22×D7311yescharacteristic
422C2×C42C22×D7311yescharacteristic
423C2×C42C22×D7311yescharacteristic
424#108—2921no—
425#108—2921no—
426#107—731no—
427#107—731no—
428#107—731no—
429#107—731no—
430#106—731no—
431#106—731no—
432#106—731no—
433#106—731no—
434C4⋊C8—731no—
435C4⋊C8—731no—
436C4⋊C8—731no—
437C4⋊C8—731no—
438C4⋊C8—731no—
439C4⋊C8—731no—
440C4⋊C8—731no—
441C4⋊C8—731no—
442C4⋊C8—1461no—
443C4⋊C8—1461no—
444C4⋊C8—1461no—
445C4⋊C8—1461no—
446C4⋊C8—1461no—
447C4⋊C8—1461no—
448C4⋊C8—1461no—
449C4⋊C8—1461no—
450C4⋊C8—1461no—
451C4⋊C8—1461no—
452#104—22no—
453#104Dic14614yescomplemented
454#103—731no—
455#103—731no—
456#103—731no—
457#103—731no—
458#102—731no—
459#102—731no—
460#102—731no—
461#102—731no—
462#97—21no—
463#97—2921no—
464#97—1461no—
465#97—1461no—
466C4×C8—21no—
467C4×C8—2921no—
468C4×C8—1461no—
469C4×C8—1461no—
470#95—21no—
471#95—21no—
472#41—21no—
473#41—21no—
474#41C2×Dic14612yes—
475#41#1192402812yes—
476C2×Q8—1461no—
477C2×Q8—1461no—
478C2×Q8C2×C4×D7311yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D7311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4#1192402711yescharacteristic
487C22×C4#1192402711yescharacteristic
488C22×C4C23×D7311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—2922no—
493M16—2922no—
494M16—1461no—
495M16—1461no—
496M16—1461no—
497M16—1461no—
498M16C2×Dic14612yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—2922no—
502C2×C8—2922no—
503C2×C8—731no—
504C2×C8—731no—
505C2×C8—731no—
506C2×C8—731no—
507C2×C8—731no—
508C2×C8—731no—
509C2×C8—731no—
510C2×C8—731no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—731no—
524C4⋊C4—731no—
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—1461no—
528C4⋊C4—1461no—
529C4⋊C4—1461no—
530C4⋊C4—1461no—
531C4⋊C4—1461no—
532C4⋊C4—1461no—
533C4⋊C4C2×C4×D7311yescharacteristic
534C4⋊C4C2×C4×D7311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—1461no—
539C22⋊C4—1461no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—1461no—
547C42—1461no—
548C42C2×C4×D7311yescharacteristic
549C42C2×C4×D7311yescharacteristic
550C42D4×D7311yescharacteristic
551C42D4×D7311yescharacteristic
552C42C2×Dic14612yes—
553C23—21no—
554C23C2×#1192402711yescharacteristic
555Q8—21no—
556Q8—2922no—
557Q8—5841no—
558Q8C4×Dic14612yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4C4×Dic14612yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4#1455655111yescharacteristic
583C2×C4#1455655111yescharacteristic
584C2×C4#1455655111yescharacteristic
585C2×C4#1455655111yescharacteristic
586C2×C4C22×C4×D7311yescharacteristic
587C2×C4C2×D4×D7311yescharacteristic
588C2×C4C22×Dic14611yescharacteristic
589C2×C4C2×#1192402811yescharacteristic
590C2×C4#1455663711yescharacteristic
591C2×C4#1455663811yescharacteristic
592C8—22no—
593C8—41no—
594C8—2921no—
595C8—2921no—
596C8—1461no—
597C8—1461no—
598C8—1461no—
599C8—1461no—
600C8—1461no—
601C8—1461no—
602C8—1461no—
603C8—1461no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×#1455655111yescharacteristic
610C22#1798927711yescharacteristic
611C22#1798929411yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—2921no—
622C4—2921no—
623C4—2921no—
624C4—2921no—
625C4C2×C4×Dic14611yescharacteristic
626C4#1798906711yescharacteristic
627C4#1798923311yescharacteristic
628C4D4×Dic14611yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#2261293411yescharacteristic
633C2#2261883011yescharacteristic
634C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1759C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C23
cosocleC22×C4×C73C24
hypercenter#1759D73
hypocenterC73#22984
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #22618878C2semidirect
4. #22610912C2semidirect
5. #22610706C2semidirect
6. #22610683C2semidirect
7. #22610678C2semidirect
8. #22610533C2semidirect
9. #22610533C2semidirect
12. #22609788C2semidirect
19. #17988894C4semidirect
20. #17988894C4semidirect
21. #17988887C4semidirect
22. #17988887C4semidirect
23. #17988882C4semidirect
24. #17988877C4semidirect
25. #17988872C4semidirect
26. #17988867C4semidirect
149. #104×C73Q8semidirect
333. C73#22984semidirect
453. #104Dic146semidirect

Maximal subgroups

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

subgroupindex
#226197192
#226188782
#226184992
#226109122
#226107062
#226106832
#226106782
#226105332
#226102042
#226097882
#226097762
#226097692
C73×#17592
#2298473