Finite Group Databasebeta

← #11888563

Subgroups — #11888563

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596295C211yesmaximal, characteristic, complemented
2#10596001C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6#10592810C211yesmaximal, characteristic, complemented
7#10592695C211yesmaximal, characteristic, complemented
8#10592517C211yesmaximal, characteristic, complemented
9#10592511C211yesmaximal, characteristic, complemented
10#10592504C211yesmaximal, characteristic, complemented
11#10592496C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic, complemented
13#10592480C211yesmaximal, characteristic, complemented
14#10592470C211yesmaximal, characteristic, complemented
15#10592462C211yesmaximal, characteristic, complemented
16#78853—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64155C2211yescharacteristic
22#64153C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64148—21no—
25#64144—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27C2×#3753C2211yescharacteristic
28#64139C2211yescharacteristic
29#64138—21no—
30C4×#638C2211yescharacteristic
31#64133C2211yescharacteristic
32C2×#3750—21no—
33C2×#3744C2211yescharacteristic
34C2×#3743C2211yescharacteristic
35#64104C2211yescharacteristic
36#64102C2211yescharacteristic
37C4⋊C4×C3⋊D3C2211yescharacteristic
38#64099C2211yescharacteristic
39#64093—21no—
40#64092—21no—
41#64085—21no—
42C4×C4⋊(C3⋊D3)—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63662C2211yescharacteristic
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55#63641C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5824—34no—
61#5530—34no—
62C3×#416D314yescomplemented
63#5238—34no—
64#5114—34no—
65#5111—34no—
66#4996—34no—
67#4818—34no—
68#4812—34no—
69#4805—34no—
70#4797—34no—
71#4785—34no—
72#4781—34no—
73#4771—34no—
74#4763—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×#638—21no—
83C2×#638—21no—
84C2×#638D411yescharacteristic
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87#3830—22no—
88#3830—41no—
89C2×C4⋊(C3⋊D3)—21no—
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C32×C8—41no—
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C42—21no—
102#3757—21no—
103#3757—21no—
104#3757D411yescharacteristic
105#3755—41no—
106#3753—22no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—41no—
126#3743—41no—
127#3307—91noSylow
128C2×C3×#41C2×D314yes—
129C2×#237—34no—
130C22×C3×C8C2×D314yes—
131C3×#117C2×D314yes—
132#946—34no—
133#944—34no—
134C2×#215—34no—
135#939—64no—
136#935—64no—
137D4×Dic3—34no—
138C2×#213—34no—
139#930—34no—
140#929—64no—
141C4×#67—34no—
142#924—34no—
143C2×Dic3⋊C4—64no—
144C2×#204—34no—
145C2×ΓL(1,𝔽25)—34no—
146#895—34no—
147#893—34no—
148D3×C4⋊C4—34no—
149#890—34no—
150#884—64no—
151#883—64no—
152#876—64no—
153C4×D12—64no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158#835—34no—
159#832—34no—
160#830—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#817—34no—
164#816—34no—
165#815—34no—
166Dic3⋊C8—34no—
167#810—34no—
168#810—34no—
169#808—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C22×C3⋊D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8—21no—
177C32×D4—21no—
178C32×D4—42no—
179C32×D4#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188#638—41no—
189#638—42no—
190#638—81no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—42no—
195C2×C3⋊Dic3—42no—
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—21no—
201C4⋊(C3⋊D3)—42no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—81no—
205C4×C3⋊D3—81no—
206#634—21no—
207#634—21no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#553—91no—
213#547—91no—
214#491—91no—
215#485—91no—
216#483—91no—
217#478—91no—
218#468—91no—
219#465—91no—
220#461—91no—
221#449—91no—
222#449—91no—
223#442—91no—
224#435—91no—
225#417—91no—
226#416C3⋊D311yescharacteristic, complemented
227C3×#41—28no—
228C3×#41—44no—
229C2×C3×Q8C22×D314yes—
230C2×C3×D4—24no—
231C2×C3×D4C22×D314yes—
232C22×C3×C4—24no—
233C22×C3×C4C22×D314yes—
234C2×#67—34no—
235C2×#67—64no—
236C2×#67—64no—
237C22×Dic3—64no—
238C22×Dic3—64no—
239#237—68no—
240#237—124no—
241C2×D12—34no—
242C2×D12—64no—
243C2×C4×D3—34no—
244C2×C4×D3—64no—
245C2×C4×D3—64no—
246C2×Dic6—34no—
247C2×C3×C8—44no—
248C2×C3×C8C22×D314yes—
249C2×C3×C8C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C4⋊C4C22×D314yes—
252C3×C22⋊C4—24no—
253C3×C42—24no—
254#217—34no—
255#217—64no—
256#217—64no—
257#215—124no—
258#213—68no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—64no—
267Dic3⋊C4—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—34no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277#204—124no—
278ΓL(1,𝔽25)—124no—
279C22×C32—22no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C32×C4—21no—
293C32×C4—41no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C2×#4111yescharacteristic
297C32×C4H(5,𝔽2)11yescharacteristic
298C3⋊Dic3—21no—
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C2×#41—91no—
305C2×#41C2×C3⋊D311yescharacteristic
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16—91no—
310C22×C8C2×C3⋊D311yescharacteristic
311C4⋊Q8—91no—
312#126—181no—
313#125—91no—
314#123—181no—
315#123—181no—
316#123—181no—
317C22⋊Q8—91no—
318C22⋊Q8—91no—
319#121—91no—
320#121—91no—
321#121—181no—
322#121—181no—
323C4×D4—91no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—181no—
327#117C2×C3⋊D311yescharacteristic
328C2×C4⋊C4—91no—
329C2×C4⋊C4—181no—
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103C2×C3⋊D311yescharacteristic
339#103C2×C3⋊D311yescharacteristic
340#102—91no—
341#102—91no—
342#102C2×C3⋊D311yescharacteristic
343#102C2×C3⋊D311yescharacteristic
344C22⋊C8—91no—
345C22⋊C8—91no—
346#97—91no—
347C23×C3—24no—
348C23×C3D3×D414yes—
349C22×D3—34no—
350C22×D3—64no—
351C3×Q8—24no—
352C3×Q8—24no—
353C3×D4—24no—
354C3×D4—48no—
355C3×D4#23518yes—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—48no—
362C2×C3×C4D3×D414yes—
363C2×C3×C4C23×D314yes—
364#67—124no—
365#67—128no—
366#67—244no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—128no—
374C2×Dic3—128no—
375D12—64no—
376D12—64no—
377D12—128no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—244no—
381C4×D3—244no—
382Dic6—64no—
383Dic6—64no—
384C3×C8—24no—
385C3×C8—24no—
386C3⋊C8—64no—
387C3⋊C8—64no—
388C2×C32—41no—
389C2×C32—42no—
390C2×C32#54611yescharacteristic
391C2×C32#57511yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—41no—
394C3⋊D3—81no—
395#41—22no—
396#41—41no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8C22×C3⋊D311yescharacteristic
401C2×D4—21no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4C22×C3⋊D311yescharacteristic
408C22×C4—21no—
409C22×C4—91no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4C22×C3⋊D311yescharacteristic
415SD16—361no—
416SD16—361no—
417D8—182no—
418M16—361no—
419C2×C8—41no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8C22×C3⋊D311yescharacteristic
423C2×C8C22×C3⋊D311yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4C22×C3⋊D311yescharacteristic
435C4⋊C4C22×C3⋊D311yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—21no—
446C42—91no—
447C22×C3—28no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3C2×D3×D414yes—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—124no—
460C3×C4—24no—
461C3×C4—44no—
462C3×C4—44no—
463C3×C4—44no—
464C3×C4C2×#23514yes—
465C3×C4#100414yes—
466Dic3—64no—
467Dic3—64no—
468Dic3—64no—
469Dic3—124no—
470Dic3—124no—
471Dic3—124no—
472C32#330711yescharacteristic, complemented, Sylow
473C23—21no—
474C23—91no—
475C23—181no—
476C23D4×C3⋊D311yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—181no—
480Q8—181no—
481D4—21no—
482D4—42no—
483D4—181no—
484D4—181no—
485D4—362no—
486D4—361no—
487D4—362no—
488D4—721no—
489D4#382812yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—42no—
496C2×C4—91no—
497C2×C4—91no—
498C2×C4—91no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4D4×C3⋊D311yescharacteristic
509C2×C4C23×C3⋊D311yescharacteristic
510C8—21no—
511C8—21no—
512C8—181no—
513C8—181no—
514C2×C3—44no—
515C2×C3—48no—
516C2×C3#549014yes—
517C2×C3#576814yes—
518C2×C3#577014yes—
519D3—124no—
520D3—244no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—41no—
526C22—41no—
527C22—181no—
528C22—181no—
529C22—181no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22C2×D4×C3⋊D311yescharacteristic
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—181no—
539C4—181no—
540C4—181no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4C2×#382811yescharacteristic
545C4#6436111yescharacteristic
546C3#7885314yescomplemented
547C2—41no—
548C2—42no—
549C2—361no—
550C2—721no—
551C2#1059596111yescharacteristic
552C2#1059623911yescharacteristic
553C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenter#416C3⋊D3
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #10596295C2semidirect
2. #10596001C2semidirect
3. C32×#416C2semidirect
4. #10592937C2semidirect
5. #10592813C2semidirect
6. #10592810C2semidirect
7. #10592695C2semidirect
8. #10592517C2semidirect
9. #10592511C2semidirect
10. #10592504C2semidirect
11. #10592496C2semidirect
12. #10592484C2semidirect
13. #10592480C2semidirect
14. #10592470C2semidirect
15. #10592462C2semidirect
62. C3×#416D3semidirect
226. #416C3⋊D3semidirect
472. C32#3307semidirect
546. C3#78853semidirect

Maximal subgroups

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

subgroupindex
#105962952
#105960012
C32×#4162
#105929372
#105928132
#105928102
#105926952
#105925172
#105925112
#105925042
#105924962
#105924842
#105924802
#105924702
#105924622
#788533