Finite Group Databasebeta

← #11870513

Subgroups — #11870513

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591172C212yesmaximal
5#10591124C212yesmaximal, complemented
6#10590365C212yesmaximal, complemented
7C4×#3716C214yesmaximal, complemented
8#10590268C212yesmaximal, complemented
9#82314—31nomaximal
10#79298—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14#64135—21no—
15#64133—21no—
16#64133C2212yes—
17#64079—21no—
18#64078C2211yescharacteristic, complemented
19#64078C2211yescharacteristic, complemented
20C4×#634—21no—
21C4×#634C2212yescomplemented
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×C4×D12—21no—
25C3×C4×D12—21no—
26C3×C4×D12C2212yes—
27C3×C4×D12C2212yes—
28C2×#3716C2214yes—
29C3×#830C2212yes—
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31C3×C4×C3⋊C8C2212yescomplemented
32#63573C2214yescomplemented
33#63567C2214yescomplemented
34#63563C2214yes—
35C2×C3×C4×D4—31no—
36C2×C4×D12D311yescharacteristic
37#5470—31no—
38#5470—31no—
39#5470—61no—
40C3×#431—31no—
41#5218—32no—
42#5019—32no—
43C4×#214—34no—
44#5008—32no—
45#4971—32no—
46#4925D311yescharacteristic, complemented
47#4842—32no—
48#4841—32no—
49#4731—32no—
50#4721—32no—
51C4×#204—34no—
52C23×C3×D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#634—21no—
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C2×C3×D12—21no—
60C2×C3×D12—24no—
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—44no—
65C32×C42D411yescharacteristic
66C32×C42D411yescharacteristic
67C32×C42C2311yescharacteristic
68C32×C42C2311yescharacteristic
69#3757—22no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—22no—
75#3750—22no—
76C4×C3⋊Dic3—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8C2314yes—
82#3716—28no—
83#3101—91noSylow
84C22×C3×D4—31no—
85C23×C3×C4—61no—
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—21no—
88C3×C4×D4—32no—
89C3×C4×D4—32no—
90C3×C4×D4—61no—
91C3×C4×D4—61no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C2×D311yescharacteristic
97C2×#214—34no—
98C2×(C2×D3)⋊C4—21no—
99#926—62no—
100#926—61no—
101#926—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103#924—32no—
104#924—32no—
105#924—62no—
106#924—62no—
107#924—61no—
108#924—61no—
109C2×#204—34no—
110C4×D12—21no—
111C4×D12—21no—
112C4×D12C2×D312yes—
113C4×D12C2×D312yes—
114#870—62no—
115#870—61no—
116#870—61no—
117#869—31no—
118#869—31no—
119#869—31no—
120#869—31no—
121#869—61no—
122#869—61no—
123C4×Dic6—32no—
124C4×Dic6—32no—
125C4×Dic6—62no—
126C4×Dic6—62no—
127C4×Dic6—61no—
128C4×Dic6—61no—
129C3×C4⋊C8—32no—
130C3×C22⋊C8—32no—
131C3×C4×C8—32no—
132#832—34no—
133#830C2×D312yes—
134#821—34no—
135#817—34no—
136#816—34no—
137#810—34no—
138#808—34no—
139C4⋊(C3⋊C8)C2×D312yescomplemented
140C4×C3⋊C8C2×D312yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C2×C32×C4—22no—
147C2×C32×C4—41no—
148C2×C32×C4SD1614yescomplemented
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157#634—24no—
158#634—42no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C3×D12—24no—
162C3×D12—22no—
163C3×D12#4114yes—
164C3×C4×D3—44no—
165C3×C4×D3—44no—
166C3×C3⋊C8—24no—
167#533—91no—
168C2×C4×D4—31no—
169#483—92no—
170#476—92no—
171#461—92no—
172#450—92no—
173C4×SD16—94no—
174#431—31no—
175C24×C3—61no—
176C23×D3—21no—
177C2×C3×D4—32no—
178C2×C3×D4—64no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—61no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—124no—
187C22×C3×C4D1211yescharacteristic
188C22×C3×C4D1211yescharacteristic
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C2×D12—21no—
195C2×D12—24no—
196C2×D12C22×D312yes—
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3—44no—
200C2×Dic6—32no—
201C2×Dic6—32no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×C3×C8—34no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—61no—
209C3×C22⋊C4—62no—
210C3×C22⋊C4—62no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42D1211yescharacteristic
216C3×C42D1211yescharacteristic
217C3×C42#6711yescharacteristic
218C3×C42#6711yescharacteristic
219C3×C42C22×D311yescharacteristic
220C3×C42C22×D311yescharacteristic
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223#217—64no—
224#217—62no—
225#217—62no—
226#214—68no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—22no—
229C4⋊Dic3—21no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3—62no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3C22×D312yes—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249C4×Dic3—64no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C2×C3⋊C8C22×D314yes—
253#204—68no—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32C2×SD1612yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—24no—
259C2×C3×D3—48no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4C2×SD1612yes—
266C32×C4C2×SD1612yes—
267C32×C4C2×#4112yes—
268C3⋊Dic3—42no—
269C3⋊Dic3—42no—
270C3×Dic3—42no—
271C22×D4—31no—
272C23×C4—61no—
273C2×SD16—94no—
274C4⋊Q8—91no—
275C4⋊Q8—91no—
276#125—181no—
277C22⋊Q8—92no—
278C22⋊Q8—181no—
279C4×Q8—92no—
280C4×Q8—181no—
281C4×D4—32no—
282C4×D4—32no—
283C4×D4—61no—
284C4×D4—61no—
285#117—181no—
286C2×C4⋊C4—31no—
287C2×C22⋊C4—61no—
288C2×C42D3211yescharacteristic
289#106—94no—
290C4⋊C8—32no—
291#103—94no—
292#102—94no—
293C22⋊C8—32no—
294C4×C8—32no—
295C23×C3—21no—
296C23×C3—64no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3C2×D1211yescharacteristic
301C23×C3C2×#6711yescharacteristic
302C22×D3—24no—
303C22×D3—22no—
304C22×D3—42no—
305C22×D3—42no—
306C3×D4—34no—
307C3×D4—64no—
308C3×D4—62no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—24no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4—124no—
325C2×C3×C4—124no—
326C2×C3×C4#20414yescomplemented
327C2×C3×C4#21414yescomplemented
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—42no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348D12—24no—
349D12—22no—
350D12#23514yes—
351C4×D3—44no—
352C4×D3—44no—
353Dic6—64no—
354Dic6—64no—
355Dic6—124no—
356Dic6—124no—
357Dic6—122no—
358Dic6—122no—
359C3×C8—64no—
360C3⋊C8—24no—
361C2×C32—22no—
362C2×C32#52511yescharacteristic
363C2×C32C22×SD1611yescharacteristic
364C2×C32#57511yescharacteristic
365C3×D3—44no—
366C24—61no—
367C2×Q8—92no—
368C2×Q8—181no—
369C2×D4—32no—
370C2×D4—64no—
371C2×D4—61no—
372C22×C4—61no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—124no—
376C22×C4#62611yescharacteristic
377C22×C4#62611yescharacteristic
378C22×C4C2×D3211yescharacteristic
379SD16—188no—
380C2×C8—34no—
381C4⋊C4—32no—
382C4⋊C4—61no—
383C4⋊C4—92no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4—181no—
389C22⋊C4—62no—
390C22⋊C4—62no—
391C22⋊C4—182no—
392C42—182no—
393C42#62611yescharacteristic
394C42#62611yescharacteristic
395C42C2×D3211yescharacteristic
396C42C2×D3211yescharacteristic
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—64no—
406C22×C3—128no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3C2×#20412yes—
410C22×C3C2×#21412yes—
411C22×C3C22×D1211yescharacteristic
412C22×C3C22×#6711yescharacteristic
413C2×D3—24no—
414C2×D3—48no—
415C2×D3—42no—
416C2×D3—42no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—22no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—122no—
430C3×C4C2×#20412yes—
431C3×C4C2×#20412yes—
432C3×C4C2×#21412yes—
433C3×C4C2×#21412yes—
434C3×C4C2×#23512yes—
435C3×C4D3×#4112yes—
436Dic3—42no—
437Dic3—124no—
438Dic3—124no—
439Dic3—122no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443C32#310111yescharacteristic, complemented, Sylow
444C23—64no—
445C23—62no—
446C23—122no—
447C23—122no—
448C23C2×#62611yescharacteristic
449Q8—184no—
450Q8—362no—
451D4—34no—
452D4—64no—
453D4—62no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—62no—
457C2×C4—122no—
458C2×C4—124no—
459C2×C4—124no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4#371614yescomplemented
463C2×C4C2×#62611yescharacteristic
464C2×C4C2×#62611yescharacteristic
465C2×C4C2×#62611yescharacteristic
466C2×C4C2×#62611yescharacteristic
467C2×C4C2×#62611yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—64no—
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3#552411yescharacteristic
478C2×C3C22×#20411yescharacteristic
479C2×C3#574811yescharacteristic
480C2×C3#579111yescharacteristic
481C2×C3C22×#21411yescharacteristic
482C2×C3#582211yescharacteristic
483D3—44no—
484C22—21no—
485C22—21no—
486C22—64no—
487C22—128no—
488C22—122no—
489C22—122no—
490C22C2×#371612yes—
491C22C22×#62611yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—122no—
496C4—362no—
497C4—362no—
498C4C2×#371612yes—
499C4C2×#371612yes—
500C4D3×#23512yes—
501C3—21no—
502C3#7929811yescharacteristic, complemented
503C3#8231411yescharacteristic, complemented
504C2—22no—
505C2—124no—
506C2C22×#371611yescharacteristic
507C2#1059479511yescharacteristic
508C2#1059502311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
3. C3×#4925C2semidirect
5. #10591124C2semidirect
6. #10590365C2semidirect
7. C4×#3716C2semidirect
8. #10590268C2semidirect
18. #64078C22semidirect
19. #64078C22semidirect
21. C4×#634C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. C3×C4×C3⋊C8C22semidirect
32. #63573C22semidirect
33. #63567C22semidirect
46. #4925D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. C4×C3⋊C8C2×D3semidirect
148. C2×C32×C4SD16semidirect
326. C2×C3×C4#204semidirect
327. C2×C3×C4#214semidirect
443. C32#3101semidirect
462. C2×C4#3716semidirect
502. C3#79298semidirect
503. C3#82314semidirect

Maximal subgroups

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

subgroupindex
#105959412
C2×C3×C4×D122
C3×#49252
#105911722
#105911242
#105903652
C4×#37162
#105902682
#823143
#792983