Finite Group Databasebeta

← #11860684

Subgroups — #11860684

Order 1152.

1225 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic
2#10595223C212yesmaximal, complemented
3C3×Dic3×D8C212yesmaximal, complemented
4#10591426C212yesmaximal, complemented
5#10591404C214yesmaximal, complemented
6#10590763C212yesmaximal, complemented
7#10590714C211yesmaximal, characteristic, complemented
8#10590700C211yesmaximal, characteristic, complemented
9#79588—32nomaximal
10C2×D4×C3⋊D3C2212yes—
11C2×C32×D8C2211yescharacteristic
12C2×#3753C2212yes—
13D8×C3⋊D3C418yescomplemented
14C2×#3745C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C3×D4×Dic3C2214yescomplemented
17#63974—22no—
18C2×#3722—22no—
19#63952—24no—
20#63894C2214yescomplemented
21#63874C2211yescharacteristic
22#63849C2212yes—
23C2×#3712C2211yescharacteristic
24C3×#832C2214yescomplemented
25C3×#818C2212yescomplemented
26C3×C8×Dic3C2212yescomplemented
27#63574C2212yescomplemented
28#63564C2214yescomplemented
29#63554C2212yescomplemented
30C2×D3×D8—32no—
31C2×D3×D8—61no—
32#5545—34no—
33C3×C4×D8—32no—
34Dic3×D8D312yescomplemented
35#5014—34no—
36#4880—32no—
37#4872—32no—
38#4785—34no—
39#4770—34no—
40C4×D24—32no—
41#4689—32no—
42C23×C3⋊D3—22no—
43C2×C32×D4C2312yes—
44C2×#638—22no—
45D4×C3⋊D3—24no—
46D4×C3⋊D3C2×C418yescomplemented
47C2×C4⋊(C3⋊D3)C2312yes—
48C2×C4×C3⋊D3C2311yescharacteristic
49C22×C3×Dic3—24no—
50C2×#624—24no—
51C32×D8C2×C414yescomplemented
52C2×C32×C8C2311yescharacteristic
53#3753C2×C418yescomplemented
54C2×C3⋊(C3⋊C8)C2311yescharacteristic
55#3745C2×C414yescomplemented
56C8×C3⋊D3C2×C414yescomplemented
57C3×#217—24no—
58C3×C4⋊Dic3C2314yes—
59C3×C4×Dic3C2312yes—
60C2×C3×C3⋊C8C2312yes—
61#3724D412yes—
62#3722—22no—
63#3722—24no—
64#3722D411yescharacteristic
65#3722D411yescharacteristic
66Dic32—22no—
67#3712—22no—
68#2948—91noSylow
69C2×D3×D4—34no—
70C2×D3×D4—62no—
71C2×C3×D8—21no—
72C2×C3×D8C2×D312yes—
73C3×C4×D4—34no—
74D4×Dic3C2×D314yescomplemented
75C2×#213—34no—
76C2×#213—62no—
77C4×#67—64no—
78C2×(C2×D3)⋊C4—64no—
79D3×D8—316no—
80D3×D8—68no—
81C2×D24—32no—
82C2×D24—61no—
83C2×ΓL(1,𝔽25)—32no—
84C2×D3×C8—32no—
85C2×D3×C8—61no—
86#893—34no—
87#892—34no—
88#67⋊C4—64no—
89D3×C22⋊C4—64no—
90C4×D12—34no—
91#872—32no—
92C3×#107—32no—
93C3×#102—34no—
94C3×C4×C8—32no—
95#832C2×D314yescomplemented
96#821—34no—
97#818C2×D312yescomplemented
98#815—32no—
99C8×Dic3C2×D312yescomplemented
100#809—34no—
101#808—34no—
102#803—32no—
103C23×C32—22no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3—28no—
106C22×C3⋊D3—84no—
107C22×C3⋊D3C2×D411yescharacteristic
108C32×D4—22no—
109C32×D4C22×C414yes—
110C2×C32×C4C2411yescharacteristic
111#638—28no—
112C2×C3⋊Dic3C2×D411yescharacteristic
113C4⋊(C3⋊D3)—22no—
114C4⋊(C3⋊D3)C22×C414yes—
115C4×C3⋊D3C22×C412yes—
116C4×C3⋊D3#4112yes—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—84no—
119C2×C3×Dic3C2×D412yes—
120C2×C3×Dic3C2×D412yes—
121#624—84no—
122C32×C8C22×C412yes—
123C3⋊(C3⋊C8)C22×C412yes—
124C3×C3⋊C8—22no—
125C22×D8—91no—
126#518—92no—
127#442—94no—
128C4×D8—32no—
129C4×D8—92no—
130#427—91no—
131#418—92no—
132#405—91no—
133C23×D3—64no—
134C23×D3—122no—
135C2×C3×D4—22no—
136C2×C3×D4C22×D314yes—
137C22×C3×C4—64no—
138C2×#67—64no—
139C2×#67—122no—
140C22×Dic3—24no—
141D3×D4—316no—
142D3×D4—68no—
143D3×D4—68no—
144D3×D4—124no—
145C2×D12—34no—
146C2×D12—62no—
147C2×C4×D3—32no—
148C2×C4×D3—61no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C3×D8—24no—
152C3×D8C4×D318yescomplemented
153C2×C3×C8—21no—
154C2×C3×C8—32no—
155C2×C3×C8C22×D312yes—
156C3×C4⋊C4—34no—
157C3×C22⋊C4—64no—
158C3×C42—32no—
159#217—24no—
160#213—316no—
161#213—68no—
162(C2×D3)⋊C4—32no—
163(C2×D3)⋊C4—32no—
164(C2×D3)⋊C4—64no—
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—64no—
167C4⋊Dic3C22×D314yes—
168Dic3⋊C4—32no—
169Dic3⋊C4—32no—
170C4×Dic3—64no—
171C4×Dic3C22×D312yes—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8C22×D312yes—
175D24—38no—
176D24—64no—
177ΓL(1,𝔽25)—64no—
178D3×C8—38no—
179D3×C8—64no—
180C22×C32—24no—
181C22×C32—44no—
182C22×C32C22×D411yescharacteristic
183C2×C3⋊D3—22no—
184C2×C3⋊D3—24no—
185C2×C3⋊D3—44no—
186C2×C3⋊D3—88no—
187C2×C3⋊D3C4×D412yes—
188C32×C4C23×C411yescharacteristic
189C32×C4C2×#4111yescharacteristic
190C3⋊Dic3C4×D412yes—
191C3×Dic3—22no—
192C3×Dic3—22no—
193C3×Dic3—44no—
194C22×D4—92no—
195C2×D8—92no—
196C2×D8—98no—
197C2×D8—91no—
198C2×D8D3211yescharacteristic
199C2×M16—91no—
200C22×C8—91no—
201C4×D4—34no—
202C4×D4—94no—
203C4×D4—184no—
204#117—91no—
205#117—92no—
206C2×C22⋊C4—182no—
207C2×C22⋊C4—182no—
208#107—32no—
209#106—92no—
210#102—34no—
211#102—94no—
212#97—92no—
213C4×C8—32no—
214C23×C3—24no—
215C23×C3—42no—
216C22×D3—32no—
217C22×D3—61no—
218C22×D3—616no—
219C22×D3—64no—
220C22×D3—128no—
221C22×D3—122no—
222C22×D3—244no—
223C22×D3—244no—
224C22×D3—248no—
225C3×D4—24no—
226C3×D4—24no—
227C3×D4—42no—
228C3×D4C2×C4×D318yes—
229C2×C3×C4—21no—
230C2×C3×C4—32no—
231C2×C3×C4—32no—
232C2×C3×C4—64no—
233C2×C3×C4—244no—
234C2×C3×C4C23×D312yes—
235#67—616no—
236#67—128no—
237C2×Dic3—24no—
238C2×Dic3—32no—
239C2×Dic3—61no—
240C2×Dic3—84no—
241C2×Dic3D3×D412yes—
242C2×Dic3D3×D412yes—
243D12—38no—
244D12—64no—
245D12—64no—
246D12—122no—
247C4×D3—34no—
248C4×D3—34no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—244no—
252C4×D3—244no—
253C3×C8—22no—
254C3×C8—62no—
255C3×C8C2×C4×D314yes—
256C3⋊C8—22no—
257C3⋊C8—34no—
258C3⋊C8—62no—
259C2×C32—44no—
260C2×C32C2×C4×D411yescharacteristic
261C2×C32#57612yes—
262C3⋊D3—22no—
263C3⋊D3—44no—
264C24—182no—
265C2×D4—98no—
266C2×D4—92no—
267C2×D4—184no—
268C2×D4—182no—
269C2×D4C2×D3212yes—
270C22×C4—64no—
271C22×C4—91no—
272C22×C4—184no—
273D8—98no—
274D8—94no—
275D8#62414yescomplemented
276M16—182no—
277C2×C8—32no—
278C2×C8—91no—
279C2×C8—94no—
280C2×C8C2×D3211yescharacteristic
281C4⋊C4—34no—
282C4⋊C4—92no—
283C22⋊C4—64no—
284C22⋊C4—91no—
285C22⋊C4—91no—
286C22⋊C4—184no—
287C22⋊C4—182no—
288C42—32no—
289C42—182no—
290C22×C3—28no—
291C22×C3—21no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—84no—
296C22×C3C2×D3×D412yes—
297C2×D3—34no—
298C2×D3—62no—
299C2×D3—64no—
300C2×D3—62no—
301C2×D3—62no—
302C2×D3—68no—
303C2×D3—124no—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—244no—
307C2×D3—2416no—
308C2×D3—2416no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—62no—
312C3×C4—62no—
313C3×C4—124no—
314C3×C4C22×C4×D312yes—
315C3×C4D3×#4112yes—
316Dic3—22no—
317Dic3—22no—
318Dic3—34no—
319Dic3—44no—
320Dic3—62no—
321C32#294811yescharacteristic, complemented, Sylow
322C23—22no—
323C23—91no—
324C23—188no—
325C23—182no—
326C23—724no—
327D4—22no—
328D4—94no—
329D4—188no—
330D4—182no—
331D4C2×#62414yes—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—64no—
335C2×C4—91no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—244no—
339C2×C4—724no—
340C2×C4C22×D3211yescharacteristic
341C8—62no—
342C8—92no—
343C8C2×#62412yes—
344C2×C3—21no—
345C2×C3—22no—
346C2×C3—48no—
347C2×C3—84no—
348C2×C3C4×D3×D412yes—
349C2×C3#575712yes—
350C2×C3#576912yes—
351D3—64no—
352D3—64no—
353D3—128no—
354D3—244no—
355C22—24no—
356C22—44no—
357C22—92no—
358C22—182no—
359C22—184no—
360C22—364no—
361C22—728no—
362C22D32×D411yescharacteristic
363C4—62no—
364C4—62no—
365C4—92no—
366C4—124no—
367C4#6431211yescharacteristic
368C4C22×#62411yescharacteristic
369C3—21no—
370C3#7958812yescomplemented
371C2—44no—
372C2—182no—
373C2—364no—
374C2#1059473412yes—
375C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×D8×C3⋊D3C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10595223C2semidirect
3. C3×Dic3×D8C2semidirect
4. #10591426C2semidirect
5. #10591404C2semidirect
6. #10590763C2semidirect
7. #10590714C2semidirect
8. #10590700C2semidirect
13. D8×C3⋊D3C4semidirect
16. C3×D4×Dic3C22semidirect
20. #63894C22semidirect
24. C3×#832C22semidirect
25. C3×#818C22semidirect
26. C3×C8×Dic3C22semidirect
27. #63574C22semidirect
28. #63564C22semidirect
29. #63554C22semidirect
34. Dic3×D8D3semidirect
46. D4×C3⋊D3C2×C4semidirect
51. C32×D8C2×C4semidirect
53. #3753C2×C4semidirect
55. #3745C2×C4semidirect
56. C8×C3⋊D3C2×C4semidirect
74. D4×Dic3C2×D3semidirect
95. #832C2×D3semidirect
97. #818C2×D3semidirect
99. C8×Dic3C2×D3semidirect
152. C3×D8C4×D3semidirect
275. D8#624semidirect
321. C32#2948semidirect
370. C3#79588semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
#105952232
C3×Dic3×D82
#105914262
#105914042
#105907632
#105907142
#105907002
#795883