Finite Group Databasebeta

← #11860710

Subgroups — #11860710

Order 1152.

1113 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1113 conjugacy classes of subgroups — too many to draw. Only its 224 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×#63797C211yesmaximal, characteristic
2#10594606C212yesmaximal, complemented
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4869C212yesmaximal, complemented
5#10590771C212yesmaximal, complemented
6#10590703C211yesmaximal, characteristic, complemented
7#10590594C212yesmaximal, complemented
8#10590452C214yesmaximal, complemented
9#79867—32nomaximal
10C2×#3802C2212yes—
11C2×C8×C3⋊D3C2211yescharacteristic
12#64101C2212yes—
13C2×C3×D24C2212yes—
14C3×#893C2214yescomplemented
15D3×(C2×D3)⋊C4—24no—
16#63902—22no—
17C4×#625—22no—
18Dic3×D12C2214yescomplemented
19#63874C2211yescharacteristic
20C2×#3713C2212yes—
21C2×#3712C2211yescharacteristic
22#63797C418yescomplemented
23C32×#106C2211yescharacteristic, complemented
24#63644C2211yescharacteristic, complemented
25#63634C2212yescomplemented
26C3×#815C2212yescomplemented
27C3×#809C2214yescomplemented
28#63563C2214yescomplemented
29Dic3×C3⋊C8C2212yescomplemented
30C2×D3×D8—32no—
31#5545—34no—
32C3×#442—32no—
33#5152—32no—
34C4×#213—34no—
35#4869D312yescomplemented
36#4860—32no—
37#4860—61no—
38#4770—34no—
39#4756—34no—
40#4711—32no—
41#4708—32no—
42C22×D32—22no—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×D12C2314yes—
45C2×C3×C4×D3—24no—
46C2×#625—22no—
47C2×D3×Dic3—24no—
48#3802—24no—
49#3802C2×C418yescomplemented
50C2×C32×C8C2311yescharacteristic
51C32×C4⋊C4C2312yes—
52#3752—22no—
53C4⋊(C3⋊Dic3)C2312yes—
54C4×C3⋊Dic3—22no—
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56C8×C3⋊D3C2×C414yescomplemented
57C3×(C2×D3)⋊C4—24no—
58C3×C4×Dic3C2312yes—
59C2×C3×C3⋊C8C2312yes—
60C3×D24C2×C418yescomplemented
61#3724D412yes—
62#3722D412yes—
63(C2×D3)⋊Dic3—24no—
64#3713C2×C418yescomplemented
65#3712—22no—
66#2948—91noSylow
67C2×D3×D4—34no—
68C2×C3×D8—32no—
69C3×C4×D4—34no—
70D4×Dic3—34no—
71C2×#213—34no—
72C4×#67—64no—
73C2×(C2×D3)⋊C4—64no—
74D3×D8—316no—
75C2×D24C2×D312yes—
76C2×ΓL(1,𝔽25)—32no—
77C2×D3×C8—32no—
78C2×D3×C8—61no—
79#893C2×D314yescomplemented
80#892—34no—
81#892—62no—
82#67⋊C4—64no—
83D3×C22⋊C4—64no—
84C4×D12—34no—
85#872—32no—
86C3×#106—21no—
87C3×#106C2×D312yescomplemented
88C3×#102—34no—
89C3×#97—32no—
90#832—34no—
91#821—34no—
92#817—32no—
93#817—61no—
94#815C2×D312yescomplemented
95C8×Dic3—32no—
96#809C2×D314yescomplemented
97#807—34no—
98#807—62no—
99C4×C3⋊C8—32no—
100C22×C3⋊D3C2×D411yescharacteristic
101C22×C3×D3—24no—
102C2×D32—28no—
103C2×D32—82no—
104C2×D32—82no—
105C2×C32×C4—22no—
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3C2×D411yescharacteristic
109C4×C3⋊D3C22×C412yes—
110C4×C3⋊D3#4112yes—
111C2×C3×Dic3C2×D414yes—
112C3×D12—24no—
113C3×D12C22×C418yes—
114C3×C4×D3—84no—
115#625—28no—
116D3×Dic3—84no—
117C32×C8C22×C412yes—
118C3⋊(C3⋊C8)C22×C412yes—
119C3×C3⋊C8—22no—
120C22×D8—91no—
121#518—92no—
122#442—32no—
123#442—92no—
124C4×D8—94no—
125#427—91no—
126#418—92no—
127#405—91no—
128C23×D3—64no—
129C2×C3×D4—34no—
130C22×C3×C4—64no—
131C2×#67—64no—
132C22×Dic3—64no—
133D3×D4—316no—
134D3×D4—68no—
135C2×D12C22×D314yes—
136C2×C4×D3—24no—
137C2×C4×D3—32no—
138C2×C4×D3—61no—
139C2×C4×D3—64no—
140C3×D8—38no—
141C2×C3×C8—21no—
142C2×C3×C8—32no—
143C2×C3×C8C22×D312yes—
144C3×C4⋊C4—22no—
145C3×C4⋊C4C22×D314yes—
146C3×C22⋊C4—64no—
147C3×C42—32no—
148#217—64no—
149#213—316no—
150(C2×D3)⋊C4—24no—
151(C2×D3)⋊C4—34no—
152(C2×D3)⋊C4—64no—
153(C2×D3)⋊C4—64no—
154(C2×D3)⋊C4—122no—
155C4⋊Dic3—34no—
156C4⋊Dic3—62no—
157Dic3⋊C4—34no—
158C4×Dic3—64no—
159C4×Dic3—122no—
160C4×Dic3C22×D312yes—
161C2×C3⋊C8—32no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8C22×D312yes—
164D24C4×D318yescomplemented
165ΓL(1,𝔽25)—64no—
166D3×C8—38no—
167D3×C8—64no—
168C22×C32C22×D411yescharacteristic
169C2×C3⋊D3—22no—
170C2×C3⋊D3C4×D412yes—
171C2×C3×D3—28no—
172C2×C3×D3—44no—
173C2×C3×D3—44no—
174D32—88no—
175C32×C4—42no—
176C32×C4C23×C411yescharacteristic
177C32×C4C2×#4111yescharacteristic
178C3⋊Dic3—42no—
179C3⋊Dic3C4×D412yes—
180C3×Dic3—24no—
181C22×D4—92no—
182C2×D8—32no—
183C2×D8—98no—
184C2×D8—92no—
185C2×M16—91no—
186C22×C8—91no—
187C4×D4—34no—
188C4×D4—94no—
189C4×D4—182no—
190C4×D4—182no—
191#117—91no—
192#117—92no—
193C2×C22⋊C4—184no—
194#107—92no—
195#106—91no—
196#106D3211yescharacteristic, complemented
197#102—34no—
198#102—94no—
199#97—32no—
200C4×C8—92no—
201C23×C3—64no—
202C22×D3—24no—
203C22×D3—32no—
204C22×D3—61no—
205C22×D3—616no—
206C22×D3—244no—
207C22×D3—244no—
208C3×D4—38no—
209C3×D4—64no—
210C2×C3×C4—24no—
211C2×C3×C4—21no—
212C2×C3×C4—34no—
213C2×C3×C4—42no—
214C2×C3×C4—244no—
215C2×C3×C4C23×D312yes—
216#67—616no—
217C2×Dic3—32no—
218C2×Dic3—61no—
219C2×Dic3—64no—
220C2×Dic3—122no—
221C2×Dic3—244no—
222C2×Dic3D3×D414yes—
223D12—24no—
224D12C2×C4×D318yes—
225C4×D3—34no—
226C4×D3—34no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—84no—
230C4×D3—244no—
231C3×C8—22no—
232C3×C8—62no—
233C3×C8C2×C4×D314yes—
234C3⋊C8—22no—
235C3⋊C8—34no—
236C3⋊C8—62no—
237C2×C32C2×C4×D411yescharacteristic
238C2×C32#57612yes—
239C3⋊D3—22no—
240C3×D3—48no—
241C24—182no—
242C2×D4—34no—
243C2×D4—98no—
244C2×D4—184no—
245C2×D4—182no—
246C22×C4—64no—
247C22×C4—91no—
248C22×C4—184no—
249D8—38no—
250D8—98no—
251M16—182no—
252C2×C8—32no—
253C2×C8—91no—
254C2×C8—94no—
255C2×C8C2×D3211yescharacteristic
256C4⋊C4—92no—
257C4⋊C4—92no—
258C4⋊C4C2×D3212yes—
259C22⋊C4—64no—
260C22⋊C4—92no—
261C22⋊C4—182no—
262C22⋊C4—184no—
263C42—32no—
264C42—182no—
265C22×C3—21no—
266C22×C3—68no—
267C22×C3—124no—
268C22×C3—124no—
269C22×C3C2×D3×D412yes—
270C2×D3—28no—
271C2×D3—34no—
272C2×D3—44no—
273C2×D3—44no—
274C2×D3—62no—
275C2×D3—64no—
276C2×D3—122no—
277C2×D3—2416no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—44no—
281C3×C4—64no—
282C3×C4—82no—
283C3×C4C22×C4×D312yes—
284C3×C4D3×#4112yes—
285Dic3—24no—
286Dic3—34no—
287Dic3—62no—
288Dic3—124no—
289Dic3—242no—
290C32#294811yescharacteristic, complemented, Sylow
291C23—64no—
292C23—91no—
293C23—188no—
294C23—722no—
295C23—722no—
296D4—38no—
297D4—64no—
298D4—188no—
299C2×C4—22no—
300C2×C4—34no—
301C2×C4—91no—
302C2×C4—92no—
303C2×C4—92no—
304C2×C4—182no—
305C2×C4—244no—
306C2×C4—724no—
307C2×C4C22×D3211yescharacteristic
308C8—62no—
309C8—92no—
310C8C4×D3212yes—
311C2×C3—21no—
312C2×C3—22no—
313C2×C3—128no—
314C2×C3C4×D3×D412yes—
315C2×C3#577414yes—
316D3—48no—
317D3—64no—
318D3—122no—
319C22—68no—
320C22—92no—
321C22—124no—
322C22—124no—
323C22—182no—
324C22—728no—
325C22D32×D411yescharacteristic
326C4—42no—
327C4—64no—
328C4—92no—
329C4—362no—
330C4C2×C4×D3211yescharacteristic
331C4#6431911yescharacteristic
332C3—21no—
333C3#7986712yescomplemented
334C2—128no—
335C2—182no—
336C2#1059460511yescharacteristic
337C2#1059475012yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63797C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594606C2semidirect
3. #10592559C2semidirect
4. C3×#4869C2semidirect
5. #10590771C2semidirect
6. #10590703C2semidirect
7. #10590594C2semidirect
8. #10590452C2semidirect
14. C3×#893C22semidirect
18. Dic3×D12C22semidirect
22. #63797C4semidirect
23. C32×#106C22semidirect
24. #63644C22semidirect
25. #63634C22semidirect
26. C3×#815C22semidirect
27. C3×#809C22semidirect
28. #63563C22semidirect
29. Dic3×C3⋊C8C22semidirect
35. #4869D3semidirect
49. #3802C2×C4semidirect
56. C8×C3⋊D3C2×C4semidirect
60. C3×D24C2×C4semidirect
64. #3713C2×C4semidirect
79. #893C2×D3semidirect
87. C3×#106C2×D3semidirect
94. #815C2×D3semidirect
96. #809C2×D3semidirect
164. D24C4×D3semidirect
196. #106D32semidirect
290. C32#2948semidirect
333. C3#79867semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105946062
#105925592
C3×#48692
#105907712
#105907032
#105905942
#105904522
#798673