Finite Group Databasebeta

← #11774341

Subgroups — #11774341

Order 1152.

555 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 555 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C4×#3797C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4C3×#4484C212yesmaximal, complemented
5#10589084C212yesmaximal, complemented
6#68231—32nomaximal
7C2×#3797C411yescharacteristic
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×Dic6C2212yes—
10C4×#627—21no—
11#63900C411yescharacteristic
12#63883—21no—
13C4×#624—21no—
14#63843C412yes—
15#63838—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63647—21no—
18C8×C3⋊Dic3—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×C4×C3⋊C8C2212yes—
21#63572—21no—
22#63557—21no—
23C4×D3×Q8—32no—
24#4833—32no—
25#4833—61no—
26#4685—32no—
27C3×Q8⋊C8—32no—
28#4535—32no—
29#4484D312yescomplemented
30#4456—32no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×Dic6C2×C412yes—
35C2×#627—21no—
36C2×#624—21no—
37C2×#624—21no—
38#3797—22no—
39#3797C814yescomplemented
40C2×C32×C8—21no—
41C32×C42C2311yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C3×C4⋊Dic3C2×C412yes—
47C3×Dic3⋊C4—22no—
48C3×C4×Dic3—22no—
49C2×C3×C3⋊C8—22no—
50#3724—21no—
51Dic3⋊Dic3—22no—
52Dic32—22no—
53#1479—91noSylow
54C2×D3×Q8—32no—
55C3×C4×Q8—32no—
56Q8×Dic3—32no—
57D3×C4⋊C4—32no—
58D3×C4⋊C4—62no—
59#887—32no—
60#887—62no—
61C42×D3—32no—
62C42×D3—61no—
63C42×D3—62no—
64C4×Dic6—62no—
65C4×Dic6C2×D312yes—
66C3×C4⋊C8—21no—
67C3×C4⋊C8C2×D312yes—
68C3×C4×C8—32no—
69(C2×D3)⋊C8—62no—
70(C2×D3)⋊C8—62no—
71(C2×D3)⋊C8—62no—
72Dic3⋊C8—62no—
73C8×Dic3—62no—
74C8×Dic3—62no—
75C4⋊(C3⋊C8)—32no—
76C4⋊(C3⋊C8)—61no—
77C4×C3⋊C8C2×D312yes—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4×C3⋊D3—21no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3C2×C812yes—
89C4×C3⋊D3M1612yes—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C3×Dic6—22no—
93C3×Dic6C2×C814yes—
94#627—24no—
95#624—24no—
96#624—42no—
97C32×C8—41no—
98C3⋊(C3⋊C8)—41no—
99C3×C3⋊C8—42no—
100C2×C4×Q8—91no—
101#431—91no—
102#431—91no—
103Q8⋊C8—32no—
104Q8⋊C8—92no—
105C2×C3×Q8—32no—
106D3×Q8—38no—
107D3×Q8—64no—
108C2×C4×D3—32no—
109C2×C4×D3—32no—
110C2×C4×D3—32no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×Dic6—62no—
117C2×Dic6C4×D312yes—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8—62no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—62no—
123C3×C42—21no—
124C3×C42—62no—
125C3×C42C22×D312yes—
126C4⋊Dic3—62no—
127C4⋊Dic3C4×D312yes—
128Dic3⋊C4—22no—
129Dic3⋊C4—62no—
130Dic3⋊C4—62no—
131C4×Dic3—22no—
132C4×Dic3—32no—
133C4×Dic3—32no—
134C4×Dic3—32no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C2×C3⋊C8—22no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—62no—
143C22×C32C2×C22⋊C411yescharacteristic
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3C22⋊C812yes—
147C32×C4—21no—
148C32×C4C22×C811yescharacteristic
149C32×C4C2×M1611yescharacteristic
150C32×C4#13711yescharacteristic
151C32×C4#13711yescharacteristic
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3C22⋊C812yes—
155C3×Dic3—24no—
156C3×Dic3—42no—
157C22×Q8—91no—
158C4×Q8—32no—
159C4×Q8—92no—
160C4×Q8—181no—
161C4×Q8—181no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—181no—
164C2×C42—91no—
165C2×C42—181no—
166C4⋊C8—91no—
167C4⋊C8—181no—
168C4⋊C8D3211yescharacteristic
169C22⋊C8—181no—
170C22⋊C8—181no—
171C4×C8—32no—
172C4×C8—181no—
173C22×D3—32no—
174C22×D3—61no—
175C3×Q8—34no—
176C3×Q8—62no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—62no—
181C2×C3×C4—62no—
182C2×C3×C4C2×C4×D312yes—
183C2×C3×C4D3×D412yes—
184C2×C3×C4D3×D412yes—
185C2×Dic3—22no—
186C2×Dic3—22no—
187C2×Dic3—32no—
188C2×Dic3—32no—
189C2×Dic3—32no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C4×D3—34no—
194C4×D3—34no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—68no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—121no—
201C4×D3—121no—
202C4×D3—124no—
203C4×D3—122no—
204C4×D3—122no—
205Dic6—22no—
206Dic6—68no—
207Dic6D3×C814yes—
208C3×C8—42no—
209C3×C8—42no—
210C3×C8—122no—
211C3⋊C8—42no—
212C3⋊C8—122no—
213C3⋊C8—122no—
214C2×C32C2×C22⋊C811yescharacteristic
215C2×C32#41911yescharacteristic
216C2×C32#42111yescharacteristic
217C3⋊D3—22no—
218C2×Q8—32no—
219C2×Q8—94no—
220C2×Q8—181no—
221C2×Q8—182no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—181no—
226C22×C4—181no—
227C2×C8—21no—
228C2×C8—62no—
229C2×C8—181no—
230C4⋊C4—32no—
231C4⋊C4—62no—
232C4⋊C4—181no—
233C4⋊C4—182no—
234C42—62no—
235C42—91no—
236C42—91no—
237C42—91no—
238C42—182no—
239C42C2×D3211yescharacteristic
240C22×C3—21no—
241C22×C3D3×C22⋊C412yes—
242C2×D3—34no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—121no—
247C2×D3—121no—
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—41no—
254C3×C4—64no—
255C3×C4—122no—
256C3×C4C2×D3×C812yes—
257C3×C4D3×M1612yes—
258C3×C4#91512yes—
259C3×C4#91812yes—
260Dic3—24no—
261Dic3—34no—
262Dic3—42no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—121no—
268C32#147911yescharacteristic, complemented, Sylow
269C23—91no—
270Q8—34no—
271Q8—62no—
272Q8—184no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—92no—
277C2×C4—92no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—184no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—361no—
284C2×C4—362no—
285C2×C4C4×D3211yescharacteristic
286C2×C4#380211yescharacteristic
287C2×C4#381111yescharacteristic
288C8—41no—
289C8—122no—
290C8—361no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3D3×C22⋊C812yes—
295C2×C3#480212yes—
296C2×C3#482112yes—
297D3—64no—
298D3—122no—
299C22—92no—
300C22—181no—
301C22—181no—
302C22#6392111yescharacteristic
303C4—21no—
304C4—64no—
305C4—92no—
306C4—122no—
307C4—181no—
308C4—181no—
309C4D32×C811yescharacteristic
310C4#6379111yescharacteristic
311C4#6393111yescharacteristic
312C4#6394511yescharacteristic
313C3—21no—
314C3#6823112yescomplemented
315C2—182no—
316C2#1059060211yescharacteristic
317C2#1059093511yescharacteristic
318C2#1059100911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4484C2semidirect
5. #10589084C2semidirect
29. #4484D3semidirect
39. #3797C8semidirect
268. C32#1479semidirect
314. C3#68231semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105925322
#105902972
C3×#44842
#105890842
#682313