Finite Group Databasebeta

← #11775087

Subgroups — #11775087

Order 1152.

577 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 577 conjugacy classes of subgroups — too many to draw. Only its 100 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
1#10594810C211yesmaximal, characteristic
2#10592348C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C3×#4452C212yesmaximal
5#10589152C212yesmaximal
6#68309—32nomaximal
7C2×#3750—21no—
8C2×C4×C3⋊Dic3—21no—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C3×#924C2212yes—
11#63982—21no—
12#63957—21no—
13#63919C411yescharacteristic, complemented
14#63873C411yescharacteristic, complemented
15#63870—21no—
16#63843C412yescomplemented
17#63838—21no—
18C32×#95C2211yescharacteristic
19#63658C2211yescharacteristic
20C3×#830C2212yes—
21#63572—21no—
22#63553—21no—
23#5622—32no—
24#4718—32no—
25#4649—32no—
26#4649—61no—
27C3×#328—32no—
28#4538—32no—
29#4467—32no—
30#4452D312yes—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C3×Dic6C2×C412yes—
37C2×#627—21no—
38#3750—24no—
39C4×C3⋊Dic3—42no—
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C3×#217—22no—
45C3×C4⋊Dic3C2×C412yes—
46C3×Dic3⋊C4—22no—
47C2×C3×C3⋊C8—22no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51Dic3⋊Dic3—22no—
52Dic32—22no—
53#1503—91noSylow
54C3×C22⋊Q8—32no—
55Q8×Dic3—32no—
56#944—32no—
57#924C2×D312yes—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—62no—
63C2×C4×Dic3—62no—
64#889—62no—
65#888—32no—
66#887—32no—
67#887—62no—
68#878—62no—
69#877—62no—
70C3×C22⋊C8—32no—
71C3×#95—21no—
72C3×#95C2×D312yes—
73C3⋊#95—32no—
74C3⋊#95—61no—
75#830C2×D312yes—
76Dic3⋊C8—62no—
77C8×Dic3—62no—
78C23×C32C2×D411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3SD1612yes—
94C2×C3⋊Dic3Q1612yes—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C3×Dic6—42no—
98#627—42no—
99C3×C3⋊C8—42no—
100#533—91no—
101#431—91no—
102C4×C4⋊C4—91no—
103#328—32no—
104#328—92no—
105C2×C3×Q8—32no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4C22×D312yes—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×Dic6—62no—
117C2×Dic6C4×D312yes—
118C2×C3×C8—62no—
119C3×C4⋊C4—32no—
120C3×C4⋊C4—62no—
121C3×C22⋊C4—62no—
122#217—22no—
123C4⋊Dic3—62no—
124C4⋊Dic3C4×D312yes—
125Dic3⋊C4—22no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129Dic3⋊C4—62no—
130Dic3⋊C4—68no—
131Dic3⋊C4—68no—
132C4×Dic3—32no—
133C4×Dic3—32no—
134C4×Dic3—32no—
135C4×Dic3—32no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—62no—
141C4×Dic3—62no—
142C4×Dic3—124no—
143C4×Dic3—124no—
144C2×C3⋊C8—22no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C2×SD1611yescharacteristic
149C22×C32C2×Q1611yescharacteristic
150C32×C4—21no—
151C32×C4—21no—
152C32×C4—42no—
153C3⋊Dic3—21no—
154C3⋊Dic3—42no—
155C3⋊Dic3#10312yes—
156C3⋊Dic3#10312yes—
157C3⋊Dic3#10412yes—
158C3×Dic3—42no—
159C3×Dic3—42no—
160C4⋊Q8—91no—
161C4⋊Q8—91no—
162#125—181no—
163C22⋊Q8—32no—
164C22⋊Q8—181no—
165C4×Q8—92no—
166C4×Q8—181no—
167#117—181no—
168C2×C4⋊C4—181no—
169C2×C42—91no—
170C2×C42—181no—
171C4⋊C8—181no—
172C22⋊C8—32no—
173C4×C8—181no—
174#95—91no—
175#95D3211yescharacteristic
176C23×C3—21no—
177C23×C3D3×D412yes—
178C3×Q8—122no—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4—42no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4C2×C4×D312yes—
192C2×C3×C4D3×D412yes—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—32no—
196C2×Dic3—32no—
197C2×Dic3—32no—
198C2×Dic3—34no—
199C2×Dic3—34no—
200C2×Dic3—32no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—122no—
214C2×Dic3—122no—
215Dic6—42no—
216Dic6—124no—
217C3×C8—122no—
218C3⋊C8—42no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32#41011yescharacteristic
222C2×C32C2×#10311yescharacteristic
223C2×C32C2×#10411yescharacteristic
224C2×Q8—32no—
225C2×Q8—181no—
226C22×C4—21no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—181no—
230C22×C4C2×D3211yescharacteristic
231C2×C8—62no—
232C4⋊C4—32no—
233C4⋊C4—62no—
234C4⋊C4—184no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—182no—
238C4⋊C4—181no—
239C22⋊C4—62no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42—91no—
244C42—182no—
245C42—362no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3D3×C22⋊C412yes—
254C22×C3D3×SD1612yes—
255C22×C3D3×Q1612yes—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—44no—
261C3×C4—44no—
262C3×C4—122no—
263C3×C4—122no—
264Dic3—34no—
265Dic3—34no—
266Dic3—34no—
267Dic3—42no—
268Dic3—42no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—124no—
275Dic3—124no—
276C32#150311yescharacteristic, complemented, Sylow
277C23#381111yescharacteristic
278Q8—122no—
279Q8—362no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—62no—
285C2×C4—62no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—92no—
290C2×C4—92no—
291C2×C4—91no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4C4×D3211yescharacteristic
297C2×C4#380211yescharacteristic
298C8—122no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3#474012yes—
307C2×C3D3×#10312yes—
308C2×C3D3×#10412yes—
309C22—21no—
310C22—21no—
311C22#6392111yescharacteristic
312C22#6393011yescharacteristic
313C22#6394411yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—92no—
318C4—92no—
319C4—92no—
320C4—122no—
321C4—122no—
322C4—181no—
323C4—362no—
324C3—21no—
325C3#6830912yescomplemented
326C2—21no—
327C2—21no—
328C2#1059039311yescharacteristic
329C2#1059040611yescharacteristic
330C2#1059060111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
13. #63919C4semidirect
14. #63873C4semidirect
16. #63843C4semidirect
276. C32#1503semidirect
325. C3#68309semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105923482
#105910612
C3×#44522
#105891522
#683093