Finite Group Databasebeta

← #11775094

Subgroups — #11775094

Order 1152.

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

normal subgroups only

This group has 539 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#10592417C211yesmaximal, characteristic
3#10591257C211yesmaximal, characteristic
4C3×#4467C212yesmaximal
5#10589153C212yesmaximal
6#68309—32nomaximal
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#924C2212yes—
9#63982—21no—
10C2×#3724—21no—
11#63957—21no—
12C2×Dic32—21no—
13#63919C411yescharacteristic, complemented
14#63873C411yescharacteristic, complemented
15#63870—21no—
16#63843C412yescomplemented
17#63838—21no—
18C32×C22⋊C8C2211yescharacteristic
19#63657C2211yescharacteristic
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C3×C3⋊#95C2212yes—
23#5622—32no—
24#4718—32no—
25#4718—61no—
26#4649—32no—
27C3×#328—32no—
28#4538—32no—
29#4467D312yes—
30#4452—32no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3×Dic3—22no—
35C2×C3×Dic6C2×C412yes—
36C2×#627—21no—
37C2×C32×C8—21no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)—21no—
43C3×#217—22no—
44C3×C4⋊Dic3C2×C412yes—
45C3×Dic3⋊C4—22no—
46#3724—24no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50Dic3⋊Dic3—22no—
51Dic32—22no—
52Dic32—42no—
53#1503—91noSylow
54C3×C22⋊Q8—32no—
55Q8×Dic3—32no—
56#944—32no—
57#924C2×D312yes—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—62no—
62#889—62no—
63#888—32no—
64#887—32no—
65#887—62no—
66#878—62no—
67#877—62no—
68C3×C22⋊C8—21no—
69C3×C22⋊C8C2×D312yes—
70C3×#95—32no—
71C3⋊#95C2×D312yes—
72#830—32no—
73#830—61no—
74Dic3⋊C8—62no—
75Dic3⋊C8—62no—
76C8×Dic3—62no—
77C8×Dic3—62no—
78C23×C32C2×D411yescharacteristic
79C2×C32×C4—41no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3SD1612yes—
88C2×C3⋊Dic3Q1612yes—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C3×Dic6—42no—
95#627—42no—
96C32×C8—41no—
97C3⋊(C3⋊C8)—41no—
98#533—91no—
99#431—91no—
100C4×C4⋊C4—91no—
101#328—32no—
102#328—92no—
103C2×C3×Q8—32no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C22×C3×C4C22×D312yes—
107C22×Dic3—22no—
108C22×Dic3—32no—
109C22×Dic3—32no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C2×Dic6—62no—
113C2×Dic6C4×D312yes—
114C2×C3×C8—22no—
115C2×C3×C8—22no—
116C3×C4⋊C4—32no—
117C3×C4⋊C4—62no—
118C3×C22⋊C4—62no—
119#217—22no—
120C4⋊Dic3—62no—
121C4⋊Dic3C4×D312yes—
122Dic3⋊C4—22no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127Dic3⋊C4—68no—
128C4×Dic3—32no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C4×Dic3—32no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C4×Dic3—124no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32C2×C22⋊C411yescharacteristic
144C22×C32C2×SD1611yescharacteristic
145C22×C32C2×Q1611yescharacteristic
146C32×C4—21no—
147C32×C4—21no—
148C3⋊Dic3—21no—
149C3⋊Dic3#10312yes—
150C3⋊Dic3#10312yes—
151C3⋊Dic3#10412yes—
152C3×Dic3—44no—
153C3×Dic3—42no—
154C3×Dic3—42no—
155C4⋊Q8—91no—
156C4⋊Q8—91no—
157#125—181no—
158C22⋊Q8—32no—
159C22⋊Q8—181no—
160C4×Q8—92no—
161C4×Q8—181no—
162#117—181no—
163C2×C4⋊C4—181no—
164C2×C42—91no—
165C2×C42—181no—
166C4⋊C8—181no—
167C22⋊C8—91no—
168C22⋊C8D3211yescharacteristic
169C4×C8—181no—
170#95—32no—
171C23×C3—21no—
172C23×C3D3×D412yes—
173C3×Q8—122no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—64no—
179C2×C3×C4—62no—
180C2×C3×C4—62no—
181C2×C3×C4—122no—
182C2×C3×C4—122no—
183C2×C3×C4C2×C4×D312yes—
184C2×C3×C4D3×D412yes—
185C2×Dic3—24no—
186C2×Dic3—22no—
187C2×Dic3—22no—
188C2×Dic3—32no—
189C2×Dic3—32no—
190C2×Dic3—32no—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—32no—
194C2×Dic3—42no—
195C2×Dic3—42no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202C2×Dic3—64no—
203C2×Dic3—122no—
204Dic6—42no—
205Dic6—124no—
206C3×C8—42no—
207C3×C8—42no—
208C3⋊C8—122no—
209C3⋊C8—122no—
210C2×C32—21no—
211C2×C32—21no—
212C2×C32#41011yescharacteristic
213C2×C32C2×#10311yescharacteristic
214C2×C32C2×#10411yescharacteristic
215C2×Q8—32no—
216C2×Q8—181no—
217C22×C4—62no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4C2×D3211yescharacteristic
221C2×C8—21no—
222C2×C8—181no—
223C4⋊C4—32no—
224C4⋊C4—62no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—182no—
228C4⋊C4—181no—
229C4⋊C4—184no—
230C22⋊C4—62no—
231C42—91no—
232C42—91no—
233C42—91no—
234C42—91no—
235C42—182no—
236C42—362no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3D3×C22⋊C412yes—
245C22×C3D3×SD1612yes—
246C22×C3D3×Q1612yes—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—41no—
251C3×C4—124no—
252C3×C4—122no—
253C3×C4—122no—
254Dic3—34no—
255Dic3—34no—
256Dic3—34no—
257Dic3—44no—
258Dic3—42no—
259Dic3—42no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—121no—
265C32#150311yescharacteristic, complemented, Sylow
266C23#380211yescharacteristic
267Q8—122no—
268Q8—362no—
269C2×C4—41no—
270C2×C4—64no—
271C2×C4—62no—
272C2×C4—62no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—122no—
280C2×C4—122no—
281C2×C4—182no—
282C2×C4C4×D3211yescharacteristic
283C2×C4#381111yescharacteristic
284C8—41no—
285C8—361no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—41no—
292C2×C3—41no—
293C2×C3#474012yes—
294C2×C3D3×#10312yes—
295C2×C3D3×#10412yes—
296C22—21no—
297C22—21no—
298C22#6379611yescharacteristic
299C22#6380211yescharacteristic
300C22#6392111yescharacteristic
301C4—21no—
302C4—21no—
303C4—92no—
304C4—92no—
305C4—92no—
306C4—124no—
307C4—122no—
308C4—122no—
309C4—181no—
310C3—21no—
311C3#6830912yescomplemented
312C2—21no—
313C2—21no—
314C2#1059040611yescharacteristic
315C2#1059067211yescharacteristic
316C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

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

Maximal subgroups

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

subgroupindex
#105948102
#105924172
#105912572
C3×#44672
#105891532
#683093