Finite Group Databasebeta

← #11775187

Subgroups — #11775187

Order 1152.

511 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 511 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592418C211yesmaximal, characteristic
3#10591252C211yesmaximal, characteristic
4C3×#4467C212yesmaximal
5#10589153C212yesmaximal
6#68310—32nomaximal
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#924C2212yes—
9#63982—21no—
10#63957—21no—
11C2×Dic32—21no—
12#63919C411yescharacteristic, complemented
13#63873C411yescharacteristic, complemented
14#63870—21no—
15#63843C412yescomplemented
16#63838—21no—
17C32×C22⋊C8C2211yescharacteristic
18#63657C2211yescharacteristic
19#63642—21no—
20#63641—21no—
21C3×C3⋊#95C2212yes—
22#63579—21no—
23#5622—32no—
24#4719—32no—
25#4719—61no—
26#4648—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—21no—
47#3724—21no—
48#3724—21no—
49Dic3⋊Dic3—22no—
50Dic32—24no—
51Dic32—22no—
52#1506—91noSylow
53C3×C22⋊Q8—32no—
54Q8×Dic3—32no—
55#944—32no—
56#924C2×D312yes—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—62no—
60#889—62no—
61#888—32no—
62#887—32no—
63#887—62no—
64#878—62no—
65#877—62no—
66C3×C22⋊C8—21no—
67C3×C22⋊C8C2×D312yes—
68C3×#95—32no—
69C3⋊#95—62no—
70C3⋊#95C2×D312yes—
71#830—32no—
72#830—61no—
73#815—62no—
74#815—62no—
75Dic3⋊C8—62no—
76Dic3⋊C8—62no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4—41no—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3×Dic3—24no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×Dic6—42no—
93#627—42no—
94C32×C8—41no—
95C3⋊(C3⋊C8)—41no—
96#533—91no—
97#432—91no—
98#376—91no—
99#328—32no—
100#328—92no—
101C2×C3×Q8—32no—
102C22×C3×C4—21no—
103C22×C3×C4—62no—
104C22×C3×C4C22×D312yes—
105C22×Dic3—22no—
106C22×Dic3—32no—
107C22×Dic3—32no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C2×Dic6—62no—
111C2×Dic6C4×D312yes—
112C2×C3×C8—22no—
113C2×C3×C8—22no—
114C3×C4⋊C4—32no—
115C3×C4⋊C4—62no—
116C3×C22⋊C4—62no—
117#217—22no—
118C4⋊Dic3—62no—
119C4⋊Dic3C4×D312yes—
120Dic3⋊C4—22no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—32no—
128C4×Dic3—32no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C4×Dic3—68no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32#13712yes—
142C32×C4—21no—
143C32×C4—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3#10412yes—
148C3×Dic3—44no—
149C3×Dic3—42no—
150C3×Dic3—42no—
151C4⋊Q8—91no—
152C4⋊Q8—91no—
153#125—181no—
154C22⋊Q8—32no—
155C22⋊Q8—181no—
156C4×Q8—92no—
157C4×Q8—181no—
158#117—181no—
159C2×C42—91no—
160C2×C42—181no—
161C4⋊C8—181no—
162C22⋊C8—91no—
163C22⋊C8D3211yescharacteristic
164#97—181no—
165#95—32no—
166#95—181no—
167C23×C3—21no—
168C23×C3D3×D412yes—
169C3×Q8—122no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—42no—
173C2×C3×C4—42no—
174C2×C3×C4—64no—
175C2×C3×C4—62no—
176C2×C3×C4—62no—
177C2×C3×C4—122no—
178C2×C3×C4—122no—
179C2×C3×C4C2×C4×D312yes—
180C2×C3×C4D3×D412yes—
181C2×Dic3—24no—
182C2×Dic3—22no—
183C2×Dic3—22no—
184C2×Dic3—32no—
185C2×Dic3—32no—
186C2×Dic3—32no—
187C2×Dic3—32no—
188C2×Dic3—42no—
189C2×Dic3—42no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—64no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199Dic6—42no—
200Dic6—124no—
201C3×C8—42no—
202C3×C8—42no—
203C3⋊C8—122no—
204C3⋊C8—122no—
205C2×C32—22no—
206C2×C32#41011yescharacteristic
207C2×C32#41911yescharacteristic
208C2×C32C2×#10411yescharacteristic
209C2×Q8—32no—
210C2×Q8—181no—
211C22×C4—62no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4C2×D3211yescharacteristic
215C2×C8—21no—
216C2×C8—181no—
217C4⋊C4—32no—
218C4⋊C4—62no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—182no—
222C4⋊C4—181no—
223C22⋊C4—62no—
224C42—91no—
225C42—91no—
226C42—91no—
227C42—91no—
228C42—182no—
229C42—184no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—41no—
235C22×C3—41no—
236C22×C3D3×C22⋊C412yes—
237C22×C3#91512yes—
238C22×C3#91812yes—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—41no—
243C3×C4—124no—
244C3×C4—122no—
245C3×C4—122no—
246Dic3—34no—
247Dic3—44no—
248Dic3—42no—
249Dic3—42no—
250Dic3—62no—
251Dic3—62no—
252Dic3—62no—
253Dic3—62no—
254Dic3—121no—
255Dic3—121no—
256Dic3—121no—
257C32#150611yescharacteristic, complemented, Sylow
258C23#380211yescharacteristic
259Q8—122no—
260Q8—362no—
261C2×C4—41no—
262C2×C4—64no—
263C2×C4—62no—
264C2×C4—62no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—122no—
270C2×C4—122no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4C4×D3211yescharacteristic
274C2×C4#381111yescharacteristic
275C8—41no—
276C8—361no—
277C2×C3—22no—
278C2×C3—22no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—42no—
283C2×C3#474012yes—
284C2×C3#480212yes—
285C2×C3D3×#10412yes—
286C22—21no—
287C22—21no—
288C22#6381112yes—
289C22#6392111yescharacteristic
290C4—21no—
291C4—21no—
292C4—92no—
293C4—124no—
294C4—122no—
295C4—122no—
296C4—181no—
297C4—181no—
298C4—181no—
299C3—21no—
300C3#6831012yescomplemented
301C2—22no—
302C2#1059040611yescharacteristic
303C2#1059069111yescharacteristic
304C2#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#1506
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
12. #63919C4semidirect
13. #63873C4semidirect
15. #63843C4semidirect
257. C32#1506semidirect
300. C3#68310semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105924182
#105912522
C3×#44672
#105891532
#683103