Finite Group Databasebeta

← #11775603

Subgroups — #11775603

Order 1152.

610 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C2×#63778C211yesmaximal, characteristic
4#10590215C212yesmaximal, complemented
5#10590158C212yesmaximal, complemented
6C2×Q8×C3⋊D3C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C22×#622—21no—
10C2×C4⋊#157—21no—
11C32×C22⋊Q8C411yescharacteristic, complemented
12#64155C2211yescharacteristic
13#64133C411yescharacteristic, complemented
14#64106C2211yescharacteristic
15#64105—21no—
16C4⋊C4×C3⋊D3—21no—
17C4⋊C4×C3⋊D3C411yescharacteristic, complemented
18C22⋊C4×C3⋊D3—21no—
19#64087—21no—
20#63781C2212yes—
21#63778—21no—
22#63778C2212yes—
23D3×C22⋊Q8—62no—
24C23×C3⋊D3D411yescharacteristic
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29Q8×C3⋊D3—42no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—42no—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634—21no—
38C2×#634C2×C411yescharacteristic
39C22⋊#157—42no—
40C2×#622—22no—
41C2×#622—42no—
42C4⋊#157—42no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C22⋊C4—21no—
46#3757—21no—
47#3752—21no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C411yescharacteristic
51#3750—21no—
52#3750—21no—
53#3750—21no—
54#1520—91nomaximal, Sylow
55C2×D3×Q8—62no—
56C22×C4×D3—62no—
57C3×C22⋊Q8—22no—
58#946—62no—
59#924—62no—
60#897—62no—
61#896—64no—
62D3×C4⋊C4—62no—
63D3×C4⋊C4—64no—
64D3×C22⋊C4—64no—
65#878—64no—
66C23×C32C22⋊C411yescharacteristic
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3C22⋊C411yescharacteristic
70C22×C3⋊D3SD1612yes—
71C22×C3⋊D3Q1612yes—
72C22×C3⋊D3C2×D411yescharacteristic
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C32×Q8—41no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C4×C3⋊D3—22no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3—42no—
93#634—42no—
94#634—41no—
95#622—42no—
96C2×C22⋊Q8—91no—
97C2×C22⋊C8—91no—
98#380—91no—
99#328—92no—
100#328—92no—
101C23×D3—62no—
102C2×C3×Q8—22no—
103C22×C3×C4—22no—
104C22×Dic3—62no—
105D3×Q8—128no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—128no—
113C2×Dic6—62no—
114C2×Dic6—64no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—22no—
117C3×C22⋊C4—24no—
118#217—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—64no—
121C4⋊Dic3—62no—
122C4⋊Dic3—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32#10312yes—
129C22×C32C2×C22⋊C411yescharacteristic
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—42no—
135C2×C3⋊D3—42no—
136C2×C3⋊D3#10312yes—
137C2×C3⋊D3C2×SD1611yescharacteristic
138C2×C3⋊D3C2×Q1611yescharacteristic
139#157—82no—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—41no—
143C32×C4—41no—
144C3⋊Dic3—21no—
145C3⋊Dic3—41no—
146C3⋊Dic3—41no—
147C3⋊Dic3#9912yes—
148C22×Q8—91no—
149C23×C4—91no—
150C22×C8—181no—
151C22⋊Q8—91no—
152C22⋊Q8—91no—
153C22⋊Q8—91no—
154C22⋊Q8—181no—
155C22⋊Q8—181no—
156C22⋊Q8#15711yescharacteristic, complemented
157C2×C4⋊C4—91no—
158C2×C4⋊C4—181no—
159C2×C4⋊C4—181no—
160C2×C22⋊C4—181no—
161C2×C22⋊C4—181no—
162C22⋊C8—92no—
163C22⋊C8—181no—
164#95—92no—
165C23×C3—22no—
166C22×D3—62no—
167C22×D3—64no—
168C22×D3—64no—
169C22×D3—62no—
170C22×D3—124no—
171C22×D3—124no—
172C3×Q8—44no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—44no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—124no—
183C4×D3—68no—
184C4×D3—124no—
185C4×D3—124no—
186C4×D3—128no—
187C4×D3—124no—
188C4×D3—128no—
189Dic6—128no—
190Dic6—124no—
191C2×C32—22no—
192C2×C32C2×#9911yescharacteristic
193C2×C32C2×#10311yescharacteristic
194C2×C32#42111yescharacteristic
195C3⋊D3—22no—
196C3⋊D3—21no—
197C3⋊D3—21no—
198C24—91no—
199C2×Q8—91no—
200C2×Q8—181no—
201C2×Q8—362no—
202C2×Q8C2×#15711yescharacteristic
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—182no—
211C22×C4—362no—
212C22×C4C2×#15711yescharacteristic
213C2×C8—182no—
214C2×C8—362no—
215C4⋊C4—21no—
216C4⋊C4—91no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—362no—
222C4⋊C4C2×#15711yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—181no—
225C22⋊C4—181no—
226C22⋊C4—181no—
227C22⋊C4—362no—
228C22×C3—22no—
229C22×C3—24no—
230C22×C3—42no—
231C22×C3—42no—
232C2×D3—64no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—64no—
236C2×D3—64no—
237C2×D3—122no—
238C2×D3—122no—
239C2×D3—128no—
240C2×D3—128no—
241C3×C4—24no—
242C3×C4—42no—
243C3×C4—44no—
244C3×C4—44no—
245Dic3—64no—
246Dic3—122no—
247Dic3—124no—
248Dic3—124no—
249C32#152011yescharacteristic, complemented, Sylow
250C23—91no—
251C23—91no—
252C23—92no—
253C23—92no—
254C23—361no—
255C23—361no—
256C23C22⋊#15711yescharacteristic
257Q8—41no—
258Q8—361no—
259Q8—362no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4—362no—
273C2×C4—362no—
274C2×C4—362no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4C22⋊#15711yescharacteristic
278C2×C4C22×#15711yescharacteristic
279C8—362no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—44no—
284D3—68no—
285D3—122no—
286D3—122no—
287C22—21no—
288C22—21no—
289C22—91no—
290C22—92no—
291C22—91no—
292C22—181no—
293C22—181no—
294C22—181no—
295C22—181no—
296C22—362no—
297C22—362no—
298C22#6378412yes—
299C22C2×C22⋊#15711yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—92no—
305C4—181no—
306C4—361no—
307C4—361no—
308C4—722no—
309C3—22no—
310C2—22no—
311C2—181no—
312C2—182no—
313C2—181no—
314C2#1059381711yescharacteristic
315C2C2×#6378411yescharacteristic
316C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊Q8#157
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10590215C2semidirect
5. #10590158C2semidirect
6. C2×Q8×C3⋊D3C4semidirect
11. C32×C22⋊Q8C4semidirect
13. #64133C4semidirect
17. C4⋊C4×C3⋊D3C4semidirect
156. C22⋊Q8#157semidirect
249. C32#1520semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105938122
C2×#637782
#105902152
#105901582
#15209