Finite Group Databasebeta

← #11775576

Subgroups — #11775576

Order 1152.

766 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#64104C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic, complemented
3#10593800C211yesmaximal, characteristic, complemented
4#10590157C214yesmaximal, complemented
5C22×C4⋊(C3⋊D3)—21no—
6C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×#3787—21no—
11C2×C32×C4⋊C4C411yescharacteristic, complemented
12C2×#3752—21no—
13#64104—21no—
14#64104—21no—
15#64104C412yescomplemented
16#64104C2212yes—
17C22⋊#622—21no—
18#63781C2212yescomplemented
19#63778C2212yescomplemented
20C2×#895—62no—
21C23×C3⋊D3—21no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—22no—
24C22×C32×C4—21no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)—42no—
31C2×C4⋊(C3⋊D3)—42no—
32C2×C4⋊(C3⋊D3)—42no—
33C2×C4⋊(C3⋊D3)C2×C412yes—
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C22⋊#157—42no—
40C2×#622—22no—
41C4⋊#157—42no—
42#3787—42no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45#3752—22no—
46#3752—22no—
47#1519—91nomaximal, Sylow
48C22×D12—62no—
49C22×D12—64no—
50C22×C4×D3—62no—
51C2×C3×C4⋊C4—22no—
52C2×(C2×D3)⋊C4—64no—
53#895—64no—
54#895—64no—
55#895—64no—
56#895—64no—
57C23×C32C22⋊C411yescharacteristic
58C22×C3⋊D3—22no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3—41no—
61C22×C3⋊D3—42no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3—42no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C22×C3⋊D3D812yes—
66C22×C3⋊D3SD1612yes—
67C22×C3⋊D3C2×D411yescharacteristic
68C2×#157—42no—
69C2×#157—42no—
70C2×#157—42no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—42no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22×C411yescharacteristic
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4⋊(C3⋊D3)—42no—
80C4⋊(C3⋊D3)—44no—
81C4⋊(C3⋊D3)—42no—
82C4⋊(C3⋊D3)—42no—
83C4⋊(C3⋊D3)—42no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—41no—
88#622—42no—
89C2×#121—91no—
90C2×C22⋊C8—91no—
91#380—91no—
92#327—94no—
93C23×D3—62no—
94C23×D3—64no—
95C22×C3×C4—24no—
96C22×C3×C4—22no—
97C22×Dic3—62no—
98C2×D12—64no—
99C2×D12—68no—
100C2×D12—68no—
101C2×D12—64no—
102C2×D12—128no—
103C2×D12—128no—
104C2×D12—128no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—128no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—24no—
112(C2×D3)⋊C4—68no—
113(C2×D3)⋊C4—68no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32#10212yes—
117C22×C32C2×C22⋊C411yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3—42no—
125C2×C3⋊D3—42no—
126C2×C3⋊D3—42no—
127C2×C3⋊D3—84no—
128C2×C3⋊D3#10212yes—
129C2×C3⋊D3C2×D811yescharacteristic
130C2×C3⋊D3C2×SD1611yescharacteristic
131#157—82no—
132C32×C4—21no—
133C32×C4—42no—
134C32×C4#9912yes—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C22×D4—91no—
138C22×D4—181no—
139C23×C4—91no—
140C22×C8—181no—
141#121—92no—
142#121—92no—
143#121—181no—
144#121—181no—
145C2×C4⋊C4—181no—
146C2×C4⋊C4#15711yescharacteristic, complemented
147C2×C22⋊C4—181no—
148C2×C22⋊C4—181no—
149C22⋊C8—92no—
150C22⋊C8—181no—
151#95—92no—
152C23×C3—22no—
153C22×D3—62no—
154C22×D3—64no—
155C22×D3—64no—
156C22×D3—62no—
157C22×D3—68no—
158C22×D3—124no—
159C22×D3—124no—
160C22×D3—128no—
161C22×D3—128no—
162C22×D3—128no—
163C2×C3×C4—28no—
164C2×C3×C4—28no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—48no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—124no—
171D12—128no—
172D12—128no—
173D12—1216no—
174D12—128no—
175D12—128no—
176C4×D3—124no—
177C4×D3—124no—
178C4×D3—124no—
179C4×D3—124no—
180C2×C32—22no—
181C2×C32C2×#9911yescharacteristic
182C2×C32C2×#10211yescharacteristic
183C2×C32#42111yescharacteristic
184C3⋊D3—21no—
185C3⋊D3—22no—
186C3⋊D3—21no—
187C3⋊D3—82no—
188C24—91no—
189C24—181no—
190C2×D4—92no—
191C2×D4—182no—
192C2×D4—182no—
193C2×D4—181no—
194C2×D4—362no—
195C2×D4—362no—
196C2×D4—362no—
197C22×C4—21no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—182no—
204C22×C4—362no—
205C22×C4C2×#15711yescharacteristic
206C2×C8—182no—
207C2×C8—362no—
208C4⋊C4—21no—
209C4⋊C4—362no—
210C4⋊C4C2×#15712yes—
211C22⋊C4—182no—
212C22⋊C4—182no—
213C22⋊C4—362no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3—22no—
217C22×C3—24no—
218C2×D3—64no—
219C2×D3—62no—
220C2×D3—62no—
221C2×D3—122no—
222C2×D3—122no—
223C2×D3—122no—
224C2×D3—122no—
225C2×D3—128no—
226C2×D3—128no—
227C2×D3—128no—
228C2×D3—128no—
229C2×D3—128no—
230C2×D3—2416no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—48no—
234Dic3—122no—
235Dic3—122no—
236C32#151911yescharacteristic, complemented, Sylow
237C23—91no—
238C23—91no—
239C23—92no—
240C23—92no—
241C23—182no—
242C23—361no—
243C23—361no—
244C23—362no—
245C23—362no—
246C23—362no—
247C23C22⋊#15711yescharacteristic
248D4—362no—
249D4—362no—
250D4—362no—
251D4—364no—
252D4—362no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4—362no—
264C2×C4—362no—
265C2×C4—362no—
266C2×C4C22⋊#15711yescharacteristic
267C2×C4C22×#15711yescharacteristic
268C8—362no—
269C2×C3—28no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273D3—122no—
274D3—124no—
275D3—122no—
276D3—248no—
277C22—21no—
278C22—21no—
279C22—91no—
280C22—91no—
281C22—92no—
282C22—181no—
283C22—181no—
284C22—181no—
285C22—181no—
286C22—362no—
287C22—362no—
288C22—362no—
289C22—362no—
290C22—362no—
291C22—724no—
292C22#6378212yes—
293C22C2×C22⋊#15711yescharacteristic
294C4—21no—
295C4—42no—
296C4—181no—
297C4—181no—
298C4—722no—
299C4#6377412yes—
300C3—22no—
301C2—22no—
302C2—181no—
303C2—181no—
304C2—182no—
305C2—722no—
306C2C2×#6377411yescharacteristic
307C2C2×#6378211yescharacteristic
308C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64104C2
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593812C2semidirect
3. #10593800C2semidirect
4. #10590157C2semidirect
6. C22×C4⋊(C3⋊D3)C4semidirect
11. C2×C32×C4⋊C4C4semidirect
15. #64104C4semidirect
18. #63781C22semidirect
19. #63778C22semidirect
146. C2×C4⋊C4#157semidirect
236. C32#1519semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
#105938122
#105938002
#105901572
#15199