Finite Group Databasebeta

← #11802764

Subgroups — #11802764

Order 1152.

1346 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 1346 conjugacy classes of subgroups — too many to draw. Only its 162 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×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593847C212yesmaximal
3#10593812C212yesmaximal, complemented
4C4×C22⋊#157C212yesmaximal, complemented
5#10593747C218yesmaximal, complemented
6C24×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C2214yes—
10C2×C22⋊#157C2214yes—
11C2×C22⋊#157C2214yes—
12C2×C4⋊#157C2214yescomplemented
13C2×C4×#157C2214yescomplemented
14C2×C32×C22⋊C4C411yescharacteristic, complemented
15C2×#3757C411yescharacteristic, complemented
16C2×#3752C411yescharacteristic, complemented
17C2×#3752C411yescharacteristic, complemented
18C22⋊C4×C3⋊D3C414yescomplemented
19C22⋊C4×C3⋊D3C2214yes—
20#63781C2214yescomplemented
21#63781C2214yescomplemented
22C2×D3×C22⋊C4—62no—
23C24×C32C2×C411yescharacteristic
24C23×C3⋊D3—24no—
25C23×C3⋊D3—42no—
26C23×C3⋊D3—42no—
27C23×C3⋊D3C2×C412yes—
28C23×C3⋊D3C2×C411yescharacteristic
29C23×C3⋊D3C2312yes—
30C23×C3⋊D3C2311yescharacteristic
31C22×#157C2318yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3C2×C412yes—
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3C2312yes—
41C2×C4×C3⋊D3C2312yes—
42C22⋊#157—28no—
43C22⋊#157—44no—
44C22⋊#157—44no—
45C4⋊#157—44no—
46C4×#157—44no—
47C32×C22⋊C4C2×C414yes—
48#3757C2×C414yes—
49#3752C2×C414yes—
50#3752C2×C414yes—
51#2312—91nomaximal, Sylow
52C24×D3—62no—
53C22×C4×D3—62no—
54C22×C4×D3—62no—
55C2×C3×C22⋊C4—22no—
56C2×#217—62no—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59D3×C22⋊C4—68no—
60D3×C22⋊C4—68no—
61C23×C32—22no—
62C23×C32—41no—
63C23×C32—41no—
64C23×C32C22×C412yes—
65C23×C32C22×C411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3—22no—
69C22×C3⋊D3—24no—
70C22×C3⋊D3—24no—
71C22×C3⋊D3—24no—
72C22×C3⋊D3—24no—
73C22×C3⋊D3—42no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3—41no—
77C22×C3⋊D3—416no—
78C22×C3⋊D3C22×C412yes—
79C22×C3⋊D3C22×C411yescharacteristic
80C22×C3⋊D3#4114yes—
81C22×C3⋊D3C2411yescharacteristic
82C2×#157—28no—
83C2×#157—28no—
84C2×#157—28no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4C22×C412yes—
88C2×C32×C4C22×C412yes—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C22×C412yes—
92C2×C3⋊Dic3C22×C412yes—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—24no—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—42no—
97C22×C22⋊C4—91no—
98#388—98no—
99#380—92no—
100#379—92no—
101C4×C22⋊C4—92no—
102C24×C3—22no—
103C23×D3—62no—
104C23×D3—64no—
105C23×D3—62no—
106C23×D3—64no—
107C23×D3—616no—
108C23×D3—128no—
109C23×D3—128no—
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—128no—
119C2×C4×D3—128no—
120C3×C22⋊C4—28no—
121#217—68no—
122(C2×D3)⋊C4—68no—
123(C2×D3)⋊C4—68no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—22no—
127C22×C32—22no—
128C22×C32—22no—
129C22×C32—44no—
130C22×C32#11712yes—
131C22×C32C23×C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—28no—
135C2×C3⋊D3—22no—
136C2×C3⋊D3—22no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3—48no—
139C2×C3⋊D3—44no—
140C2×C3⋊D3—48no—
141C2×C3⋊D3#11712yes—
142C2×C3⋊D3C2×#4112yes—
143C2×C3⋊D3H(5,𝔽2)12yes—
144C2×C3⋊D3H(5,𝔽2)12yes—
145#157—48no—
146C32×C4—22no—
147C32×C4—22no—
148C3⋊Dic3—22no—
149C3⋊Dic3—22no—
150C25—91no—
151C23×C4—91no—
152C23×C4—91no—
153C2×C4⋊C4—94no—
154C2×C22⋊C4—91no—
155C2×C22⋊C4—91no—
156C2×C22⋊C4—91no—
157C2×C22⋊C4—94no—
158C2×C22⋊C4—94no—
159C2×C22⋊C4—94no—
160C2×C22⋊C4—94no—
161C2×C22⋊C4—94no—
162C2×C22⋊C4#15711yescharacteristic, complemented
163C2×C42—94no—
164#95—94no—
165#95—94no—
166C23×C3—28no—
167C23×C3—22no—
168C23×C3—24no—
169C23×C3—44no—
170C23×C3—44no—
171C22×D3—62no—
172C22×D3—68no—
173C22×D3—62no—
174C22×D3—64no—
175C22×D3—68no—
176C22×D3—68no—
177C22×D3—616no—
178C22×D3—616no—
179C22×D3—68no—
180C22×D3—128no—
181C22×D3—128no—
182C22×D3—128no—
183C22×D3—128no—
184C22×D3—1264no—
185C22×D3—124no—
186C22×D3—124no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—44no—
190C2×C3×C4—44no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—124no—
194C2×Dic3—124no—
195C4×D3—128no—
196C4×D3—128no—
197C4×D3—128no—
198C4×D3—128no—
199C2×C32—22no—
200C2×C32—42no—
201C2×C32C2×#11711yescharacteristic
202C2×C32#51811yescharacteristic
203C2×C32#51811yescharacteristic
204C3⋊D3—22no—
205C3⋊D3—42no—
206C3⋊D3#53814yes—
207C24—91no—
208C24—92no—
209C24—92no—
210C24—91no—
211C24—184no—
212C24—362no—
213C24—362no—
214C24C2×#15711yescharacteristic
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—92no—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—98no—
222C22×C4—362no—
223C22×C4—362no—
224C22×C4C2×#15711yescharacteristic
225C22×C4C2×#15711yescharacteristic
226C4⋊C4—364no—
227C22⋊C4—94no—
228C22⋊C4—94no—
229C22⋊C4—94no—
230C22⋊C4—188no—
231C22⋊C4—364no—
232C22⋊C4—364no—
233C22⋊C4C2×#15714yes—
234C42—364no—
235C22×C3—24no—
236C22×C3—24no—
237C22×C3—28no—
238C22×C3—24no—
239C22×C3—22no—
240C22×C3—44no—
241C22×C3—44no—
242C22×C3—416no—
243C2×D3—64no—
244C2×D3—64no—
245C2×D3—64no—
246C2×D3—64no—
247C2×D3—64no—
248C2×D3—64no—
249C2×D3—632no—
250C2×D3—68no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—1232no—
254C2×D3—1232no—
255C2×D3—1216no—
256C3×C4—44no—
257C3×C4—44no—
258Dic3—124no—
259Dic3—124no—
260C32#231211yescharacteristic, complemented, Sylow
261C23—22no—
262C23—41no—
263C23—41no—
264C23—91no—
265C23—94no—
266C23—91no—
267C23—92no—
268C23—182no—
269C23—182no—
270C23—184no—
271C23—184no—
272C23—184no—
273C23—184no—
274C23—182no—
275C23—361no—
276C23—361no—
277C23—362no—
278C23—362no—
279C23—3616no—
280C23C22×#15712yes—
281C23C22×#15711yescharacteristic
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—184no—
287C2×C4—184no—
288C2×C4—188no—
289C2×C4—188no—
290C2×C4—188no—
291C2×C4—362no—
292C2×C4—362no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4C22×#15712yes—
296C2×C4C22×#15712yes—
297C2×C3—28no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—48no—
302D3—68no—
303D3—68no—
304D3—128no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—44no—
311C22—92no—
312C22—92no—
313C22—92no—
314C22—92no—
315C22—188no—
316C22—181no—
317C22—181no—
318C22—182no—
319C22—182no—
320C22—182no—
321C22—364no—
322C22—368no—
323C22—368no—
324C22#6428612yes—
325C22C23×#15711yescharacteristic
326C4—22no—
327C4—22no—
328C4—182no—
329C4—182no—
330C4—368no—
331C3—22no—
332C2—22no—
333C2—42no—
334C2—94no—
335C2—182no—
336C2—362no—
337C2C2×#6428611yescharacteristic
338C2#1059664211yescharacteristic
339C2#1059664211yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C22⋊C4C4
prime radicalC24×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC2×C22⋊C4#157
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10593812C2semidirect
4. C4×C22⋊#157C2semidirect
5. #10593747C2semidirect
12. C2×C4⋊#157C22semidirect
13. C2×C4×#157C22semidirect
14. C2×C32×C22⋊C4C4semidirect
15. C2×#3757C4semidirect
16. C2×#3752C4semidirect
17. C2×#3752C4semidirect
18. C22⋊C4×C3⋊D3C4semidirect
20. #63781C22semidirect
21. #63781C22semidirect
162. C2×C22⋊C4#157semidirect
260. C32#2312semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
#105938472
#105938122
C4×C22⋊#1572
#105937472
#23129