Finite Group Databasebeta

← #14664394

Subgroups — #14664394

Order 2816.

516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#66898C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066640C214yesmaximal, complemented
4C11×#2542C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C11×C22⋊Q8—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#399C412yescomplemented
10C11×#399C2212yes—
11C11×#390—21no—
12C11×#384—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15C4×C22⋊Dic11—21no—
16#10622820—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C11×C22⋊Q8—44no—
27C11×C22⋊Q8—44no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C22⋊Dic11—22no—
43C2×C4×Dic11—41no—
44C2×#4318—41no—
45C11×#95C2×C412yes—
46#66898—24no—
47C11⋊#95—41no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—41no—
50#11788—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—41no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—42no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—44no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—44no—
83C11×C22⋊C4—44no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—42no—
87C22⋊Dic11—24no—
88C22⋊Dic11—42no—
89C4×Dic11—82no—
90#4318—82no—
91C2×C11⋊C8—42no—
92#2542D1111yescharacteristic
93C4×#99—111no—
94#1465—111no—
95#1352—114no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11#13712yes—
107Q8×C11—82no—
108Q8×C11—82no—
109D4×C11—44no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—24no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10412yes—
132C2×Dic11—44no—
133C2×Dic11—82no—
134C2×Dic11—82no—
135C11⋊C8—82no—
136C2×C4⋊Q8Dic1111yescharacteristic, complemented
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C4×D4C2×D1111yescharacteristic
140C2×#99—221no—
141#407—221no—
142#399Dic1112yescomplemented
143#399C2×D1112yes—
144#390—21no—
145#384—21no—
146C4×C4⋊C4Dic1111yescharacteristic, complemented
147C4×C22⋊C4—221no—
148#342—112no—
149#324—221no—
150#323—112no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—22no—
154C22×C11—42no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11C2×#9911yescharacteristic
164C22×C11#41911yescharacteristic
165C22×C11C2×#10411yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—82no—
173C4×C11#35312yes—
174Dic11—84no—
175C22×Q8—21no—
176C22×D4C22⋊D1111yescharacteristic
177C23×C4C22⋊D1111yescharacteristic
178C23×C4C22⋊D1111yescharacteristic
179C2×M16—441no—
180C4⋊Q8—41no—
181C4⋊Q8—41no—
182C22⋊Q8—44no—
183C22⋊Q8—44no—
184C4×D4—41no—
185C4×D4—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4C2×Dic1112yes—
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—222no—
195C2×C22⋊C4C2×Dic1111yescharacteristic
196C2×C22⋊C4C22×D1111yescharacteristic
197C2×C42—21no—
198C2×C42—441no—
199C2×C42C2×Dic1111yescharacteristic
200#99—224no—
201C22⋊C8—222no—
202C22⋊C8—441no—
203#95—441no—
204#95C2×Dic1112yes—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11—81no—
209C2×C11#150811yescharacteristic
210C2×C11#212311yescharacteristic
211C2×C11C2×#35311yescharacteristic
212C24C22⋊Dic1111yescharacteristic
213C24C2×C22⋊D1111yescharacteristic
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—442no—
230C22×C4C22⋊Dic1111yescharacteristic
231C22×C4C22⋊Dic1111yescharacteristic
232C22×C4C22⋊Dic1111yescharacteristic
233C22×C4C22×Dic1111yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235M16—882no—
236C2×C8—442no—
237C4⋊C4—24no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—44no—
241C4⋊C4—44no—
242C4⋊C4—42no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—44no—
246C22⋊C4—44no—
247C22⋊C4—224no—
248C22⋊C4—442no—
249C42—21no—
250C42—21no—
251C42—42no—
252C42—882no—
253C11#1178811yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23#6699512yes—
264C23C2×C22⋊Dic1111yescharacteristic
265Q8—82no—
266Q8—82no—
267D4—44no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—444no—
288C2×C4—882no—
289C2×C4—882no—
290C2×C4#6689811yescharacteristic
291C2×C4#6689811yescharacteristic
292C2×C4#6690112yes—
293C8—882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22—81no—
306C22C2×#6689811yescharacteristic
307C22#1062283811yescharacteristic
308C22C2×#6690111yescharacteristic
309C4—22no—
310C4—21no—
311C4—44no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—82no—
316C4—884no—
317C4#1062218312yes—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—81no—
322C2#1306713611yescharacteristic
323C2#1307027011yescharacteristic
324C2C2×#1062218311yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2542C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2542D11
hypocenterC11#11788
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
3. #13066640C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
9. C11×#399C4semidirect
13. C4×C11×C4⋊C4C4semidirect
136. C2×C4⋊Q8Dic11semidirect
142. #399Dic11semidirect
146. C4×C4⋊C4Dic11semidirect
253. C11#11788semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669542
#130666402
C11×#25422
#1178811