Finite Group Databasebeta

← #14664490

Subgroups — #14664490

Order 2816.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068693C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066640C212yesmaximal
4#13066637C212yesmaximal
5C11×#2396C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic, complemented
7C2×C11×#117C2211yescharacteristic
8C11×#400C411yescharacteristic, complemented
9C11×#399C2211yescharacteristic
10C11×#398—21no—
11C11×#396—21no—
12C11×#395C411yescharacteristic, complemented
13C11×#393C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17#10622824—21no—
18#10622539—21no—
19#10622166—21no—
20#10622164—21no—
21#10622164C2212yes—
22#10622163C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C22⋊Dic11—22no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51C11⋊#95—41no—
52C11⋊#95—41no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55#66867—41no—
56#11810—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C2×Q8×C11—42no—
59C2×Q8×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—42no—
91C42×C11—41no—
92C42×C11—41no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C2×C11⋊C8—42no—
96#2396D1111yescharacteristic
97#1820—111no—
98#1464—111no—
99#1352—112no—
100#1351—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11#13712yes—
107Q8×C11—42no—
108Q8×C11—42no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#9911yescharacteristic
138C2×Dic11—82no—
139C2×Dic11—82no—
140C2×Dic11—82no—
141C11⋊C8—82no—
142C2×C4×Q8Dic1111yescharacteristic, complemented
143C2×#117C2×D1111yescharacteristic
144#432—221no—
145#400Dic1111yescharacteristic, complemented
146#399C2×D1111yescharacteristic
147#398—21no—
148#396—21no—
149#395Dic1111yescharacteristic, complemented
150#393C2×D1111yescharacteristic
151#381—221no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4Dic1111yescharacteristic, complemented
154C4×C22⋊C4—21no—
155#342—112no—
156#342—221no—
157#324—221no—
158#323—112no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—42no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—42no—
172C4×C11—41no—
173C4×C11—42no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—81no—
180Dic11—162no—
181C22×Q8C2×Dic1111yescharacteristic
182C23×C4C22⋊D1111yescharacteristic
183C4×Q8—41no—
184C4×Q8—41no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C2×Dic1111yescharacteristic
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4C22×D1111yescharacteristic
199C2×C42—21no—
200C2×C42—21no—
201C2×C42C2×Dic1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C4⋊C8—441no—
204C22⋊C8—222no—
205#97—441no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—441no—
211#95—441no—
212#95C2×Dic1111yescharacteristic
213#95C2×Dic1111yescharacteristic
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—42no—
217C2×C11#151111yescharacteristic
218C2×C11#212011yescharacteristic
219C2×C11#212611yescharacteristic
220C24C2×C22⋊D1111yescharacteristic
221C2×Q8—42no—
222C2×Q8—41no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—442no—
232C22×C4C22⋊Dic1111yescharacteristic
233C22×C4C22⋊Dic1111yescharacteristic
234C22×C4C22⋊Dic1111yescharacteristic
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22×Dic1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—442no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—442no—
251C22⋊C4—442no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—42no—
257C42—41no—
258C42—41no—
259C11#1181011yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23#6699512yes—
265C23C2×C22⋊Dic1111yescharacteristic
266Q8—42no—
267Q8—42no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—882no—
296C2×C4—882no—
297C2×C4—882no—
298C2×C4#6689811yescharacteristic
299C2×C4#6689811yescharacteristic
300C8—882no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#6689811yescharacteristic
309C22#1062283811yescharacteristic
310C22#1062284911yescharacteristic
311C4—21no—
312C4—21no—
313C4—42no—
314C4—41no—
315C4—42no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—81no—
321C4—81no—
322C4—1762no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1306714911yescharacteristic
327C2#1307025711yescharacteristic
328C2#1307028111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2396C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2396D11
hypocenterC11#11810
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2396

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C11C4semidirect
8. C11×#400C4semidirect
12. C11×#395C4semidirect
15. C4×C11×C4⋊C4C4semidirect
142. C2×C4×Q8Dic11semidirect
145. #400Dic11semidirect
149. #395Dic11semidirect
153. C4×C4⋊C4Dic11semidirect
259. C11#11810semidirect

Maximal subgroups

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

subgroupindex
#130686932
#130669502
#130666402
#130666372
C11×#23962
#1181011