Finite Group Databasebeta

← #14657490

Subgroups — #14657490

Order 2816.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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#13068612C211yesmaximal, characteristic
2#13067371C211yesmaximal, characteristic
3#13067306C211yesmaximal, characteristic
4#13067071C211yesmaximal, characteristic
5C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#3078C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#479—22no—
11C11×#477—21no—
12C11×#475—21no—
13C11×#428—21no—
14C11×#423C2211yescharacteristic
15C11×#419—21no—
16C2×#66900—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622185—21no—
22#10622184—21no—
23Q8⋊(C11⋊C8)—21no—
24Q8⋊(C11⋊C8)—21no—
25Q8⋊(C11⋊C8)—21no—
26Q8⋊(C11⋊C8)—21no—
27#10622168—21no—
28#10622118—22no—
29C22×Q8×C11D411yescharacteristic
30C2×C11×M16—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8D411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4318—21no—
48C2×#4318—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C11×#107—22no—
52C11×#106—22no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C11×#103—22no—
56C11×#103—22no—
57#66900—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8D411yescharacteristic
66C4×C11⋊C8D411yescharacteristic
67#10462—111nomaximal, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11SD1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—22no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102#4318—41no—
103#4318—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—81no—
113#3078D1111yescharacteristic
114#1801—111no—
115#1566—111no—
116#1550—111no—
117#1493—111no—
118C2×Q8⋊C8—111no—
119#1292—111no—
120C23×C11#12311yescharacteristic
121Q8×C11—22no—
122Q8×C11—22no—
123Q8×C11—41no—
124Q8×C11—41no—
125Q8×C11—41no—
126Q8×C11—41no—
127Q8×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C8×C11—42no—
149C11⋊C8—22no—
150C11⋊C8—41no—
151C11⋊C8—81no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#533C2×D1111yescharacteristic
155C2×C4×Q8C2×D1111yescharacteristic
156#479—22no—
157#477—21no—
158#475—21no—
159#428—21no—
160#423—111no—
161#423—111no—
162#423C2×D1111yescharacteristic
163C2×C4⋊C8—111no—
164#419—21no—
165C2×#101—221no—
166C2×C4×C8—111no—
167#343—221no—
168#334—222no—
169#333—221no—
170#332—221no—
171Q8⋊C8—221no—
172Q8⋊C8—221no—
173Q8⋊C8—221no—
174Q8⋊C8—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39411yescharacteristic
178C22×C11#48311yescharacteristic
179C22×C11#48511yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11#44811yescharacteristic
188C4×C11#45211yescharacteristic
189C4×C11#46511yescharacteristic
190C4×C11#47011yescharacteristic
191C4×C11#47111yescharacteristic
192C4×C11#47311yescharacteristic
193C22×Q8C22⋊D1111yescharacteristic
194C2×M16—21no—
195C2×M16—221no—
196C2×M16—221no—
197C22×C8—221no—
198C22×C8—221no—
199C4⋊Q8C22⋊D1111yescharacteristic
200C4⋊Q8C22⋊D1111yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210#117—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C42—21no—
214C2×C42C22×D1111yescharacteristic
215#107—22no—
216#106—22no—
217C4⋊C8—21no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8C22⋊D1112yes—
225#103—22no—
226#103—22no—
227#101—442no—
228C4×C8—111no—
229C4×C8—111no—
230C4×C8—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#203511yescharacteristic
234C2×C11#205011yescharacteristic
235C2×C11#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8#432512yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4#434111yescharacteristic
247C22×C4#434111yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249M16—41no—
250M16—41no—
251M16—441no—
252M16—441no—
253M16—441no—
254M16—441no—
255C2×C8—22no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—442no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—881no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42D4×D1111yescharacteristic
278C42#434111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C11#1046211yescharacteristic, complemented, Sylow
282C23#6698811yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4#6698811yescharacteristic
301C2×C4#6698911yescharacteristic
302C2×C4#6699111yescharacteristic
303C2×C4#6699211yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4C2×#432511yescharacteristic
306C2×C4#6699511yescharacteristic
307C2×C4#6700311yescharacteristic
308C2×C4#6700411yescharacteristic
309C2×C4#6700611yescharacteristic
310C8—42no—
311C8—222no—
312C8—441no—
313C8—881no—
314C8—881no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22#1062265611yescharacteristic
319C22#1062265811yescharacteristic
320C22#1062283511yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4#1062266111yescharacteristic
329C4#1062266511yescharacteristic
330C4#1062281611yescharacteristic
331C4#1062281711yescharacteristic
332C4#1062284011yescharacteristic
333C4#1062285211yescharacteristic
334C2—21no—
335C2—21no—
336C2#1306980911yescharacteristic
337C2#1306990011yescharacteristic
338C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#3078D11
hypocenterC11#10462
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
281. C11#10462semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130673712
#130673062
#130670712
C2×Q8⋊(C11⋊C8)2
#130664902
C11×#30782
#1046211