Finite Group Databasebeta

← #14643108

Subgroups — #14643108

Order 2816.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#13076575C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic
3#13070155C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066440C211yesmaximal, characteristic
7C11×#2095C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×#103—21no—
10C11×#391C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622842—21no—
13#10622585—21no—
14C2×#66874—21no—
15C2×#66871—21no—
16#10622542C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622270—21no—
19#10622270—21no—
20#10622266—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C11×#107—42no—
47C11×#103—42no—
48C11×#95—21no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66874—42no—
57#66871—42no—
58#7836—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22Q1612yes—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C42×C11—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11Q1612yes—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—81no—
94Dic11⋊C4—81no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97C4×Dic11—81no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2806—111no—
105#2100—111no—
106#2095—111no—
107#2095D1111yescharacteristic
108#1272—111no—
109#1272—111no—
110#1271—111no—
111C23×C11#12011yescharacteristic
112Q8×C11—42no—
113Q8×C11—81no—
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—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147Dic22—42no—
148Dic22—81no—
149C8×C11—42no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152C2×#107—21no—
153C2×#107—221no—
154C2×#103—21no—
155C2×#103—221no—
156#398—221no—
157#398—221no—
158#395—221no—
159#391—111no—
160#391—221no—
161#391C2×D1111yescharacteristic
162#389—111no—
163#389—221no—
164#387—221no—
165#384C2×D1111yescharacteristic
166#340—221no—
167#340—221no—
168#336—111no—
169#336—111no—
170#336C2×D1111yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45111yescharacteristic
173C22×C11#45211yescharacteristic
174C22×C11#45311yescharacteristic
175C22×C11#45311yescharacteristic
176C22×C11#45411yescharacteristic
177C22×C11#45811yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—161no—
187Dic11—42no—
188Dic11—42no—
189Dic11—81no—
190Dic11—81no—
191C22×Q8—111no—
192C22×Q8C22⋊D1111yescharacteristic
193C22×C8—21no—
194C22×C8—221no—
195C22×C8—221no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C42—221no—
209C2×C42C22×D1111yescharacteristic
210#107—42no—
211#107—442no—
212#103—42no—
213#103—442no—
214#95—21no—
215#95—21no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11#161411yescharacteristic
223C2×C11#161711yescharacteristic
224C2×C11#161811yescharacteristic
225C2×C11#163211yescharacteristic
226C2×C11#163311yescharacteristic
227C2×C11#163611yescharacteristic
228C2×C11#165611yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—112no—
234C2×Q8—221no—
235C2×Q8—441no—
236C2×Q8—441no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4D4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—222no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C2×C8—441no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—112no—
263C4⋊C4—221no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—881no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C42—41no—
273C42—881no—
274C11#783611yescharacteristic, complemented, Sylow
275C23#6699011yescharacteristic
276Q8—42no—
277Q8—81no—
278Q8—442no—
279Q8—881no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4Q16×D1111yescharacteristic
308C2×C4Q16×D1111yescharacteristic
309C2×C4#6697111yescharacteristic
310C2×C4#6697111yescharacteristic
311C2×C4#6699511yescharacteristic
312C2×C4#6700311yescharacteristic
313C8—42no—
314C8—442no—
315C8—881no—
316C22#1062266011yescharacteristic
317C22#1062266611yescharacteristic
318C22#1062269011yescharacteristic
319C22#1062279911yescharacteristic
320C22#1062279911yescharacteristic
321C22#1062281111yescharacteristic
322C22#1062281411yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4—442no—
333C4—442no—
334C4—881no—
335C4—881no—
336C2#1306763911yescharacteristic
337C2#1306765611yescharacteristic
338C2#1306766211yescharacteristic
339C2#1306774911yescharacteristic
340C2#1306775411yescharacteristic
341C2#1306777211yescharacteristic
342C2#1306790711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2095C2
socle, prime radicalC23×C11#120
hypercenter#2095D11
hypocenterC11#7836
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
274. C11#7836semidirect

Maximal subgroups

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

subgroupindex
#130765752
#130701782
#130701552
#130664422
#130664412
#130664402
C11×#20952
#783611