Finite Group Databasebeta

← #14642263

Subgroups — #14642263

Order 2816.

410 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 103 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#13076999C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic
3#13068464C211yesmaximal, characteristic
4#13066441C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C11×#389C2211yescharacteristic
9C2×#66879—21no—
10C2×Dic11⋊C8—21no—
11C2×Dic11⋊C8—21no—
12C2×C8×Dic11—21no—
13#10622598C411yescharacteristic
14#10622594—21no—
15#10622591—21no—
16#10622587C411yescharacteristic
17#10622587C411yescharacteristic
18#10622586C411yescharacteristic
19C42×Dic11C2211yescharacteristic
20#10622542C2211yescharacteristic
21#10622267—21no—
22#10622264—21no—
23C11×#336C2211yescharacteristic
24C11×#336C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22C2×C411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C11×#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54#66879—42no—
55Dic11⋊C8—24no—
56Dic11⋊C8—24no—
57C8×Dic11—42no—
58#7689—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C411yescharacteristic
69C22×Dic11C22⋊C411yescharacteristic
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×C8×C11—22no—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—42no—
88Dic11⋊C4—42no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—41no—
96C4×Dic11SD1612yes—
97C4×Dic11Q1612yes—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2863—111no—
105#1767—111no—
106C4×C4⋊C8—111no—
107#1272—111no—
108#1272—111no—
109#1271—111no—
110#1271D1111yescharacteristic
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11#13111yescharacteristic
125C2×C4×C11#13111yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11C2×Q1611yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11#10312yes—
145C2×Dic11#10312yes—
146C2×Dic11#10412yes—
147C2×Dic11#10412yes—
148Dic22—81no—
149Dic22—81no—
150C8×C11—42no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C2×C4⋊C8—221no—
155C2×C4⋊C8—221no—
156C2×#97—221no—
157C2×C4×C8—221no—
158#391—111no—
159#391—111no—
160#391—111no—
161#389—111no—
162#389—111no—
163#389C2×D1111yescharacteristic
164#387—221no—
165#387—221no—
166#387—221no—
167#383—221no—
168C43—111no—
169#336—111no—
170#336—111no—
171#336C2×D1111yescharacteristic
172#336C2×D1111yescharacteristic
173C22×C11#40811yescharacteristic
174C22×C11#41011yescharacteristic
175C22×C11#41311yescharacteristic
176C22×C11C2×#10311yescharacteristic
177C22×C11#41711yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11C2×#10411yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—81no—
188Dic11—22no—
189Dic11—22no—
190Dic11—22no—
191Dic11—22no—
192Dic11—81no—
193Dic11—81no—
194C22×Q8—111no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—221no—
198C22×C8—221no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C4×D1111yescharacteristic
204C2×C4⋊C4C4×D1111yescharacteristic
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—224no—
213C4⋊C8—224no—
214#97—442no—
215C4×C8—442no—
216#95—21no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11#147311yescharacteristic
226C2×C11#148311yescharacteristic
227C2×C11#149311yescharacteristic
228C2×C11#150311yescharacteristic
229C2×C11#150911yescharacteristic
230C2×C11#152411yescharacteristic
231C2×C11#155011yescharacteristic
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8—441no—
235C2×Q8—441no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—222no—
254C2×C8—222no—
255C2×C8—441no—
256C2×C8—441no—
257C2×C8—441no—
258C2×C8—441no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C42—41no—
268C42—112no—
269C42—112no—
270C42—222no—
271C42—222no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—441no—
277C11#768911yescharacteristic, complemented, Sylow
278C23C22⋊C4×D1111yescharacteristic
279Q8—881no—
280Q8—881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—112no—
294C2×C4—112no—
295C2×C4—112no—
296C2×C4—112no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4#6695411yescharacteristic
312C2×C4#6696011yescharacteristic
313C2×C4#6696411yescharacteristic
314C2×C4SD16×D1111yescharacteristic
315C2×C4#6696811yescharacteristic
316C2×C4Q16×D1111yescharacteristic
317C8—42no—
318C8—42no—
319C8—442no—
320C8—442no—
321C22#1062234011yescharacteristic
322C22#1062235311yescharacteristic
323C22#1062236411yescharacteristic
324C22#1062238411yescharacteristic
325C22D11×#10311yescharacteristic
326C22D11×#10411yescharacteristic
327C22D11×#10411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—222no—
337C4—222no—
338C4—222no—
339C4—222no—
340C4—881no—
341C4—881no—
342C2#1306698411yescharacteristic
343C2#1306702611yescharacteristic
344C2#1306706911yescharacteristic
345C2#1306711311yescharacteristic
346C2#1306713811yescharacteristic
347C2#1306720311yescharacteristic
348C2#1306730511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7689
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
277. C11#7689semidirect

Maximal subgroups

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

subgroupindex
#130769992
#130684682
#130684642
#130664412
#130664392
C11×#12712
#768911