Finite Group Databasebeta

← #14642211

Subgroups — #14642211

Order 2816.

396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077002C211yesmaximal, characteristic
2#13068464C211yesmaximal, characteristic
3#13068363C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C11×#389C2211yescharacteristic
9C2×#66879—21no—
10C2×Dic11⋊C8—21no—
11C2×C8×Dic11—21no—
12#10622598C411yescharacteristic
13#10622594—21no—
14#10622591—21no—
15#10622590C411yescharacteristic
16#10622590C411yescharacteristic
17#10622586C411yescharacteristic
18C42×Dic11C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622266—21no—
21#10622265—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—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—24no—
55Dic11⋊C8—24no—
56C8×Dic11—42no—
57#7677—111nomaximal, Sylow
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11C22⋊C411yescharacteristic
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C411yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11—41no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—41no—
84C4⋊Dic11—42no—
85Dic11⋊C4—42no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88C4×Dic11—22no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#2864—111no—
104C4×C4⋊C8—111no—
105#1745—111no—
106#1271—111no—
107#1271—111no—
108#1271—111no—
109#1271D1111yescharacteristic
110C23×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11#13111yescharacteristic
124C2×C4×C11#13111yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—21no—
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#10112yes—
145C2×Dic11#10412yes—
146C2×Dic11#10412yes—
147C8×C11—42no—
148C8×C11—42no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C2×C4⋊C8—221no—
152C2×#97—221no—
153C2×C4×C8—221no—
154#389—111no—
155#389—111no—
156#389—111no—
157#389C2×D1111yescharacteristic
158#387—221no—
159#387—221no—
160#387—221no—
161#387—221no—
162#382—111no—
163#382—111no—
164C43—111no—
165#336—111no—
166#336—111no—
167#336—221no—
168#336C2×D1111yescharacteristic
169#336C2×D1111yescharacteristic
170C22×C11#40811yescharacteristic
171C22×C11#41011yescharacteristic
172C22×C11C2×#10111yescharacteristic
173C22×C11#41611yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11C2×#10411yescharacteristic
176C22×C11C2×#10411yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—81no—
184C4×C11—81no—
185Dic11—22no—
186Dic11—22no—
187Dic11—22no—
188Dic11—41no—
189Dic11—81no—
190Dic11—81no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—221no—
194C22×C8—221no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C42—111no—
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—224no—
211#97—224no—
212C4×C8—442no—
213#95—21no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221C2×C11#147011yescharacteristic
222C2×C11#148311yescharacteristic
223C2×C11#149411yescharacteristic
224C2×C11#150011yescharacteristic
225C2×C11#150911yescharacteristic
226C2×C11#152611yescharacteristic
227C2×C11#155211yescharacteristic
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C42—41no—
264C42—222no—
265C42—222no—
266C42—222no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—221no—
273C11#767711yescharacteristic, complemented, Sylow
274C23C22⋊C4×D1111yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—112no—
288C2×C4—112no—
289C2×C4—112no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4#6695411yescharacteristic
306C2×C4#6696011yescharacteristic
307C2×C4#6696411yescharacteristic
308C2×C4#6696811yescharacteristic
309C2×C4#6696911yescharacteristic
310C2×C4#6697211yescharacteristic
311C8—42no—
312C8—42no—
313C8—442no—
314C8—442no—
315C22#1062234011yescharacteristic
316C22#1062235311yescharacteristic
317C22D11×#10111yescharacteristic
318C22#1062238411yescharacteristic
319C22#1062241711yescharacteristic
320C22D11×#10411yescharacteristic
321C22D11×#10411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—222no—
331C4—222no—
332C4—222no—
333C4—441no—
334C4—881no—
335C4—881no—
336C2#1306697011yescharacteristic
337C2#1306702611yescharacteristic
338C2#1306707511yescharacteristic
339C2#1306710111yescharacteristic
340C2#1306713811yescharacteristic
341C2#1306720911yescharacteristic
342C2#1306731511yescharacteristic
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#7677
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
273. C11#7677semidirect

Maximal subgroups

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

subgroupindex
#130770022
#130684642
#130683632
#130664402
#130664392
#130664382
C11×#12712
#767711