Finite Group Databasebeta

← #14642953

Subgroups — #14642953

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#13070158C211yesmaximal, characteristic
3#13070089C211yesmaximal, characteristic
4#13070024C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic
8C11×#391C2211yescharacteristic
9#10622842—21no—
10C2×#66899—21no—
11C2×#66882—21no—
12C2×#66881—21no—
13C2×#66880—21no—
14#10622585—21no—
15#10622548C2211yescharacteristic
16#10622542C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622270—21no—
19#10622270—21no—
20#10622266—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—21no—
46C11×#95—21no—
47C11×#95—21no—
48#66899—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66882—42no—
56#66881—42no—
57#66880—42no—
58#7809—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×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22Q1612yes—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C42×C11—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11SD1612yes—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101C4×Dic11—81no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2806—111no—
106#2096—111no—
107#2083—111no—
108#2072—111no—
109#1272—111no—
110#1272D1111yescharacteristic
111#1271—111no—
112C23×C11#12011yescharacteristic
113Q8×C11—42no—
114Q8×C11—81no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11C2×Q1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
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—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148Dic22—42no—
149Dic22—81no—
150C8×C11—42no—
151C8×C11—42no—
152C11⋊C8—81no—
153C2×#107—221no—
154C2×#106—221no—
155C2×#103—221no—
156C2×#103—221no—
157#398—221no—
158#398—221no—
159#395—221no—
160#391—111no—
161#391—221no—
162#391C2×D1111yescharacteristic
163#389—111no—
164#389—221no—
165#387—221no—
166#384—111no—
167#340—221no—
168#340—221no—
169#336—111no—
170#336C2×D1111yescharacteristic
171#336C2×D1111yescharacteristic
172C22×C11#44811yescharacteristic
173C22×C11#44911yescharacteristic
174C22×C11#45111yescharacteristic
175C22×C11#45311yescharacteristic
176C22×C11#45511yescharacteristic
177C22×C11#45611yescharacteristic
178C22×C11#45811yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187Dic11—42no—
188Dic11—42no—
189Dic11—81no—
190Dic11—81no—
191Dic11—161no—
192C22×Q8—111no—
193C22×Q8D4411yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—221no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4D4411yescharacteristic
209C2×C42—221no—
210C2×C42C22×D1111yescharacteristic
211#107—442no—
212#106—442no—
213#103—442no—
214#103—442no—
215#95—21no—
216#95—21no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223C2×C11#161111yescharacteristic
224C2×C11#161211yescharacteristic
225C2×C11#161411yescharacteristic
226C2×C11#162211yescharacteristic
227C2×C11#164511yescharacteristic
228C2×C11#164811yescharacteristic
229C2×C11#166111yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—112no—
235C2×Q8—221no—
236C2×Q8—441no—
237C2×Q8—441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—441no—
245C22×C4C2×D4411yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C22×C4D4×D1111yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—441no—
255C2×C8—441no—
256C2×C8—441no—
257C4⋊C4—41no—
258C4⋊C4—112no—
259C4⋊C4—221no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C42—41no—
275C42—881no—
276C11#780911yescharacteristic, complemented, Sylow
277C23#6693511yescharacteristic
278Q8—42no—
279Q8—81no—
280Q8—442no—
281Q8—881no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—441no—
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—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4#6695711yescharacteristic
310C2×C4#6696111yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4#6696811yescharacteristic
313C2×C4Q16×D1111yescharacteristic
314C2×C4#6697111yescharacteristic
315C8—42no—
316C8—42no—
317C8—881no—
318C22#1062234711yescharacteristic
319C22#1062235511yescharacteristic
320C22#1062235911yescharacteristic
321C22#1062241911yescharacteristic
322C22#1062242111yescharacteristic
323C22#1062243511yescharacteristic
324C22#1062243911yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—442no—
334C4—442no—
335C4—881no—
336C4—881no—
337C4—1761no—
338C2#1306762511yescharacteristic
339C2#1306763211yescharacteristic
340C2#1306764211yescharacteristic
341C2#1306769111yescharacteristic
342C2#1306783811yescharacteristic
343C2#1306786011yescharacteristic
344C2#1306793611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11#120
hypercenter#1272D11
hypocenterC11#7809
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
276. C11#7809semidirect

Maximal subgroups

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

subgroupindex
#130765752
#130701582
#130700892
#130700242
#130664412
#130664382
C11×#12722
#780911