Finite Group Databasebeta

← #14642938

Subgroups — #14642938

Order 2816.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070159C211yesmaximal, characteristic
2#13070092C211yesmaximal, characteristic
3#13070087C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#2805C211yesmaximal, characteristic
8C11×#400—21no—
9C11×#400—21no—
10C11×#395—21no—
11C11×#391C2211yescharacteristic
12C11×#389—21no—
13C11×#389C2211yescharacteristic
14C11×#389C2211yescharacteristic
15C11×#387—21no—
16C11×#387—21no—
17C2×#66899—21no—
18C2×#66872—21no—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8—21no—
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#66899—42no—
55#66872—42no—
56#66872—42no—
57#66871—42no—
58#7807—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—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—41no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—81no—
85C11×C4⋊C4SD1612yes—
86C42×C11—41no—
87C42×C11—81no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#2805D1111yescharacteristic
104#2096—111no—
105#2084—111no—
106#2083—111no—
107#1272—111no—
108#1271—111no—
109#1271—111no—
110C23×C11#12011yescharacteristic
111Q8×C11—42no—
112Q8×C11—81no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
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—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
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×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149C2×#107—221no—
150C2×#106—221no—
151C2×#106—221no—
152C2×#103—221no—
153#400—21no—
154#400—21no—
155#395—21no—
156#391C2×D1111yescharacteristic
157#389—21no—
158#389C2×D1111yescharacteristic
159#389C2×D1111yescharacteristic
160#387—21no—
161#387—21no—
162#384—111no—
163#340—221no—
164#340—221no—
165#336—111no—
166#336—111no—
167#336—111no—
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45211yescharacteristic
171C22×C11#45311yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11#45611yescharacteristic
174C22×C11#45811yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187Dic11—161no—
188C22×Q8C22⋊D1111yescharacteristic
189C22×C8—221no—
190C22×C8—221no—
191C22×C8—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C42—21no—
205C2×C42C22×D1111yescharacteristic
206#107—442no—
207#106—442no—
208#106—442no—
209#103—442no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219C2×C11#160911yescharacteristic
220C2×C11#161111yescharacteristic
221C2×C11#161811yescharacteristic
222C2×C11#162211yescharacteristic
223C2×C11#165011yescharacteristic
224C2×C11#165311yescharacteristic
225C2×C11#166011yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—441no—
237C22×C4C2×C22⋊D1111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C2×C8—222no—
241C2×C8—222no—
242C2×C8—222no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4#432512yes—
268C42—41no—
269C42—81no—
270C11#780711yescharacteristic, complemented, Sylow
271C23#6700611yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×#432511yescharacteristic
302C2×C4#6699511yescharacteristic
303C2×C4#6700211yescharacteristic
304C2×C4#6700311yescharacteristic
305C2×C4#6700311yescharacteristic
306C2×C4#6700411yescharacteristic
307C8—442no—
308C8—442no—
309C8—442no—
310C22#1062284011yescharacteristic
311C22#1062285111yescharacteristic
312C22#1062285211yescharacteristic
313C22#1062285411yescharacteristic
314C22#1062285611yescharacteristic
315C22#1062285911yescharacteristic
316C22#1062285911yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—1761no—
330C2#1306761311yescharacteristic
331C2#1306762411yescharacteristic
332C2#1306766411yescharacteristic
333C2#1306768811yescharacteristic
334C2#1306787211yescharacteristic
335C2#1306789311yescharacteristic
336C2#1306792711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2805C2
socle, prime radicalC23×C11#120
hypercenter#2805D11
hypocenterC11#7807
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
270. C11#7807semidirect

Maximal subgroups

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

subgroupindex
#130701592
#130700922
#130700872
#130664422
#130664392
C11×#28052
#780711