Finite Group Databasebeta

← #14642995

Subgroups — #14642995

Order 2816.

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

normal subgroups only

This group has 362 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#13070173C211yesmaximal, characteristic
3#13070025C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066440C211yesmaximal, characteristic
7C11×#2072C211yesmaximal, characteristic
8C2×C11×#103—21no—
9C11×#391C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622842—21no—
12#10622585—21no—
13C2×#66874—21no—
14#10622542C2211yescharacteristic
15#10622541C2211yescharacteristic
16#10622270—21no—
17#10622270—21no—
18#10622266—21no—
19#10622259—21no—
20C11×#340—21no—
21C11×#336C2211yescharacteristic
22#10622167—21no—
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×#103—42no—
47C11×#95—21no—
48C11×#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66874—42no—
56#7816—111nomaximal, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22SD1612yes—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11Q1612yes—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—81no—
92Dic11⋊C4—81no—
93Dic11⋊C4—81no—
94Dic11⋊C4—81no—
95C4×Dic11—81no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#2806—111no—
103#2099—111no—
104#2072—111no—
105#2072D1111yescharacteristic
106#1272—111no—
107#1272—111no—
108#1271—111no—
109C23×C11#12011yescharacteristic
110Q8×C11—42no—
111Q8×C11—81no—
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—81no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
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—
145Dic22—42no—
146Dic22—81no—
147C8×C11—81no—
148C11⋊C8—81no—
149C11⋊C8—81no—
150C2×#103—21no—
151C2×#103—221no—
152#398—221no—
153#398—221no—
154#395—221no—
155#391—111no—
156#391—221no—
157#391C2×D1111yescharacteristic
158#389—111no—
159#389—221no—
160#387—221no—
161#384C2×D1111yescharacteristic
162#340—21no—
163#340—221no—
164#340—221no—
165#340—221no—
166#336—111no—
167#336—111no—
168#336C2×D1111yescharacteristic
169C22×C11#44811yescharacteristic
170C22×C11#44911yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45411yescharacteristic
173C22×C11#45511yescharacteristic
174C22×C11#45511yescharacteristic
175C22×C11#45811yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—161no—
185Dic11—42no—
186Dic11—42no—
187Dic11—81no—
188Dic11—81no—
189C22×Q8—111no—
190C22×Q8C22⋊D1111yescharacteristic
191C22×C8—21no—
192C22×C8—221no—
193C22×C8—221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
206C2×C42—221no—
207C2×C42C22×D1111yescharacteristic
208#103—42no—
209#103—442no—
210#95—21no—
211#95—21no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218C2×C11#160811yescharacteristic
219C2×C11#161211yescharacteristic
220C2×C11#161711yescharacteristic
221C2×C11#162611yescharacteristic
222C2×C11#164411yescharacteristic
223C2×C11#164511yescharacteristic
224C2×C11#166211yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—112no—
230C2×Q8—221no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—112no—
259C4⋊C4—221no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—881no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C4⋊C4—881no—
268C42—41no—
269C42—881no—
270C11#781611yescharacteristic, complemented, Sylow
271C23#6699011yescharacteristic
272Q8—42no—
273Q8—81no—
274Q8—442no—
275Q8—881no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4SD16×D1111yescharacteristic
304C2×C4#6696811yescharacteristic
305C2×C4Q16×D1111yescharacteristic
306C2×C4#6697111yescharacteristic
307C2×C4#6698511yescharacteristic
308C2×C4#6700311yescharacteristic
309C8—81no—
310C8—881no—
311C8—881no—
312C22#1062265011yescharacteristic
313C22#1062266611yescharacteristic
314C22#1062267411yescharacteristic
315C22#1062278311yescharacteristic
316C22#1062279911yescharacteristic
317C22#1062281411yescharacteristic
318C22#1062281511yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—161no—
328C4—442no—
329C4—442no—
330C4—881no—
331C4—881no—
332C2#1306760511yescharacteristic
333C2#1306762811yescharacteristic
334C2#1306765611yescharacteristic
335C2#1306771011yescharacteristic
336C2#1306782811yescharacteristic
337C2#1306783411yescharacteristic
338C2#1306793811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2072C2
socle, prime radicalC23×C11#120
hypercenter#2072D11
hypocenterC11#7816
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
270. C11#7816semidirect

Maximal subgroups

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

subgroupindex
#130765752
#130701732
#130700252
#130664422
#130664412
#130664402
C11×#20722
#781611