Finite Group Databasebeta

← #14642997

Subgroups — #14642997

Order 2816.

362 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 91 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#13070174C211yesmaximal, characteristic
2#13070024C211yesmaximal, characteristic
3#13070024C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066442C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#2806C211yesmaximal, characteristic
8C11×#398—21no—
9C11×#398—21no—
10C11×#395—21no—
11C11×#391—21no—
12C11×#391C2211yescharacteristic
13C11×#391C2211yescharacteristic
14C11×#389—21no—
15C11×#389C2211yescharacteristic
16C11×#387—21no—
17C2×#66899—21no—
18C2×#66899—21no—
19#10622548C2211yescharacteristic
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C22×C11⋊C8—21no—
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#66899—42no—
55#66899—42no—
56#7816—111nomaximal, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11SD1612yes—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—41no—
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—81no—
82C11×C4⋊C4—81no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—81no—
85C11×C4⋊C4Q1612yes—
86C42×C11—41no—
87C42×C11—81no—
88C4⋊Dic11—42no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
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#2806D1111yescharacteristic
103#2099—111no—
104#2072—111no—
105#2072—111no—
106#1272—111no—
107#1272—111no—
108#1271—111no—
109C23×C11#12011yescharacteristic
110Q8×C11—42no—
111Q8×C11—42no—
112Q8×C11—81no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
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×C11—41no—
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×Q1611yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149C11⋊C8—81no—
150C2×#103—221no—
151C2×#103—221no—
152#398—21no—
153#398—21no—
154#395—21no—
155#391—21no—
156#391C2×D1111yescharacteristic
157#391C2×D1111yescharacteristic
158#389—21no—
159#389C2×D1111yescharacteristic
160#387—21no—
161#384—111no—
162#340—221no—
163#340—221no—
164#340—221no—
165#340—221no—
166#336—111no—
167#336—111no—
168#336—111no—
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—42no—
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188Dic11—161no—
189C22×Q8C22⋊D1111yescharacteristic
190C22×Q8C22⋊D1111yescharacteristic
191C22×C8—221no—
192C22×C8—221no—
193C22×C8—221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C4⋊C4C22⋊D1111yescharacteristic
206C2×C42—21no—
207C2×C42C22×D1111yescharacteristic
208#103—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—
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—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8#432512yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—441no—
240C22×C4C2×C22⋊D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—442no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4#432612yes—
268C42—41no—
269C42—81no—
270C11#781611yescharacteristic, complemented, Sylow
271C23#6700611yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
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—41no—
299C2×C4—41no—
300C2×C4—881no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4C2×#432511yescharacteristic
304C2×C4#6699511yescharacteristic
305C2×C4#6699511yescharacteristic
306C2×C4C2×#432611yescharacteristic
307C2×C4#6700211yescharacteristic
308C2×C4#6700311yescharacteristic
309C8—881no—
310C8—881no—
311C8—881no—
312C22#1062284011yescharacteristic
313C22#1062284111yescharacteristic
314C22#1062285111yescharacteristic
315C22#1062285511yescharacteristic
316C22#1062285511yescharacteristic
317C22#1062285611yescharacteristic
318C22#1062285811yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—1761no—
332C2#1306760711yescharacteristic
333C2#1306763011yescharacteristic
334C2#1306765811yescharacteristic
335C2#1306771211yescharacteristic
336C2#1306783011yescharacteristic
337C2#1306783711yescharacteristic
338C2#1306793911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2806C2
socle, prime radicalC23×C11#120
hypercenter#2806D11
hypocenterC11#7816
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

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
#130701742
#130700242
#130664422
#130664392
C11×#28062
#781611