Finite Group Databasebeta

← #14642980

Subgroups — #14642980

Order 2816.

378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 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#13076578C211yesmaximal, characteristic
2#13070160C211yesmaximal, characteristic
3#13070025C211yesmaximal, characteristic
4#13066441C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#2084C211yesmaximal, characteristic
8C2×C11×#106—21no—
9C11×#389C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622598—21no—
12#10622597—21no—
13#10622594—21no—
14#10622592—21no—
15C2×#66874—21no—
16C2×#66874—21no—
17C2×#66872—21no—
18#10622542C2211yescharacteristic
19#10622542C2211yescharacteristic
20#10622274—21no—
21#10622259—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×C8×C11—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×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C11×#106—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#66874—42no—
57#66872—42no—
58#7814—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22SD1612yes—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4SD1612yes—
91C42×C11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—81no—
95C4⋊Dic11—81no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98C4×Dic11—81no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2806—111no—
106#2096—111no—
107#2084D1111yescharacteristic
108#2072—111no—
109#1272—111no—
110#1272—111no—
111#1271—111no—
112C23×C11#12011yescharacteristic
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—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
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—41no—
146Dic22—42no—
147Dic22—42no—
148Dic22—81no—
149Dic22—81no—
150C8×C11—42no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C2×#106—21no—
154C2×#106—221no—
155C2×#103—221no—
156C2×#103—221no—
157#398—221no—
158#398—221no—
159#395—221no—
160#391—111no—
161#391—111no—
162#391—221no—
163#389—221no—
164#389C2×D1111yescharacteristic
165#387—221no—
166#384C2×D1111yescharacteristic
167#340—21no—
168#340—221no—
169#336—111no—
170#336—111no—
171#336C2×D1111yescharacteristic
172C22×C11#44811yescharacteristic
173C22×C11#44811yescharacteristic
174C22×C11#45211yescharacteristic
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—42no—
186C4×C11—81no—
187C4×C11—161no—
188Dic11—42no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—111no—
193C22×Q8—111no—
194C22×C8—21no—
195C22×C8—221no—
196C22×C8—221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C4⋊C4C22⋊D1111yescharacteristic
209C2×C42—221no—
210C2×C42C22×D1111yescharacteristic
211#106—42no—
212#106—442no—
213#103—442no—
214#103—442no—
215#95—21no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223C2×C11#160811yescharacteristic
224C2×C11#161111yescharacteristic
225C2×C11#161811yescharacteristic
226C2×C11#162311yescharacteristic
227C2×C11#164311yescharacteristic
228C2×C11#165311yescharacteristic
229C2×C11#166111yescharacteristic
230C2×Q8—112no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8—441no—
235C2×Q8—441no—
236C2×Q8—441no—
237C2×Q8—441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4D4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—222no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C2×C8—441no—
256C2×C8—441no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C4⋊C4#432412yes—
274C42—41no—
275C42—881no—
276C11#781411yescharacteristic, complemented, Sylow
277C23#6699011yescharacteristic
278Q8—442no—
279Q8—442no—
280Q8—881no—
281Q8—881no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—222no—
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—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4SD16×D1111yescharacteristic
310C2×C4#6696811yescharacteristic
311C2×C4#6696811yescharacteristic
312C2×C4#6696911yescharacteristic
313C2×C4C2×#432411yescharacteristic
314C2×C4#6700411yescharacteristic
315C8—42no—
316C8—442no—
317C8—881no—
318C22#1062265311yescharacteristic
319C22#1062266611yescharacteristic
320C22#1062270811yescharacteristic
321C22#1062278311yescharacteristic
322C22#1062278611yescharacteristic
323C22#1062281111yescharacteristic
324C22#1062281511yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—161no—
334C4—442no—
335C4—881no—
336C4—881no—
337C4—881no—
338C2#1306760511yescharacteristic
339C2#1306762311yescharacteristic
340C2#1306766111yescharacteristic
341C2#1306769311yescharacteristic
342C2#1306782111yescharacteristic
343C2#1306789011yescharacteristic
344C2#1306793111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2084C2
socle, prime radicalC23×C11#120
hypercenter#2084D11
hypocenterC11#7814
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
276. C11#7814semidirect

Maximal subgroups

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

subgroupindex
#130765782
#130701602
#130700252
#130664412
#130664392
C11×#20842
#781411