Finite Group Databasebeta

← #14655893

Subgroups — #14655893

Order 2816.

486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079958C211yesmaximal, characteristic
2#13079561C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic
4#13069564C211yesmaximal, characteristic
5#13067114C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic
7C11×#1986C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622734—22no—
14#10622706—21no—
15#10622705—21no—
16#10622704—21no—
17#10622703—21no—
18#10622664—22no—
19#10622663—22no—
20#10622644—22no—
21#10622644—21no—
22#10622634—21no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622315—22no—
26#10622295—21no—
27#10622293—21no—
28C11×#339—22no—
29#10622167—22no—
30#10622090—22no—
31C22×Dic22—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4326—24no—
45C2×#4326—22no—
46#66979—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49#66977—21no—
50#66977—21no—
51C22×C11⋊C8D412yes—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×#97—21no—
62C4×C8×C11—21no—
63C11×#95—21no—
64#66899—22no—
65C22⋊(C11⋊C8)D412yes—
66#66882—24no—
67#66881—24no—
68#66874—24no—
69#66874—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10199—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—41no—
83C2×Dic22—21no—
84C2×Dic22—22no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22—82no—
88C11×M16—22no—
89C11×M16Q1614yescomplemented
90C2×C8×C11—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C42×C11—42no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107#4326—84no—
108#4326—82no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—42no—
123#3249—111no—
124#3209—111no—
125#3165—111no—
126#1987—111no—
127#1986D1111yescharacteristic
128#1503—111no—
129#1283—111no—
130C23×C11#12711yescharacteristic
131Q8×C11—42no—
132Q8×C11—41no—
133Q8×C11—41no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C2×Q1612yes—
149C2×C4×C11#13712yes—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—82no—
154Dic22—44no—
155Dic22—41no—
156Dic22—41no—
157Dic22—82no—
158Dic22—81no—
159C8×C11—24no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162#533—111no—
163#533C2×D1111yescharacteristic
164C2×C4⋊Q8—111no—
165#501—222no—
166#500—221no—
167#498—221no—
168#494—221no—
169#487—221no—
170#477—221no—
171#477—221no—
172#467—222no—
173#462—222no—
174#462—221no—
175#462—221no—
176#451—222no—
177#431—111no—
178#428—222no—
179C2×C4⋊C8—111no—
180C4×M16C2×D1111yescharacteristic
181C4×C4⋊C4C2×D1111yescharacteristic
182#340—222no—
183#339—22no—
184#328—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#39211yescharacteristic
188C22×C11#49411yescharacteristic
189C22×C11#49711yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#45112yes—
197C4×C11#45511yescharacteristic
198C4×C11#45611yescharacteristic
199C4×C11#46212yes—
200Dic11—81no—
201Dic11—82no—
202Dic11—81no—
203C22×Q8—221no—
204C2×Q16—224no—
205C2×Q16—222no—
206C2×M16C22⋊D1112yes—
207C22×C8—112no—
208C4⋊Q8—112no—
209C4⋊Q8—111no—
210C4⋊Q8—111no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8D4411yescharacteristic
215C4⋊Q8D4411yescharacteristic
216#125—21no—
217#125—221no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—221no—
225C4×Q8—221no—
226#117—21no—
227#117—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42—21no—
232C2×C42C22×D1111yescharacteristic
233#107—222no—
234#107—224no—
235#106—224no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239#103—224no—
240#103—222no—
241#103—222no—
242C22⋊C8—112no—
243#97—21no—
244C4×C8—21no—
245C4×C8—221no—
246#95—21no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#200711yescharacteristic
250C2×C11#200811yescharacteristic
251C2×C11#201611yescharacteristic
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—221no—
255C2×Q8—222no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—882no—
259C22×C4—41no—
260C22×C4—441no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—884no—
265Q16—882no—
266M16—22no—
267M16#432614yescomplemented
268C2×C8—22no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—442no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—221no—
281C4⋊C4—222no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—222no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—41no—
291C22⋊C4—441no—
292C42—41no—
293C42—42no—
294C42—441no—
295C42C2×D4411yescharacteristic
296C42#433911yescharacteristic
297C42D4×D1111yescharacteristic
298C42D4×D1111yescharacteristic
299C11#1019911yescharacteristic, complemented, Sylow
300C23#6699311yescharacteristic
301Q8—42no—
302Q8—41no—
303Q8—41no—
304Q8—444no—
305Q8—441no—
306Q8—441no—
307Q8—881no—
308Q8—882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—882no—
321C2×C4#6693511yescharacteristic
322C2×C4#6693511yescharacteristic
323C2×C4#6693711yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6698311yescharacteristic
326C2×C4#6699011yescharacteristic
327C2×C4C2×#432612yes—
328C2×C4#6700412yes—
329C8—24no—
330C8—442no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22#1062257311yescharacteristic
335C22#1062267311yescharacteristic
336C22#1062270511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—81no—
342C4—81no—
343C4—881no—
344C4—882no—
345C4—881no—
346C4#1062243811yescharacteristic
347C4#1062243911yescharacteristic
348C4#1062264412yes—
349C4#1062266312yes—
350C2—21no—
351C2—21no—
352C2#1306966411yescharacteristic
353C2#1306967011yescharacteristic
354C2#1306971511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1986C2
socleC22×C11#392
prime radicalC23×C11#127
hypercenter#1986D11
hypocenterC11#10199
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
89. C11×M16Q16semidirect
267. M16#4326semidirect
299. C11#10199semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130795612
#130791622
#130695642
#130671142
#130664672
C11×#19862
#1019911