Finite Group Databasebeta

← #14655318

Subgroups — #14655318

Order 2816.

470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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#13080007C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic
4#13067211C211yesmaximal, characteristic
5#13067036C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic
7C11×#3230C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16C2×#66900—22no—
17#10622707—21no—
18#10622703—21no—
19#10622693—22no—
20#10622692—21no—
21#10622691—21no—
22#10622665—22no—
23#10622644—21no—
24#10622633—21no—
25#10622577—22no—
26#10622537C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622181—22no—
30#10622122—22no—
31C22×Q8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—22no—
48#66979—21no—
49#66977—21no—
50#66977—21no—
51C2×#4318—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×#107—24no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66900—44no—
65#66899—22no—
66#66874—22no—
67#66872—24no—
68#66872—22no—
69#66871—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10117—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×C8×C11—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—22no—
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×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—41no—
107#4326—82no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114C4×Dic11—41no—
115#4318—24no—
116#4318—22no—
117#4318—42no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3255—111no—
123#3230D1111yescharacteristic
124#3165—111no—
125#1966—111no—
126#1526—111no—
127#1485—111no—
128#1299—111no—
129C23×C11#12111yescharacteristic
130Q8×C11—41no—
131Q8×C11—41no—
132Q8×C11—42no—
133Q8×C11—82no—
134Q8×C11—81no—
135Q8×C11—81no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—44no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—41no—
153Dic22—41no—
154Dic22—42no—
155C8×C11—42no—
156C11⋊C8—24no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159#533—111no—
160#533C2×D1111yescharacteristic
161C2×C4⋊Q8C2×D1111yescharacteristic
162#501—222no—
163#500—21no—
164#500—221no—
165#498—221no—
166#487—21no—
167#484—22no—
168#477—22no—
169#475—221no—
170#475—221no—
171#470—222no—
172#462—221no—
173#462—221no—
174#431C2×D1111yescharacteristic
175#428—222no—
176#423—111no—
177C2×#101—222no—
178C4×M16—111no—
179C4×M16—111no—
180#330—222no—
181Q8⋊C8—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#39211yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—82no—
191C4×C11—81no—
192C4×C11#45311yescharacteristic
193C4×C11#45411yescharacteristic
194C4×C11#45612yes—
195C4×C11#47312yes—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—21no—
199C2×Q16—222no—
200C2×M16—112no—
201C2×M16—221no—
202C2×M16—221no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—111no—
208C4⋊Q8—111no—
209C4⋊Q8C22⋊D1111yescharacteristic
210C4⋊Q8C22⋊D1111yescharacteristic
211#125—21no—
212#125—221no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—221no—
220C4×Q8—221no—
221#117—21no—
222#117—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C22⋊D1112yes—
225C2×C42C22×D1111yescharacteristic
226#107—24no—
227#107—224no—
228#106—224no—
229#106—222no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232C4⋊C8C22⋊D1112yes—
233#103—24no—
234#103—222no—
235#103—222no—
236#101—444no—
237C22⋊C8—21no—
238#97—112no—
239#97—221no—
240C4×C8—21no—
241C4×C8—221no—
242C4×C8—221no—
243C2×C11—41no—
244C2×C11#200511yescharacteristic
245C2×C11#200611yescharacteristic
246C2×C11#202011yescharacteristic
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—221no—
254C2×Q8—221no—
255C22×C4—22no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259Q16—882no—
260M16—224no—
261M16—222no—
262M16—441no—
263M16—442no—
264C2×C8—22no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C22⋊C4—441no—
286C42—41no—
287C42—441no—
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C11#1011711yescharacteristic, complemented, Sylow
293C23#6699211yescharacteristic
294Q8—41no—
295Q8—41no—
296Q8—42no—
297Q8—82no—
298Q8—81no—
299Q8—81no—
300Q8—442no—
301Q8—441no—
302Q8—441no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—44no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4#6699011yescharacteristic
314C2×C4#6699011yescharacteristic
315C2×C4#6699111yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C2×C4#6700611yescharacteristic
319C8—42no—
320C8—224no—
321C8—442no—
322C8—442no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22#1062283611yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—82no—
332C4—81no—
333C4—881no—
334C4—881no—
335C4#1062280512yes—
336C4#1062281111yescharacteristic
337C4#1062281411yescharacteristic
338C4#1062285912yes—
339C2—41no—
340C2#1306965011yescharacteristic
341C2#1306965611yescharacteristic
342C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3230D11
hypocenterC11#10117
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
292. C11#10117semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130791582
#130694612
#130672112
#130670362
#130665072
C11×#32302
#1011711