Finite Group Databasebeta

← #14655332

Subgroups — #14655332

Order 2816.

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

normal subgroups only

This group has 454 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#13069606C211yesmaximal, characteristic
4#13067211C211yesmaximal, characteristic
5#13067036C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic
7C11×#3229C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#498—21no—
12C11×#487—21no—
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16#10622707—21no—
17#10622703—21no—
18#10622693—22no—
19#10622692—21no—
20#10622691—21no—
21#10622665—22no—
22#10622644—21no—
23#10622633—21no—
24#10622577—22no—
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622168—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×#106—24no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66899—22no—
65#66874—22no—
66#66872—24no—
67#66872—22no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10119—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×C8×C11—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C22⋊Dic11—41no—
105#4326—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113#4318—24no—
114#4318—22no—
115#4318—42no—
116#4318—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3255—111no—
121#3229D1111yescharacteristic
122#3165—111no—
123#1997—111no—
124#1526—111no—
125#1485—111no—
126#1299—111no—
127C23×C11#12111yescharacteristic
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11—42no—
131Q8×C11—82no—
132Q8×C11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—41no—
149Dic22—41no—
150Dic22—41no—
151Dic22—42no—
152C8×C11—42no—
153C11⋊C8—24no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156#533—111no—
157#533C2×D1111yescharacteristic
158C2×C4⋊Q8C2×D1111yescharacteristic
159#501—222no—
160#500—221no—
161#498—21no—
162#498—221no—
163#487—21no—
164#483—22no—
165#475—22no—
166#475—221no—
167#475—221no—
168#470—222no—
169#462—221no—
170#462—221no—
171#431C2×D1111yescharacteristic
172#428—222no—
173#423—111no—
174C4×M16—111no—
175C4×M16—111no—
176#343—222no—
177#330—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—82no—
189C4×C11#45511yescharacteristic
190C4×C11#45611yescharacteristic
191C4×C11#45612yes—
192C4×C11#47112yes—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—21no—
196C2×Q16—222no—
197C2×M16—112no—
198C2×M16—221no—
199C2×M16—221no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206C4⋊Q8C22⋊D1111yescharacteristic
207C4⋊Q8C22⋊D1111yescharacteristic
208#125—21no—
209#125—221no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—221no—
217C4×Q8—221no—
218#117—21no—
219#117—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22⋊D1112yes—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224#106—24no—
225#106—224no—
226#106—222no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8C22⋊D1112yes—
230#103—24no—
231#103—222no—
232#103—222no—
233C22⋊C8—21no—
234#97—112no—
235#97—221no—
236C4×C8—21no—
237C4×C8—221no—
238C4×C8—221no—
239C2×C11—41no—
240C2×C11#200511yescharacteristic
241C2×C11#200711yescharacteristic
242C2×C11#201911yescharacteristic
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×Q8—221no—
249C2×Q8—221no—
250C22×C4—22no—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254Q16—882no—
255M16—224no—
256M16—222no—
257M16—441no—
258M16—442no—
259C2×C8—22no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—441no—
281C42—41no—
282C42—441no—
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C11#1011911yescharacteristic, complemented, Sylow
288C23#6699211yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—42no—
292Q8—82no—
293Q8—82no—
294Q8—442no—
295Q8—441no—
296Q8—441no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4#6699011yescharacteristic
308C2×C4#6699011yescharacteristic
309C2×C4#6699111yescharacteristic
310C2×C4#6699211yescharacteristic
311C2×C4#6699311yescharacteristic
312C2×C4#6700611yescharacteristic
313C8—42no—
314C8—224no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1062283611yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—82no—
327C4—881no—
328C4—881no—
329C4#1062279012yes—
330C4#1062281511yescharacteristic
331C4#1062281811yescharacteristic
332C4#1062285912yes—
333C2—41no—
334C2#1306965011yescharacteristic
335C2#1306966111yescharacteristic
336C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3229D11
hypocenterC11#10119
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
287. C11#10119semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130791582
#130696062
#130672112
#130670362
#130665072
C11×#32292
#1011911