Finite Group Databasebeta

← #14655490

Subgroups — #14655490

Order 2816.

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

normal subgroups only

This group has 456 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#13079806C211yesmaximal, characteristic
2#13079737C211yesmaximal, characteristic
3#13067342C211yesmaximal, characteristic, complemented
4#13067226C211yesmaximal, characteristic
5#13066972C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C2×C11×#501C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#501—22no—
12C11×#501—22no—
13C2×C11×#107—21no—
14C2×C11×#106—21no—
15C2×C11×#97C2211yescharacteristic
16#10622701—21no—
17#10622700—22no—
18#10622691—21no—
19#10622680—21no—
20#10622679—22no—
21#10622678—21no—
22#10622581—21no—
23#10622580—21no—
24#10622580—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622184—22no—
29#10622166—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49#66983—21no—
50#66983—21no—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66922D411yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×#97—21no—
59C11×#97D412yes—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)D412yes—
63#66873—22no—
64#66873—24no—
65#66873—22no—
66#66872—22no—
67#66871—22no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10142—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—41no—
86#4339—82no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3234—111no—
118#3226—111no—
119C2×#501D1111yescharacteristic, complemented
120#1558—111no—
121#1530—111no—
122#1470—111no—
123#1302—111no—
124C23×C11#12111yescharacteristic
125C22×D11—41no—
126Q8×C11—82no—
127Q8×C11—82no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—82no—
136C2×C4×C11—81no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C22⋊D11—82no—
144C2×Dic11—41no—
145D44—42no—
146D44—42no—
147D44—81no—
148C4×D11—82no—
149Dic22—81no—
150C8×C11—24no—
151C11⋊C8—42no—
152C11⋊C8—42no—
153C11⋊C8—81no—
154#532—111no—
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×#125C2×D1111yescharacteristic
157#501—22no—
158#501—22no—
159#501—221no—
160#500—221no—
161#490—221no—
162#486—221no—
163#481—221no—
164#480—222no—
165#480—221no—
166#478—222no—
167#474—222no—
168#432—111no—
169#432—111no—
170#431—111no—
171C2×#107—21no—
172C2×#106—21no—
173C2×#97C2×D1111yescharacteristic
174#333—222no—
175#329—222no—
176#324—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#39211yescharacteristic
180C22×C11#47212yes—
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—82no—
192C4×C11#45612yes—
193Dic11—81no—
194C2×#41—221no—
195C22×Q8—21no—
196C22×C8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—111no—
201C4⋊Q8C22⋊D1112yes—
202#127—111no—
203#125—21no—
204#125—21no—
205#125—21no—
206#125—21no—
207#124—221no—
208#121—221no—
209#121—221no—
210C4×D4—221no—
211C4×D4—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C4⋊C4C22⋊D1111yescharacteristic
218C2×C42C22×D1111yescharacteristic
219#107—24no—
220#107—224no—
221#107—222no—
222#106—24no—
223#106—222no—
224C4⋊C8—112no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227#102—224no—
228#102—222no—
229#102—222no—
230C22⋊C8—112no—
231C22⋊C8—221no—
232C22⋊C8—221no—
233#97—21no—
234#97—221no—
235#97—221no—
236#97C22⋊D1112yes—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11#200511yescharacteristic
240C2×C11#200911yescharacteristic
241C2×C11#201811yescharacteristic
242D11—161no—
243#41—882no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—82no—
247C2×Q8—221no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—441no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C2×C8—24no—
260C2×C8—22no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#1014211yescharacteristic, complemented, Sylow
285C23—441no—
286C23#6699211yescharacteristic
287Q8—82no—
288Q8—82no—
289Q8—881no—
290D4—442no—
291D4—442no—
292D4—881no—
293D4—882no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4—441no—
304C2×C4—882no—
305C2×C4#6699011yescharacteristic
306C2×C4#6699011yescharacteristic
307C2×C4#6699111yescharacteristic
308C2×C4#6699211yescharacteristic
309C2×C4#6699311yescharacteristic
310C2×C4#6700611yescharacteristic
311C8—24no—
312C8—442no—
313C8—442no—
314C8—881no—
315C22—21no—
316C22—21no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22#1062281212yes—
321C22#1062283611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—81no—
329C4—82no—
330C4—881no—
331C4#1062270812yes—
332C2—22no—
333C2—1761no—
334C2#1306965211yescharacteristic
335C2#1306967411yescharacteristic
336C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#501C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#501D11
hypocenterC11#10142
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13067342C2semidirect
5. #13066972C2semidirect
6. #13066515C2semidirect
7. C2×C11×#501C2semidirect
119. C2×#501D11semidirect
284. C11#10142semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130797372
#130673422
#130672262
#130669722
#130665152
C2×C11×#5012
#1014211