Finite Group Databasebeta

← #14655435

Subgroups — #14655435

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#13079802C211yesmaximal, characteristic
2C2×#10622695C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic
5#13066971C211yesmaximal, characteristic, complemented
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#498—21no—
12C11×#486—21no—
13C11×#481—22no—
14C11×#476—22no—
15C11×#431C2211yescharacteristic
16C2×#66899—21no—
17C2×#66899—21no—
18#10622695—22no—
19#10622695—22no—
20#10622693—21no—
21#10622684—21no—
22#10622647—21no—
23#10622646—21no—
24#10622622—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622185—22no—
29#10622178—22no—
30#10622107—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C22×C11⋊C8—21no—
52#66923—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56C11×#106—24no—
57C11×C4⋊C8—21no—
58C11×#102—24no—
59C11×C22⋊C8D412yes—
60C4×C8×C11—21no—
61#66899—24no—
62#66899—24no—
63#66896—22no—
64#66896—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10134—111nomaximal, Sylow
76C11×#41—82no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—44no—
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—41no—
117#3234—111no—
118#3227D1111yescharacteristic
119C2×#491—111no—
120#1556—111no—
121#1530—111no—
122#1470—111no—
123#1302—111no—
124C23×C11—41no—
125C23×C11#12111yescharacteristic
126Q8×C11—44no—
127Q8×C11—81no—
128Q8×C11—82no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—81no—
132D4×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11—82no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—81no—
150C8×C11—42no—
151C11⋊C8—42no—
152C11⋊C8—42no—
153C11⋊C8—81no—
154#532C2×D1111yescharacteristic
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×#125—111no—
157#501—221no—
158#498—21no—
159#491—222no—
160#491—222no—
161#490—221no—
162#486—21no—
163#481—22no—
164#481—221no—
165#480—221no—
166#478—222no—
167#476—22no—
168#432—111no—
169#432—111no—
170#431C2×D1111yescharacteristic
171C2×#103—221no—
172C2×#103—221no—
173C2×#97—111no—
174#332—222no—
175#329—222no—
176#324—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11#39211yescharacteristic
183C22×C11#47112yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11#45412yes—
192Dic11—81no—
193Dic11—81no—
194C2×#41—21no—
195C22×Q8—21no—
196C22×C8—221no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8C22⋊D1112yes—
201C4⋊Q8C22⋊D1111yescharacteristic
202#127C22⋊D1111yescharacteristic
203#125—221no—
204#125—221no—
205#125—221no—
206#125—221no—
207#124—21no—
208#121—21no—
209#121—21no—
210C4×D4—21no—
211C4×D4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C42C22×D1111yescharacteristic
219#107—222no—
220#106—24no—
221#106—222no—
222C4⋊C8—21no—
223C4⋊C8—112no—
224C4⋊C8—221no—
225#103—224no—
226#103—224no—
227#102—24no—
228#102—222no—
229#102—222no—
230C22⋊C8—221no—
231C22⋊C8—221no—
232C22⋊C8C22⋊D1112yes—
233#97—112no—
234#97—221no—
235#97—221no—
236#97—221no—
237C4×C8—21no—
238C2×C11—22no—
239C2×C11—161no—
240C2×C11#200311yescharacteristic
241C2×C11#200911yescharacteristic
242C2×C11#201911yescharacteristic
243#41—82no—
244C2×Q8—22no—
245C2×Q8—21no—
246C2×Q8—44no—
247C2×Q8—41no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C2×C8—22no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#1013411yescharacteristic, complemented, Sylow
285C23—41no—
286C23#6699111yescharacteristic
287Q8—44no—
288Q8—81no—
289Q8—82no—
290D4—42no—
291D4—42no—
292D4—81no—
293D4—82no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—442no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—881no—
305C2×C4#6699011yescharacteristic
306C2×C4#6699011yescharacteristic
307C2×C4#6699211yescharacteristic
308C2×C4#6699211yescharacteristic
309C2×C4#6699311yescharacteristic
310C2×C4#6700611yescharacteristic
311C8—42no—
312C8—442no—
313C8—442no—
314C8—881no—
315C22—21no—
316C22—21no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#1062279012yes—
321C22#1062283611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—81no—
329C4—881no—
330C4—881no—
331C4#1062281412yes—
332C2—22no—
333C2—161no—
334C2#1306963511yescharacteristic
335C2#1306967611yescharacteristic
336C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3227D11
hypocenterC11#10134
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×#10622695C2semidirect
3. #13067333C2semidirect
5. #13066971C2semidirect
6. #13066516C2semidirect
284. C11#10134semidirect

Maximal subgroups

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

subgroupindex
#130798022
C2×#106226952
#130673332
#130672272
#130669712
#130665162
C11×#32272
#1013411