Finite Group Databasebeta

← #14655414

Subgroups — #14655414

Order 2816.

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

normal subgroups only

This group has 498 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#13079818C211yesmaximal, characteristic, complemented
2C2×#10622684C211yesmaximal, characteristic
3#13067330C211yesmaximal, characteristic
4#13067231C211yesmaximal, characteristic, complemented
5#13066971C211yesmaximal, characteristic, complemented
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3208C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#492—21no—
12C11×#486—21no—
13C11×#460—22no—
14C11×#450—22no—
15C11×#431C2211yescharacteristic
16C2×#66896—21no—
17C2×#66896—21no—
18#10622695—21no—
19#10622693—21no—
20#10622684—22no—
21#10622684—22no—
22#10622657—21no—
23#10622656—21no—
24#10622635—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622182—22no—
29#10622181—22no—
30#10622107—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×C11×SD16—24no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127D412yes—
41C11×#125—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C11×#117—21no—
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C22×C11⋊C8—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56#66923—21no—
57C11×C4⋊C8—21no—
58C11×#102—24no—
59C11×C22⋊C8D412yes—
60C4×C8×C11—21no—
61#66899—22no—
62#66899—22no—
63#66896—24no—
64#66896—24no—
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#10131—111nomaximal, Sylow
76C24×C11—41no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—82no—
87C2×D4×C11—82no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C11×SD16—84no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—41no—
119#3236—111no—
120#3208D1111yescharacteristic
121C2×#490—111no—
122#1555—111no—
123#1531—111no—
124#1470—111no—
125#1302—111no—
126C23×C11—42no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11—82no—
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132Q8×C11—42no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
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—
152C2×Dic11—42no—
153C2×Dic11—81no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#533C2×D1111yescharacteristic
159C2×#127C2×D1111yescharacteristic
160C2×#125—111no—
161#501—221no—
162#492—21no—
163#491—221no—
164#490—222no—
165#490—222no—
166#486—21no—
167#484—221no—
168#483—221no—
169#479—222no—
170#460—22no—
171#450—22no—
172#432—111no—
173#432—111no—
174#431C2×D1111yescharacteristic
175C2×#102—221no—
176C2×#102—221no—
177C2×#97—111no—
178#331—222no—
179#330—222no—
180#324—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—164no—
187C22×C11#39211yescharacteristic
188C22×C11#47112yes—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#45412yes—
197Dic11—81no—
198Dic11—81no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C2×SD16—24no—
203C22×C8—221no—
204C4⋊Q8C22⋊D1111yescharacteristic
205C4⋊Q8C22⋊D1111yescharacteristic
206#127—21no—
207#127—21no—
208#127—21no—
209#127C22⋊D1112yes—
210#125—21no—
211#125—221no—
212#125—221no—
213#125—221no—
214#125—221no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225#107—222no—
226#106—222no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230#103—222no—
231#103—222no—
232#102—24no—
233#102—224no—
234#102—224no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237C22⋊C8C22⋊D1112yes—
238#97—112no—
239#97—221no—
240#97—221no—
241#97—221no—
242C4×C8—21no—
243C2×C11—22no—
244C2×C11—162no—
245C2×C11#200311yescharacteristic
246C2×C11#200811yescharacteristic
247C2×C11#201911yescharacteristic
248C24—41no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—82no—
259C2×D4—82no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4D4×D1111yescharacteristic
263C22×C4#434111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—84no—
266C2×C8—22no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—442no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—41no—
286C42—41no—
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1013111yescharacteristic, complemented, Sylow
292C23—42no—
293C23—82no—
294C23—82no—
295C23—82no—
296C23#6699111yescharacteristic
297Q8—42no—
298Q8—42no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—82no—
303D4—82no—
304D4—82no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—881no—
314C2×C4#6699011yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700611yescharacteristic
320C8—42no—
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#1062279012yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—81no—
338C4—81no—
339C4—881no—
340C4—881no—
341C4#1062281412yes—
342C2—22no—
343C2—162no—
344C2#1306963511yescharacteristic
345C2#1306966911yescharacteristic
346C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3208C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#3208D11
hypocenterC11#10131
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13079818C2semidirect
4. #13067231C2semidirect
5. #13066971C2semidirect
6. #13066516C2semidirect
291. C11#10131semidirect

Maximal subgroups

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

subgroupindex
#130798182
C2×#106226842
#130673302
#130672312
#130669712
#130665162
C11×#32082
#1013111