Finite Group Databasebeta

← #14655472

Subgroups — #14655472

Order 2816.

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

normal subgroups only

This group has 446 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#13079561C211yesmaximal, characteristic
2C2×#10622678C211yesmaximal, characteristic
3#13067332C211yesmaximal, characteristic
4#13067231C211yesmaximal, characteristic
5#13066972C211yesmaximal, characteristic
6#13066514C211yesmaximal, characteristic
7C11×#3236C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#484—21no—
14C11×#483—21no—
15C11×#479—22no—
16C11×#432C2211yescharacteristic
17#10622706—21no—
18#10622705—21no—
19#10622678—22no—
20#10622678—22no—
21#10622663—22no—
22#10622644—22no—
23C2×#66872—21no—
24C2×#66871—21no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622166—22no—
30#10622124—22no—
31C22×Dic22—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
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⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C22×C11⋊C8—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57C11×#107—22no—
58C11×#106—22no—
59C11×C4⋊C8D412yes—
60C11×#103—22no—
61C11×#103—22no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66#66874—24no—
67#66872—24no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10139—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—41no—
84C2×Dic22—22no—
85C2×Dic22—41no—
86C2×Dic22—82no—
87C2×C8×C11—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
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×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#4326—84no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3236D1111yescharacteristic
118#3209—111no—
119C2×#501—111no—
120#1556—111no—
121#1531—111no—
122#1470—111no—
123#1302—111no—
124C23×C11#12111yescharacteristic
125Q8×C11—42no—
126Q8×C11—42no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—82no—
144Dic22—44no—
145Dic22—82no—
146C8×C11—42no—
147C11⋊C8—24no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150#533C2×D1111yescharacteristic
151C2×C4⋊Q8—111no—
152C2×#125C2×D1111yescharacteristic
153#501—21no—
154#501—222no—
155#501—222no—
156#494—221no—
157#491—21no—
158#487—221no—
159#484—21no—
160#483—21no—
161#479—22no—
162#462—222no—
163#451—222no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431—111no—
167C2×#107—221no—
168C2×#106—221no—
169C2×#97—111no—
170#332—222no—
171#330—222no—
172#324—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#39211yescharacteristic
176C22×C11#47312yes—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11#45612yes—
187Dic11—82no—
188C22×Q8—221no—
189C2×Q16—224no—
190C22×C8—221no—
191C4⋊Q8—112no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8C22⋊D1111yescharacteristic
196C4⋊Q8C22⋊D1111yescharacteristic
197#125—21no—
198#125—21no—
199#125—21no—
200#125—21no—
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206#117—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22⋊D1111yescharacteristic
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C42C22×D1111yescharacteristic
214#107—22no—
215#107—224no—
216#106—22no—
217#106—224no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8C22⋊D1112yes—
221#103—22no—
222#103—22no—
223#103—224no—
224C22⋊C8—21no—
225C22⋊C8—112no—
226C22⋊C8—221no—
227#97—21no—
228#97—112no—
229#97—221no—
230#97—221no—
231C4×C8—221no—
232C2×C11—22no—
233C2×C11#200511yescharacteristic
234C2×C11#200811yescharacteristic
235C2×C11#202011yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—222no—
239C2×Q8—441no—
240C2×Q8—882no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—441no—
244C22×C4D4×D1111yescharacteristic
245C22×C4#434111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247Q16—884no—
248C2×C8—22no—
249C2×C8—224no—
250C2×C8—222no—
251C2×C8—222no—
252C2×C8—441no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—41no—
272C42—41no—
273C42D4×D1111yescharacteristic
274C42D4×D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C42C2×C22⋊D1111yescharacteristic
277C11#1013911yescharacteristic, complemented, Sylow
278C23#6699211yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—444no—
282Q8—882no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—442no—
293C2×C4—882no—
294C2×C4#6699011yescharacteristic
295C2×C4#6699011yescharacteristic
296C2×C4#6699111yescharacteristic
297C2×C4#6699211yescharacteristic
298C2×C4#6699311yescharacteristic
299C2×C4#6700611yescharacteristic
300C8—42no—
301C8—224no—
302C8—442no—
303C8—881no—
304C22—21no—
305C22—21no—
306C22#1062281712yes—
307C22#1062283611yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4—81no—
317C4—882no—
318C4#1062285912yes—
319C2—22no—
320C2#1306965011yescharacteristic
321C2#1306966611yescharacteristic
322C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3236D11
hypocenterC11#10139
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
277. C11#10139semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106226782
#130673322
#130672312
#130669722
#130665142
C11×#32362
#1013911