Finite Group Databasebeta

← #14657685

Subgroups — #14657685

Order 2816.

394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079543C211yesmaximal, characteristic
2#13069460C211yesmaximal, characteristic, complemented
3#13067404C211yesmaximal, characteristic, complemented
4#13067349C211yesmaximal, characteristic
5#13067298C211yesmaximal, characteristic, complemented
6#13067034C211yesmaximal, characteristic
7C11×#1299C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×#66888—22no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622454—21no—
17#10622454—21no—
18#10622351—22no—
19#10622306—21no—
20#10622294—21no—
21#10622123—21no—
22#10622119—21no—
23#10622119—22no—
24#10622118—21no—
25#10622117—21no—
26#10622097—22no—
27C2×#4339—21no—
28C22×Dic22D412yes—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×#4318—21no—
37C2×#4314—22no—
38C2×#4314—22no—
39#66928—21no—
40#66927D411yescharacteristic
41C4×D44—21no—
42C4×D44—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922D411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D411yescharacteristic
51C11×C4⋊C8D411yescharacteristic
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C22⋊(C11⋊C8)—21no—
57#66888—44no—
58#66880—22no—
59#66880—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#10489—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C2×C22⋊D11—41no—
69C22×Dic11—22no—
70#4339—82no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×C4×D11—41no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—21no—
78C2×Dic22—42no—
79C2×Dic22—42no—
80C11×M16—22no—
81C11×M16—41no—
82C11×M16—81no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99#4318—42no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102#4314—82no—
103#4314—82no—
104#3206—111no—
105#1966—111no—
106#1574—111no—
107#1560—111no—
108#1548—111no—
109#1484—111no—
110#1299D1111yescharacteristic, complemented
111C23×C11#12311yescharacteristic
112C22×D11—41no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11#12411yescharacteristic
124C22⋊D11—82no—
125C2×Dic11—44no—
126C2×Dic11—41no—
127C2×Dic11—42no—
128D44—41no—
129D44—41no—
130D44—41no—
131D44—41no—
132D44—81no—
133C4×D11—82no—
134Dic22—42no—
135Dic22—42no—
136Dic22—82no—
137Dic22—81no—
138C8×C11—42no—
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—81no—
142C11⋊C8—42no—
143C11⋊C8—81no—
144#532—111no—
145C2×C4⋊Q8—111no—
146#492—221no—
147#487—221no—
148#461—221no—
149#461—221no—
150#448—222no—
151#431—111no—
152#431C2×D1111yescharacteristic
153#423—111no—
154#423C2×D1111yescharacteristic
155C2×#101—222no—
156C4×M16C2×D1111yescharacteristic
157#335—221no—
158#334—221no—
159#333—222no—
160#333—221no—
161#331—221no—
162D4⋊C8—222no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#39411yescharacteristic
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11#45311yescharacteristic
174C4×C11#45511yescharacteristic
175C4×C11#47112yes—
176C4×C11#47111yescharacteristic
177C4×C11#47311yescharacteristic
178Dic11—82no—
179Dic11—81no—
180C2×#41—221no—
181C22×Q8—112no—
182C2×SD16—222no—
183C2×SD16—222no—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—221no—
187C4⋊Q8—111no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192#127—111no—
193#124—221no—
194#121—221no—
195#121—221no—
196C4×D4—221no—
197C4×D4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—112no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8D4411yescharacteristic
207C4⋊C8D4411yescharacteristic
208#103—222no—
209#103—222no—
210#101—444no—
211C22⋊C8—21no—
212C22⋊C8—221no—
213#97—21no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—221no—
217C2×C11—41no—
218C2×C11#203711yescharacteristic
219C2×C11#204611yescharacteristic
220C2×C11#205211yescharacteristic
221D11—161no—
222#41—882no—
223C2×Q8—222no—
224C2×Q8—222no—
225C2×Q8—221no—
226C2×Q8—442no—
227C2×Q8—442no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4—441no—
232C22×C4—222no—
233C22×C4—441no—
234C22×C4#433911yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4#434311yescharacteristic
237SD16—882no—
238SD16—882no—
239M16—22no—
240M16—41no—
241M16—81no—
242M16—442no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—222no—
248C2×C8—441no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C42C2×D4411yescharacteristic
258C42#433911yescharacteristic
259C42D4×D1111yescharacteristic
260C42D4×D1111yescharacteristic
261C11#1048911yescharacteristic, complemented, Sylow
262C23—441no—
263C23#6694711yescharacteristic
264Q8—442no—
265Q8—442no—
266Q8—882no—
267Q8—881no—
268D4—441no—
269D4—441no—
270D4—441no—
271D4—441no—
272D4—881no—
273D4—882no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—444no—
280C2×C4—441no—
281C2×C4—442no—
282C2×C4—882no—
283C2×C4#6692811yescharacteristic
284C2×C4#6693511yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6694711yescharacteristic
288C2×C4#6694811yescharacteristic
289C8—42no—
290C8—41no—
291C8—41no—
292C8—81no—
293C8—442no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—881no—
299C22—881no—
300C22—881no—
301C22#1062228511yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—882no—
306C4—881no—
307C4#1062236111yescharacteristic
308C4#1062236811yescharacteristic
309C4#1062243511yescharacteristic
310C4#1062243811yescharacteristic
311C4#1062251112yes—
312C2—41no—
313C2—1761no—
314C2#1306982911yescharacteristic
315C2#1306988011yescharacteristic
316C2#1306991811yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1299C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1299D11
hypocenterC11#10489
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
2. #13069460C2semidirect
3. #13067404C2semidirect
5. #13067298C2semidirect
7. C11×#1299C2semidirect
110. #1299D11semidirect
261. C11#10489semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130694602
#130674042
#130673492
#130672982
#130670342
C11×#12992
#1048911