Finite Group Databasebeta

← #14657680

Subgroups — #14657680

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#13079538C211yesmaximal, characteristic
2#13069459C211yesmaximal, characteristic, complemented
3#13067407C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic
6#13066505C211yesmaximal, characteristic, complemented
7C11×#1560C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66888—22no—
13#10622706—21no—
14#10622689—21no—
15#10622653—22no—
16#10622632—21no—
17#10622632—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#333—21no—
22C11×#331—21no—
23D4⋊(C11⋊C8)—22no—
24#10622119—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×Dic22D412yes—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×#127D411yescharacteristic
33C11×#124—21no—
34C11×#121—21no—
35C11×#121—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4324—22no—
40C2×#4324—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×#4318—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66888—44no—
55#66874—22no—
56#66874—22no—
57C4⋊(C11⋊C8)D411yescharacteristic
58C4⋊(C11⋊C8)D411yescharacteristic
59C4⋊(C11⋊C8)D412yes—
60#66867—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10489—111nomaximal, Sylow
65C11×#41—82no—
66C2×Q8×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—22no—
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22—42no—
79C2×Dic22—42no—
80C11×M16—42no—
81C11×M16—81no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92#4324—82no—
93#4324—82no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98#4318—22no—
99#4318—41no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104#3206—111no—
105#1966—111no—
106#1574—111no—
107#1560D1111yescharacteristic
108#1548—111no—
109#1484—111no—
110#1299—111no—
111C23×C11—41no—
112C23×C11#12311yescharacteristic
113Q8×C11—81no—
114D4×C11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—41no—
118D4×C11—81no—
119D4×C11—82no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—82no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×Dic11—44no—
134C2×Dic11—42no—
135Dic22—42no—
136Dic22—42no—
137Dic22—82no—
138C8×C11—81no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—41no—
142C11⋊C8—41no—
143C11⋊C8—42no—
144#532C2×D1111yescharacteristic
145C2×C4⋊Q8—111no—
146#492—221no—
147#487—221no—
148#461—221no—
149#461—221no—
150#448—222no—
151#431—111no—
152#431—111no—
153#423C2×D1111yescharacteristic
154#423C2×D1111yescharacteristic
155C2×#101—222no—
156C4×M16—111no—
157#335—221no—
158#334—221no—
159#333—21no—
160#333—222no—
161#331—21no—
162D4⋊C8—222no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11—81no—
169C22×C11#39411yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11#45311yescharacteristic
175C4×C11#45511yescharacteristic
176C4×C11#47111yescharacteristic
177C4×C11#47112yes—
178C4×C11#47311yescharacteristic
179Dic11—82no—
180C2×#41—21no—
181C22×Q8—112no—
182C2×SD16—222no—
183C2×SD16—222no—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—221no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8C22⋊D1111yescharacteristic
192#127C22⋊D1111yescharacteristic
193#124—21no—
194#121—21no—
195#121—21no—
196C4×D4—21no—
197C4×D4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—112no—
206C4⋊C8—111no—
207C4⋊C8—111no—
208#103—222no—
209#103—222no—
210#101—444no—
211C22⋊C8—221no—
212C22⋊C8—221no—
213#97—221no—
214C4×C8—221no—
215C4×C8—221no—
216C4×C8—221no—
217C2×C11—41no—
218C2×C11—161no—
219C2×C11#203711yescharacteristic
220C2×C11#204611yescharacteristic
221C2×C11#205211yescharacteristic
222#41—82no—
223C2×Q8—21no—
224C2×Q8—222no—
225C2×Q8—222no—
226C2×Q8—442no—
227C2×Q8—442no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—41no—
232C22×C4—41no—
233C22×C4—222no—
234C22×C4#433911yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237SD16—882no—
238SD16—882no—
239M16—42no—
240M16—81no—
241M16—222no—
242M16—441no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42#433911yescharacteristic
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1048911yescharacteristic, complemented, Sylow
262C23—41no—
263C23#6693611yescharacteristic
264Q8—81no—
265Q8—442no—
266Q8—442no—
267Q8—882no—
268D4—41no—
269D4—41no—
270D4—41no—
271D4—41no—
272D4—81no—
273D4—82no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—82no—
281C2×C4—444no—
282C2×C4—442no—
283C2×C4#6693711yescharacteristic
284C2×C4#6693711yescharacteristic
285C2×C4#6693811yescharacteristic
286C2×C4#6698211yescharacteristic
287C2×C4#6699011yescharacteristic
288C2×C4#6699211yescharacteristic
289C8—81no—
290C8—81no—
291C8—442no—
292C8—441no—
293C8—441no—
294C8—442no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—81no—
299C22—81no—
300C22—81no—
301C22#1062257211yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—81no—
306C4—882no—
307C4#1062236112yes—
308C4#1062281111yescharacteristic
309C4#1062281311yescharacteristic
310C4#1062281511yescharacteristic
311C4#1062281711yescharacteristic
312C2—41no—
313C2—161no—
314C2#1306982411yescharacteristic
315C2#1306987711yescharacteristic
316C2#1306991311yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1560C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#1560D11
hypocenterC11#10489
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

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

NH ≅ G/Ntype
2. #13069459C2semidirect
3. #13067407C2semidirect
4. #13067298C2semidirect
6. #13066505C2semidirect
261. C11#10489semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130694592
#130674072
#130672982
#130670332
#130665052
C11×#15602
#1048911