Finite Group Databasebeta

← #14664644

Subgroups — #14664644

Order 2816.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074193C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066636C212yesmaximal
4#13066615C212yesmaximal
5C11×#1820C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic, complemented
8C11×#381—21no—
9#10622823—21no—
10#10622596C411yescharacteristic, complemented
11#10622592C411yescharacteristic, complemented
12#10622591—21no—
13#10622566C2211yescharacteristic
14#10622560C2211yescharacteristic
15#10622557—21no—
16#10622550C411yescharacteristic, complemented
17#10622546—21no—
18#10622538—21no—
19C11×#342—21no—
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C4×Dic22—41no—
42C4×Dic22—41no—
43C11×#95—41no—
44C11×#95—41no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11842—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11—42no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C22⋊Dic11—42no—
86C22⋊Dic11—42no—
87C4⋊Dic11—41no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92C4×Dic11—42no—
93C2×C11⋊C8—42no—
94#2599—111no—
95#1820D1111yescharacteristic
96#1458—111no—
97#1351—112no—
98#1344—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#13512yes—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—82no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11#9911yescharacteristic
124C2×C4×C11#9911yescharacteristic
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137Dic22—42no—
138Dic22—42no—
139C11⋊C8—82no—
140C2×C4×Q8—111no—
141C2×#117C2×D1111yescharacteristic
142#431—221no—
143#398—111no—
144#397—111no—
145#395—111no—
146#393—111no—
147#388—221no—
148#387—221no—
149#387—221no—
150#385—221no—
151#383—111no—
152#381—21no—
153#342—21no—
154#342C2×D1112yes—
155#324—221no—
156#323—112no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—81no—
164C22×C11C2×#9911yescharacteristic
165C22×C11#41611yescharacteristic
166C22×C11#42111yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—162no—
175Dic11—42no—
176Dic11—81no—
177Dic11—81no—
178Dic11—81no—
179C22×Q8—111no—
180C23×C4C22⋊D1111yescharacteristic
181C4×Q8—441no—
182C4×Q8—441no—
183#117—41no—
184#117—41no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4C4×D1111yescharacteristic
190C2×C4⋊C4D4411yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—221no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4C22⋊D1111yescharacteristic
195C2×C22⋊C4C22×D1111yescharacteristic
196C2×C42—221no—
197C2×C42C4×D1111yescharacteristic
198C2×C42D4411yescharacteristic
199C4⋊C8—441no—
200C22⋊C8—222no—
201C4×C8—441no—
202#95—41no—
203#95—41no—
204#95—111no—
205#95—111no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11—42no—
215C2×C11#151611yescharacteristic
216C2×C11#212011yescharacteristic
217C2×C11#212911yescharacteristic
218C24C2×C22⋊D1111yescharacteristic
219C2×Q8—441no—
220C2×Q8—442no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4C2×D4411yescharacteristic
236C2×C8—442no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—441no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—442no—
249C22⋊C4—442no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—442no—
255C11#1184211yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23C2×(C2×D11)⋊C411yescharacteristic
261C23#6700312yes—
262Q8—442no—
263Q8—442no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—222no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4#6687011yescharacteristic
295C2×C4#6687011yescharacteristic
296C8—882no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22C2×#6687011yescharacteristic
305C22#1062261511yescharacteristic
306C22#1062261811yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—162no—
315C4—442no—
316C4—881no—
317C4—881no—
318C4—881no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2#1306717011yescharacteristic
323C2#1307025511yescharacteristic
324C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1820C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1820D11
hypocenterC11#11842
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic22C4semidirect
10. #10622596C4semidirect
11. #10622592C4semidirect
16. #10622550C4semidirect
255. C11#11842semidirect

Maximal subgroups

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

subgroupindex
#130741932
#130669302
#130666362
#130666152
C11×#18202
#1184211