Finite Group Databasebeta

← #14663453

Subgroups — #14663453

Order 2816.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073959C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066565C212yesmaximal, complemented
4#13066563C212yesmaximal, complemented
5C11×#1460C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×Dic11⋊C4C411yescharacteristic
8C11×#431—21no—
9#10622833C411yescharacteristic
10#10622833C411yescharacteristic
11#10622825C411yescharacteristic
12#10622823—21no—
13#10622820—21no—
14#10622597—21no—
15#10622561—21no—
16#10622559C2211yescharacteristic
17#10622559C2211yescharacteristic
18#10622546—21no—
19C11×#323—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11C2×C411yescharacteristic
37C2×C22⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—41no—
44C2×Dic11⋊C4—41no—
45C2×#4318—41no—
46C11×C4⋊C8—41no—
47C11×C22⋊C8—22no—
48C4×C8×C11—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—41no—
56#11577—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22×C411yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11—81no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—42no—
80C22×Dic11—81no—
81C2×C8×C11—42no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—21no—
86C42×C11—21no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—42no—
90C22⋊Dic11—81no—
91C4⋊Dic11—81no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—81no—
97#4318—82no—
98C2×C11⋊C8—42no—
99#2579—111no—
100#1465—111no—
101#1460D1111yescharacteristic
102#1326—112no—
103#1326—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11C2×C22⋊C411yescharacteristic
114C23×C11#13112yes—
115D4×C11—44no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10112yes—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—82no—
147C8×C11—82no—
148C11⋊C8—82no—
149C2×C4×D4C2×D1111yescharacteristic
150C22×C4⋊C4—111no—
151#431—21no—
152#407—221no—
153#398—221no—
154#396—221no—
155#387—221no—
156#386—111no—
157#386—111no—
158#385—111no—
159#385—111no—
160#385—221no—
161#380—111no—
162#324—221no—
163#323—21no—
164#323—112no—
165#323C2×D1112yes—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—22no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—81no—
178C22×C11#40811yescharacteristic
179C22×C11C2×#9911yescharacteristic
180C22×C11C2×#10111yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187Dic11—42no—
188Dic11—81no—
189Dic11—81no—
190Dic11—81no—
191C22×D4C4×D1111yescharacteristic
192C23×C4—111no—
193C23×C4—111no—
194C23×C4C4×D1111yescharacteristic
195C23×C4D4411yescharacteristic
196C2×M16—441no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—441no—
205C2×C4⋊C4—441no—
206C2×C4⋊C4D4411yescharacteristic
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4C22⋊D1111yescharacteristic
212C2×C22⋊C4C22×D1111yescharacteristic
213C2×C42C22⋊D1111yescharacteristic
214C4⋊C8—41no—
215C22⋊C8—22no—
216C22⋊C8—222no—
217C22⋊C8—441no—
218C4×C8—41no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—42no—
227C2×C11—81no—
228C2×C11#147211yescharacteristic
229C2×C11#212011yescharacteristic
230C2×C11#212111yescharacteristic
231C24(C2×D11)⋊C411yescharacteristic
232C24C2×C4×D1111yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—442no—
247C22×C4—441no—
248C22×C4—441no—
249C22×C4—881no—
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4C2×D4411yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255M16—882no—
256C2×C8—42no—
257C2×C8—442no—
258C4⋊C4—41no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—881no—
264C4⋊C4—881no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—222no—
268C22⋊C4—222no—
269C22⋊C4—442no—
270C22⋊C4—881no—
271C42—21no—
272C42—21no—
273C11#1157711yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#6695412yes—
284C23C2×(C2×D11)⋊C411yescharacteristic
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—222no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—882no—
314C2×C4#6687011yescharacteristic
315C2×C4#6687011yescharacteristic
316C2×C4#6688812yes—
317C8—82no—
318C8—882no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#6687011yescharacteristic
332C22#1062272311yescharacteristic
333C22C2×#6688811yescharacteristic
334C4—21no—
335C4—21no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—442no—
341C4—881no—
342C4—881no—
343C4—881no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1306697911yescharacteristic
349C2#1307025511yescharacteristic
350C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11577
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13066565C2semidirect
4. #13066563C2semidirect
273. C11#11577semidirect

Maximal subgroups

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

subgroupindex
#130739592
#130669542
#130665652
#130665632
C11×#14602
#1157711