Finite Group Databasebeta

← #14663401

Subgroups — #14663401

Order 2816.

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

normal subgroups only

This group has 412 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#13073592C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic, complemented
3#13066549C212yesmaximal, complemented
4#13066547C212yesmaximal
5C11×#1461C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C411yescharacteristic
8C2×#66997C411yescharacteristic
9C2×#66928C411yescharacteristic
10C11×#431—21no—
11#10622607—21no—
12#10622607—21no—
13#10622601C2211yescharacteristic
14#10622587C2211yescharacteristic
15#10622553—21no—
16#10622553—21no—
17C4×C4⋊Dic11C411yescharacteristic
18#10622539—21no—
19C11×#324—21no—
20C11×#324C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×Dic22C2×C411yescharacteristic
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34#67000—42no—
35#66997—42no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47#66928—41no—
48#66928—41no—
49C11×C4⋊C8—41no—
50C11×C22⋊C8—22no—
51C4×C8×C11—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11565—111nomaximal, Sylow
59C23×D11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
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×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×D44—22no—
74C2×D44—41no—
75C2×D44—41no—
76C2×Dic22—22no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—42no—
96C4⋊Dic11—42no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—42no—
102#2545—111no—
103#1467—111no—
104#1461D1111yescharacteristic, complemented
105#1319—112no—
106#1318—112no—
107C23×C11C2×C22⋊C411yescharacteristic
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115Q8×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—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#10012yes—
133C2×C4×C11#13112yes—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143D44—82no—
144Dic22—82no—
145C8×C11—82no—
146C11⋊C8—82no—
147C2×C4⋊Q8—111no—
148C2×#124—111no—
149C2×#124—111no—
150C2×C4×Q8C2×D1111yescharacteristic
151#432—221no—
152#431—21no—
153#396—221no—
154#396—221no—
155#391—111no—
156#390—111no—
157#388—221no—
158#388—221no—
159C4×C4⋊C4—111no—
160#324—21no—
161#324—112no—
162#324—221no—
163#324C2×D1112yes—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#40811yescharacteristic
167C22×C11C2×#9911yescharacteristic
168C22×C11C2×#10011yescharacteristic
169C2×D11—81no—
170C2×D11—81no—
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—42no—
185Dic11—81no—
186Dic11—81no—
187C22×Q8—111no—
188C22×Q8C4×D1111yescharacteristic
189C22×D4—111no—
190C4⋊Q8—442no—
191#124—441no—
192#124—441no—
193#124—442no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4D4411yescharacteristic
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C4⋊C4C22×D1111yescharacteristic
202C2×C22⋊C4—221no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42C4×D1111yescharacteristic
211C2×C42D4411yescharacteristic
212C2×C42C22⋊D1111yescharacteristic
213C4⋊C8—41no—
214C4⋊C8—441no—
215C22⋊C8—22no—
216C22⋊C8—222no—
217#97—441no—
218C4×C8—41no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11#147111yescharacteristic
225C2×C11#212611yescharacteristic
226C2×C11#213311yescharacteristic
227D11—161no—
228C24—221no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—222no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×D4—222no—
236C2×D4—441no—
237C2×D4—441no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4C2×C4×D1111yescharacteristic
246C22×C4C2×D4411yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C2×C8—42no—
249C2×C8—442no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—442no—
254C4⋊C4—442no—
255C4⋊C4—442no—
256C22⋊C4—442no—
257C22⋊C4—442no—
258C22⋊C4—442no—
259C22⋊C4—442no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—442no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—441no—
270C42—441no—
271C11#1156511yescharacteristic, complemented, Sylow
272C23—441no—
273C23—441no—
274C23—441no—
275C23—441no—
276C23—441no—
277C23—441no—
278C23—441no—
279C23C2×(C2×D11)⋊C411yescharacteristic
280Q8—44no—
281Q8—882no—
282D4—882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—222no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4#6687011yescharacteristic
307C2×C4#6687011yescharacteristic
308C2×C4#6688712yes—
309C2×C4#6695412yes—
310C8—82no—
311C8—882no—
312C22—21no—
313C22—21no—
314C22—881no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C2×#6687011yescharacteristic
322C22#1062272311yescharacteristic
323C22C2×#6688711yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—442no—
333C4—881no—
334C4—881no—
335C2—21no—
336C2—21no—
337C2—1761no—
338C2#1306697511yescharacteristic
339C2#1307027911yescharacteristic
340C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1461C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1461D11
hypocenterC11#11565
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13066960C2semidirect
3. #13066549C2semidirect
5. C11×#1461C2semidirect
104. #1461D11semidirect
271. C11#11565semidirect

Maximal subgroups

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

subgroupindex
#130735922
#130669602
#130665492
#130665472
C11×#14612
#1156511