Finite Group Databasebeta

← #14663341

Subgroups — #14663341

Order 2816.

366 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 69 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#13073068C211yesmaximal, characteristic
2#13066949C211yesmaximal, characteristic
3#13066929C211yesmaximal, characteristic
4#13066561C211yesmaximal, characteristic, complemented
5#13066561C211yesmaximal, characteristic, complemented
6#13066550C211yesmaximal, characteristic, complemented
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×#66945C2211yescharacteristic
10C11×#391C2211yescharacteristic
11#10622843C411yescharacteristic
12#10622589C2211yescharacteristic
13C4×(C2×D11)⋊C4C411yescharacteristic
14#10622549C411yescharacteristic
15#10622332—21no—
16#10622331—21no—
17#10622288—21no—
18#10622288—21no—
19#10622265—21no—
20#10622265—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31#66999—41no—
32#66999—41no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4D411yescharacteristic
36C2×(C2×D11)⋊C4D411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45#66945—41no—
46#66945—41no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11552—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C42×C11—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2499—111no—
106#1464—111no—
107#1458—111no—
108#1325—111no—
109#1325—111no—
110#1319—111no—
111#1319D1111yescharacteristic, complemented
112C23×C11C2×C22⋊C411yescharacteristic
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—41no—
117C22×D11—41no—
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#13111yescharacteristic
133C2×C4×C11#13111yescharacteristic
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—22no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11#9911yescharacteristic
147C2×Dic11#9911yescharacteristic
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—41no—
151C4×D11—41no—
152C8×C11—81no—
153C8×C11—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156C2×C22⋊Q8—111no—
157C2×#117—111no—
158#432—221no—
159#431—221no—
160#397—221no—
161#397—221no—
162#391—111no—
163#391C2×D1111yescharacteristic
164#387—221no—
165#387—221no—
166#384—111no—
167#382—111no—
168C4×C22⋊C4—111no—
169#324—111no—
170#324—111no—
171#324C2×D1111yescharacteristic
172#324C2×D1111yescharacteristic
173#323—221no—
174#323—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#40811yescharacteristic
178C22×C11C2×#9911yescharacteristic
179C22×C11#41311yescharacteristic
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—81no—
184C2×D11—81no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—81no—
190C4×C11—81no—
191Dic11—21no—
192Dic11—21no—
193Dic11—42no—
194Dic11—41no—
195Dic11—41no—
196Dic11—81no—
197C22×Q8C4×D1111yescharacteristic
198C23×C4—111no—
199C22⋊Q8—441no—
200C22⋊Q8—441no—
201#117—441no—
202#117—441no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C22⋊C4—111no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C42—111no—
214C2×C42—111no—
215C2×C42—111no—
216C2×C42C4×D1111yescharacteristic
217C4⋊C8—441no—
218C4⋊C8—441no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#97—441no—
224C4×C8—441no—
225#95—21no—
226#95—21no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11#146811yescharacteristic
235C2×C11#212611yescharacteristic
236C2×C11#213511yescharacteristic
237D11—81no—
238C24—111no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—441no—
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—41no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C22⋊C4—441no—
270C22⋊C4—441no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C42—41no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42—221no—
279C42—221no—
280C11#1155211yescharacteristic, complemented, Sylow
281C23—221no—
282C23—221no—
283C23—221no—
284C23—441no—
285C23—441no—
286C23C22⋊C4×D1111yescharacteristic
287Q8—81no—
288Q8—81no—
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—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—222no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4#6695411yescharacteristic
320C2×C4#6696011yescharacteristic
321C8—81no—
322C8—81no—
323C8—881no—
324C8—881no—
325C22—21no—
326C22—21no—
327C22—441no—
328C22—441no—
329C22—441no—
330C22—881no—
331C22—881no—
332C22#1062234011yescharacteristic
333C22D11×#9911yescharacteristic
334C22#1062235811yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—221no—
342C4—221no—
343C4—442no—
344C4—441no—
345C4—441no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—881no—
350C2#1306696111yescharacteristic
351C2#1307028011yescharacteristic
352C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1319D11
hypocenterC11#11552
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #13066561C2semidirect
5. #13066561C2semidirect
6. #13066550C2semidirect
7. C11×#1319C2semidirect
111. #1319D11semidirect
280. C11#11552semidirect

Maximal subgroups

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

subgroupindex
#130730682
#130669492
#130669292
#130665612
#130665502
C11×#13192
#1155211