Finite Group Databasebeta

← #14647387

Subgroups — #14647387

Order 2816.

384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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#13071576C211yesmaximal, characteristic
2C4×#66888C211yesmaximal, characteristic
3#13066959C211yesmaximal, characteristic
4#13066510C211yesmaximal, characteristic
5#13066508C211yesmaximal, characteristic
6#13066480C211yesmaximal, characteristic
7C11×#1288C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C11×#383C2211yescharacteristic
12C2×#66888—21no—
13#10622545C2211yescharacteristic
14#10622539C2211yescharacteristic
15C4×#4318C2211yescharacteristic
16#10622267—21no—
17#10622265—21no—
18#10622264C411yescharacteristic
19#10622263C411yescharacteristic
20#10622262—21no—
21#10622262C411yescharacteristic
22#10622261C411yescharacteristic
23#10622259—21no—
24#10622192—21no—
25#10622107—21no—
26#10622107—21no—
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11D411yescharacteristic
31C2×Dic11⋊C4—21no—
32C2×Dic11⋊C4—21no—
33C2×Dic11⋊C4D411yescharacteristic
34C2×Dic11⋊C4D411yescharacteristic
35C2×C4×Dic11—21no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×#4318—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C11×#97—21no—
48C11×#97—21no—
49C4×C8×C11—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66888—24no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67#8774—111nomaximal, Sylow
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
78C22×Dic11C22⋊C411yescharacteristic
79C2×Dic22—22no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C11×M16—22no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—42no—
104C4×Dic11—42no—
105C4×Dic11—42no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2356—111no—
111C4×#101—111no—
112#1467—111no—
113#1300—111no—
114#1300—111no—
115#1288—111no—
116#1288D1111yescharacteristic
117C23×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#11711yescharacteristic
129C2×C4×C11#11711yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—22no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11#10412yes—
150Dic22—42no—
151Dic22—42no—
152C8×C11—42no—
153C8×C11—81no—
154C11⋊C8—42no—
155C11⋊C8—81no—
156C2×C4×Q8—111no—
157#432—111no—
158#432C2×D1111yescharacteristic
159C2×#101—221no—
160C4×M16—111no—
161C4×M16C2×D1111yescharacteristic
162#391—221no—
163#387—221no—
164#387—221no—
165#383—111no—
166#383C2×D1111yescharacteristic
167#382—111no—
168C4×C4⋊C4—111no—
169C4×C4⋊C4—221no—
170#376—111no—
171#376—111no—
172#343—221no—
173#324—221no—
174#324—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38111yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11#42111yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—81no—
188Dic11—22no—
189Dic11—42no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—81no—
194C22×Q8—111no—
195C2×M16—21no—
196C2×M16—221no—
197C4×Q8—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—221no—
209C2×C42—221no—
210C2×C42—221no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—221no—
214#101—224no—
215C22⋊C8—21no—
216C22⋊C8—221no—
217#97—21no—
218#97—21no—
219#97—221no—
220#97—221no—
221C4×C8—21no—
222C4×C8—221no—
223#95—21no—
224#95—21no—
225#95—111no—
226#95—111no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95C4×D1111yescharacteristic
233#95C4×D1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#182611yescharacteristic
237C2×C11#182711yescharacteristic
238C2×C11#183011yescharacteristic
239C2×Q8—222no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254M16—22no—
255M16—41no—
256M16—222no—
257M16—441no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—442no—
275C42—442no—
276C42—442no—
277C42#433911yescharacteristic
278C42#433911yescharacteristic
279C42#434111yescharacteristic
280C42#434311yescharacteristic
281C11#877411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1111yescharacteristic
283Q8—442no—
284Q8—442no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—112no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—222no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4#6692511yescharacteristic
312C2×C4#6693611yescharacteristic
313C2×C4#6693611yescharacteristic
314C2×C4#6694511yescharacteristic
315C2×C4#6694711yescharacteristic
316C2×C4#6694711yescharacteristic
317C8—42no—
318C8—81no—
319C8—442no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22#1062227711yescharacteristic
324C22D11×#10411yescharacteristic
325C22#1062243411yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—222no—
335C4—442no—
336C4—441no—
337C4—441no—
338C4—441no—
339C4—881no—
340C2—21no—
341C2—21no—
342C2#1306871411yescharacteristic
343C2#1306871811yescharacteristic
344C2#1306872911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1288C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1288D11
hypocenterC11#8774
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
281. C11#8774semidirect

Maximal subgroups

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

subgroupindex
#130715762
C4×#668882
#130669592
#130665102
#130665082
#130664802
C11×#12882
#877411