Finite Group Databasebeta

← #14651484

Subgroups — #14651484

Order 2816.

536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077700C211yesmaximal, characteristic, complemented
2#13073619C211yesmaximal, characteristic
3#13067330C211yesmaximal, characteristic
4#13066959C211yesmaximal, characteristic, complemented
5#13066473C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1555C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66989C412yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13#10622835—21no—
14#10622835—21no—
15#10622834—21no—
16#10622834—21no—
17#10622834C412yes—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622441—22no—
22#10622332—21no—
23#10622331—21no—
24#10622314—22no—
25C11×#331—22no—
26#10622182—22no—
27#10622107—21no—
28#10622107—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C412yes—
32C22×Dic22C2×C411yescharacteristic
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—22no—
42#66989—44no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11C2×C412yes—
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#97—21no—
59C11×#97—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66879—22no—
64Dic11⋊C8—22no—
65Dic11⋊C8—22no—
66C8×Dic11—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70#66867—21no—
71#9458—111nomaximal, Sylow
72C24×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—82no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C2×Dic22—22no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—41no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102C22⋊Dic11—44no—
103C22⋊Dic11—44no—
104C22⋊Dic11—82no—
105C22⋊Dic11—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—42no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117C4×Dic11—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#2983—111no—
121#2548—111no—
122#1555—111no—
123#1555D1111yescharacteristic
124#1467—111no—
125#1285—111no—
126#1285—111no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11C2×C22⋊C411yescharacteristic
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11#10012yes—
164Dic22—42no—
165Dic22—42no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#127C2×D1111yescharacteristic
171C2×#124—112no—
172C2×C4×Q8—111no—
173#446—222no—
174#446—222no—
175#432—111no—
176#432—111no—
177#432—221no—
178#432C2×D1111yescharacteristic
179#432C2×D1111yescharacteristic
180#431—221no—
181#394—221no—
182#394—221no—
183#390—112no—
184#390—221no—
185#390—221no—
186C4×C4⋊C4—111no—
187#331—22no—
188#331—222no—
189#324—221no—
190#324—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11#38611yescharacteristic
201C22×C11C2×#10011yescharacteristic
202C22×C11#41311yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11#45412yes—
209Dic11—22no—
210Dic11—41no—
211Dic11—41no—
212Dic11—41no—
213Dic11—82no—
214C22×Q8—111no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C4×D1112yes—
218#127—21no—
219#127—21no—
220#127—21no—
221#127—21no—
222#124—444no—
223C4×Q8—221no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C22⋊C4—222no—
232C2×C22⋊C4—222no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4—222no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—112no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—112no—
241C4⋊C8—222no—
242C4⋊C8—222no—
243C4⋊C8—221no—
244C4⋊C8C22⋊D1112yes—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249#97—21no—
250#97—21no—
251#97—222no—
252#97—221no—
253#97—221no—
254C4×C8—222no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—162no—
259C2×C11#188811yescharacteristic
260C2×C11#190011yescharacteristic
261C2×C11#191011yescharacteristic
262C24—22no—
263C2×Q8—222no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—441no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—82no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—222no—
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—222no—
289C2×C8—441no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—442no—
297C22⋊C4—444no—
298C22⋊C4—444no—
299C22⋊C4—882no—
300C22⋊C4—882no—
301C42—221no—
302C42—221no—
303C42—221no—
304C42—221no—
305C42—442no—
306C42#433911yescharacteristic
307C42D4×D1111yescharacteristic
308C42#434111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#945811yescharacteristic, complemented, Sylow
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23C22⋊C4×D1111yescharacteristic
319Q8—442no—
320Q8—442no—
321D4—82no—
322D4—82no—
323D4—82no—
324D4—82no—
325D4—82no—
326D4—82no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—112no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4(C22⋊D11)⋊C411yescharacteristic
345C2×C4#6693611yescharacteristic
346C2×C4#6693711yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699111yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—82no—
357C22—82no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22—82no—
362C22—82no—
363C22D11×#10011yescharacteristic
364C22#1062235811yescharacteristic
365C22#1062256911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—222no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4—882no—
376C4#1062281412yes—
377C2—21no—
378C2—21no—
379C2—162no—
380C2#1306901611yescharacteristic
381C2#1306907611yescharacteristic
382C2#1306914011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1555C2
socleC22×C11#386
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1555D11
hypocenterC11#9458
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
1. #13077700C2semidirect
4. #13066959C2semidirect
5. #13066473C2semidirect
6. #13066471C2semidirect
310. C11#9458semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130736192
#130673302
#130669592
#130664732
#130664712
C11×#15552
#945811