Finite Group Databasebeta

← #14684573

Subgroups — #14684573

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066884C213yesmaximal, complemented
2#13066881C211yesmaximal, characteristic, complemented
3#13066878C211yesmaximal, characteristic, complemented
4#13066869C213yesmaximal, complemented
5#13066861C213yesmaximal
6#13066838C213yesmaximal
7C2×C11×#396C211yesmaximal, characteristic
8C24×Dic11C2211yescharacteristic
9C22×C11×C4⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C22×C22⋊Dic11C2213yes—
12C22×C4⋊Dic11C2213yes—
13C11×#396C418yescomplemented
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C25×C11C2311yescharacteristic
23C23×C4×C11C2313yes—
24C23×C4×C11C2313yes—
25C23×Dic11—43no—
26C23×Dic11—43no—
27C23×Dic11Q814yes—
28C23×Dic11C2313yes—
29C23×Dic11C2313yes—
30C23×Dic11C2311yescharacteristic
31C23×Dic11C2311yescharacteristic
32C2×C11×C4⋊C4—43no—
33C2×C11×C4⋊C4—43no—
34C2×C11×C4⋊C4C2×C4112yescomplemented
35C2×C11×C22⋊C4—43no—
36C2×C11×C22⋊C4—43no—
37C2×C11×C22⋊C4C2×C4112yes—
38C2×C22⋊Dic11—26no—
39C2×C22⋊Dic11—43no—
40C2×C22⋊Dic11—43no—
41C2×C4⋊Dic11—43no—
42C2×C4⋊Dic11—43no—
43C2×C4⋊Dic11—43no—
44C11×#95C2×C414yescomplemented
45C11⋊#95—43no—
46C11⋊#95—43no—
47C11⋊#95—43no—
48C11⋊#95—43no—
49C11⋊#95—43no—
50C11⋊#95—43no—
51C11⋊#95—43no—
52#14637—111nomaximal, Sylow
53C24×C11—23no—
54C24×C11—23no—
55C24×C11—23no—
56C24×C11—23no—
57C24×C11C22×C412yes—
58C24×C11C2×Q812yes—
59C24×C11#4112yes—
60C24×C11C2411yescharacteristic
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—23no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—23no—
72C22×C4×C11—23no—
73C22×C4×C11C22×C416yes—
74C22×C4×C11C22×C416yes—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11—23no—
84C22×Dic11—23no—
85C22×Dic11—23no—
86C22×Dic11—23no—
87C22×Dic11—23no—
88C22×Dic11—23no—
89C22×Dic11—23no—
90C22×Dic11—23no—
91C22×Dic11—23no—
92C22×Dic11—23no—
93C22×Dic11—412no—
94C22×Dic11—44no—
95C22×Dic11—412no—
96C22×Dic11C2×Q812yes—
97C22×Dic11C2×Q812yes—
98C11×C4⋊C4—412no—
99C11×C22⋊C4—412no—
100C22⋊Dic11—412no—
101C4⋊Dic11—412no—
102C2×#396D1111yescharacteristic
103#1445—113no—
104#1444—111no—
105#1443—111no—
106#1441—113no—
107#1439—113no—
108C22⋊#95—113no—
109C23×C11—26no—
110C23×C11—26no—
111C23×C11—26no—
112C23×C11—26no—
113C23×C11—26no—
114C23×C11—26no—
115C23×C11—41no—
116C23×C11—43no—
117C23×C11—43no—
118C23×C11—43no—
119C23×C11—43no—
120C23×C11—43no—
121C23×C11C4×Q814yes—
122C23×C11C23×C411yescharacteristic
123C23×C11C22×Q811yescharacteristic
124C23×C11C2×#4111yescharacteristic
125C23×C11H(5,𝔽2)13yes—
126C23×C11H(5,𝔽2)13yes—
127C23×C11H(5,𝔽2)13yes—
128C23×C112−1+413yes—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—26no—
132C2×C4×C11—26no—
133C2×C4×C11—26no—
134C2×C4×C11—26no—
135C2×C4×C11—43no—
136C2×C4×C11—43no—
137C2×C4×C11—43no—
138C2×C4×C11—43no—
139C2×C4×C11—43no—
140C2×C4×C11—43no—
141C2×C4×C11—43no—
142C2×C4×C11—43no—
143C2×Dic11—26no—
144C2×Dic11—26no—
145C2×Dic11—416no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—43no—
149C2×Dic11—43no—
150C2×Dic11—43no—
151C2×Dic11—43no—
152C2×Dic11—43no—
153C2×Dic11—43no—
154C2×Dic11—43no—
155C2×Dic11—43no—
156C2×Dic11—43no—
157C2×Dic11—43no—
158C2×Dic11—43no—
159C2×Dic11—43no—
160C2×Dic11—43no—
161C2×Dic11—43no—
162C2×Dic11—43no—
163C2×Dic11—43no—
164C24×C4—111no—
165C22×C4⋊C4—113no—
166C22×C4⋊C4C2×D1113yes—
167C22×C22⋊C4—113no—
168C22×C22⋊C4C2×D1113yes—
169#396Dic1118yescomplemented
170C2×#95—113no—
171C2×#95—113no—
172C2×#95—113no—
173C2×#95—113no—
174C2×#95—113no—
175C2×#95—113no—
176C2×#95—113no—
177C2×#95C2×D1111yescharacteristic
178C22×C11—212no—
179C22×C11—42no—
180C22×C11—46no—
181C22×C11—46no—
182C22×C11—42no—
183C22×C11—46no—
184C22×C11—42no—
185C22×C11C2×C4×Q811yescharacteristic
186C22×C11#51813yes—
187C22×C11#52013yes—
188C22×C11#53813yes—
189C22×C11#53913yes—
190C22×C11#54313yes—
191C22×C11#54413yes—
192C22×C11#56011yescharacteristic
193C22×C11#56013yes—
194C22×C11#56013yes—
195C22×C11#56213yes—
196C22×C11#56213yes—
197C22×C11#56313yes—
198C4×C11—46no—
199C4×C11—46no—
200Dic11—42no—
201Dic11—42no—
202Dic11—83no—
203Dic11—83no—
204C25C22×D1111yescharacteristic
205C23×C4—111no—
206C23×C4—111no—
207C23×C4—114no—
208C23×C4—113no—
209C23×C4—113no—
210C23×C4—443no—
211C23×C4—443no—
212C23×C4C22×D1113yes—
213C23×C4C22×D1113yes—
214C2×C4⋊C4—43no—
215C2×C4⋊C4—43no—
216C2×C4⋊C4—443no—
217C2×C4⋊C4—443no—
218C2×C4⋊C4—443no—
219C2×C4⋊C4C2×Dic11112yescomplemented
220C2×C22⋊C4—43no—
221C2×C22⋊C4—43no—
222C2×C22⋊C4—226no—
223C2×C22⋊C4—443no—
224C2×C22⋊C4—443no—
225C2×C22⋊C4C2×Dic11112yes—
226#95—443no—
227#95—443no—
228#95—443no—
229#95—443no—
230#95—443no—
231#95—443no—
232#95—443no—
233#95C2×Dic1114yescomplemented
234C2×C11—44no—
235C2×C11#232913yes—
236C2×C11#237713yes—
237C2×C11#238311yescharacteristic
238C2×C11#282511yescharacteristic
239C2×C11#282713yes—
240C2×C11#284113yes—
241C2×C11#284211yescharacteristic
242C24—23no—
243C24—23no—
244C24—23no—
245C24—23no—
246C24Q8×D1112yes—
247C24#434312yes—
248C24C22×Dic1112yes—
249C24C23×D1111yescharacteristic
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—112no—
263C22×C4—112no—
264C22×C4—223no—
265C22×C4—223no—
266C22×C4—223no—
267C22×C4—223no—
268C22×C4—223no—
269C22×C4—223no—
270C22×C4—223no—
271C22×C4—223no—
272C22×C4—223no—
273C22×C4—223no—
274C22×C4—223no—
275C22×C4—223no—
276C22×C4—223no—
277C22×C4—223no—
278C22×C4—223no—
279C22×C4—223no—
280C22×C4—223no—
281C22×C4—223no—
282C22×C4—4412no—
283C22×C4—444no—
284C22×C4—4412no—
285C22×C4C22×Dic1116yes—
286C22×C4C22×Dic1116yes—
287C4⋊C4—412no—
288C4⋊C4—4412no—
289C22⋊C4—412no—
290C22⋊C4—4412no—
291C11#1463711yescharacteristic, complemented, Sylow
292C23—26no—
293C23—26no—
294C23—26no—
295C23—26no—
296C23—26no—
297C23—26no—
298C23—41no—
299C23—43no—
300C23—43no—
301C23—43no—
302C23—43no—
303C23—43no—
304C23Q8×Dic1114yes—
305C23#6703713yes—
306C23#6703713yes—
307C23C2×Q8×D1111yescharacteristic
308C23C2×#434311yescharacteristic
309C23#6704213yes—
310C23#6704313yes—
311C23C23×Dic1111yescharacteristic
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—226no—
327C2×C4—226no—
328C2×C4—4416no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—443no—
332C2×C4—443no—
333C2×C4—443no—
334C2×C4—443no—
335C2×C4—443no—
336C2×C4—443no—
337C2×C4—443no—
338C2×C4—443no—
339C2×C4—443no—
340C2×C4—443no—
341C2×C4—443no—
342C2×C4—443no—
343C2×C4—443no—
344C2×C4—443no—
345C2×C4—443no—
346C2×C4—443no—
347C22—212no—
348C22—46no—
349C22—42no—
350C22—46no—
351C22—42no—
352C22—42no—
353C22—46no—
354C22#1062315113yes—
355C22#1062315113yes—
356C22#1062315213yes—
357C22#1062315213yes—
358C22#1062315413yes—
359C22#1062316513yes—
360C22#1062317513yes—
361C22#1062317613yes—
362C22#1062324211yescharacteristic
363C22#1062324313yes—
364C22#1062332913yes—
365C22C2×Q8×Dic1111yescharacteristic
366C22#1062335813yes—
367C4—46no—
368C4—46no—
369C4—442no—
370C4—442no—
371C4—883no—
372C4—883no—
373C2—44no—
374C2#1307135113yes—
375C2#1307177313yes—
376C2#1307180811yescharacteristic
377C2#1307670711yescharacteristic
378C2#1307673013yes—
379C2#1307687713yes—
380C2#1307687911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#396C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#396D11
hypocenterC11#14637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13066884C2semidirect
2. #13066881C2semidirect
3. #13066878C2semidirect
4. #13066869C2semidirect
13. C11×#396C4semidirect
34. C2×C11×C4⋊C4C2×C4semidirect
44. C11×#95C2×C4semidirect
169. #396Dic11semidirect
219. C2×C4⋊C4C2×Dic11semidirect
233. #95C2×Dic11semidirect
291. C11#14637semidirect

Maximal subgroups

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

subgroupindex
#130668842
#130668812
#130668782
#130668692
#130668612
#130668382
C2×C11×#3962
#1463711