Finite Group Databasebeta

← #14675605

Subgroups — #14675605

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622290C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C213yesmaximal, complemented
3C2×#10622279C213yesmaximal
4#13066885C213yesmaximal, complemented
5#13066858C213yesmaximal
6#95×Dic11C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×C11×C4⋊C4C2213yes—
10C22×(C2×D11)⋊C4C2213yes—
11C22×(C2×D11)⋊C4C2213yes—
12C22×C4⋊Dic11C2213yes—
13C22×C4×Dic11C2213yes—
14C22×C4×Dic11C2213yes—
15C2×C11×#95C2213yes—
16C2×C11×#95C2211yescharacteristic
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2216yes—
20C4⋊C4×Dic11—212no—
21#10622290C418yescomplemented
22#10622279—212no—
23C24×D11C2311yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×C4×C11C2313yes—
27C23×Dic11C2313yes—
28C23×Dic11C2313yes—
29C23×Dic11C2311yescharacteristic
30C22×C4×D11—26no—
31C22×C4×D11—26no—
32C22×C4×D11Q814yes—
33C2×C11×C4⋊C4—26no—
34C2×C11×C4⋊C4—212no—
35C2×(C2×D11)⋊C4—26no—
36C2×(C2×D11)⋊C4—26no—
37C2×(C2×D11)⋊C4—26no—
38C2×(C2×D11)⋊C4—26no—
39C2×(C2×D11)⋊C4—26no—
40C2×(C2×D11)⋊C4C2×C4112yes—
41C2×C4⋊Dic11—26no—
42C2×C4⋊Dic11—26no—
43C2×C4⋊Dic11C2×C4112yescomplemented
44C2×C4×Dic11—212no—
45C2×C4×Dic11—26no—
46C2×C4×Dic11—212no—
47C2×C4×Dic11D4112yes—
48C11×#95—26no—
49C11×#95C2×C414yescomplemented
50C11⋊#95—26no—
51C11⋊#95—26no—
52C11⋊#95—212no—
53C4×#399—111nomaximal, Sylow
54C24×C11C2411yescharacteristic
55C23×D11—23no—
56C23×D11—23no—
57C23×D11—23no—
58C23×D11—23no—
59C23×D11C22×C412yes—
60C23×D11C2×Q812yes—
61C23×D11#4112yes—
62C22×C4×C11—26no—
63C22×C4×C11—26no—
64C22×C4×C11—23no—
65C22×C4×C11—26no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—26no—
69C22×C4×C11—23no—
70C22×C4×C11C22×C416yes—
71C22×C4×C11C2×D416yes—
72C22×C4×C11C2×Q812yes—
73C22×C4×C11#4116yes—
74C22×C4×C11#4116yes—
75C22×Dic11—26no—
76C22×Dic11—23no—
77C22×Dic11—26no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11C22×C416yes—
84C22×Dic11C2×D416yes—
85C22×Dic11C2×D416yes—
86C22×Dic11C2×Q812yes—
87C22×Dic11#4116yes—
88C2×C4×D11—224no—
89C2×C4×D11—412no—
90C2×C4×D11—44no—
91C11×C4⋊C4—224no—
92(C2×D11)⋊C4—224no—
93(C2×D11)⋊C4—224no—
94C4⋊Dic11—224no—
95C4×Dic11—224no—
96C4×Dic11—412no—
97C2×#399—111no—
98C2×C4×C4⋊C4—113no—
99C2×C4×C22⋊C4—113no—
100#1445—113no—
101#1444D1111yescharacteristic, complemented
102#1439—113no—
103C4×#95—111no—
104C23×C11C23×C411yescharacteristic
105C23×C11C22×D413yes—
106C23×C11C22×Q811yescharacteristic
107C23×C11C2×#4113yes—
108C23×C11C2×#4113yes—
109C23×C11C2×#4111yescharacteristic
110C23×C11C2×#4113yes—
111C22×D11—26no—
112C22×D11—26no—
113C22×D11—26no—
114C22×D11—26no—
115C22×D11—26no—
116C22×D11—26no—
117C22×D11—43no—
118C22×D11—43no—
119C22×D11—46no—
120C22×D11—41no—
121C22×D11—43no—
122C22×D11C4×Q814yes—
123C2×C4×C11—212no—
124C2×C4×C11—26no—
125C2×C4×C11—26no—
126C2×C4×C11—212no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11—212no—
130C2×C4×C11—43no—
131C2×C4×C11—43no—
132C2×C4×C11—46no—
133C2×C4×C11—43no—
134C2×C4×C11—41no—
135C2×C4×C11C4×D4112yes—
136C2×Dic11—212no—
137C2×Dic11—26no—
138C2×Dic11—26no—
139C2×Dic11—26no—
140C2×Dic11—26no—
141C2×Dic11—46no—
142C2×Dic11—46no—
143C2×Dic11—43no—
144C2×Dic11—46no—
145C2×Dic11—43no—
146C2×Dic11C22⋊Q8112yes—
147C2×Dic11#123112yes—
148C2×Dic11#12714yes—
149C4×D11—416no—
150C24×C4—111no—
151C22×C4⋊C4—113no—
152C22×C4⋊C4C2×D1113yes—
153C22×C22⋊C4—113no—
154C22×C22⋊C4—113no—
155C22×C42—113no—
156C22×C42—113no—
157#399—118no—
158C4×C4⋊C4—2212no—
159C4×C22⋊C4—2212no—
160C2×#95—113no—
161C2×#95—116no—
162C2×#95—113no—
163C2×#95C2×D1113yes—
164C2×#95C2×D1111yescharacteristic
165C22×C11C2×C4×D413yes—
166C22×C11C2×C4×Q811yescharacteristic
167C22×C11C4×#4113yes—
168C22×C11C2×C22⋊Q813yes—
169C22×C11C2×#12313yes—
170C22×C11#52513yes—
171C22×C11#52513yes—
172C22×C11#52916yes—
173C22×C11#52913yes—
174C22×C11C2×#12711yescharacteristic
175C22×C11#53213yes—
176C22×C11#53313yes—
177C2×D11—212no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—46no—
181C2×D11—46no—
182C2×D11—42no—
183C2×D11—46no—
184C4×C11—212no—
185C4×C11—42no—
186C4×C11—46no—
187Dic11—46no—
188Dic11—46no—
189Dic11#39918yescomplemented
190C25—111no—
191C23×C4—111no—
192C23×C4—113no—
193C23×C4—113no—
194C23×C4—114no—
195C23×C4—226no—
196C23×C4—226no—
197C23×C4C22×D1113yes—
198C23×C4C22×D1111yescharacteristic
199C23×C4C22×D1113yes—
200C2×C4⋊C4—26no—
201C2×C4⋊C4—212no—
202C2×C4⋊C4—1112no—
203C2×C4⋊C4—226no—
204C2×C4⋊C4—226no—
205C2×C22⋊C4—1112no—
206C2×C22⋊C4—226no—
207C2×C22⋊C4—226no—
208C2×C22⋊C4—226no—
209C2×C22⋊C4—226no—
210C2×C22⋊C4—226no—
211C2×C42—1112no—
212C2×C42—2212no—
213C2×C42—226no—
214C2×C42—2212no—
215#95—26no—
216#95—226no—
217#95—2212no—
218#95—226no—
219#95C4×D1114yescomplemented
220C2×C11C4×#12313yes—
221C2×C11C4×C22⋊Q813yes—
222C2×C11C4×#12711yescharacteristic
223C2×C11C2×#39911yescharacteristic
224C2×C11#239513yes—
225C2×C11#239613yes—
226C2×C11#239711yescharacteristic
227D11—44no—
228C24—112no—
229C24—112no—
230C24—112no—
231C24—223no—
232C24—223no—
233C24—223no—
234C24—223no—
235C24C23×D1111yescharacteristic
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—116no—
245C22×C4—112no—
246C22×C4—116no—
247C22×C4—116no—
248C22×C4—116no—
249C22×C4—2224no—
250C22×C4—223no—
251C22×C4—226no—
252C22×C4—223no—
253C22×C4—226no—
254C22×C4—223no—
255C22×C4—226no—
256C22×C4—226no—
257C22×C4—223no—
258C22×C4—444no—
259C22×C4—4412no—
260C22×C4C2×C4×D1116yes—
261C22×C4D4×D1116yes—
262C22×C4#434116yes—
263C22×C4Q8×D1112yes—
264C22×C4#434316yes—
265C4⋊C4—224no—
266C4⋊C4—2224no—
267C22⋊C4—2224no—
268C22⋊C4—2224no—
269C42—2224no—
270C42—4412no—
271C11C4×#39911yescharacteristic, complemented, Sylow
272C23—114no—
273C23—226no—
274C23—226no—
275C23—226no—
276C23—226no—
277C23—226no—
278C23—226no—
279C23—441no—
280C23—443no—
281C23—443no—
282C23—446no—
283C23—443no—
284C23C22×C4×D1111yescharacteristic
285C23C2×D4×D1113yes—
286C23C2×#434113yes—
287C23C2×Q8×D1111yescharacteristic
288C23C2×#434313yes—
289C23#41×D1113yes—
290C23#41×D1111yescharacteristic
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—26no—
295C2×C4—212no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—43no—
299C2×C4—41no—
300C2×C4—43no—
301C2×C4—46no—
302C2×C4—43no—
303C2×C4—114no—
304C2×C4—1112no—
305C2×C4—1112no—
306C2×C4—226no—
307C2×C4—226no—
308C2×C4—2212no—
309C2×C4—226no—
310C2×C4—226no—
311C2×C4—4416no—
312C2×C4—443no—
313C2×C4—443no—
314C2×C4—446no—
315C2×C4—446no—
316C2×C4—446no—
317C2×C4#66946112yes—
318C22—2212no—
319C22—446no—
320C22—446no—
321C22—442no—
322C22—446no—
323C22—442no—
324C22—442no—
325C22C2×#6694613yes—
326C22C4×#434113yes—
327C22C4×Q8×D1111yescharacteristic
328C22#1062311713yes—
329C22#1062313713yes—
330C22#1062315516yes—
331C22D11×C22⋊Q813yes—
332C22D11×#12313yes—
333C22#1062322213yes—
334C22D11×#12711yescharacteristic
335C22#1062325613yes—
336C22#1062325913yes—
337C4—212no—
338C4—46no—
339C4—42no—
340C4—118no—
341C4—446no—
342C4—446no—
343C2—444no—
344C2#1307113513yes—
345C2#1307114613yes—
346C2#1307117811yescharacteristic
347C2D11×#39911yescharacteristic
348C2#1307188013yes—
349C2#1307188713yes—
350C2#1307189411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11C4×#399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic11C2semidirect
4. #13066885C2semidirect
6. #95×Dic11C2semidirect
7. C11×#1444C2semidirect
21. #10622290C4semidirect
43. C2×C4⋊Dic11C2×C4semidirect
49. C11×#95C2×C4semidirect
101. #1444D11semidirect
189. Dic11#399semidirect
219. #95C4×D11semidirect
271. C11C4×#399semidirect

Maximal subgroups

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

subgroupindex
C2×#106222902
C2×C4⋊C4×Dic112
C2×#106222792
#130668852
#130668582
#95×Dic112
C11×#14442
C4×#39911