Finite Group Databasebeta

← Dic11×#393 #14675579

Subgroups — Dic11×#393 #14675579

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic11C213yesmaximal
3#13066887C211yesmaximal, characteristic, complemented
4#13066873C213yesmaximal, complemented
5#13066861C213yesmaximal
6#95×Dic11C213yesmaximal, complemented
7C2×C11×#393C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2213yes—
11C22×C22⋊Dic11C2213yes—
12C2×Q8×Dic11—212no—
13C22×C4⋊Dic11C2213yes—
14C22×C4×Dic11C2213yes—
15C22×C4×Dic11C2213yes—
16C11×#393C418yescomplemented
17C2×C11×#95C2213yes—
18C2×C11⋊#95C2216yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C22⋊C4×Dic11—212no—
23C25×C11C2311yescharacteristic
24C22×Q8×C11—26no—
25C22×Q8×C11—26no—
26C22×Q8×C11C2×C414yescomplemented
27C23×C4×C11C2313yes—
28C23×C4×C11C2313yes—
29C23×Dic11—26no—
30C23×Dic11—26no—
31C23×Dic11Q814yescomplemented
32C23×Dic11C2313yes—
33C23×Dic11C2311yescharacteristic
34C23×Dic11C2313yes—
35C23×Dic11C2311yescharacteristic
36C2×C11×C22⋊C4—26no—
37C2×C11×C22⋊C4—26no—
38C2×C11×C22⋊C4C2×C4112yes—
39C2×C22⋊Dic11—26no—
40C2×C22⋊Dic11—26no—
41C2×C22⋊Dic11—26no—
42Q8×Dic11—232no—
43C2×C4⋊Dic11—26no—
44C2×C4⋊Dic11—212no—
45C2×C4×Dic11—212no—
46C2×C4×Dic11—26no—
47C2×C4×Dic11—212no—
48C2×C4×Dic11D4112yes—
49C11×#95C2×C4112yescomplemented
50C11⋊#95—26no—
51C11⋊#95—26no—
52C11⋊#95—26no—
53C11⋊#95—212no—
54C4×#393—111nomaximal, Sylow
55C24×C11—23no—
56C24×C11—23no—
57C24×C11—23no—
58C24×C11—23no—
59C24×C11C22×C412yes—
60C24×C11C2×Q812yes—
61C24×C11#4112yes—
62C24×C11C2411yescharacteristic
63C2×Q8×C11—28no—
64C2×Q8×C11—224no—
65C2×Q8×C11—224no—
66C22×C4×C11—26no—
67C22×C4×C11—26no—
68C22×C4×C11—23no—
69C22×C4×C11—26no—
70C22×C4×C11—26no—
71C22×C4×C11—23no—
72C22×C4×C11C22×C416yes—
73C22×C4×C11C22×C416yes—
74C22×C4×C11C2×D416yes—
75C22×C4×C11#4116yes—
76C22×Dic11—224no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—26no—
80C22×Dic11—26no—
81C22×Dic11—26no—
82C22×Dic11—26no—
83C22×Dic11—23no—
84C22×Dic11—23no—
85C22×Dic11—23no—
86C22×Dic11—23no—
87C22×Dic11—44no—
88C22×Dic11—412no—
89C22×Dic11C2×D416yes—
90C22×Dic11C2×D416yes—
91C22×Dic11C2×Q812yes—
92C22×Dic11C2×Q812yes—
93C22×Dic11#4116yes—
94C22×Dic11#4116yes—
95C11×C22⋊C4—224no—
96C22⋊Dic11—224no—
97C4⋊Dic11—224no—
98C4×Dic11—224no—
99C4×Dic11—412no—
100C22×C4×Q8—111no—
101C2×#393D1111yescharacteristic
102C2×C4×C22⋊C4—113no—
103#1446—111no—
104#1442—113no—
105#1439—113no—
106C4×#95—113no—
107C23×C11—26no—
108C23×C11—26no—
109C23×C11—26no—
110C23×C11—26no—
111C23×C11—26no—
112C23×C11—26no—
113C23×C11—41no—
114C23×C11—43no—
115C23×C11—43no—
116C23×C11—46no—
117C23×C11—43no—
118C23×C11C4×Q814yescomplemented
119C23×C11C23×C411yescharacteristic
120C23×C11C22×D413yes—
121C23×C11C22×Q811yescharacteristic
122C23×C11C2×#4113yes—
123C23×C11C2×#4111yescharacteristic
124C23×C11C2×#4113yes—
125C23×C11C2×#4113yes—
126Q8×C11—232no—
127C2×C4×C11—212no—
128C2×C4×C11—26no—
129C2×C4×C11—26no—
130C2×C4×C11—212no—
131C2×C4×C11—26no—
132C2×C4×C11—212no—
133C2×C4×C11—43no—
134C2×C4×C11—46no—
135C2×C4×C11—43no—
136C2×C4×C11C4×D4112yes—
137C2×Dic11—26no—
138C2×Dic11—26no—
139C2×Dic11—26no—
140C2×Dic11—26no—
141C2×Dic11—212no—
142C2×Dic11—26no—
143C2×Dic11—41no—
144C2×Dic11—43no—
145C2×Dic11—46no—
146C2×Dic11—43no—
147C2×Dic11—43no—
148C2×Dic11—46no—
149C2×Dic11—46no—
150C2×Dic11—416no—
151C2×Dic11#12014yes—
152C2×Dic11C22⋊Q8112yes—
153C2×Dic11#124112yes—
154C23×Q8C2×D1111yescharacteristic
155C24×C4—111no—
156C2×C4×Q8—2212no—
157C22×C4⋊C4—113no—
158C22×C22⋊C4—113no—
159C22×C22⋊C4C2×D1113yes—
160C22×C42—113no—
161C22×C42—113no—
162#393Dic1118yesdirect product factor
163C4×C22⋊C4—2212no—
164C2×#95—116no—
165C2×#95—113no—
166C2×#95—113no—
167C2×#95—113no—
168C2×#95C2×D1113yes—
169C22×C11—212no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—46no—
173C22×C11—46no—
174C22×C11—42no—
175C22×C11—46no—
176C22×C11C2×C4×D413yes—
177C22×C11C2×C4×Q811yescharacteristic
178C22×C11C4×#4113yes—
179C22×C11C2×#12011yescharacteristic
180C22×C11C2×C22⋊Q813yes—
181C22×C11#52513yes—
182C22×C11#52513yes—
183C22×C11C2×#12413yes—
184C22×C11#52913yes—
185C22×C11#52916yes—
186C22×C11#53213yes—
187C22×C11#53313yes—
188C4×C11—212no—
189C4×C11—46no—
190Dic11—42no—
191Dic11—46no—
192Dic11—46no—
193Dic11#39318yesdirect product factor
194C25C22×D1111yescharacteristic
195C22×Q8—26no—
196C22×Q8—26no—
197C22×Q8C2×Dic1114yescomplemented
198C23×C4—111no—
199C23×C4—114no—
200C23×C4—113no—
201C23×C4—113no—
202C23×C4—111no—
203C23×C4—226no—
204C23×C4—226no—
205C23×C4C22×D1113yes—
206C23×C4C22×D1113yes—
207C4×Q8—2232no—
208C2×C4⋊C4—2212no—
209C2×C4⋊C4—226no—
210C2×C22⋊C4—26no—
211C2×C22⋊C4—26no—
212C2×C22⋊C4—226no—
213C2×C22⋊C4—226no—
214C2×C22⋊C4—226no—
215C2×C22⋊C4C2×Dic11112yes—
216C2×C42—1112no—
217C2×C42—2212no—
218C2×C42—226no—
219C2×C42—2212no—
220#95—2212no—
221#95—226no—
222#95—226no—
223#95—226no—
224#95C2×Dic11112yescomplemented
225C2×C11—44no—
226C2×C11C4×#12011yescharacteristic
227C2×C11C4×C22⋊Q813yes—
228C2×C11C4×#12413yes—
229C2×C11C2×#39311yescharacteristic
230C2×C11#238811yescharacteristic
231C2×C11#239613yes—
232C2×C11#239813yes—
233C24—23no—
234C24—23no—
235C24—23no—
236C24—23no—
237C24Q8×D1112yes—
238C24#434312yes—
239C24C22×Dic1112yes—
240C24C23×D1111yescharacteristic
241C2×Q8—28no—
242C2×Q8—224no—
243C2×Q8—224no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—116no—
251C22×C4—112no—
252C22×C4—116no—
253C22×C4—116no—
254C22×C4—112no—
255C22×C4—116no—
256C22×C4—2224no—
257C22×C4—223no—
258C22×C4—223no—
259C22×C4—226no—
260C22×C4—226no—
261C22×C4—223no—
262C22×C4—223no—
263C22×C4—226no—
264C22×C4—226no—
265C22×C4—223no—
266C22×C4—223no—
267C22×C4—444no—
268C22×C4—4412no—
269C22×C4D4×D1116yes—
270C22×C4#434116yes—
271C22×C4C22×Dic1116yes—
272C22×C4C22×Dic1116yes—
273C4⋊C4—2224no—
274C22⋊C4—224no—
275C22⋊C4—2224no—
276C42—2224no—
277C42—4412no—
278C11C4×#39311yescharacteristic, complemented, Sylow
279C23—26no—
280C23—26no—
281C23—26no—
282C23—26no—
283C23—26no—
284C23—26no—
285C23—43no—
286C23—41no—
287C23—43no—
288C23—43no—
289C23—46no—
290C23Q8×Dic1114yescomplemented
291C23C2×D4×D1113yes—
292C23C2×#434113yes—
293C23C2×Q8×D1111yescharacteristic
294C23C2×#434311yescharacteristic
295C23#41×D1113yes—
296C23#41×D1113yes—
297C23C23×Dic1111yescharacteristic
298Q8—232no—
299C2×C4—212no—
300C2×C4—26no—
301C2×C4—212no—
302C2×C4—26no—
303C2×C4—26no—
304C2×C4—212no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—46no—
308C2×C4—114no—
309C2×C4—1112no—
310C2×C4—1112no—
311C2×C4—226no—
312C2×C4—226no—
313C2×C4—226no—
314C2×C4—226no—
315C2×C4—226no—
316C2×C4—2212no—
317C2×C4—4416no—
318C2×C4—443no—
319C2×C4—441no—
320C2×C4—446no—
321C2×C4—446no—
322C2×C4—446no—
323C2×C4—443no—
324C2×C4—443no—
325C2×C4D4×Dic11112yes—
326C22—212no—
327C22—46no—
328C22—42no—
329C22—46no—
330C22—46no—
331C22—42no—
332C22—42no—
333C22#1062311713yes—
334C22D11×#12011yescharacteristic
335C22#1062315313yes—
336C22#1062315513yes—
337C22D11×C22⋊Q813yes—
338C22#1062315813yes—
339C22#1062319913yes—
340C22D11×#12413yes—
341C22#1062321116yes—
342C22C2×D4×Dic1113yes—
343C22C2×Q8×Dic1111yescharacteristic
344C22#41×Dic1113yes—
345C4—212no—
346C4—46no—
347C4—118no—
348C4—446no—
349C4—442no—
350C4—446no—
351C2—44no—
352C2#120×Dic1111yescharacteristic
353C2C22⋊Q8×Dic1113yes—
354C2#124×Dic1113yes—
355C2D11×#39311yescharacteristic
356C2#1307183311yescharacteristic
357C2#1307188313yes—
358C2#1307189813yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#393C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#393D11
hypocenterC11C4×#393
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
3. #13066887C2semidirect
4. #13066873C2semidirect
6. #95×Dic11C2semidirect
16. C11×#393C4semidirect
26. C22×Q8×C11C2×C4semidirect
31. C23×Dic11Q8semidirect
49. C11×#95C2×C4semidirect
118. C23×C11C4×Q8semidirect
162. #393Dic11direct (N × H)
193. Dic11#393direct (N × H)
197. C22×Q8C2×Dic11semidirect
224. #95C2×Dic11semidirect
278. C11C4×#393semidirect
290. C23Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×C22⋊C4×Dic112
#130668872
#130668732
#130668612
#95×Dic112
C2×C11×#3932
C4×#39311