Finite Group Databasebeta

← #14675580

Subgroups — #14675580

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×#10622844C211yesmaximal, characteristic
3C2×#10622279C213yesmaximal
4#13066872C213yesmaximal, complemented
5#13066862C213yesmaximal
6#95×Dic11C213yesmaximal, complemented
7C11×#1446C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C2×Q8×Dic11—212no—
11C22×(C2×D11)⋊C4C2213yes—
12C22×(C2×D11)⋊C4C2213yes—
13C22×C4⋊Dic11C2213yes—
14C22×C4×Dic11C2213yes—
15C22×C4×Dic11C2213yes—
16C2×C11×#95C2213yes—
17C2×C11×#95C2213yes—
18#10622844C418yescomplemented
19C2×C11⋊#95C2216yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22#10622279—212no—
23C24×D11C2311yescharacteristic
24C22×Q8×C11—26no—
25C22×Q8×C11—26no—
26C22×Q8×C11C2×C414yescomplemented
27C23×C4×C11C2311yescharacteristic
28C23×C4×C11C2313yes—
29C23×C4×C11C2313yes—
30C23×Dic11C2313yes—
31C23×Dic11C2313yes—
32C23×Dic11C2311yescharacteristic
33C22×C4×D11—26no—
34C22×C4×D11—26no—
35C22×C4×D11Q814yescomplemented
36Q8×Dic11—232no—
37C2×(C2×D11)⋊C4—26no—
38C2×(C2×D11)⋊C4—26no—
39C2×(C2×D11)⋊C4—26no—
40C2×(C2×D11)⋊C4—26no—
41C2×(C2×D11)⋊C4—26no—
42C2×(C2×D11)⋊C4C2×C4112yes—
43C2×C4⋊Dic11—26no—
44C2×C4⋊Dic11—212no—
45C2×C4×Dic11—212no—
46C2×C4×Dic11—26no—
47C2×C4×Dic11—212no—
48C2×C4×Dic11D4112yes—
49C11×#95—26no—
50C11×#95—26no—
51C11⋊#95—212no—
52C11⋊#95—26no—
53C11⋊#95C2×C4112yescomplemented
54C4×#393—111nomaximal, Sylow
55C24×C11C2411yescharacteristic
56C23×D11—23no—
57C23×D11—23no—
58C23×D11—23no—
59C23×D11—23no—
60C23×D11C22×C412yes—
61C23×D11C2×Q812yes—
62C23×D11#4112yes—
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—23no—
70C22×C4×C11—26no—
71C22×C4×C11—26no—
72C22×C4×C11—23no—
73C22×C4×C11—23no—
74C22×C4×C11C22×C416yes—
75C22×C4×C11C2×D416yes—
76C22×C4×C11C2×Q812yes—
77C22×C4×C11#4116yes—
78C22×C4×C11#4116yes—
79C22×Dic11—23no—
80C22×Dic11—26no—
81C22×Dic11—26no—
82C22×Dic11—26no—
83C22×Dic11—26no—
84C22×Dic11—23no—
85C22×Dic11—23no—
86C22×Dic11—23no—
87C22×Dic11C22×C416yes—
88C22×Dic11C2×D416yes—
89C22×Dic11C2×D416yes—
90C22×Dic11C2×Q812yes—
91C22×Dic11#4116yes—
92C2×C4×D11—224no—
93C2×C4×D11—44no—
94C2×C4×D11—412no—
95(C2×D11)⋊C4—224no—
96(C2×D11)⋊C4—224no—
97C4⋊Dic11—224no—
98C4×Dic11—224no—
99C4×Dic11—412no—
100C22×C4×Q8—111no—
101C2×#393—111no—
102C2×C4×C22⋊C4—113no—
103#1446D1111yescharacteristic, complemented
104#1442—113no—
105#1439—113no—
106C4×#95—113no—
107C23×C11C23×C411yescharacteristic
108C23×C11C22×D413yes—
109C23×C11C22×Q811yescharacteristic
110C23×C11C2×#4113yes—
111C23×C11C2×#4113yes—
112C23×C11C2×#4111yescharacteristic
113C23×C11C2×#4113yes—
114C22×D11—26no—
115C22×D11—26no—
116C22×D11—26no—
117C22×D11—26no—
118C22×D11—26no—
119C22×D11—26no—
120C22×D11—41no—
121C22×D11—43no—
122C22×D11—43no—
123C22×D11—46no—
124C22×D11—43no—
125C22×D11C4×Q814yescomplemented
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—26no—
133C2×C4×C11—212no—
134C2×C4×C11—41no—
135C2×C4×C11—43no—
136C2×C4×C11—43no—
137C2×C4×C11—43no—
138C2×C4×C11—46no—
139C2×C4×C11C4×D4112yes—
140C2×Dic11—26no—
141C2×Dic11—212no—
142C2×Dic11—26no—
143C2×Dic11—26no—
144C2×Dic11—26no—
145C2×Dic11—46no—
146C2×Dic11—43no—
147C2×Dic11—46no—
148C2×Dic11—46no—
149C2×Dic11—43no—
150C2×Dic11#12014yes—
151C2×Dic11C22⋊Q8112yes—
152C2×Dic11#124112yes—
153C4×D11—416no—
154C23×Q8C2×D1111yescharacteristic
155C24×C4—111no—
156C2×C4×Q8—2212no—
157C22×C4⋊C4—113no—
158C22×C22⋊C4—113no—
159C22×C22⋊C4—113no—
160C22×C42—113no—
161C22×C42—113no—
162#393—118no—
163C4×C22⋊C4—2212no—
164C2×#95—113no—
165C2×#95—116no—
166C2×#95—113no—
167C2×#95C2×D1113yes—
168C2×#95C2×D1113yes—
169C22×C11C2×C4×D413yes—
170C22×C11C2×C4×Q811yescharacteristic
171C22×C11C4×#4113yes—
172C22×C11C2×#12011yescharacteristic
173C22×C11C2×C22⋊Q813yes—
174C22×C11#52513yes—
175C22×C11#52513yes—
176C22×C11C2×#12413yes—
177C22×C11#52916yes—
178C22×C11#52913yes—
179C22×C11#53213yes—
180C22×C11#53313yes—
181C2×D11—212no—
182C2×D11—42no—
183C2×D11—42no—
184C2×D11—46no—
185C2×D11—46no—
186C2×D11—42no—
187C2×D11—46no—
188C4×C11—212no—
189C4×C11—42no—
190C4×C11—46no—
191Dic11—46no—
192Dic11—46no—
193Dic11#39318yescomplemented
194C25—111no—
195C22×Q8—26no—
196C22×Q8—26no—
197C22×Q8C4×D1114yescomplemented
198C23×C4—111no—
199C23×C4—113no—
200C23×C4—113no—
201C23×C4—114no—
202C23×C4—226no—
203C23×C4—226no—
204C23×C4C22×D1111yescharacteristic
205C23×C4C22×D1113yes—
206C23×C4C22×D1113yes—
207C4×Q8—2232no—
208C2×C4⋊C4—2212no—
209C2×C4⋊C4—226no—
210C2×C22⋊C4—1112no—
211C2×C22⋊C4—226no—
212C2×C22⋊C4—226no—
213C2×C22⋊C4—226no—
214C2×C22⋊C4—226no—
215C2×C22⋊C4—226no—
216C2×C42—1112no—
217C2×C42—2212no—
218C2×C42—226no—
219C2×C42—2212no—
220#95—26no—
221#95—26no—
222#95—1112no—
223#95—226no—
224#95—2212no—
225C2×C11C4×#12011yescharacteristic
226C2×C11C4×C22⋊Q813yes—
227C2×C11C4×#12413yes—
228C2×C11C2×#39311yescharacteristic
229C2×C11#238811yescharacteristic
230C2×C11#239613yes—
231C2×C11#239813yes—
232D11—44no—
233C24—112no—
234C24—112no—
235C24—112no—
236C24—223no—
237C24—223no—
238C24—223no—
239C24—223no—
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—23no—
251C22×C4—23no—
252C22×C4—116no—
253C22×C4—112no—
254C22×C4—116no—
255C22×C4—116no—
256C22×C4—116no—
257C22×C4—2224no—
258C22×C4—223no—
259C22×C4—226no—
260C22×C4—223no—
261C22×C4—226no—
262C22×C4—226no—
263C22×C4—223no—
264C22×C4—226no—
265C22×C4—223no—
266C22×C4—444no—
267C22×C4—4412no—
268C22×C4C2×C4×D1116yes—
269C22×C4D4×D1116yes—
270C22×C4#434116yes—
271C22×C4Q8×D1112yes—
272C22×C4#434316yes—
273C4⋊C4—2224no—
274C22⋊C4—2224no—
275C22⋊C4—2224no—
276C42—2224no—
277C42—4412no—
278C11C4×#39311yescharacteristic, complemented, Sylow
279C23—114no—
280C23—226no—
281C23—226no—
282C23—226no—
283C23—226no—
284C23—226no—
285C23—226no—
286C23—443no—
287C23—443no—
288C23—441no—
289C23—446no—
290C23—443no—
291C23C22×C4×D1111yescharacteristic
292C23C2×D4×D1113yes—
293C23C2×#434113yes—
294C23C2×Q8×D1111yescharacteristic
295C23C2×#434313yes—
296C23#41×D1111yescharacteristic
297C23#41×D1113yes—
298Q8—232no—
299C2×C4—212no—
300C2×C4—26no—
301C2×C4—212no—
302C2×C4—26no—
303C2×C4—212no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—43no—
307C2×C4—41no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—46no—
311C2×C4—114no—
312C2×C4—1112no—
313C2×C4—1112no—
314C2×C4—226no—
315C2×C4—226no—
316C2×C4—2212no—
317C2×C4—226no—
318C2×C4—226no—
319C2×C4—4416no—
320C2×C4—443no—
321C2×C4—446no—
322C2×C4—446no—
323C2×C4—446no—
324C2×C4—443no—
325C2×C4(C22⋊D11)⋊C4112yes—
326C22—2212no—
327C22—442no—
328C22—446no—
329C22—446no—
330C22—446no—
331C22—442no—
332C22—442no—
333C22C2×(C22⋊D11)⋊C413yes—
334C22C4×Q8×D1111yescharacteristic
335C22C4×#434313yes—
336C22#1062311713yes—
337C22D11×#12011yescharacteristic
338C22#1062315516yes—
339C22D11×C22⋊Q813yes—
340C22#1062315813yes—
341C22D11×#12413yes—
342C22#1062321113yes—
343C22#1062325613yes—
344C22#1062325913yes—
345C4—212no—
346C4—46no—
347C4—42no—
348C4—118no—
349C4—446no—
350C4—446no—
351C2—444no—
352C2#1307111511yescharacteristic
353C2#1307115413yes—
354C2#1307115913yes—
355C2D11×#39311yescharacteristic
356C2#1307183411yescharacteristic
357C2#1307188713yes—
358C2#1307189813yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1446D11
hypocenterC11C4×#393
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
4. #13066872C2semidirect
6. #95×Dic11C2semidirect
7. C11×#1446C2semidirect
18. #10622844C4semidirect
26. C22×Q8×C11C2×C4semidirect
35. C22×C4×D11Q8semidirect
53. C11⋊#95C2×C4semidirect
103. #1446D11semidirect
125. C22×D11C4×Q8semidirect
193. Dic11#393semidirect
197. C22×Q8C4×D11semidirect
278. C11C4×#393semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228442
C2×#106222792
#130668722
#130668622
#95×Dic112
C11×#14462
C4×#39311