Finite Group Databasebeta

← #14920093

Subgroups — #14920093

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071923C216yesmaximal, complemented
2#13071910C213yesmaximal, complemented
3#13071907C213yesmaximal, complemented
4#13071892C216yesmaximal
5#13071888C213yesmaximal
6#13071886C213yesmaximal
7C42×Dic22C213yesmaximal, complemented
8C4×#66925C213yesmaximal
9C42×Q8×C11C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2213yes—
11C2×#66925C2213yes—
12C2×#66925C2213yes—
13C2×C42×D11C2211yescharacteristic
14C2×C4×Dic22C2213yes—
15C2×C4×Dic22C2216yes—
16C4×C11×C4⋊C4C2213yes—
17C4×C11×C4⋊C4C2216yes—
18C43×C11C2213yes—
19#10622844C2211yescharacteristic
20#10622842C2213yes—
21#10622607C2216yes—
22#10622605C2213yes—
23#10622597C2216yes—
24#10622596C2216yes—
25#10622595C2213yes—
26#10622593C2216yes—
27#10622592C2216yes—
28C4×(C2×D11)⋊C4C2216yes—
29C4×(C2×D11)⋊C4C2216yes—
30C4×C4⋊Dic11C2213yes—
31C4×C4⋊Dic11C2216yes—
32#10622545C2213yes—
33#10622545C2213yes—
34C4×Dic11⋊C4C2216yes—
35C4×Dic11⋊C4C2216yes—
36C4×Dic11⋊C4C2216yes—
37C4×Dic11⋊C4C2216yes—
38C4×Dic11⋊C4C2216yes—
39C42×Dic11C2213yes—
40#10622290C2211yescharacteristic
41#10622289C2212yes—
42#10622286C2213yes—
43#10622272C2213yes—
44#10622271C2216yes—
45#10622270C2216yes—
46#10622269C2213yes—
47C22×Q8×C11C2311yescharacteristic
48C22×C4×D11C2313yes—
49C22×Dic22C2313yes—
50C4×Q8×C11—212no—
51C2×C11×C4⋊C4C2316yes—
52C2×C11×C4⋊C4C2313yes—
53C2×C42×C11C2316yes—
54C2×C42×C11C2313yes—
55C2×C42×C11C2316yes—
56C2×C42×C11C2313yes—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4C2316yes—
59C2×(C2×D11)⋊C4C2313yes—
60C2×(C2×D11)⋊C4C2313yes—
61C2×C4⋊Dic11C2316yes—
62C2×C4⋊Dic11C2313yes—
63C2×Dic11⋊C4C2316yes—
64C2×Dic11⋊C4C2316yes—
65C2×Dic11⋊C4C2316yes—
66C2×Dic11⋊C4C2313yes—
67C2×Dic11⋊C4C2316yes—
68C2×Dic11⋊C4C2313yes—
69C2×C4×Dic11C2316yes—
70C2×C4×Dic11C2316yes—
71C2×C4×Dic11C2313yes—
72C2×C4×Dic11C2313yes—
73C2×C4×Dic11C2313yes—
74#66925—212no—
75#66925—212no—
76C42×D11Q818yescomplemented
77C4×Dic22—212no—
78C4×Dic22—224no—
79C11×#95C2311yescharacteristic
80C11×#95C2313yes—
81C11×#95C2312yes—
82C11⋊#95C2316yes—
83C11⋊#95C2316yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2313yes—
88C11⋊#95C2313yes—
89C11⋊#95C2316yes—
90#34552—111nomaximal, Sylow
91C23×D11C2411yescharacteristic
92C2×Q8×C11—26no—
93C22×C4×C11C2416yes—
94C22×C4×C11C2413yes—
95C22×C4×C11C2413yes—
96C22×C4×C11C2413yes—
97C22×Dic11C2413yes—
98C22×Dic11C2413yes—
99C22×Dic11C2413yes—
100C22×Dic11C2416yes—
101C2×C4×D11—26no—
102C2×C4×D11—26no—
103C2×C4×D11C2×Q8112yes—
104C2×Dic22—212no—
105C2×Dic22—26no—
106C11×C4⋊C4—212no—
107C11×C4⋊C4—26no—
108C42×C11—212no—
109C42×C11—26no—
110C42×C11—212no—
111C42×C11C2×Q814yes—
112C42×C11#41112yes—
113(C2×D11)⋊C4—212no—
114(C2×D11)⋊C4—26no—
115(C2×D11)⋊C4—26no—
116C4⋊Dic11—212no—
117C4⋊Dic11—26no—
118Dic11⋊C4—212no—
119Dic11⋊C4—212no—
120Dic11⋊C4—212no—
121Dic11⋊C4—212no—
122Dic11⋊C4—26no—
123Dic11⋊C4—26no—
124C4×Dic11—212no—
125C4×Dic11—212no—
126C4×Dic11—26no—
127C4×Dic11C2×Q8112yes—
128C4×Dic11#41112yes—
129#2402—116no—
130#2399—113no—
131#2399—113no—
132#2396—113no—
133#2396—116no—
134#2396—113no—
135C42×Q8—113no—
136C42×Q8D1111yescharacteristic, complemented
137C4×#117—113no—
138C23×C11C2511yescharacteristic
139C22×D11—23no—
140C22×D11—23no—
141C22×D11C22×Q812yes—
142Q8×C11—28no—
143C2×C4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—26no—
146C2×C4×C11—26no—
147C2×C4×C11—26no—
148C2×C4×C11C22×Q816yes—
149C2×C4×C11C2×#4116yes—
150C2×C4×C11C2×#4116yes—
151C2×C4×C11C2×#4116yes—
152C2×C4×C11C2×#4116yes—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—23no—
156C2×Dic11—23no—
157C2×Dic11—26no—
158C2×Dic11—26no—
159C2×Dic11—23no—
160C2×Dic11—23no—
161C2×Dic11C22×Q816yes—
162C2×Dic11C2×#41112yes—
163C4×D11—224no—
164Dic22—224no—
165C2×C4×Q8—116no—
166C2×C4×Q8—113no—
167C2×C4×Q8C2×D1113yes—
168C2×#117—113no—
169C2×#117—113no—
170C22×C42—111no—
171#400—113no—
172#400—116no—
173#400—113no—
174#399—113no—
175#399—111no—
176#398—116no—
177#398—116no—
178#398—116no—
179#398—116no—
180#396—116no—
181#396—112no—
182#395—113no—
183#395—116no—
184#395—113no—
185#393—111no—
186#393—113no—
187C4×C4⋊C4—116no—
188C4×C4⋊C4—116no—
189C4×C4⋊C4—116no—
190C4×C4⋊C4—116no—
191C4×C4⋊C4—116no—
192C4×C4⋊C4—113no—
193C4×C4⋊C4—116no—
194C4×C4⋊C4C2×D1113yes—
195C4×C4⋊C4C2×D1116yes—
196C4×C22⋊C4—116no—
197C4×C22⋊C4—116no—
198#376—113no—
199#376—113no—
200C43—113no—
201C43C2×D1113yes—
202C22×C11C23×Q811yescharacteristic
203C22×C11C22×#4113yes—
204C22×C11C22×#4113yes—
205C2×D11—26no—
206C2×D11—43no—
207C2×D11—41no—
208C4×C11—26no—
209C4×C11—26no—
210C4×C11—46no—
211C4×C11#533112yes—
212Dic11—26no—
213Dic11—212no—
214Dic11—43no—
215Dic11—43no—
216C22×Q8—113no—
217C22×Q8C22×D1111yescharacteristic
218C23×C4—113no—
219C4×Q8—212no—
220C4×Q8—2224no—
221C4×Q8—2212no—
222#117—2212no—
223#117—2212no—
224C2×C4⋊C4—116no—
225C2×C4⋊C4—113no—
226C2×C4⋊C4—113no—
227C2×C4⋊C4—116no—
228C2×C4⋊C4—116no—
229C2×C4⋊C4—116no—
230C2×C4⋊C4—116no—
231C2×C4⋊C4—113no—
232C2×C4⋊C4C22×D1116yes—
233C2×C4⋊C4C22×D1113yes—
234C2×C22⋊C4—116no—
235C2×C22⋊C4—113no—
236C2×C22⋊C4—113no—
237C2×C42—113no—
238C2×C42—113no—
239C2×C42—118no—
240C2×C42—113no—
241C2×C42—116no—
242C2×C42—116no—
243C2×C42C22×D1113yes—
244C2×C42C22×D1116yes—
245C2×C42C22×D1116yes—
246C2×C42C22×D1113yes—
247C2×C42C22×D1111yescharacteristic
248#95—116no—
249#95—116no—
250#95—116no—
251#95—116no—
252#95—116no—
253#95—113no—
254#95—113no—
255#95—116no—
256#95C22×D1113yes—
257#95C22×D1111yescharacteristic
258#95C22×D1112yes—
259C2×C11C2×#53313yes—
260C2×C11#344413yes—
261C2×C11#344411yescharacteristic
262D11—42no—
263C24—111no—
264C2×Q8—26no—
265C2×Q8—2212no—
266C2×Q8—226no—
267C22×C4—113no—
268C22×C4—116no—
269C22×C4—1112no—
270C22×C4—113no—
271C22×C4—113no—
272C22×C4—226no—
273C22×C4—226no—
274C22×C4C23×D1116yes—
275C22×C4C23×D1113yes—
276C22×C4C23×D1113yes—
277C22×C4C23×D1113yes—
278C4⋊C4—212no—
279C4⋊C4—26no—
280C4⋊C4—2212no—
281C4⋊C4—2212no—
282C4⋊C4—2212no—
283C4⋊C4—2212no—
284C4⋊C4—226no—
285C4⋊C4—226no—
286C4⋊C4—2212no—
287C4⋊C4—226no—
288C22⋊C4—2212no—
289C22⋊C4—226no—
290C22⋊C4—226no—
291C42—212no—
292C42—26no—
293C42—212no—
294C42—1112no—
295C42—1112no—
296C42—226no—
297C42—2212no—
298C42—2212no—
299C42#4339112yes—
300C42Q8×D1114yes—
301C11#3455211yescharacteristic, complemented, Sylow
302C23—112no—
303C23—223no—
304C23—223no—
305C23C24×D1111yescharacteristic
306Q8—28no—
307Q8—2224no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—116no—
314C2×C4—1112no—
315C2×C4—226no—
316C2×C4—223no—
317C2×C4—226no—
318C2×C4—223no—
319C2×C4—2224no—
320C2×C4—223no—
321C2×C4—223no—
322C2×C4—226no—
323C2×C4—226no—
324C2×C4C2×#433916yes—
325C2×C4C2×#433916yes—
326C2×C4C2×#433916yes—
327C2×C4C2×Q8×D1116yes—
328C2×C4#41×D1116yes—
329C22—226no—
330C22—443no—
331C22—441no—
332C22C22×#433913yes—
333C22C22×Q8×D1111yescharacteristic
334C22C2×#41×D1113yes—
335C4—26no—
336C4—26no—
337C4—46no—
338C4—226no—
339C4—2212no—
340C4—443no—
341C4—443no—
342C4#10623109112yes—
343C2—442no—
344C2C2×#1062310913yes—
345C2#1308190913yes—
346C2#1308191211yescharacteristic
subgroupG/H
centerC2×C42C22×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC42×Q8×C11C2
prime radicalC23×D11C24
hypercenterC42×Q8D11
hypocenterC11#34552
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
1. #13071923C2semidirect
2. #13071910C2semidirect
3. #13071907C2semidirect
7. C42×Dic22C2semidirect
9. C42×Q8×C11C2semidirect
76. C42×D11Q8semidirect
136. C42×Q8D11semidirect
301. C11#34552semidirect

Maximal subgroups

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

subgroupindex
#130719232
#130719102
#130719072
#130718922
#130718882
#130718862
C42×Dic222
C4×#669252
C42×Q8×C112
#3455211