Finite Group Databasebeta

← #46780968

Subgroups — #46780968

Order 33664.

1088 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
1C23×C4×D263C211yesmaximal, characteristic
2C22×(C2×D263)⋊C4C212yesmaximal
3C2×C263⋊#95C212yesmaximal, complemented
4C2×C263⋊#95C211yesmaximal, characteristic, complemented
5C2×#95×C263C211yesmaximal, characteristic, complemented
6C24×D263C2211yescharacteristic
7C23×Dic263C2212yes—
8C23×Dic263C2211yescharacteristic
9C22×C4×D263—24no—
10C22×C4×D263—24no—
11C22×C4×D263—22no—
12C22×C4×D263—22no—
13C22×C4×D263C414yescomplemented
14C2×(C2×D263)⋊C4—24no—
15C2×(C2×D263)⋊C4—24no—
16C2×(C2×D263)⋊C4C418yescomplemented
17C263⋊#95—24no—
18C263⋊#95—22no—
19C23×C4×C263C2212yes—
20C23×C4×C263C2211yescharacteristic
21#95×C263—22no—
22C23×D263—22no—
23C23×D263—21no—
24C23×D263—21no—
25C23×D263—21no—
26C23×D263—22no—
27C23×D263—21no—
28C23×D263C2×C414yes—
29C23×D263C2×C412yes—
30C23×D263D412yes—
31C23×D263D414yes—
32C23×D263Q812yes—
33C22×Dic263—22no—
34C22×Dic263—21no—
35C22×Dic263—21no—
36C22×Dic263—22no—
37C22×Dic263—22no—
38C22×Dic263—22no—
39C22×Dic263—22no—
40C22×Dic263—22no—
41C22×Dic263—22no—
42C22×Dic263C2×C412yes—
43C22×Dic263C2×C414yescomplemented
44C22×Dic263D414yes—
45C2×C4×D263—216no—
46C2×C4×D263—216no—
47C2×C4×D263—28no—
48C2×C4×D263—28no—
49C2×C4×D263—28no—
50(C2×D263)⋊C4—216no—
51C24×C263C2311yescharacteristic
52C22×C4×C263—22no—
53C22×C4×C263—22no—
54C22×C4×C263—22no—
55C22×C4×C263—22no—
56C22×C4×C263—22no—
57C22×C4×C263—22no—
58C22×C4×C263—22no—
59C22×C4×C263—22no—
60C22×C4×C263C2×C412yes—
61C22×C4×C263C2×C414yescomplemented
62C22×C4×C263D412yes—
63C22×C4×C263D412yes—
64C22×D263—22no—
65C22×D263—22no—
66C22×D263—22no—
67C22×D263—22no—
68C22×D263—24no—
69C22×D263—24no—
70C22×D263—24no—
71C22×D263—24no—
72C22×D263—24no—
73C22×D263—24no—
74C22×D263—22no—
75C22×D263—24no—
76C22×D263—22no—
77C22×D263—22no—
78C22×D263—24no—
79C22×D263—22no—
80C22×D263—24no—
81C22×D263—24no—
82C22×D263C4214yes—
83C22×D263C22⋊C418yes—
84C22×D263C22⋊C414yes—
85C22×D263C4⋊C414yes—
86C22×D263C4⋊C418yes—
87C2×Dic263—22no—
88C2×Dic263—22no—
89C2×Dic263—24no—
90C2×Dic263—24no—
91C2×Dic263—24no—
92C2×Dic263—24no—
93C2×Dic263—24no—
94C2×Dic263—42no—
95C2×Dic263—42no—
96C2×Dic263—42no—
97C2×Dic263—42no—
98C2×Dic263C22⋊C414yescomplemented
99C4×D263—232no—
100C23×C263C22×C411yescharacteristic
101C23×C263C22×C412yes—
102C23×C263C2×D412yes—
103C23×C263C2×D411yescharacteristic
104C23×C263C2×D412yes—
105C23×C263C2×D411yescharacteristic
106C23×C263C2×D411yescharacteristic
107C23×C263C2×Q811yescharacteristic
108C23×C263#4111yescharacteristic
109C23×C263#4112yes—
110C23×C263#4111yescharacteristic
111C2×C4×C263—22no—
112C2×C4×C263—22no—
113C2×C4×C263—24no—
114C2×C4×C263—24no—
115C2×C4×C263—24no—
116C2×C4×C263—24no—
117C2×C4×C263—24no—
118C2×C4×C263—42no—
119C2×C4×C263—42no—
120C2×C4×C263—42no—
121C2×C4×C263—42no—
122C2×C4×C263C22⋊C414yescomplemented
123C22×C263C2×C4211yescharacteristic
124C22×C263C2×C22⋊C411yescharacteristic
125C22×C263C2×C22⋊C412yes—
126C22×C263C2×C22⋊C411yescharacteristic
127C22×C263C2×C22⋊C411yescharacteristic
128C22×C263C2×C4⋊C411yescharacteristic
129C22×C263C2×C4⋊C412yes—
130C22×C263#11711yescharacteristic
131C22×C263#11711yescharacteristic
132C22×C263C4×D412yes—
133C22×C263C4×D412yes—
134C22×C263C4×D412yes—
135C22×C263C4×D412yes—
136C22×C263#12012yes—
137C22×C263#12012yes—
138C22×C263#12111yescharacteristic
139C22×C263#12112yes—
140C22×C263#12111yescharacteristic
141C22×C263C22⋊Q811yescharacteristic
142C22×C263C22⋊Q812yes—
143C22×C263C22⋊Q811yescharacteristic
144C22×C263#12312yes—
145C22×C263#12312yes—
146C2×D263—24no—
147C2×D263—24no—
148C2×D263—24no—
149C2×D263—24no—
150C2×D263—24no—
151C2×D263—24no—
152C2×D263—28no—
153C2×D263—28no—
154C2×D263—28no—
155C2×D263—28no—
156C2×D263#9518yescomplemented
157C4×C263—24no—
158C4×C263—44no—
159Dic263—24no—
160Dic263—44no—
161C2×C263C2×#9511yescharacteristic
162C2×C263C4×C22⋊C411yescharacteristic
163C2×C263C4×C22⋊C411yescharacteristic
164C2×C263#37911yescharacteristic
165C2×C263#38011yescharacteristic
166C2×C263#38011yescharacteristic
167C2×C263#38111yescharacteristic
168C2×C263#38512yes—
169C2×C263#38512yes—
170C2×C263#38612yes—
171C2×C263#38612yes—
172D263—28no—
173C263C22⋊#9511yescharacteristic, complemented, Sylow
174C22⋊#95—2631nomaximal, Sylow
175C24×C4—2631no—
176C22×C22⋊C4—2632no—
177C2×#95—2632no—
178C2×#95—2631no—
179C2×#95D26311yescharacteristic, complemented
180C25—2631no—
181C23×C4—2631no—
182C23×C4—2632no—
183C23×C4—2634no—
184C23×C4—5264no—
185C23×C4—5264no—
186C23×C4—5262no—
187C23×C4—5262no—
188C23×C4C2×D26312yes—
189C23×C4C2×D26311yescharacteristic
190C2×C22⋊C4—2638no—
191C2×C22⋊C4—5264no—
192C2×C22⋊C4—5264no—
193#95—22no—
194#95—5264no—
195#95—5262no—
196C24—2634no—
197C24—2632no—
198C24—2632no—
199C24—2634no—
200C24—2632no—
201C24—5262no—
202C24—5261no—
203C24—5261no—
204C24—5261no—
205C24—5262no—
206C24—5261no—
207C24C22×D26311yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—2632no—
217C22×C4—2634no—
218C22×C4—2634no—
219C22×C4—5268no—
220C22×C4—5268no—
221C22×C4—52616no—
222C22×C4—52616no—
223C22×C4—5262no—
224C22×C4—5261no—
225C22×C4—5261no—
226C22×C4—5268no—
227C22×C4—5262no—
228C22×C4—5262no—
229C22×C4—5262no—
230C22×C4—5262no—
231C22×C4—5262no—
232C22×C4—5262no—
233C22×C4C4×D26312yes—
234C22×C4C4×D26314yescomplemented
235C22×C4C22⋊D26312yes—
236C22×C4D105212yes—
237C22⋊C4—52616no—
238C23—2634no—
239C23—2638no—
240C23—2634no—
241C23—2634no—
242C23—2638no—
243C23—5262no—
244C23—5262no—
245C23—5262no—
246C23—5262no—
247C23—5264no—
248C23—5264no—
249C23—5264no—
250C23—5264no—
251C23—5264no—
252C23—5264no—
253C23—5262no—
254C23—5264no—
255C23—5262no—
256C23—5262no—
257C23—5264no—
258C23—5262no—
259C23—5264no—
260C23—5264no—
261C23C2×C4×D26311yescharacteristic
262C23C2×C4×D26312yes—
263C23D4×D26312yes—
264C23D4×D26311yescharacteristic
265C23D4×D26312yes—
266C23C2×C22⋊D26311yescharacteristic
267C23C2×D105211yescharacteristic
268C23Q8×D26311yescharacteristic
269C23#1686237511yescharacteristic
270C23#1686237612yes—
271C23#1686237711yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—2634no—
284C2×C4—52632no—
285C2×C4—5262no—
286C2×C4—5262no—
287C2×C4—5264no—
288C2×C4—5264no—
289C2×C4—5264no—
290C2×C4—5264no—
291C2×C4—5264no—
292C2×C4—10522no—
293C2×C4—10522no—
294C2×C4—10522no—
295C2×C4—10522no—
296C2×C4(C2×D263)⋊C414yescomplemented
297C22—2638no—
298C22—5264no—
299C22—5264no—
300C22—5264no—
301C22—5264no—
302C22—5264no—
303C22—5264no—
304C22—5268no—
305C22—5268no—
306C22—5268no—
307C22—5268no—
308C22C42×D26311yescharacteristic
309C22C22⋊C4×D26311yescharacteristic
310C22C22⋊C4×D26312yes—
311C22C22⋊C4×D26311yescharacteristic
312C22C2×(C2×D263)⋊C411yescharacteristic
313C22C4⋊C4×D26311yescharacteristic
314C22C4⋊C4×D26312yes—
315C22#2255442711yescharacteristic
316C22#2255442811yescharacteristic
317C22(C22⋊D263)⋊C412yes—
318C22C4×C22⋊D26312yes—
319C22#2255443212yes—
320C22C4×D105212yes—
321C22#2255443812yes—
322C22#2255444012yes—
323C22#2255444111yescharacteristic
324C22#2255444312yes—
325C22#2255444511yescharacteristic
326C22#2255444611yescharacteristic
327C22#2255444812yes—
328C22#2255445011yescharacteristic
329C22#2255445212yes—
330C22#2255445512yes—
331C4—24no—
332C4—44no—
333C4—5264no—
334C4—10524no—
335C2—5268no—
336C2#95×D26311yescharacteristic
337C2#3068178511yescharacteristic
338C2C4×(C2×D263)⋊C411yescharacteristic
339C2#3068179311yescharacteristic
340C2#3068179511yescharacteristic
341C2#3068179711yescharacteristic
342C2#3068180011yescharacteristic
343C2#3068180912yes—
344C2#3068181212yes—
345C2#3068181412yes—
346C2#3068181612yes—
subgroupG/H
center, FrattiniC24C22×D263
commutatorC22×C263C2×C42
FittingC2×#95×C263C2
socle, cosocleC24×C263C23
prime radicalC24×D263C22
hypercenterC2×#95D263
hypocenterC263C22⋊#95
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×C263⋊#95C2semidirect
4. C2×C263⋊#95C2semidirect
5. C2×#95×C263C2semidirect
13. C22×C4×D263C4semidirect
16. C2×(C2×D263)⋊C4C4semidirect
43. C22×Dic263C2×C4semidirect
61. C22×C4×C263C2×C4semidirect
98. C2×Dic263C22⋊C4semidirect
122. C2×C4×C263C22⋊C4semidirect
156. C2×D263#95semidirect
173. C263C22⋊#95semidirect
179. C2×#95D263semidirect
234. C22×C4C4×D263semidirect
296. C2×C4(C2×D263)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D2632
C22×(C2×D263)⋊C42
C2×C263⋊#952
C2×#95×C2632
C22⋊#95263