Finite Group Databasebeta

← #46781008

Subgroups — #46781008

Order 33664.

476 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C263⋊#95C211yesmaximal, characteristic
2C2×C263⋊#95C211yesmaximal, characteristic
3C2×C263⋊#95C211yesmaximal, characteristic
4C2×C263⋊#95C211yesmaximal, characteristic
5C2×C263⋊#95C211yesmaximal, characteristic
6C2×C263⋊#95C211yesmaximal, characteristic
7C2×#95×C263C211yesmaximal, characteristic
8C23×Dic263C2211yescharacteristic
9C23×Dic263C2211yescharacteristic
10C23×Dic263C2211yescharacteristic
11C23×Dic263C2211yescharacteristic
12C263⋊#95—22no—
13C263⋊#95—22no—
14C263⋊#95—22no—
15C263⋊#95—22no—
16C263⋊#95—22no—
17C263⋊#95C414yescomplemented
18C23×C4×C263C2211yescharacteristic
19C23×C4×C263C2211yescharacteristic
20C23×C4×C263C2211yescharacteristic
21#95×C263—22no—
22C22×Dic263—21no—
23C22×Dic263—21no—
24C22×Dic263—21no—
25C22×Dic263—21no—
26C22×Dic263—21no—
27C22×Dic263—21no—
28C22×Dic263—21no—
29C22×Dic263—21no—
30C22×Dic263—21no—
31C22×Dic263—21no—
32C22×Dic263—21no—
33C22×Dic263—21no—
34C22×Dic263—21no—
35C22×Dic263—21no—
36C22×Dic263—21no—
37C22×Dic263—21no—
38C22×Dic263—21no—
39C22×Dic263—21no—
40C22×Dic263—21no—
41C22×Dic263—21no—
42C22×Dic263—21no—
43C22×Dic263—21no—
44C22×Dic263—21no—
45C22×Dic263—21no—
46C22×Dic263C2×C412yes—
47C22×Dic263C2×C412yes—
48C22×Dic263D412yes—
49C22×Dic263D412yes—
50C24×C263C2311yescharacteristic
51C22×C4×C263—21no—
52C22×C4×C263—21no—
53C22×C4×C263—21no—
54C22×C4×C263—21no—
55C22×C4×C263—21no—
56C22×C4×C263—21no—
57C22×C4×C263—21no—
58C22×C4×C263—21no—
59C22×C4×C263—21no—
60C22×C4×C263—21no—
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263—21no—
64C22×C4×C263—21no—
65C22×C4×C263—21no—
66C22×C4×C263—21no—
67C22×C4×C263—21no—
68C22×C4×C263—21no—
69C22×C4×C263C2×C412yes—
70C22×C4×C263D412yes—
71C22×C4×C263Q812yes—
72C2×Dic263—22no—
73C2×Dic263—22no—
74C2×Dic263—22no—
75C2×Dic263—22no—
76C2×Dic263—22no—
77C2×Dic263—22no—
78C2×Dic263—22no—
79C2×Dic263—22no—
80C2×Dic263—22no—
81C2×Dic263—22no—
82C2×Dic263—22no—
83C2×Dic263—22no—
84C2×Dic263—41no—
85C2×Dic263—41no—
86C2×Dic263—41no—
87C2×Dic263—41no—
88C2×Dic263—41no—
89C2×Dic263—41no—
90C2×Dic263—41no—
91C2×Dic263—41no—
92C2×Dic263—41no—
93C2×Dic263—41no—
94C2×Dic263—41no—
95C2×Dic263—41no—
96C2×Dic263—41no—
97C2×Dic263—41no—
98C2×Dic263—41no—
99C2×Dic263—41no—
100C23×C263C22×C411yescharacteristic
101C23×C263C2×D411yescharacteristic
102C23×C263C2×D411yescharacteristic
103C23×C263C2×D411yescharacteristic
104C23×C263C2×Q811yescharacteristic
105C23×C263#4111yescharacteristic
106C23×C263#4111yescharacteristic
107C23×C263#4111yescharacteristic
108C23×C263#4111yescharacteristic
109C23×C263#4111yescharacteristic
110C23×C263#4111yescharacteristic
111C23×C263#4111yescharacteristic
112C23×C263#4111yescharacteristic
113C23×C263#4111yescharacteristic
114C23×C263#4111yescharacteristic
115C2×C4×C263—22no—
116C2×C4×C263—22no—
117C2×C4×C263—22no—
118C2×C4×C263—22no—
119C2×C4×C263—22no—
120C2×C4×C263—22no—
121C2×C4×C263—22no—
122C2×C4×C263—22no—
123C2×C4×C263—22no—
124C2×C4×C263—41no—
125C2×C4×C263—41no—
126C2×C4×C263—41no—
127C2×C4×C263—41no—
128C2×C4×C263—41no—
129C2×C4×C263—41no—
130C2×C4×C263—41no—
131C2×C4×C263—41no—
132C2×C4×C263—41no—
133C2×C4×C263—41no—
134C2×C4×C263—41no—
135C2×C4×C263—41no—
136C22×C263#11711yescharacteristic
137C22×C263#11711yescharacteristic
138C22×C263#11711yescharacteristic
139C22×C263C4×D411yescharacteristic
140C22×C263C4×D411yescharacteristic
141C22×C263C4×D411yescharacteristic
142C22×C263C4×Q811yescharacteristic
143C22×C263#12111yescharacteristic
144C22×C263#12111yescharacteristic
145C22×C263#12111yescharacteristic
146C22×C263C22⋊Q811yescharacteristic
147C22×C263C22⋊Q811yescharacteristic
148C22×C263C22⋊Q811yescharacteristic
149C22×C263#12311yescharacteristic
150C22×C263#12311yescharacteristic
151C22×C263#12311yescharacteristic
152C22×C263#12311yescharacteristic
153C22×C263#12311yescharacteristic
154C22×C263#12311yescharacteristic
155C22×C263#12411yescharacteristic
156C22×C263#12411yescharacteristic
157C22×C263#12411yescharacteristic
158C22×C263#12511yescharacteristic
159C22×C263#12511yescharacteristic
160C22×C263#12511yescharacteristic
161C22×C263#12611yescharacteristic
162C22×C263#12611yescharacteristic
163C22×C263#12611yescharacteristic
164C22×C263#12611yescharacteristic
165C22×C263#12611yescharacteristic
166C22×C263#12611yescharacteristic
167C22×C263#12611yescharacteristic
168C22×C263#12611yescharacteristic
169C22×C263#12611yescharacteristic
170C22×C263#12611yescharacteristic
171C4×C263—42no—
172C4×C263—42no—
173C4×C263—42no—
174Dic263—42no—
175Dic263—42no—
176Dic263—42no—
177Dic263—42no—
178C2×C263#38311yescharacteristic
179C2×C263#38711yescharacteristic
180C2×C263#38711yescharacteristic
181C2×C263#38711yescharacteristic
182C2×C263#38811yescharacteristic
183C2×C263#38811yescharacteristic
184C2×C263#38811yescharacteristic
185C2×C263#39611yescharacteristic
186C2×C263#39711yescharacteristic
187C2×C263#39711yescharacteristic
188C2×C263#39711yescharacteristic
189C2×C263#40011yescharacteristic
190C2×C263#40011yescharacteristic
191C2×C263#40011yescharacteristic
192C2×C263#40111yescharacteristic
193C263#144311yescharacteristic, complemented, Sylow
194#1443—2631nomaximal, Sylow
195C2×#95—2631no—
196C2×#95—2631no—
197C2×#95—2631no—
198C2×#95—2631no—
199C2×#95—2631no—
200C2×#95—2631no—
201C2×#95D26311yescharacteristic
202C23×C4—2631no—
203C23×C4—2631no—
204C23×C4—2631no—
205C23×C4—2631no—
206C23×C4C2×D26311yescharacteristic
207C23×C4C2×D26311yescharacteristic
208C23×C4C2×D26311yescharacteristic
209#95—22no—
210#95—2634no—
211#95—5262no—
212#95—5262no—
213#95—5262no—
214#95—5262no—
215#95—5262no—
216C24C22×D26311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—2632no—
236C22×C4—2632no—
237C22×C4—2632no—
238C22×C4—2632no—
239C22×C4—5261no—
240C22×C4—5261no—
241C22×C4—5261no—
242C22×C4—5261no—
243C22×C4—5261no—
244C22×C4—5261no—
245C22×C4—5261no—
246C22×C4—5261no—
247C22×C4—5261no—
248C22×C4—5261no—
249C22×C4—5261no—
250C22×C4—5261no—
251C22×C4—5261no—
252C22×C4—5261no—
253C22×C4—5261no—
254C22×C4—5261no—
255C22×C4—5261no—
256C22×C4—5261no—
257C22×C4—5261no—
258C22×C4—5261no—
259C22×C4—5261no—
260C22×C4—5261no—
261C22×C4—5261no—
262C22×C4—5261no—
263C22×C4C4×D26312yes—
264C22×C4C22⋊D26312yes—
265C22×C4Dic52612yes—
266C23C2×C4×D26311yescharacteristic
267C23D4×D26311yescharacteristic
268C23D4×D26311yescharacteristic
269C23C2×C22⋊D26311yescharacteristic
270C23C2×Dic52611yescharacteristic
271C23#1686237511yescharacteristic
272C23#1686237511yescharacteristic
273C23#1686237511yescharacteristic
274C23#1686237511yescharacteristic
275C23#1686237611yescharacteristic
276C23#1686237611yescharacteristic
277C23#1686237611yescharacteristic
278C23#1686237611yescharacteristic
279C23#1686237711yescharacteristic
280C23#1686237711yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—5262no—
303C2×C4—5262no—
304C2×C4—5262no—
305C2×C4—5262no—
306C2×C4—5262no—
307C2×C4—5262no—
308C2×C4—5262no—
309C2×C4—5262no—
310C2×C4—5262no—
311C2×C4—5262no—
312C2×C4—5262no—
313C2×C4—5262no—
314C2×C4—10521no—
315C2×C4—10521no—
316C2×C4—10521no—
317C2×C4—10521no—
318C2×C4—10521no—
319C2×C4—10521no—
320C2×C4—10521no—
321C2×C4—10521no—
322C2×C4—10521no—
323C2×C4—10521no—
324C2×C4—10521no—
325C2×C4—10521no—
326C2×C4—10521no—
327C2×C4—10521no—
328C2×C4—10521no—
329C2×C4—10521no—
330C22#2255442611yescharacteristic
331C22#2255442711yescharacteristic
332C22#2255442811yescharacteristic
333C22(C22⋊D263)⋊C411yescharacteristic
334C22C4×C22⋊D26311yescharacteristic
335C22#2255443211yescharacteristic
336C22C4×Dic52611yescharacteristic
337C22#2255444111yescharacteristic
338C22#2255444211yescharacteristic
339C22#2255444311yescharacteristic
340C22#2255444711yescharacteristic
341C22#2255444711yescharacteristic
342C22#2255444911yescharacteristic
343C22#2255445111yescharacteristic
344C22#2255445211yescharacteristic
345C22#2255445311yescharacteristic
346C22#2255445511yescharacteristic
347C22#2255445511yescharacteristic
348C22#2255445511yescharacteristic
349C22#2255445611yescharacteristic
350C22#2255445611yescharacteristic
351C22#2255445911yescharacteristic
352C22#2255446111yescharacteristic
353C22#2255446111yescharacteristic
354C22#2255446211yescharacteristic
355C22#2255446311yescharacteristic
356C22#2255446311yescharacteristic
357C22#2255446311yescharacteristic
358C22#2255446311yescharacteristic
359C22#2255446411yescharacteristic
360C22#2255446511yescharacteristic
361C22#2255446511yescharacteristic
362C22#2255446511yescharacteristic
363C22#2255446511yescharacteristic
364C22#2255446511yescharacteristic
365C4—42no—
366C4—42no—
367C4—42no—
368C4—10522no—
369C4—10522no—
370C4—10522no—
371C4—10522no—
372C2#3068180511yescharacteristic
373C2#3068182111yescharacteristic
374C2#3068182211yescharacteristic
375C2#3068182511yescharacteristic
376C2#3068182611yescharacteristic
377C2#3068182711yescharacteristic
378C2#3068182811yescharacteristic
379C2#3068186111yescharacteristic
380C2#3068186411yescharacteristic
381C2#3068186611yescharacteristic
382C2#3068186711yescharacteristic
383C2#3068187711yescharacteristic
384C2#3068188011yescharacteristic
385C2#3068188011yescharacteristic
386C2C263⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D263
commutatorC23×C263C22×C4
FittingC2×#95×C263C2
socle, prime radical, cosocleC24×C263C23
hypercenterC2×#95D263
hypocenterC263#1443
LCSG ▷ C23×C263 ▷ C263
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. C263⋊#95C4semidirect
193. C263#1443semidirect

Maximal subgroups

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

subgroupindex
C2×C263⋊#952
C2×#95×C2632
#1443263