Finite Group Databasebeta

← #46783048

Subgroups — #46783048

Order 33664.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D263C211yesmaximal, characteristic, complemented
2#30682450C211yesmaximal, characteristic
3C2×#22554398C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5C4×(C2×D263)⋊C4C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#339×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×C4×D263C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11C2×#16862359—21no—
12M16×D263—22no—
13M16×D263—22no—
14C2×C8×D263—21no—
15#22554454—21no—
16#22554450C411yescharacteristic, complemented
17#22554450C411yescharacteristic, complemented
18#22554445C411yescharacteristic, complemented
19#22554445C411yescharacteristic, complemented
20#22554440—21no—
21C4×D1052—21no—
22C4×D1052—21no—
23C2×(C2×D263)⋊C4—21no—
24C2×C4×Dic263C2211yescharacteristic
25#22554398—22no—
26#22554396—22no—
27C263⋊#95—21no—
28C2×M16×C263C2211yescharacteristic
29#117×C263C2211yescharacteristic
30C2×C42×C263C2211yescharacteristic
31C23×D263D411yescharacteristic
32#16862376—21no—
33#16862376—21no—
34#16862376—21no—
35#16862376—21no—
36C2×Dic526C2×C411yescharacteristic
37C2×D1052—21no—
38C2×D1052—21no—
39C2×D1052C2×C411yescharacteristic
40C2×C22⋊D263—21no—
41C22×Dic263—21no—
42C22×Dic263D411yescharacteristic
43C2×C4×D263—21no—
44C2×C4×D263—21no—
45C2×C4×D263—21no—
46C2×C4×D263—21no—
47C2×C4×D263—21no—
48C2×C4×D263C2×C411yescharacteristic
49C2×C4×D263C2×C411yescharacteristic
50C2×C4×D263D411yescharacteristic
51C2×C4×D263D411yescharacteristic
52#16862360—21no—
53#16862360D412yescomplemented
54#16862359—24no—
55C2×C263⋊C8—21no—
56C8×D263—24no—
57C4⋊Dic263—21no—
58C4⋊Dic263—21no—
59(C2×D263)⋊C4—24no—
60(C2×D263)⋊C4—21no—
61(C2×D263)⋊C4—21no—
62(C2×D263)⋊C4—21no—
63(C2×D263)⋊C4—21no—
64C4×Dic263—21no—
65C4×Dic263—21no—
66C22×C4×C263—21no—
67C22×C4×C263C2311yescharacteristic
68M16×C263—21no—
69M16×C263D412yescomplemented
70C2×C8×C263—21no—
71C4⋊C4×C263C2×C411yescharacteristic
72C4⋊C4×C263C2×C411yescharacteristic
73C22⋊C4×C263—21no—
74C42×C263—21no—
75C42×C263—21no—
76C42×C263—21no—
77C22×D263—21no—
78C22×D263—21no—
79C22×D263—22no—
80C22×D263—21no—
81C22×D263—41no—
82C22×D263C22⋊C411yescharacteristic
83C22×D263C22⋊C411yescharacteristic
84Dic526—21no—
85Dic526—21no—
86D1052—21no—
87D1052—21no—
88D1052—42no—
89D1052—42no—
90C22⋊D263—41no—
91C22⋊D263—41no—
92C2×Dic263—21no—
93C2×Dic263—21no—
94C2×Dic263—22no—
95C2×Dic263—21no—
96C2×Dic263—41no—
97C2×Dic263—41no—
98C2×Dic263C22⋊C411yescharacteristic
99C2×Dic263C22⋊C411yescharacteristic
100C4×D263—21no—
101C4×D263—21no—
102C4×D263—21no—
103C4×D263—21no—
104C4×D263—21no—
105C4×D263—21no—
106C4×D263—21no—
107C4×D263—21no—
108C4×D263—41no—
109C4×D263—41no—
110C263⋊C8—22no—
111C23×C263C2×D411yescharacteristic
112C2×C4×C263—22no—
113C2×C4×C263—21no—
114C2×C4×C263—21no—
115C2×C4×C263—41no—
116C2×C4×C263—41no—
117C2×C4×C263C22×C411yescharacteristic
118C2×C4×C263C2×D411yescharacteristic
119C2×C4×C263C2×D411yescharacteristic
120C2×C4×C263C2×D411yescharacteristic
121C2×C4×C263#4111yescharacteristic
122C2×C4×C263#4111yescharacteristic
123C8×C263—22no—
124C22×C263—21no—
125C22×C263—21no—
126C22×C263C2×C22⋊C411yescharacteristic
127C22×C263#12111yescharacteristic
128C22×C263#12111yescharacteristic
129C2×D263—21no—
130C2×D263—21no—
131C2×D263—21no—
132C2×D263—21no—
133C2×D263—21no—
134C2×D263—42no—
135C2×D263—42no—
136C2×D263—41no—
137C2×D263—41no—
138C2×D263—41no—
139C2×D263#10412yescomplemented
140C4×C263—42no—
141C4×C263—41no—
142C4×C263—41no—
143C4×C263C4×D411yescharacteristic
144C4×C263C4×D411yescharacteristic
145C4×C263#12011yescharacteristic
146C4×C263#12311yescharacteristic
147Dic263—21no—
148Dic263—21no—
149Dic263—42no—
150Dic263—41no—
151C2×C263—21no—
152C2×C263—21no—
153C2×C263#38611yescharacteristic
154C2×C263C2×#10411yescharacteristic
155C2×C263#42111yescharacteristic
156D263—22no—
157D263—41no—
158D263—81no—
159C263#187111yescharacteristic, complemented, Sylow
160#1871—2631nomaximal, Sylow
161C22×M16—2631no—
162#525—2631no—
163C2×#104—2631no—
164C2×#104—2631no—
165C4×C22⋊C4—2631no—
166#339—2631no—
167#339D26311yescharacteristic, complemented
168C2×#41—2631no—
169C23×C4—2631no—
170C2×M16—2631no—
171C2×M16—5261no—
172C2×M16—5262no—
173C2×M16—5262no—
174C2×M16C2×D26311yescharacteristic
175C22×C8—5261no—
176#123—5261no—
177C22⋊Q8—2631no—
178C22⋊Q8—2631no—
179#121—2631no—
180#121—2631no—
181#120—5261no—
182C4×D4—5261no—
183C4×D4—5261no—
184#117C2×D26311yescharacteristic
185C2×C22⋊C4—5261no—
186C2×C42—2631no—
187C2×C42C2×D26311yescharacteristic
188#104—5262no—
189#104—5262no—
190#95—5261no—
191C24—2631no—
192#41—5261no—
193#41—5261no—
194#41—5261no—
195#41—5261no—
196C2×Q8—2631no—
197C2×D4—2631no—
198C2×D4—5261no—
199C2×D4—5261no—
200C2×D4—5261no—
201C22×C4—21no—
202C22×C4—2631no—
203C22×C4—2631no—
204C22×C4—2631no—
205C22×C4—2631no—
206C22×C4—2631no—
207C22×C4—5261no—
208C22×C4—5261no—
209C22×C4—5261no—
210C22×C4—5261no—
211C22×C4—5261no—
212C22×C4—5261no—
213C22×C4C22×D26311yescharacteristic
214M16—21no—
215M16—2632no—
216M16—5264no—
217M16—5261no—
218M16D105212yescomplemented
219C2×C8—21no—
220C2×C8—5264no—
221C2×C8—5261no—
222C4⋊C4—5261no—
223C4⋊C4—5261no—
224C4⋊C4C4×D26311yescharacteristic
225C4⋊C4C4×D26311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—5261no—
228C22⋊C4—5261no—
229C22⋊C4—5261no—
230C22⋊C4—5261no—
231C22⋊C4—5264no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—5261no—
236C42—5261no—
237C23—2631no—
238C23—2631no—
239C23—5262no—
240C23—5261no—
241C23—5261no—
242C23—5261no—
243C23—10521no—
244C23D4×D26311yescharacteristic
245Q8—5261no—
246Q8—5261no—
247D4—5261no—
248D4—5261no—
249D4—10522no—
250D4—10522no—
251D4—10521no—
252D4—10521no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—2631no—
259C2×C4—2631no—
260C2×C4—5261no—
261C2×C4—5261no—
262C2×C4—5261no—
263C2×C4—5261no—
264C2×C4—5261no—
265C2×C4—5261no—
266C2×C4—5261no—
267C2×C4—5261no—
268C2×C4—5261no—
269C2×C4—5261no—
270C2×C4—5262no—
271C2×C4—5261no—
272C2×C4—10521no—
273C2×C4—10521no—
274C2×C4—10521no—
275C2×C4—10521no—
276C2×C4C2×C4×D26311yescharacteristic
277C2×C4D4×D26311yescharacteristic
278C2×C4D4×D26311yescharacteristic
279C2×C4C2×D105211yescharacteristic
280C2×C4#1686237611yescharacteristic
281C2×C4#1686237711yescharacteristic
282C8—22no—
283C8—5262no—
284C22—21no—
285C22—21no—
286C22—2632no—
287C22—5261no—
288C22—5261no—
289C22—5261no—
290C22—5261no—
291C22—5261no—
292C22—10522no—
293C22—10522no—
294C22—10521no—
295C22—10521no—
296C22—10521no—
297C22C22⋊C4×D26311yescharacteristic
298C22#2255444311yescharacteristic
299C22#2255444511yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—5261no—
304C4—5261no—
305C4—10522no—
306C4—10521no—
307C4#2255443211yescharacteristic
308C4C4×D105211yescharacteristic
309C4#2255444011yescharacteristic
310C4#2255445511yescharacteristic
311C2—21no—
312C2—21no—
313C2—5262no—
314C2—10521no—
315C2—21041no—
316C2#3068181611yescharacteristic
317C2#104×D26311yescharacteristic
318C2#3068195311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682450C2
cosocleC22×C4×C263C23
hypercenter#339D263
hypocenterC263#1871
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D263C2semidirect
3. C2×#22554398C2semidirect
4. C2×#22554396C2semidirect
5. C4×(C2×D263)⋊C4C2semidirect
6. #30681697C2semidirect
7. #339×C263C2semidirect
16. #22554450C4semidirect
17. #22554450C4semidirect
18. #22554445C4semidirect
19. #22554445C4semidirect
53. #16862360D4semidirect
69. M16×C263D4semidirect
139. C2×D263#104semidirect
159. C263#1871semidirect
167. #339D263semidirect
218. M16D1052semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D2632
#306824502
C2×#225543982
C2×#225543962
C4×(C2×D263)⋊C42
#306816972
#339×C2632
#1871263