Finite Group Databasebeta

← #46783046

Subgroups — #46783046

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#30682445C211yesmaximal, characteristic
3C2×#22554397C211yesmaximal, characteristic, complemented
4C4×(C2×D263)⋊C4C211yesmaximal, characteristic, complemented
5#30681699C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C22×C4×D263C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×#16862359—21no—
11M16×D263—22no—
12M16×D263—22no—
13C2×C8×D263—21no—
14#22554451—21no—
15#22554446C411yescharacteristic, complemented
16#22554446C411yescharacteristic, complemented
17#22554441C411yescharacteristic, complemented
18#22554441C411yescharacteristic, complemented
19#22554438—21no—
20C4×C22⋊D263—21no—
21C4×C22⋊D263—21no—
22#22554429C2211yescharacteristic
23C2×(C2×D263)⋊C4—21no—
24C2×C4×Dic263C2211yescharacteristic
25#22554397—22no—
26C263⋊#95—21no—
27C2×#41×C263C2211yescharacteristic
28C2×M16×C263C2211yescharacteristic
29C2×C42×C263C2211yescharacteristic
30#104×C263—22no—
31C23×D263D411yescharacteristic
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C22×Dic263—21no—
35C22×Dic263D411yescharacteristic
36C2×C4×D263—21no—
37C2×C4×D263—21no—
38C2×C4×D263—21no—
39C2×C4×D263—21no—
40C2×C4×D263C2×C411yescharacteristic
41C2×C4×D263C2×C411yescharacteristic
42C2×C4×D263D411yescharacteristic
43C2×C4×D263D411yescharacteristic
44#16862360—21no—
45#16862360D412yescomplemented
46#16862359—24no—
47C2×C263⋊C8—21no—
48C8×D263—24no—
49C4⋊Dic263C2×C411yescharacteristic
50C4⋊Dic263C2×C411yescharacteristic
51Dic263⋊C4—21no—
52Dic263⋊C4—21no—
53C22⋊Dic263—21no—
54C22⋊Dic263—21no—
55C22⋊Dic263—21no—
56(C2×D263)⋊C4—24no—
57(C2×D263)⋊C4—21no—
58(C2×D263)⋊C4—21no—
59C4×Dic263—21no—
60C4×Dic263—21no—
61C4×Dic263—21no—
62#41×C263—21no—
63#41×C263—21no—
64#41×C263—21no—
65#41×C263—21no—
66C2×Q8×C263C2×C411yescharacteristic
67C2×D4×C263—21no—
68C2×D4×C263C2×C411yescharacteristic
69C22×C4×C263—21no—
70C22×C4×C263—21no—
71C22×C4×C263C2311yescharacteristic
72M16×C263—21no—
73M16×C263D412yescomplemented
74C2×C8×C263—21no—
75C42×C263—21no—
76C42×C263—21no—
77C22×D263—21no—
78C22×D263—21no—
79C22×D263—22no—
80C22×D263—41no—
81C22×D263C22⋊C411yescharacteristic
82C22×D263C22⋊C411yescharacteristic
83C22⋊D263—42no—
84C22⋊D263—42no—
85C2×Dic263—21no—
86C2×Dic263—21no—
87C2×Dic263—22no—
88C2×Dic263—21no—
89C2×Dic263—21no—
90C2×Dic263—41no—
91C2×Dic263—41no—
92C2×Dic263C22⋊C411yescharacteristic
93C2×Dic263C22⋊C411yescharacteristic
94C4×D263—21no—
95C4×D263—21no—
96C4×D263—21no—
97C4×D263—21no—
98C4×D263—21no—
99C4×D263—21no—
100C4×D263—21no—
101C4×D263—21no—
102C263⋊C8—22no—
103C23×C263—21no—
104C23×C263C2×D411yescharacteristic
105Q8×C263—21no—
106Q8×C263—21no—
107D4×C263—21no—
108D4×C263—21no—
109D4×C263—41no—
110D4×C263—41no—
111C2×C4×C263—22no—
112C2×C4×C263—21no—
113C2×C4×C263—41no—
114C2×C4×C263—41no—
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×C263—41no—
127C22×C263—41no—
128C22×C263—41no—
129C22×C263C2×C22⋊C411yescharacteristic
130C22×C263#12111yescharacteristic
131C22×C263#12111yescharacteristic
132C2×D263—21no—
133C2×D263—21no—
134C2×D263—21no—
135C2×D263—21no—
136C2×D263—21no—
137C2×D263—42no—
138C2×D263—42no—
139C2×D263#10412yescomplemented
140C4×C263—42no—
141C4×C263—41no—
142C4×C263C4×D411yescharacteristic
143C4×C263C4×D411yescharacteristic
144C4×C263#12011yescharacteristic
145C4×C263#12311yescharacteristic
146Dic263—21no—
147Dic263—21no—
148Dic263—42no—
149Dic263—41no—
150Dic263—41no—
151C2×C263—21no—
152C2×C263—21no—
153C2×C263—81no—
154C2×C263#38611yescharacteristic
155C2×C263C2×#10411yescharacteristic
156C2×C263#42111yescharacteristic
157D263—22no—
158D263—41no—
159C263#187111yescharacteristic, complemented, Sylow
160#1871—2631nomaximal, Sylow
161C22×M16—2631no—
162#525—2631no—
163C2×#104—2631no—
164C2×#104D26311yescharacteristic, complemented
165C4×C22⋊C4—2631no—
166#339—2631no—
167#339—2631no—
168C2×#41C2×D26311yescharacteristic
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#117—2631no—
185C2×C22⋊C4—5261no—
186C2×C42—2631no—
187C2×C42C2×D26311yescharacteristic
188#104—22no—
189#104—5262no—
190#95—5261no—
191C24—2631no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D26311yescharacteristic
197C2×D4—21no—
198C2×D4—5261no—
199C2×D4—5261no—
200C2×D4C4×D26311yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—2631no—
204C22×C4—2631no—
205C22×C4—2631no—
206C22×C4—2631no—
207C22×C4—2631no—
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—
218M16C22⋊D26312yescomplemented
219C2×C8—21no—
220C2×C8—5264no—
221C2×C8—5261no—
222C4⋊C4—2631no—
223C4⋊C4—2631no—
224C4⋊C4—5261no—
225C4⋊C4—5261no—
226C22⋊C4—5261no—
227C22⋊C4—5261no—
228C22⋊C4—5264no—
229C22⋊C4—5261no—
230C22⋊C4—5261no—
231C22⋊C4—5261no—
232C42—21no—
233C42—21no—
234C42—5261no—
235C42—5261no—
236C42—5261no—
237C23—21no—
238C23—2631no—
239C23—2631no—
240C23—5262no—
241C23—5261no—
242C23—5261no—
243C23—10521no—
244C23D4×D26311yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—10522no—
252D4—10522no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—2631no—
260C2×C4—2631no—
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—5261no—
271C2×C4—5262no—
272C2×C4—5261no—
273C2×C4—5261no—
274C2×C4—10521no—
275C2×C4—10521no—
276C2×C4C2×C4×D26311yescharacteristic
277C2×C4D4×D26311yescharacteristic
278C2×C4D4×D26311yescharacteristic
279C2×C4C2×C22⋊D26311yescharacteristic
280C2×C4#1686237511yescharacteristic
281C2×C4#1686237611yescharacteristic
282C8—22no—
283C8—5262no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—2632no—
290C22—5261no—
291C22—5261no—
292C22—5261no—
293C22—5261no—
294C22—5261no—
295C22—10522no—
296C22—10522no—
297C22C22⋊C4×D26311yescharacteristic
298C22#2255444111yescharacteristic
299C22#2255444311yescharacteristic
300C4—42no—
301C4—41no—
302C4—5261no—
303C4—5261no—
304C4—10522no—
305C4—10521no—
306C4—10521no—
307C4(C22⋊D263)⋊C411yescharacteristic
308C4C4×C22⋊D26311yescharacteristic
309C4#2255443811yescharacteristic
310C4#2255445211yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—5262no—
315C2—10521no—
316C2#3068181411yescharacteristic
317C2#104×D26311yescharacteristic
318C2#3068195311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682445C2
cosocleC22×C4×C263C23
hypercenterC2×#104D263
hypocenterC263#1871
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D263C2semidirect
3. C2×#22554397C2semidirect
4. C4×(C2×D263)⋊C4C2semidirect
5. #30681699C2semidirect
6. #30681698C2semidirect
7. C2×#104×C263C2semidirect
15. #22554446C4semidirect
16. #22554446C4semidirect
17. #22554441C4semidirect
18. #22554441C4semidirect
45. #16862360D4semidirect
73. M16×C263D4semidirect
139. C2×D263#104semidirect
159. C263#1871semidirect
164. C2×#104D263semidirect
218. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D2632
#306824452
C2×#225543972
C4×(C2×D263)⋊C42
#306816992
#306816982
C2×#104×C2632
#1871263