Finite Group Databasebeta

← #46783248

Subgroups — #46783248

Order 33664.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#30682736C211yesmaximal, characteristic
2#30681955C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4#30681911C211yesmaximal, characteristic, complemented
5#30681708C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C4×#41×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—21no—
10#22554500C412yescomplemented
11#22554496—21no—
12#22554495C412yescomplemented
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15C2×#16862360C2211yescharacteristic
16#22554429C2211yescharacteristic
17#22554398—21no—
18#22554398—21no—
19#22554397—22no—
20#22554384—22no—
21C2×#41×C263C2211yescharacteristic
22C4×Q8×C263—21no—
23C4×D4×C263—21no—
24C4×D4×C263—22no—
25#117×C263—21no—
26#117×C263C2211yescharacteristic
27C2×C42×C263—21no—
28C2×C42×C263C2211yescharacteristic
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33C2×Dic526C2×C411yescharacteristic, complemented
34C2×D1052C2×C411yescharacteristic, complemented
35C2×C22⋊D263—21no—
36C2×C4×D263—21no—
37#16862366—22no—
38#16862364—22no—
39#16862363—22no—
40#16862361—22no—
41#16862360—21no—
42#16862360—21no—
43#16862360—21no—
44#16862360C2×C412yescomplemented
45C2×C263⋊C8—21no—
46C2×C263⋊C8—21no—
47C4⋊Dic263—21no—
48C22⋊Dic263—21no—
49C4×Dic263—21no—
50#41×C263—21no—
51#41×C263—21no—
52#41×C263C2×C412yes—
53#41×C263D412yes—
54C2×Q8×C263D411yescharacteristic
55C2×D4×C263—21no—
56C2×D4×C263D411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263—22no—
59C22×C4×C263—21no—
60C22×C4×C263C2311yescharacteristic
61C4⋊C4×C263—22no—
62C4⋊C4×C263—21no—
63C22⋊C4×C263—22no—
64C22⋊C4×C263D412yes—
65C42×C263—22no—
66C42×C263—21no—
67C42×C263—21no—
68C42×C263D411yescharacteristic
69C42×C263D411yescharacteristic
70C22×D263—21no—
71Dic526—21no—
72Dic526—21no—
73D1052—21no—
74D1052—21no—
75C22⋊D263—41no—
76C22⋊D263—41no—
77C2×Dic263—21no—
78C2×Dic263—41no—
79C4×D263—41no—
80C4×D263—41no—
81C263⋊C8—22no—
82C263⋊C8—41no—
83C23×C263—21no—
84C23×C263C2×D411yescharacteristic
85Q8×C263—21no—
86Q8×C263C22⋊C412yes—
87D4×C263—22no—
88D4×C263—22no—
89D4×C263—21no—
90D4×C263C22⋊C412yes—
91C2×C4×C263—21no—
92C2×C4×C263—21no—
93C2×C4×C263—22no—
94C2×C4×C263—22no—
95C2×C4×C263—22no—
96C2×C4×C263—21no—
97C2×C4×C263—42no—
98C2×C4×C263—44no—
99C2×C4×C263C22×C411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263#4111yescharacteristic
104C2×C4×C263#4111yescharacteristic
105C22×C263—22no—
106C22×C263—41no—
107C22×C263—42no—
108C22×C263C4×D411yescharacteristic
109C22×C263#12011yescharacteristic
110C22×C263#12111yescharacteristic
111C2×D263—41no—
112C2×D263—81no—
113C4×C263—22no—
114C4×C263—22no—
115C4×C263—42no—
116C4×C263—41no—
117C4×C263C2×C22⋊C411yescharacteristic
118C4×C263C4×D411yescharacteristic
119C4×C263#12111yescharacteristic
120C4×C263#12311yescharacteristic
121Dic263—41no—
122Dic263—81no—
123C2×C263—21no—
124C2×C263—21no—
125C2×C263—21no—
126C2×C263—42no—
127C2×C263#38611yescharacteristic
128D263—81no—
129C263#190611yescharacteristic, complemented, Sylow
130#1906—2631nomaximal, Sylow
131#575—2631no—
132C4×#41D26311yescharacteristic, complemented
133#421—2631no—
134C2×#104—2631no—
135#410—2631no—
136#344—2631no—
137#339—2631no—
138C2×#41—2631no—
139C2×#41C2×D26311yescharacteristic
140#137—2632no—
141#137—5261no—
142AGL(1,ℤ/8)—2632no—
143AGL(1,ℤ/8)—5261no—
144#135—5262no—
145C2×M16—2631no—
146C2×M16—2631no—
147C4×Q8—21no—
148C4×D4—21no—
149C4×D4—22no—
150#117—21no—
151#117—2631no—
152#117C2×D26311yescharacteristic
153C2×C42—21no—
154C2×C42C2×D26311yescharacteristic
155#104—5262no—
156#104—5261no—
157#104—5261no—
158#99—5262no—
159#41—21no—
160#41—21no—
161#41—5261no—
162#41—5261no—
163#41—5261no—
164#41—5261no—
165#41C4×D26312yes—
166#41D105212yes—
167C2×Q8—2631no—
168C2×Q8C22⋊D26311yescharacteristic
169C2×D4—21no—
170C2×D4—2631no—
171C2×D4—5261no—
172C2×D4C22⋊D26311yescharacteristic
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—5261no—
177C22×C4C22×D26311yescharacteristic
178Q16—5262no—
179SD16—5262no—
180SD16—5262no—
181D8—5262no—
182M16—2632no—
183M16—5261no—
184M16—5261no—
185M16—5261no—
186C2×C8—5261no—
187C2×C8—5261no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—5261no—
191C22⋊C4—22no—
192C22⋊C4—5261no—
193C22⋊C4C22⋊D26312yes—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—5261no—
198C42C22⋊D26311yescharacteristic
199C42C22⋊D26311yescharacteristic
200C23—21no—
201C23—5261no—
202C23C2×C22⋊D26311yescharacteristic
203Q8—21no—
204Q8—5261no—
205Q8—5261no—
206Q8(C2×D263)⋊C412yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—5261no—
211D4—5261no—
212D4—10521no—
213D4—10521no—
214D4(C2×D263)⋊C412yes—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—5261no—
224C2×C4—10521no—
225C2×C4—10521no—
226C2×C4—10521no—
227C2×C4C2×C4×D26311yescharacteristic
228C2×C4C2×C22⋊D26311yescharacteristic
229C2×C4C2×C22⋊D26311yescharacteristic
230C2×C4C2×D105211yescharacteristic
231C2×C4#1686237611yescharacteristic
232C2×C4#1686237611yescharacteristic
233C8—5262no—
234C8—10521no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—10521no—
239C22—21041no—
240C22C4×C22⋊D26311yescharacteristic
241C22#2255443911yescharacteristic
242C22#2255444411yescharacteristic
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—10521no—
248C4—21041no—
249C4C2×(C2×D263)⋊C411yescharacteristic
250C4C4×C22⋊D26311yescharacteristic
251C4#2255444411yescharacteristic
252C4#2255445311yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—42no—
257C2—21041no—
258C2#3068181711yescharacteristic
subgroupG/H
centerC4#22554444
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC4×#41×C263C2
socleC2×C263#386
prime radical#30682736C2
cosocleC22×C4×C263C23
hypercenterC4×#41D263
hypocenterC263#1906
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #30681955C2semidirect
3. C2×#22554398C2semidirect
4. #30681911C2semidirect
5. #30681708C2semidirect
6. #30681698C2semidirect
7. C4×#41×C263C2semidirect
10. #22554500C4semidirect
12. #22554495C4semidirect
33. C2×Dic526C2×C4semidirect
34. C2×D1052C2×C4semidirect
44. #16862360C2×C4semidirect
129. C263#1906semidirect
132. C4×#41D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306819552
C2×#225543982
#306819112
#306817082
#306816982
C4×#41×C2632
#1906263