Finite Group Databasebeta

← #46782705

Subgroups — #46782705

Order 33664.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22554518C211yesmaximal, characteristic
2C2×#22554398C212yesmaximal, complemented
3#30681937C212yesmaximal, complemented
4C2×#22554389C211yesmaximal, characteristic, complemented
5#391×C263C211yesmaximal, characteristic, complemented
6#22554518—24no—
7#22554518—22no—
8#22554518C414yescomplemented
9C2×#16862377—22no—
10C2×#16862376—22no—
11C2×#16862376C2212yes—
12C2×Q8×D263—22no—
13C2×#16862360C2212yes—
14#22554398—24no—
15#22554393—22no—
16#22554390—22no—
17#22554389—22no—
18C22×Q8×C263C2211yescharacteristic
19C2×C4⋊C4×C263C2211yescharacteristic
20C2×C42×C263C2211yescharacteristic
21#95×C263—22no—
22#16862377—28no—
23#16862377—28no—
24#16862376—28no—
25#16862376—28no—
26#16862376—22no—
27#16862376—22no—
28#16862376C2×C414yes—
29#16862376D414yes—
30C2×Dic526—22no—
31C2×Dic526D412yes—
32Q8×D263—28no—
33Q8×D263—28no—
34C2×D1052—22no—
35C2×D1052D412yes—
36C2×C22⋊D263—22no—
37C2×C4×D263—24no—
38C2×C4×D263—22no—
39#16862360—22no—
40#16862360—22no—
41C2×C263⋊C8—22no—
42C2×Q8×C263—22no—
43C2×Q8×C263—22no—
44C2×Q8×C263C2×C412yes—
45C2×Q8×C263D412yes—
46C22×C4×C263—21no—
47C22×C4×C263—21no—
48C22×C4×C263D412yes—
49C22×C4×C263C2311yescharacteristic
50C4⋊C4×C263—22no—
51C42×C263—22no—
52C22×D263—22no—
53Dic526—28no—
54Dic526—22no—
55Dic526C22⋊C414yes—
56D1052—28no—
57D1052—22no—
58D1052C22⋊C414yes—
59C22⋊D263—24no—
60C22⋊D263—24no—
61C2×Dic263—22no—
62C4×D263—216no—
63C4×D263—24no—
64C4×D263—24no—
65C263⋊C8—42no—
66C23×C263C2×D411yescharacteristic
67Q8×C263—24no—
68Q8×C263—24no—
69C2×C4×C263—22no—
70C2×C4×C263—22no—
71C2×C4×C263—22no—
72C2×C4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263—42no—
75C2×C4×C263—41no—
76C2×C4×C263C22⋊C414yes—
77C2×C4×C263C22×C411yescharacteristic
78C2×C4×C263C2×D412yes—
79C2×C4×C263C2×D412yes—
80C2×C4×C263C2×D411yescharacteristic
81C22×C263—21no—
82C22×C263—21no—
83C22×C263C2×C22⋊C411yescharacteristic
84C22×C263#12011yescharacteristic
85C22×C263#12011yescharacteristic
86C2×D263—24no—
87C2×D263—42no—
88C2×D263—42no—
89C4×C263—24no—
90C4×C263—42no—
91C4×C263—81no—
92C4×C263C2×C22⋊C412yes—
93C4×C263#12012yes—
94Dic263—24no—
95C2×C263—21no—
96C2×C263—21no—
97C2×C263#37911yescharacteristic
98C2×C263#45411yescharacteristic
99C2×C263#45611yescharacteristic
100D263—44no—
101C263#179311yescharacteristic, complemented, Sylow
102#1793—2631nomaximal, Sylow
103C2×2−1+4—2631no—
104C2×#104—2632no—
105#417—2632no—
106C2×#101—2631no—
107#391D26311yescharacteristic, complemented
1082−1+4—2634no—
1092−1+4—5264no—
1102−1+4—5262no—
111C2×#41—2632no—
112C2×#41—5262no—
113C2×#41—5262no—
114C22×Q8—5262no—
115C22×Q8C2×D26311yescharacteristic
116C2×M16—2632no—
117C2×C4⋊C4C2×D26311yescharacteristic
118C2×C42C2×D26311yescharacteristic
119#104—5264no—
120#103—5262no—
121#102—5262no—
122#101—5262no—
123#95—22no—
124#41—2634no—
125#41—2634no—
126#41—5268no—
127#41—5268no—
128#41—5268no—
129#41—5268no—
130#41—5262no—
131#41—5262no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2632no—
135C2×Q8—5262no—
136C2×Q8—5268no—
137C2×Q8—5268no—
138C2×Q8C4×D26312yes—
139C2×Q8D105212yes—
140C2×D4—2632no—
141C2×D4—5262no—
142C2×D4—5262no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—5264no—
146C22×C4—5262no—
147C22×C4C22⋊D26312yes—
148C22×C4C22×D26311yescharacteristic
149M16—5262no—
150M16—5262no—
151C2×C8—5262no—
152C4⋊C4—22no—
153C42—22no—
154C23—5262no—
155C23C2×C22⋊D26311yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2634no—
159Q8—5268no—
160Q8—5262no—
161D4—2634no—
162D4—5268no—
163D4—5264no—
164D4—5264no—
165D4—5262no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—52616no—
174C2×C4—5262no—
175C2×C4—5264no—
176C2×C4—5264no—
177C2×C4(C2×D263)⋊C414yes—
178C2×C4C2×C4×D26311yescharacteristic
179C2×C4D4×D26312yes—
180C2×C4D4×D26312yes—
181C2×C4C2×D105211yescharacteristic
182C8—10522no—
183C22—21no—
184C22—21no—
185C22—5264no—
186C22—10522no—
187C22—10522no—
188C22C2×(C2×D263)⋊C411yescharacteristic
189C22#2255443811yescharacteristic
190C22#2255443811yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—5264no—
195C4C22⋊C4×D26312yes—
196C4#2255444012yes—
197C2—21no—
198C2—21no—
199C2—10524no—
200C2#3068179311yescharacteristic
201C2#3068211011yescharacteristic
202C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#391×C263C2
socleC22×C263#120
prime radicalC2×#22554518C2
cosocleC22×C4×C263C23
hypercenter#391D263
hypocenterC263#1793
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#22554398C2semidirect
3. #30681937C2semidirect
4. C2×#22554389C2semidirect
5. #391×C263C2semidirect
8. #22554518C4semidirect
101. C263#1793semidirect
107. #391D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545182
C2×#225543982
#306819372
C2×#225543892
#391×C2632
#1793263