Finite Group Databasebeta

← #46781752

Subgroups — #46781752

Order 33664.

254 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682519C211yesmaximal, characteristic
2#30682252C212yesmaximal, complemented
3#30681868C211yesmaximal, characteristic, complemented
4#30681673C212yesmaximal, complemented
5#324×C263C211yesmaximal, characteristic, complemented
6C2×#16862376—21no—
7#22554450—22no—
8#22554445—22no—
9#22554444—21no—
10#22554444C2212yes—
11C2×C4⋊Dic263C2211yescharacteristic
12C2×Dic263⋊C4—21no—
13#22554404—22no—
14#22554392—22no—
15C263⋊#95—21no—
16C263⋊#95C2211yescharacteristic
17C2×C4⋊C4×C263C2211yescharacteristic
18C22⋊C8×C263C2212yes—
19#16862376—42no—
20#16862376—42no—
21C2×Dic526—21no—
22C2×D1052—21no—
23C2×D1052—21no—
24C2×D1052D412yes—
25C2×C22⋊D263—22no—
26C22×Dic263—21no—
27C22×Dic263—21no—
28C2×C4×D263—22no—
29C4⋊Dic263—21no—
30C4⋊Dic263—22no—
31C4⋊Dic263D412yes—
32Dic263⋊C4—42no—
33(C2×D263)⋊C4—22no—
34(C2×D263)⋊C4—22no—
35C22×C4×C263D411yescharacteristic
36C22×C4×C263D411yescharacteristic
37C22×C4×C263C2311yescharacteristic
38C2×C8×C263—22no—
39C4⋊C4×C263—22no—
40C22×D263—22no—
41Dic526—42no—
42D1052—42no—
43D1052—42no—
44D1052—81no—
45C22⋊D263—42no—
46C22⋊D263—42no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C2×Dic263—41no—
50C2×Dic263—41no—
51C2×Dic263—41no—
52C2×Dic263—41no—
53C2×Dic263—41no—
54C4×D263—44no—
55C23×C263C2×D411yescharacteristic
56C2×C4×C263—21no—
57C2×C4×C263—21no—
58C2×C4×C263—21no—
59C2×C4×C263—41no—
60C2×C4×C263—41no—
61C2×C4×C263D812yes—
62C2×C4×C263C2×D412yes—
63C8×C263—42no—
64C22×C263—21no—
65C22×C263—21no—
66C22×C263#12011yescharacteristic
67C22×C263C2×D811yescharacteristic
68C22×C263AGL(1,ℤ/8)11yescharacteristic
69C2×D263—42no—
70C2×D263—42no—
71C2×D263—42no—
72C4×C263—22no—
73C4×C263—22no—
74C4×C263—41no—
75Dic263—42no—
76Dic263—42no—
77Dic263—81no—
78C2×C263—21no—
79C2×C263—21no—
80C2×C263#44711yescharacteristic
81C2×C263#45611yescharacteristic
82C2×C263#45811yescharacteristic
83D263—82no—
84C263#161011yescharacteristic, complemented, Sylow
85#1610—2631nomaximal, Sylow
86#537—2631no—
87#480—2632no—
88#398—2631no—
89#327—2632no—
90#324D26311yescharacteristic, complemented
91C2×#41—5261no—
92C22⋊Q8—5262no—
93#121—2632no—
94#121—5262no—
95#121—5261no—
96C2×C4⋊C4—2631no—
97C2×C4⋊C4—5261no—
98C2×C4⋊C4C2×D26311yescharacteristic
99#107—5262no—
100#102—5262no—
101C22⋊C8C2×D26312yes—
102#95—2631no—
103#95—5261no—
104#41—10522no—
105#41—10522no—
106C2×Q8—5261no—
107C2×D4—2632no—
108C2×D4—5261no—
109C2×D4—5261no—
110C2×D4—5262no—
111C22×C4—5262no—
112C22×C4—5261no—
113C22×C4—5261no—
114C22×C4D105211yescharacteristic
115C22×C4D105211yescharacteristic
116C22×C4C22×D26311yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—2632no—
120C4⋊C4—5261no—
121C4⋊C4—5262no—
122C4⋊C4—10522no—
123C22⋊C4—5262no—
124C22⋊C4—5262no—
125C23—5262no—
126C23C2×D105211yescharacteristic
127Q8—10522no—
128D4—10522no—
129D4—10522no—
130D4—10522no—
131D4—10522no—
132D4—21041no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—5262no—
139C2×C4—5262no—
140C2×C4—10524no—
141C2×C4—10521no—
142C2×C4—10521no—
143C2×C4—10521no—
144C2×C4—10521no—
145C2×C4—10521no—
146C2×C4D210412yes—
147C2×C4D4×D26312yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—10522no—
152C22—10522no—
153C22—10522no—
154C22#2255444011yescharacteristic
155C22C2×D210411yescharacteristic
156C22#2255449811yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—10522no—
161C4—10522no—
162C4—21041no—
163C2—21no—
164C2—21no—
165C2—21042no—
166C2#3068207411yescharacteristic
167C2#3068212311yescharacteristic
168C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#324×C263C2
socleC22×C263#120
prime radical#30682519C2
hypercenter#324D263
hypocenterC263#1610
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #30682252C2semidirect
3. #30681868C2semidirect
4. #30681673C2semidirect
5. #324×C263C2semidirect
84. C263#1610semidirect
90. #324D263semidirect

Maximal subgroups

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

subgroupindex
#306825192
#306822522
#306818682
#306816732
#324×C2632
#1610263