Finite Group Databasebeta

← #46783300

Subgroups — #46783300

Order 33664.

308 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 93 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#30682705C211yesmaximal, characteristic
2#30681922C211yesmaximal, characteristic
3C2×#22554389C212yesmaximal, complemented
4#30681708C212yesmaximal, complemented
5#536×C263C211yesmaximal, characteristic
6#22554477—24no—
7C2×#16862360—22no—
8C2×#16862360C2212yes—
9C2×#16862360C2212yes—
10#22554389—24no—
11#22554389—21no—
12#22554387—21no—
13C2×#41×C263C2211yescharacteristic
14C22×Q8×C263C2211yescharacteristic
15C4⋊Q8×C263—21no—
16#124×C263—21no—
17#123×C263C414yes—
18C22⋊Q8×C263—22no—
19#117×C263C2211yescharacteristic
20#16862360—24no—
21#16862360—22no—
22#16862360—22no—
23#16862360—22no—
24#16862360D414yes—
25C2×C263⋊C8—24no—
26C2×C263⋊C8—22no—
27C2×C263⋊C8—22no—
28#41×C263—22no—
29#41×C263—22no—
30C2×Q8×C263—22no—
31C2×Q8×C263—21no—
32C2×Q8×C263—21no—
33C2×Q8×C263—22no—
34C2×Q8×C263D411yescharacteristic
35C2×D4×C263C2×C412yes—
36C2×D4×C263D411yescharacteristic
37C22×C4×C263C2×C412yes—
38C22×C4×C263D412yes—
39C22×C4×C263C2311yescharacteristic
40C4⋊C4×C263—24no—
41C4⋊C4×C263—21no—
42C22⋊C4×C263—24no—
43C22⋊C4×C263C2×C412yes—
44C42×C263—21no—
45C263⋊C8—24no—
46C263⋊C8—42no—
47C23×C263C22⋊C412yes—
48C23×C263C22×C411yescharacteristic
49Q8×C263—22no—
50Q8×C263—41no—
51Q8×C263—42no—
52Q8×C263—41no—
53D4×C263—24no—
54D4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263—22no—
59C2×C4×C263—24no—
60C2×C4×C263C22⋊C412yes—
61C2×C4×C263C2×D412yes—
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263#4112yes—
65C22×C263—22no—
66C22×C263—41no—
67C22×C263—42no—
68C22×C263C2×C22⋊C411yescharacteristic
69C22×C263C4×D412yes—
70C4×C263—22no—
71C4×C263—42no—
72C4×C263—42no—
73C4×C263#12011yescharacteristic
74C4×C263#12112yes—
75C4×C263#12311yescharacteristic
76C2×C263—21no—
77C2×C263—22no—
78C2×C263—42no—
79C2×C263#38611yescharacteristic
80C263#191511yescharacteristic, complemented, Sylow
81#1915—2631nomaximal, Sylow
82#568—2631no—
83#536D26311yescharacteristic
84#413—2631no—
85C2×#101—2632no—
86#344—2632no—
87C2×#41C2×D26311yescharacteristic
88C22×Q8C2×D26311yescharacteristic
89#131—5264no—
90C2×M16—2632no—
91C2×M16—2632no—
92C2×M16—5262no—
93C4⋊Q8—21no—
94#124—21no—
95#123Dic26314yes—
96C22⋊Q8—22no—
97#117C2×D26311yescharacteristic
98#101—5264no—
99#101—5261no—
100#100—5261no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—21no—
105C2×Q8—21no—
106C2×Q8—22no—
107C2×Q8C22⋊D26311yescharacteristic
108C2×D4C2×Dic26312yes—
109C2×D4C22⋊D26311yescharacteristic
110C22×C4C2×Dic26312yes—
111C22×C4C22⋊D26312yes—
112C22×C4C22×D26311yescharacteristic
113M16—2634no—
114M16—5264no—
115M16—5262no—
116M16—5262no—
117M16—5262no—
118C2×C8—5264no—
119C2×C8—5262no—
120C2×C8—5262no—
121C4⋊C4—24no—
122C4⋊C4—21no—
123C22⋊C4—24no—
124C22⋊C4C2×Dic26312yes—
125C42—21no—
126C23C22⋊Dic26312yes—
127C23C22×Dic26311yescharacteristic
128Q8—22no—
129Q8—41no—
130Q8—42no—
131Q8—41no—
132D4—24no—
133D4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4C22⋊Dic26312yes—
140C2×C4D4×D26312yes—
141C2×C4C2×C22⋊D26311yescharacteristic
142C2×C4C2×C22⋊D26311yescharacteristic
143C2×C4#1686237512yes—
144C8—5264no—
145C8—10522no—
146C22—22no—
147C22—41no—
148C22—42no—
149C22C2×C22⋊Dic26311yescharacteristic
150C22D4×Dic26312yes—
151C4—22no—
152C4—42no—
153C4—42no—
154C4#2255443811yescharacteristic
155C4#2255444212yes—
156C4#2255445111yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#3068181811yescharacteristic
subgroupG/H
centerC2#30681818
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#536×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#536D263
hypocenterC263#1915
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
3. C2×#22554389C2semidirect
4. #30681708C2semidirect
80. C263#1915semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306819222
C2×#225543892
#306817082
#536×C2632
#1915263