Finite Group Databasebeta

← #46783163

Subgroups — #46783163

Order 33664.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 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
1#30682705C211yesmaximal, characteristic, complemented
2#30682445C211yesmaximal, characteristic
3#30681901C212yesmaximal, complemented
4#30681710C212yesmaximal, complemented
5#413×C263C211yesmaximal, characteristic, complemented
6C22×C4×D263C2211yescharacteristic
7#22554477—24no—
8C2×#16862360—22no—
9C2×#16862360C2212yes—
10#22554451C412yes—
11#22554446—21no—
12#22554441—21no—
13#22554438C412yes—
14C4×C22⋊D263—22no—
15#22554429C2211yescharacteristic
16(C2×D263)⋊C8—24no—
17C2×#41×C263C2211yescharacteristic
18C2×M16×C263C2212yes—
19#101×C263—21no—
20#100×C263—21no—
21C23×D263C2×C411yescharacteristic
22C2×C22⋊D263—22no—
23C22×Dic263C2×C411yescharacteristic
24C2×C4×D263—22no—
25C2×C4×D263—21no—
26C2×C4×D263—21no—
27C2×C4×D263—22no—
28#16862360—24no—
29#16862360—22no—
30#16862360—22no—
31C2×C263⋊C8—24no—
32C2×C263⋊C8D414yescomplemented
33C4⋊Dic263—21no—
34Dic263⋊C4—22no—
35C22⋊Dic263—22no—
36C22⋊Dic263C2×C412yes—
37(C2×D263)⋊C4—22no—
38C4×Dic263—21no—
39#41×C263—22no—
40#41×C263—22no—
41C2×Q8×C263D411yescharacteristic
42C2×D4×C263C2×C412yes—
43C2×D4×C263D411yescharacteristic
44C22×C4×C263D412yes—
45C22×C4×C263C2311yescharacteristic
46M16×C263—22no—
47M16×C263—22no—
48C2×C8×C263—22no—
49C22×D263—21no—
50C22×D263—22no—
51C22×D263—42no—
52C22⋊D263—44no—
53C2×Dic263—22no—
54C2×Dic263—21no—
55C2×Dic263—22no—
56C4×D263—41no—
57C4×D263—42no—
58C4×D263—41no—
59C263⋊C8—24no—
60C23×C263C22⋊C412yes—
61C23×C263C22×C411yescharacteristic
62Q8×C263—22no—
63D4×C263—24no—
64D4×C263—22no—
65C2×C4×C263—22no—
66C2×C4×C263—22no—
67C2×C4×C263C22⋊C412yes—
68C2×C4×C263C2×D412yes—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263#4112yes—
72C8×C263—42no—
73C22×C263—22no—
74C22×C263—41no—
75C22×C263—42no—
76C22×C263C2×C22⋊C411yescharacteristic
77C22×C263C4×D412yes—
78C2×D263—22no—
79C2×D263—24no—
80C2×D263—41no—
81C2×D263—42no—
82C2×D263—41no—
83C4×C263—22no—
84C4×C263#12011yescharacteristic
85C4×C263#12112yes—
86C4×C263#12311yescharacteristic
87Dic263—42no—
88Dic263—41no—
89C2×C263—21no—
90C2×C263—22no—
91C2×C263—42no—
92C2×C263#38611yescharacteristic
93D263—42no—
94C263#189111yescharacteristic, complemented, Sylow
95#1891—2631nomaximal, Sylow
96#568—2631no—
97#525—2631no—
98#413D26311yescharacteristic, complemented
99#407—2632no—
100#344—2632no—
101C2×#41C2×D26311yescharacteristic
102C23×C4—2631no—
103#131—5264no—
104C2×M16—2632no—
105C2×M16—5262no—
106C2×M16C2×D26312yes—
107#123—2632no—
108C22⋊Q8—5261no—
109#121—5261no—
110#120—2632no—
111C4×D4—5262no—
112#117—2631no—
113#101—21no—
114#100—21no—
115C22⋊C8—5264no—
116C24—2631no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D26311yescharacteristic
120C2×D4—5262no—
121C2×D4C4×D26312yes—
122C2×D4C22⋊D26311yescharacteristic
123C22×C4—2631no—
124C22×C4—5262no—
125C22×C4—5261no—
126C22×C4—5261no—
127C22×C4—5262no—
128C22×C4D105212yes—
129C22×C4C22×D26311yescharacteristic
130M16—22no—
131M16—22no—
132M16—5264no—
133M16—5262no—
134M16—5262no—
135C2×C8—22no—
136C2×C8—2634no—
137C2×C8—5264no—
138C4⋊C4—5262no—
139C4⋊C4—5261no—
140C22⋊C4—2632no—
141C22⋊C4—5262no—
142C22⋊C4—5262no—
143C42—5261no—
144C23—5261no—
145C23—5262no—
146C23—10522no—
147C23(C2×D263)⋊C412yes—
148C23C2×C4×D26311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—10524no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—5262no—
156C2×C4—5261no—
157C2×C4—5262no—
158C2×C4—10521no—
159C2×C4—10522no—
160C2×C4—10521no—
161C2×C4(C2×D263)⋊C412yes—
162C2×C4D4×D26312yes—
163C2×C4C2×C22⋊D26311yescharacteristic
164C2×C4C2×D105211yescharacteristic
165C2×C4#1686237512yes—
166C8—42no—
167C8—5264no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—5262no—
172C22—5264no—
173C22—10521no—
174C22—10522no—
175C22—10521no—
176C22C2×(C2×D263)⋊C411yescharacteristic
177C22(C22⋊D263)⋊C412yes—
178C4—22no—
179C4—10522no—
180C4—10521no—
181C4#2255444011yescharacteristic
182C4#2255444212yes—
183C4#2255445411yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—10522no—
188C2#3068181511yescharacteristic
subgroupG/H
centerC4#22554440
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#413×C263C2
socleC2×C263#386
prime radical#30682445C2
cosocleC22×C4×C263C23
hypercenter#413D263
hypocenterC263#1891
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #30682705C2semidirect
3. #30681901C2semidirect
4. #30681710C2semidirect
5. #413×C263C2semidirect
32. C2×C263⋊C8D4semidirect
94. C263#1891semidirect
98. #413D263semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306824452
#306819012
#306817102
#413×C2632
#1891263