Finite Group Databasebeta

← #46783299

Subgroups — #46783299

Order 33664.

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

normal subgroups only

This group has 308 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#30682509C211yesmaximal, characteristic
2#30681922C211yesmaximal, characteristic
3C2×#22554388C212yesmaximal, complemented
4#30681710C212yesmaximal, complemented
5#568×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7C2×#16862360C2212yes—
8#22554468—21no—
9#22554457—21no—
10#22554451C414yes—
11#22554449—22no—
12#22554429C2211yescharacteristic
13#22554389—21no—
14#22554388—24no—
15#22554387—21no—
16C2×#41×C263C2211yescharacteristic
17#131×C263—24no—
18C2×M16×C263—22no—
19C2×M16×C263C2212yes—
20C2×Dic526—22no—
21C2×Dic526—21no—
22C2×Dic526—21no—
23C2×Dic526—22no—
24C22×Dic263C2×C412yes—
25#16862360—22no—
26#16862360—22no—
27C2×C263⋊C8—22no—
28C4⋊Dic263—21no—
29Dic263⋊C4—24no—
30C22⋊Dic263—24no—
31C22⋊Dic263C2×C412yes—
32C4×Dic263—21no—
33#41×C263—22no—
34#41×C263—22no—
35C2×Q8×C263D411yescharacteristic
36C2×D4×C263C2×C412yes—
37C2×D4×C263D411yescharacteristic
38C22×C4×C263D412yes—
39C22×C4×C263C2311yescharacteristic
40M16×C263—24no—
41M16×C263—22no—
42M16×C263D414yes—
43C2×C8×C263—24no—
44C2×C8×C263—22no—
45Dic526—41no—
46Dic526—42no—
47Dic526—41no—
48C2×Dic263—22no—
49C2×Dic263—22no—
50C2×Dic263—24no—
51C263⋊C8—42no—
52C23×C263C22⋊C412yes—
53C23×C263C22×C411yescharacteristic
54Q8×C263—22no—
55D4×C263—24no—
56D4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263—22no—
59C2×C4×C263C22⋊C412yes—
60C2×C4×C263C2×D412yes—
61C2×C4×C263C2×D411yescharacteristic
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263#4112yes—
64C8×C263—24no—
65C22×C263—22no—
66C22×C263—41no—
67C22×C263—42no—
68C22×C263C2×C22⋊C411yescharacteristic
69C22×C263C4×D412yes—
70C4×C263—22no—
71C4×C263#12011yescharacteristic
72C4×C263#12112yes—
73C4×C263#12311yescharacteristic
74Dic263—42no—
75Dic263—42no—
76C2×C263—21no—
77C2×C263—22no—
78C2×C263—42no—
79C2×C263#38611yescharacteristic
80C263#191511yescharacteristic, complemented, Sylow
81#1915—2631nomaximal, Sylow
82#568D26311yescharacteristic
83#536—2631no—
84#413—2631no—
85C2×#101—2632no—
86#344—2632no—
87C2×#41C2×D26311yescharacteristic
88C22×Q8—2631no—
89#131—24no—
90C2×M16—22no—
91C2×M16—2632no—
92C2×M16C2×D26312yes—
93C4⋊Q8—5261no—
94#124—5261no—
95#123—2634no—
96C22⋊Q8—5262no—
97#117—2631no—
98#101—5261no—
99#101—5264no—
100#100—5261no—
101#41—22no—
102#41—22no—
103C2×Q8—5262no—
104C2×Q8—5261no—
105C2×Q8—5261no—
106C2×Q8—5262no—
107C2×Q8D105211yescharacteristic
108C2×D4C4×D26312yes—
109C2×D4D105211yescharacteristic
110C22×C4—2632no—
111C22×C4C22⋊D26312yes—
112C22×C4C22×D26311yescharacteristic
113M16—24no—
114M16—22no—
115M16—5262no—
116M16—5262no—
117M16C22⋊D26314yes—
118C2×C8—24no—
119C2×C8—22no—
120C2×C8—5262no—
121C4⋊C4—5264no—
122C4⋊C4—5261no—
123C22⋊C4—2632no—
124C22⋊C4—5264no—
125C42—5261no—
126C23(C2×D263)⋊C412yes—
127C23C2×C4×D26311yescharacteristic
128Q8—22no—
129Q8—10521no—
130Q8—10522no—
131Q8—10521no—
132D4—24no—
133D4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—5262no—
137C2×C4—5262no—
138C2×C4—5264no—
139C2×C4(C2×D263)⋊C412yes—
140C2×C4C2×C22⋊D26312yes—
141C2×C4C2×C22⋊D26311yescharacteristic
142C2×C4C2×D105211yescharacteristic
143C2×C4#1686237612yes—
144C8—24no—
145C8—10522no—
146C22—22no—
147C22—41no—
148C22—42no—
149C22C2×(C2×D263)⋊C411yescharacteristic
150C22C4×C22⋊D26312yes—
151C4—22no—
152C4—10522no—
153C4—10522no—
154C4#2255443911yescharacteristic
155C4#2255444412yes—
156C4#2255445311yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#568×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#568D263
hypocenterC263#1915
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
3. C2×#22554388C2semidirect
4. #30681710C2semidirect
80. C263#1915semidirect

Maximal subgroups

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

subgroupindex
#306825092
#306819222
C2×#225543882
#306817102
#568×C2632
#1915263