Finite Group Databasebeta

← #46782847

Subgroups — #46782847

Order 33664.

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

normal subgroups only

This group has 306 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
1C2×#22554429C211yesmaximal, characteristic
2#30681902C211yesmaximal, characteristic
3#30681698C214yesmaximal, complemented
4C4×C22⋊C4×C263C211yesmaximal, characteristic
5C2×#16862360C2212yes—
6#22554429—21no—
7#22554429—21no—
8#22554429C412yescomplemented
9#22554429C2212yes—
10C2×C4⋊Dic263C411yescharacteristic, complemented
11C2×C4⋊Dic263C411yescharacteristic, complemented
12C2×C22⋊Dic263—21no—
13C2×C4×Dic263—21no—
14C22⋊(C263⋊C8)—21no—
15C22⋊(C263⋊C8)—21no—
16C23×C4×C263C2211yescharacteristic
17C2×C22⋊C4×C263—21no—
18C2×C42×C263C2212yes—
19#95×C263—21no—
20C22×Dic263—21no—
21C22×Dic263—21no—
22#16862360—24no—
23C2×C263⋊C8—22no—
24C4⋊Dic263—21no—
25C4⋊Dic263—21no—
26C4⋊Dic263C2×C412yes—
27C4⋊Dic263C2×C412yes—
28C22⋊Dic263—22no—
29C22⋊Dic263—22no—
30C4×Dic263—22no—
31C4×Dic263—22no—
32C24×C263D411yescharacteristic
33C22×C4×C263—24no—
34C22×C4×C263—22no—
35C22×C4×C263C2×C411yescharacteristic
36C22×C4×C263C2×C411yescharacteristic
37C22×C4×C263D411yescharacteristic
38C22×C4×C263D411yescharacteristic
39C22×C4×C263D411yescharacteristic
40C22×C4×C263C2311yescharacteristic
41C22⋊C4×C263—24no—
42C42×C263—24no—
43C2×Dic263—22no—
44C2×Dic263—22no—
45C2×Dic263—42no—
46C2×Dic263—42no—
47C263⋊C8—42no—
48C23×C263—22no—
49C23×C263—22no—
50C23×C263—41no—
51C23×C263C22⋊C411yescharacteristic
52C23×C263C22⋊C411yescharacteristic
53C23×C263C2×D411yescharacteristic
54C2×C4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263—22no—
59C2×C4×C263—24no—
60C2×C4×C263—42no—
61C2×C4×C263—42no—
62C2×C4×C263C22⋊C411yescharacteristic
63C2×C4×C263C22⋊C411yescharacteristic
64C2×C4×C263C22×C411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263#4114yes—
67C22×C263—21no—
68C22×C263—21no—
69C22×C263—21no—
70C22×C263—21no—
71C22×C263—21no—
72C22×C263—21no—
73C22×C263—21no—
74C22×C263—44no—
75C22×C263#10412yes—
76C22×C263C2×C22⋊C411yescharacteristic
77C22×C263#12312yes—
78C4×C263—21no—
79C4×C263—21no—
80C4×C263—44no—
81C4×C263#11712yes—
82C4×C263#12312yes—
83Dic263—42no—
84Dic263—42no—
85C2×C263—22no—
86C2×C263—22no—
87C2×C263—41no—
88C2×C263#38111yescharacteristic
89C2×C263C2×#10411yescharacteristic
90C2×C263#42111yescharacteristic
91C263#182611yescharacteristic, complemented, Sylow
92#1826—2631nomaximal, Sylow
93C2×#117—2631no—
94#407—2631no—
95C4×C22⋊C4D26311yescharacteristic
96#339—2634no—
97C23×C4C2×D26311yescharacteristic
98C2×M16—2632no—
99#117—2632no—
100#117—2632no—
101#117—5261no—
102#117—5261no—
103C2×C4⋊C4—2631no—
104C2×C4⋊C4—2631no—
105C2×C22⋊C4—21no—
106C2×C22⋊C4—5261no—
107C2×C42—5261no—
108C2×C42C2×D26312yes—
109C22⋊C8—5261no—
110C22⋊C8—5261no—
111#95—21no—
112C24C22⋊D26311yescharacteristic
113C22×C4—24no—
114C22×C4—22no—
115C22×C4—5261no—
116C22×C4—5261no—
117C22×C4C4×D26311yescharacteristic
118C22×C4C4×D26311yescharacteristic
119C22×C4C22⋊D26311yescharacteristic
120C22×C4D105211yescharacteristic
121C22×C4D105211yescharacteristic
122C22×C4C22×D26311yescharacteristic
123M16—5264no—
124C2×C8—5262no—
125C4⋊C4—2632no—
126C4⋊C4—2632no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C22⋊C4—24no—
130C22⋊C4—5262no—
131C22⋊C4—5262no—
132C42—24no—
133C42—5262no—
134C42—5262no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23(C2×D263)⋊C411yescharacteristic
139C23(C2×D263)⋊C411yescharacteristic
140C23C2×C22⋊D26311yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—5262no—
150C2×C4—5262no—
151C2×C4—10522no—
152C2×C4—10522no—
153C2×C4(C2×D263)⋊C411yescharacteristic
154C2×C4(C2×D263)⋊C411yescharacteristic
155C2×C4C2×C4×D26311yescharacteristic
156C2×C4C2×D105211yescharacteristic
157C2×C4#1686237514yes—
158C8—10522no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#2255439812yes—
168C22C2×(C2×D263)⋊C411yescharacteristic
169C22#2255445112yes—
170C4—21no—
171C4—21no—
172C4—44no—
173C4—10522no—
174C4—10522no—
175C4#2255442612yes—
176C4#2255445412yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#3068179911yescharacteristic
181C2C2×#2255439811yescharacteristic
182C2#3068195611yescharacteristic
subgroupG/H
centerC2×C4C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC4×C22⋊C4×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenterC4×C22⋊C4D263
hypocenterC263#1826
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #30681698C2semidirect
8. #22554429C4semidirect
10. C2×C4⋊Dic263C4semidirect
11. C2×C4⋊Dic263C4semidirect
91. C263#1826semidirect

Maximal subgroups

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

subgroupindex
C2×#225544292
#306819022
#306816982
C4×C22⋊C4×C2632
#1826263