Finite Group Databasebeta

← #46783474

Subgroups — #46783474

Order 33664.

248 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 103 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×#22554401C211yesmaximal, characteristic
2C2×#22554401C211yesmaximal, characteristic
3C2×C8×Dic263C211yesmaximal, characteristic
4#30681837C211yesmaximal, characteristic
5#30681834C211yesmaximal, characteristic
6#30681701C211yesmaximal, characteristic
7#340×C263C211yesmaximal, characteristic
8C22×C263⋊C8C2211yescharacteristic
9C2×C4⋊Dic263—21no—
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12C2×Dic263⋊C4—21no—
13C2×C4×Dic263C2211yescharacteristic
14#22554401—22no—
15#22554401C414yescomplemented
16C8×Dic263—22no—
17C263⋊#95—21no—
18C263⋊#95—21no—
19C22×C8×C263C2211yescharacteristic
20C2×C4⋊C4×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22C22×Dic263—21no—
23C22×Dic263—21no—
24C22×Dic263D411yescharacteristic
25C22×Dic263D411yescharacteristic
26C2×C263⋊C8C2×C412yes—
27C2×C263⋊C8D412yes—
28C2×C263⋊C8Q812yes—
29C4⋊Dic263—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263—42no—
33C4⋊Dic263C2×C412yes—
34Dic263⋊C4—42no—
35C4×Dic263—21no—
36C4×Dic263—21no—
37C22×C4×C263—21no—
38C22×C4×C263—21no—
39C22×C4×C263C2311yescharacteristic
40C2×C8×C263—21no—
41C2×C8×C263—21no—
42C2×C8×C263Q812yes—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263C2×C412yes—
47C2×Dic263—21no—
48C2×Dic263—21no—
49C2×Dic263—21no—
50C2×Dic263—21no—
51C2×Dic263—22no—
52C2×Dic263—41no—
53C2×Dic263—41no—
54C2×Dic263—41no—
55C2×Dic263—41no—
56C2×Dic263—41no—
57C2×Dic263SD1612yes—
58C2×Dic263SD1612yes—
59C263⋊C8C4⋊C414yescomplemented
60C23×C263C2×D411yescharacteristic
61C2×C4×C263—22no—
62C2×C4×C263—41no—
63C2×C4×C263—41no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263C22×C411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×Q811yescharacteristic
70C2×C4×C263C2×Q811yescharacteristic
71C2×C4×C263#4111yescharacteristic
72C2×C4×C263#4111yescharacteristic
73C8×C263—22no—
74C22×C263C4×D411yescharacteristic
75C22×C263#12111yescharacteristic
76C22×C263C4⋊Q811yescharacteristic
77C22×C263C2×SD1611yescharacteristic
78C22×C263C2×SD1611yescharacteristic
79C22×C263#13511yescharacteristic
80C22×C263#13511yescharacteristic
81C4×C263—42no—
82C4×C263—81no—
83C4×C263C2×C4⋊C411yescharacteristic
84C4×C263C4×Q811yescharacteristic
85C4×C263C22⋊Q811yescharacteristic
86C4×C263#12511yescharacteristic
87Dic263—22no—
88Dic263—22no—
89Dic263—42no—
90Dic263—81no—
91C2×C263#38911yescharacteristic
92C2×C263C4×SD1611yescharacteristic
93C2×C263C4×SD1611yescharacteristic
94C2×C263#46511yescharacteristic
95C2×C263#46511yescharacteristic
96C2×C263#49811yescharacteristic
97C2×C263#49911yescharacteristic
98C263#194111yescharacteristic, complemented, Sylow
99#1941—2631nomaximal, Sylow
100C2×#106—2631no—
101C2×#106—2631no—
102C2×C4×C8—2631no—
103#389—2631no—
104#389—2631no—
105#340—2631no—
106#340D26311yescharacteristic
107C22×C8—2631no—
108C22×C8C2×D26311yescharacteristic
109C2×C4⋊C4—2631no—
110C2×C4⋊C4—2631no—
111C2×C4⋊C4—5261no—
112C2×C4⋊C4—5261no—
113C2×C4⋊C4C2×D26311yescharacteristic
114C2×C4⋊C4C2×D26311yescharacteristic
115C2×C42—2631no—
116#106—2634no—
117#106—5262no—
118C4×C8—5262no—
119#95—5261no—
120#95—5261no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—2631no—
124C22×C4—2631no—
125C22×C4—5261no—
126C22×C4—5261no—
127C22×C4C22×D26311yescharacteristic
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2632no—
131C2×C8—2632no—
132C2×C8—2632no—
133C2×C8Dic52612yes—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—2632no—
138C4⋊C4—5261no—
139C4⋊C4—5261no—
140C4⋊C4—5261no—
141C4⋊C4—10522no—
142C4⋊C4—10522no—
143C4⋊C4C4×D26312yes—
144C42—5261no—
145C42—5261no—
146C23D4×D26311yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—2632no—
154C2×C4—2632no—
155C2×C4—5261no—
156C2×C4—5261no—
157C2×C4—5261no—
158C2×C4—5261no—
159C2×C4—5262no—
160C2×C4—10521no—
161C2×C4—10521no—
162C2×C4—10521no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4C2×C4×D26311yescharacteristic
166C2×C4D4×D26311yescharacteristic
167C2×C4Q8×D26311yescharacteristic
168C2×C4C2×Dic52611yescharacteristic
169C2×C4#1686237511yescharacteristic
170C2×C4#1686237611yescharacteristic
171C8—22no—
172C8—2634no—
173C22(C22⋊D263)⋊C411yescharacteristic
174C22#2255444311yescharacteristic
175C22#2255446911yescharacteristic
176C22SD16×D26311yescharacteristic
177C22SD16×D26311yescharacteristic
178C22#2255448911yescharacteristic
179C22#2255449311yescharacteristic
180C4—42no—
181C4—81no—
182C4—5262no—
183C4—5262no—
184C4—10522no—
185C4—21041no—
186C4C4⋊C4×D26311yescharacteristic
187C4C4×Dic52611yescharacteristic
188C4#2255444711yescharacteristic
189C4#2255446011yescharacteristic
190C2#3068183511yescharacteristic
191C2#3068202311yescharacteristic
192C2#3068202911yescharacteristic
193C2#3068216611yescharacteristic
194C2#3068217011yescharacteristic
195C2#3068233511yescharacteristic
196C2#3068233911yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#340×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#340D263
hypocenterC263#1941
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
15. #22554401C4semidirect
59. C263⋊C8C4⋊C4semidirect
98. C263#1941semidirect

Maximal subgroups

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

subgroupindex
C2×#225544012
C2×C8×Dic2632
#306818372
#306818342
#306817012
#340×C2632
#1941263