Finite Group Databasebeta

← #46783401

Subgroups — #46783401

Order 33664.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#30681946C211yesmaximal, characteristic
2C2×#22554393C211yesmaximal, characteristic
3C2×#22554388C211yesmaximal, characteristic
4#30681894C211yesmaximal, characteristic
5#30681707C211yesmaximal, characteristic
6#30681702C211yesmaximal, characteristic
7#428×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11C22×C263⋊C8C2211yescharacteristic
12#22554393—21no—
13#22554393—21no—
14#22554393—21no—
15#22554393—21no—
16#22554388C414yescomplemented
17#22554381—21no—
18C4×C263⋊C8—21no—
19C2×M16×C263C2211yescharacteristic
20#117×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22#107×C263—21no—
23#106×C263—21no—
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C22×Dic263—21no—
31#16862360—21no—
32#16862360—21no—
33#16862360—21no—
34#16862360C2×C412yes—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8D411yescharacteristic
40C2×C263⋊C8D411yescharacteristic
41C22×C4×C263—21no—
42C22×C4×C263C2311yescharacteristic
43M16×C263—21no—
44M16×C263C2×C412yes—
45C2×C8×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263D411yescharacteristic
49C4⋊C4×C263D411yescharacteristic
50C22⋊C4×C263—21no—
51C42×C263—21no—
52Dic526—22no—
53Dic526—22no—
54Dic526—41no—
55Dic526—41no—
56C2×Dic263—22no—
57C2×Dic263—41no—
58C2×Dic263—41no—
59C263⋊C8—22no—
60C263⋊C8—21no—
61C263⋊C8—21no—
62C263⋊C8—41no—
63C23×C263#4111yescharacteristic
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—41no—
67C2×C4×C263—81no—
68C2×C4×C263C22×C411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263#4111yescharacteristic
72C2×C4×C263#4111yescharacteristic
73C2×C4×C263#4111yescharacteristic
74C8×C263—22no—
75C22×C263—21no—
76C22×C263—21no—
77C22×C263#11711yescharacteristic
78C22×C263#12111yescharacteristic
79C22×C263#12611yescharacteristic
80C4×C263—41no—
81C4×C263—41no—
82C4×C263—81no—
83C4×C263C4×D411yescharacteristic
84C4×C263C4×D411yescharacteristic
85C4×C263#12311yescharacteristic
86C4×C263#12411yescharacteristic
87Dic263—42no—
88C2×C263—21no—
89C2×C263—21no—
90C2×C263#38811yescharacteristic
91C2×C263#47111yescharacteristic
92C2×C263#47311yescharacteristic
93C263#193011yescharacteristic, complemented, Sylow
94#1930—2631nomaximal, Sylow
95#428D26311yescharacteristic
96#419—2631no—
97C2×#103—2631no—
98C2×#101—2631no—
99#405—2631no—
100#343—2631no—
101#341—2631no—
102C22×Q8—2631no—
103C2×M16—2631no—
104C2×M16—2631no—
105C2×M16C2×D26311yescharacteristic
106C22×C8—2631no—
107#117C2×D26311yescharacteristic
108C2×C4⋊C4C2×D26311yescharacteristic
109#107—21no—
110#106—21no—
111#103—5261no—
112#103—5261no—
113#103—5261no—
114#103—5261no—
115#101—2634no—
116#97—5261no—
117C4×C8—5261no—
118C2×Q8—2632no—
119C2×Q8—5261no—
120C2×Q8—5261no—
121C2×Q8—5261no—
122C2×Q8—5261no—
123C2×Q8—5261no—
124C22×C4—21no—
125C22×C4—5261no—
126C22×C4C22×D26311yescharacteristic
127M16—21no—
128M16—2632no—
129M16—5261no—
130M16—5261no—
131M16—5261no—
132M16C4×D26312yes—
133C2×C8—21no—
134C2×C8—2631no—
135C2×C8—2631no—
136C2×C8—5261no—
137C2×C8—5261no—
138C2×C8—5261no—
139C2×C8—5261no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4C22⋊D26311yescharacteristic
143C4⋊C4C22⋊D26311yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1686237511yescharacteristic
147Q8—5262no—
148Q8—5262no—
149Q8—10521no—
150Q8—10521no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—5262no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4C2×C4×D26311yescharacteristic
159C2×C4D4×D26311yescharacteristic
160C2×C4C2×C22⋊D26311yescharacteristic
161C2×C4#1686237611yescharacteristic
162C2×C4#1686237711yescharacteristic
163C2×C4#1686237711yescharacteristic
164C8—22no—
165C8—5262no—
166C8—5261no—
167C8—5261no—
168C8—10521no—
169C22—21no—
170C22—21no—
171C22#2255442811yescharacteristic
172C22#2255444211yescharacteristic
173C22#2255446511yescharacteristic
174C4—41no—
175C4—41no—
176C4—81no—
177C4—10522no—
178C4C4×C22⋊D26311yescharacteristic
179C4#2255443211yescharacteristic
180C4#2255445511yescharacteristic
181C4#2255445911yescharacteristic
182C2—21no—
183C2—21no—
184C2#3068182811yescharacteristic
185C2#3068219911yescharacteristic
186C2#3068221111yescharacteristic
subgroupG/H
centerC22#22554442
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#428×C263C2
socleC22×C263#121
prime radicalC23×C263#41
cosocleC22×C4×C263C23
hypercenter#428D263
hypocenterC263#1930
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
16. #22554388C4semidirect
93. C263#1930semidirect

Maximal subgroups

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

subgroupindex
#306819462
C2×#225543932
C2×#225543882
#306818942
#306817072
#306817022
#428×C2632
#1930263