Finite Group Databasebeta

← #46784096

Subgroups — #46784096

Order 33664.

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

normal subgroups only

This group has 230 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#30682566C211yesmaximal, characteristic
2#30681981C211yesmaximal, characteristic
3#30681980C211yesmaximal, characteristic
4#30681804C211yesmaximal, characteristic
5#30681706C211yesmaximal, characteristic
6#30681698C211yesmaximal, characteristic
7#339×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9#22554470—21no—
10#22554469—21no—
11#22554462—21no—
12#22554461—21no—
13#22554447—22no—
14#22554429C2211yescharacteristic
15C2×C4⋊Dic263C2211yescharacteristic
16C2×C4⋊Dic263C2211yescharacteristic
17#22554404—21no—
18#22554403—21no—
19#22554402—21no—
20#22554401—21no—
21C263⋊#95—22no—
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24C2×C42×C263C2211yescharacteristic
25C2×Dic526—22no—
26C22×Dic263—21no—
27C22×Dic263D412yes—
28#16862360—21no—
29#16862360Q812yescomplemented
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—22no—
39Dic263⋊C4—22no—
40C22⋊Dic263—21no—
41C4×Dic263—21no—
42C22×C4×C263—21no—
43C22×C4×C263C2311yescharacteristic
44M16×C263—21no—
45M16×C263Q812yescomplemented
46C2×C8×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C4⋊C4×C263D411yescharacteristic
49C22⋊C4×C263—21no—
50C42×C263—21no—
51C42×C263—21no—
52C42×C263Q812yescomplemented
53Dic526—82no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—42no—
58C2×Dic263—42no—
59C2×Dic263—41no—
60C263⋊C8—22no—
61C23×C263C2×D411yescharacteristic
62C2×C4×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263—22no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×Q811yescharacteristic
70C2×C4×C263C2×Q811yescharacteristic
71C2×C4×C263C2×Q811yescharacteristic
72C2×C4×C263#4111yescharacteristic
73C8×C263—22no—
74C22×C263—21no—
75C22×C263—21no—
76C22×C263#12011yescharacteristic
77C22×C263C22⋊Q811yescharacteristic
78C22×C263C4⋊Q811yescharacteristic
79C4×C263—42no—
80C4×C263—41no—
81C4×C263—41no—
82C4×C263C22⋊Q811yescharacteristic
83C4×C263C22⋊Q811yescharacteristic
84C4×C263C4⋊Q811yescharacteristic
85C4×C263C4⋊Q811yescharacteristic
86Dic263—41no—
87Dic263—42no—
88Dic263—41no—
89Dic263—81no—
90C2×C263—21no—
91C2×C263—21no—
92C2×C263#39511yescharacteristic
93C2×C263#45411yescharacteristic
94C2×C263#45511yescharacteristic
95C263#206111yescharacteristic, complemented, Sylow
96#2061—2631nomaximal, Sylow
97#544—2631no—
98#428—2631no—
99#428—2631no—
100#382—2631no—
101#343—2631no—
102#339—2631no—
103#339D26311yescharacteristic
104C2×M16—2631no—
105C2×M16C2×D26311yescharacteristic
106C4⋊Q8—5261no—
107C4⋊Q8—5261no—
108#125—5261no—
109#125—5261no—
110C22⋊Q8—5262no—
111#117—2631no—
112#117C2×D26311yescharacteristic
113C2×C4⋊C4—2631no—
114C2×C4⋊C4—2631no—
115C2×C42C2×D26311yescharacteristic
116#107—5261no—
117#107—5261no—
118#106—5261no—
119#106—5261no—
120#95—5262no—
121C2×Q8—5262no—
122C22×C4—21no—
123C22×C4—2632no—
124C22×C4—5261no—
125C22×C4C22×D26311yescharacteristic
126M16—21no—
127M16—2632no—
128M16—5261no—
129M16Dic52612yescomplemented
130C2×C8—21no—
131C2×C8—5261no—
132C4⋊C4—2631no—
133C4⋊C4—2631no—
134C4⋊C4—5262no—
135C4⋊C4—5262no—
136C4⋊C4—5262no—
137C4⋊C4—5261no—
138C4⋊C4—5261no—
139C4⋊C4—5261no—
140C4⋊C4—5261no—
141C4⋊C4D105211yescharacteristic
142C4⋊C4D105211yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—5261no—
145C42—21no—
146C42—21no—
147C42—5261no—
148C42Dic52612yescomplemented
149C23D4×D26311yescharacteristic
150Q8—21042no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5261no—
157C2×C4—5261no—
158C2×C4—5262no—
159C2×C4—10522no—
160C2×C4—10522no—
161C2×C4—10521no—
162C2×C4D4×D26311yescharacteristic
163C2×C4C2×D105211yescharacteristic
164C2×C4Q8×D26311yescharacteristic
165C2×C4C2×Dic52611yescharacteristic
166C2×C4C2×Dic52611yescharacteristic
167C2×C4#1686237511yescharacteristic
168C8—22no—
169C8—5262no—
170C22—21no—
171C22—21no—
172C22#2255444011yescharacteristic
173C22#2255444711yescharacteristic
174C22#2255446911yescharacteristic
175C4—42no—
176C4—41no—
177C4—41no—
178C4—10521no—
179C4—10522no—
180C4—10521no—
181C4—21041no—
182C4#2255444711yescharacteristic
183C4#2255445011yescharacteristic
184C4#2255446911yescharacteristic
185C4#2255447011yescharacteristic
186C2—21no—
187C2—21no—
188C2#3068185911yescharacteristic
189C2#3068211211yescharacteristic
190C2#3068211711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#339D263
hypocenterC263#2061
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #16862360Q8semidirect
45. M16×C263Q8semidirect
52. C42×C263Q8semidirect
95. C263#2061semidirect
129. M16Dic526semidirect
148. C42Dic526semidirect

Maximal subgroups

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

subgroupindex
#306825662
#306819812
#306819802
#306818042
#306817062
#306816982
#339×C2632
#2061263