Finite Group Databasebeta

← #46782986

Subgroups — #46782986

Order 33664.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#30682704C211yesmaximal, characteristic
2#30681986C211yesmaximal, characteristic, complemented
3#30681954C211yesmaximal, characteristic
4C2×#22554398C211yesmaximal, characteristic
5#30681709C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7#423×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554478—22no—
10#22554476—22no—
11C2×#16862360C2211yescharacteristic
12C2×#16862360C2211yescharacteristic
13M16×D263—22no—
14#22554429C2211yescharacteristic
15#22554405—22no—
16#22554398C412yescomplemented
17#22554398C412yescomplemented
18#22554396—22no—
19C2×M16×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic
21C2×C42×C263C2211yescharacteristic
22C4⋊C8×C263—22no—
23#16862376—21no—
24#16862376—21no—
25#16862376C2×C412yes—
26#16862376D412yes—
27C2×Dic526Q811yescharacteristic
28C2×D1052Q811yescharacteristic
29C2×C22⋊D263—21no—
30C2×C4×D263—21no—
31#16862360—21no—
32#16862360—21no—
33#16862360C2×C412yes—
34#16862360D412yes—
35#16862359—24no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C8×D263—24no—
39C4⋊Dic263—21no—
40C22⋊Dic263—21no—
41C4×Dic263—21no—
42C22×C4×C263—21no—
43C22×C4×C263C2311yescharacteristic
44M16×C263—21no—
45M16×C263—21no—
46M16×C263—21no—
47M16×C263—21no—
48C2×C8×C263—21no—
49C2×C8×C263D412yes—
50C42×C263—21no—
51C42×C263C2×C411yescharacteristic
52C42×C263C2×C411yescharacteristic
53C22×D263—21no—
54Dic526—21no—
55Dic526C4⋊C412yes—
56D1052—21no—
57D1052C4⋊C412yes—
58C22⋊D263—22no—
59C22⋊D263—22no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C4×D263—22no—
63C4×D263—22no—
64C263⋊C8—22no—
65C263⋊C8—22no—
66C23×C263#4111yescharacteristic
67C2×C4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—42no—
70C2×C4×C263C22×C411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×Q811yescharacteristic
75C2×C4×C263#4111yescharacteristic
76C8×C263—22no—
77C8×C263—41no—
78C22×C263—41no—
79C22×C263C4×D411yescharacteristic
80C22×C263C22⋊Q811yescharacteristic
81C22×C263#12311yescharacteristic
82C2×D263—22no—
83C2×D263—81no—
84C4×C263—22no—
85C4×C263—41no—
86C4×C263C2×C4⋊C411yescharacteristic
87C4×C263C4×D411yescharacteristic
88C4×C263#12011yescharacteristic
89C4×C263C22⋊Q811yescharacteristic
90Dic263—22no—
91Dic263—81no—
92C2×C263—21no—
93C2×C263—21no—
94C2×C263—21no—
95C2×C263#38511yescharacteristic
96D263—42no—
97C263#186111yescharacteristic, complemented, Sylow
98#1861—2631nomaximal, Sylow
99#568—2631no—
100#430—2631no—
101#423D26311yescharacteristic, complemented
102#421—2631no—
103C2×#104—2631no—
104#344—2631no—
105#339—2631no—
106C2×#41—2631no—
107#131—5262no—
108#131—5262no—
109C2×M16—2631no—
110C2×M16—2631no—
111C2×M16—5262no—
112C2×M16C2×D26311yescharacteristic
113C2×M16C2×D26311yescharacteristic
114#117—2631no—
115C2×C42C2×D26311yescharacteristic
116#108—5262no—
117C4⋊C8—22no—
118#104—2632no—
119#104—2632no—
120#104—5262no—
121#41—2632no—
122#41—2632no—
123#41—5261no—
124#41—5261no—
125C2×Q8—2631no—
126C2×D4—2631no—
127C2×D4—5261no—
128C22×C4—21no—
129C22×C4—5261no—
130C22×C4C22×D26311yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—2632no—
136M16—2632no—
137M16—5264no—
138M16—5261no—
139M16—5261no—
140C2×C8—21no—
141C2×C8—5264no—
142C2×C8—5261no—
143C2×C8—5261no—
144C2×C8C22⋊D26312yes—
145C4⋊C4—5261no—
146C22⋊C4—5261no—
147C42—21no—
148C42—5261no—
149C42C4×D26311yescharacteristic
150C42C4×D26311yescharacteristic
151C23—5261no—
152C23#1686237611yescharacteristic
153Q8—2632no—
154Q8—5261no—
155D4—2632no—
156D4—5262no—
157D4—5262no—
158D4—5261no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—5261no—
163C2×C4—5262no—
164C2×C4—5262no—
165C2×C4—10521no—
166C2×C4C2×C4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C2×C4D4×D26311yescharacteristic
169C2×C4C2×C22⋊D26311yescharacteristic
170C2×C4Q8×D26311yescharacteristic
171C2×C4#1686237711yescharacteristic
172C8—22no—
173C8—41no—
174C8—5262no—
175C8—5262no—
176C22—41no—
177C22—5262no—
178C22—21041no—
179C22C4×C22⋊D26311yescharacteristic
180C22#2255444811yescharacteristic
181C22#2255445511yescharacteristic
182C4—22no—
183C4—41no—
184C4—5262no—
185C4—21041no—
186C4C4⋊C4×D26311yescharacteristic
187C4#2255443211yescharacteristic
188C4#2255443811yescharacteristic
189C4#2255444611yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—10522no—
194C2#3068180911yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#423×C263C2
socleC2×C263#385
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#423D263
hypocenterC263#1861
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #30681986C2semidirect
5. #30681709C2semidirect
6. #30681698C2semidirect
7. #423×C263C2semidirect
16. #22554398C4semidirect
17. #22554398C4semidirect
97. C263#1861semidirect
101. #423D263semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306819862
#306819542
C2×#225543982
#306817092
#306816982
#423×C2632
#1861263