Finite Group Databasebeta

← #46783793

Subgroups — #46783793

Order 33664.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22554501C212yesmaximal, complemented
2#30682519C211yesmaximal, characteristic
3C2×#22554398C212yesmaximal, complemented
4#30681707C211yesmaximal, characteristic, complemented
5#391×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2212yes—
7#22554501—24no—
8#22554501—24no—
9C2×#16862366—22no—
10C2×#16862363—22no—
11C2×#16862360C2212yes—
12#22554450—22no—
13#22554445—22no—
14#22554444—22no—
15#22554398—24no—
16C22×Q8×C263C2211yescharacteristic
17C2×C4⋊C4×C263C2211yescharacteristic
18C2×C42×C263C2211yescharacteristic
19#95×C263—22no—
20#16862376—22no—
21#16862376—22no—
22#16862376—22no—
23#16862376—22no—
24C2×Dic526D412yes—
25C2×D1052—22no—
26C2×D1052D412yes—
27C2×C22⋊D263—22no—
28C2×C4×D263—22no—
29#16862366—28no—
30#16862363—28no—
31#16862360—22no—
32#16862360D414yescomplemented
33C2×C263⋊C8—22no—
34C4⋊Dic263—22no—
35(C2×D263)⋊C4—24no—
36C2×Q8×C263—21no—
37C2×Q8×C263—22no—
38C2×Q8×C263—22no—
39C2×Q8×C263D412yescomplemented
40C22×C4×C263—21no—
41C22×C4×C263—21no—
42C22×C4×C263D412yes—
43C22×C4×C263C2311yescharacteristic
44C4⋊C4×C263—22no—
45C42×C263—22no—
46C22×D263—22no—
47Dic526—22no—
48Dic526—22no—
49D1052—22no—
50D1052—22no—
51D1052—82no—
52C22⋊D263—42no—
53C22⋊D263—42no—
54C2×Dic263—22no—
55C4×D263—42no—
56C4×D263—42no—
57C263⋊C8—24no—
58C23×C263C2×D411yescharacteristic
59Q8×C263—24no—
60Q8×C263—42no—
61C2×C4×C263—22no—
62C2×C4×C263—22no—
63C2×C4×C263—22no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263—42no—
69C2×C4×C263C2×D412yes—
70C2×C4×C263C2×D412yes—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263#4111yescharacteristic
73C22×C263—21no—
74C22×C263—21no—
75C22×C263#12011yescharacteristic
76C22×C263#12111yescharacteristic
77C22×C263#12711yescharacteristic
78C2×D263—42no—
79C2×D263—42no—
80C2×D263—42no—
81C4×C263—42no—
82C4×C263—42no—
83C4×C263—42no—
84C4×C263#12012yes—
85C4×C263#12112yes—
86Dic263—42no—
87C2×C263—21no—
88C2×C263—21no—
89C2×C263#39211yescharacteristic
90C2×C263#45511yescharacteristic
91C2×C263#45611yescharacteristic
92D263—82no—
93C263#200711yescharacteristic, complemented, Sylow
94#2007—2631nomaximal, Sylow
95C2×#137—2632no—
96#537—2631no—
97C2×#104—2632no—
98#391D26311yescharacteristic, complemented
99#343—2631no—
100C2×#41—2632no—
101C22×Q8C2×D26311yescharacteristic
102#137—5264no—
103#137—5264no—
104C2×Q16—5262no—
105C2×SD16—5262no—
106C2×M16—2632no—
107C22⋊Q8—5262no—
108#121—5262no—
109#121—5262no—
110C2×C4⋊C4C2×D26311yescharacteristic
111C2×C42C2×D26311yescharacteristic
112#104—5264no—
113#95—22no—
114#41—5262no—
115#41—5262no—
116#41—5262no—
117#41—5262no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—2632no—
122C2×Q8D105212yescomplemented
123C2×D4—2632no—
124C2×D4—5262no—
125C2×D4—5262no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—5262no—
129C22×C4C22⋊D26312yes—
130C22×C4C22×D26311yescharacteristic
131Q16—5268no—
132SD16—5268no—
133M16—2634no—
134M16—5262no—
135C2×C8—5262no—
136C4⋊C4—22no—
137C4⋊C4—5262no—
138C22⋊C4—5264no—
139C42—22no—
140C23—5262no—
141C23C2×C22⋊D26311yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—5262no—
145Q8—5262no—
146D4—5262no—
147D4—5262no—
148D4—10522no—
149D4—10522no—
150D4—21042no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—5262no—
160C2×C4—10522no—
161C2×C4—10522no—
162C2×C4D4×D26312yes—
163C2×C4D4×D26312yes—
164C2×C4C2×D105211yescharacteristic
165C2×C4#1686237611yescharacteristic
166C8—5264no—
167C22—21no—
168C22—21no—
169C22—10522no—
170C22—10522no—
171C22—10522no—
172C22#2255443811yescharacteristic
173C22#2255444411yescharacteristic
174C22#2255446611yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—10522no—
179C4#2255444012yes—
180C4#2255444312yes—
181C2—21no—
182C2—21no—
183C2—21042no—
184C2#3068184711yescharacteristic
185C2#3068211511yescharacteristic
186C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#391×C263C2
socleC22×C263#120
prime radical#30682519C2
hypercenter#391D263
hypocenterC263#2007
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#22554501C2semidirect
3. C2×#22554398C2semidirect
4. #30681707C2semidirect
5. #391×C263C2semidirect
32. #16862360D4semidirect
39. C2×Q8×C263D4semidirect
93. C263#2007semidirect
98. #391D263semidirect
122. C2×Q8D1052semidirect

Maximal subgroups

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

subgroupindex
C2×#225545012
#306825192
C2×#225543982
#306817072
#391×C2632
#2007263