Finite Group Databasebeta

← #44508491

Subgroups — #44508491

Order 30848.

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×#21440673C212yesmaximal, complemented
2#29508298C211yesmaximal, characteristic
3C2×#21440570C212yesmaximal, complemented
4#29507486C211yesmaximal, characteristic, complemented
5#391×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7#21440673—24no—
8#21440673—24no—
9C2×#16838760—22no—
10C2×#16838757—22no—
11C2×#16838754C2212yes—
12#21440622—22no—
13#21440617—22no—
14#21440616—22no—
15#21440570—24no—
16C22×Q8×C241C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C2×C42×C241C2211yescharacteristic
19#95×C241—22no—
20#16838770—22no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24C2×Dic482D412yes—
25C2×D964—22no—
26C2×D964D412yes—
27C2×C22⋊D241—22no—
28C2×C4×D241—22no—
29#16838760—28no—
30#16838757—28no—
31#16838754—22no—
32#16838754D414yescomplemented
33C2×#14515349—22no—
34C4⋊Dic241—22no—
35#16838747—24no—
36C2×Q8×C241—21no—
37C2×Q8×C241—22no—
38C2×Q8×C241—22no—
39C2×Q8×C241D412yescomplemented
40C22×C4×C241—21no—
41C22×C4×C241—21no—
42C22×C4×C241D412yes—
43C22×C4×C241C2311yescharacteristic
44C4⋊C4×C241—22no—
45C42×C241—22no—
46C22×D241—22no—
47Dic482—22no—
48Dic482—22no—
49D964—22no—
50D964—22no—
51D964—82no—
52C22⋊D241—42no—
53C22⋊D241—42no—
54C2×Dic241—22no—
55C4×D241—42no—
56C4×D241—42no—
57#14515349—24no—
58C23×C241C2×D411yescharacteristic
59Q8×C241—24no—
60Q8×C241—42no—
61C2×C4×C241—22no—
62C2×C4×C241—22no—
63C2×C4×C241—22no—
64C2×C4×C241—41no—
65C2×C4×C241—41no—
66C2×C4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241—42no—
69C2×C4×C241C2×D412yes—
70C2×C4×C241C2×D412yes—
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241#4111yescharacteristic
73C22×C241—21no—
74C22×C241—21no—
75C22×C241#12011yescharacteristic
76C22×C241#12111yescharacteristic
77C22×C241#12711yescharacteristic
78C2×D241—42no—
79C2×D241—42no—
80C2×D241—42no—
81C4×C241—42no—
82C4×C241—42no—
83C4×C241—42no—
84C4×C241#12012yes—
85C4×C241#12112yes—
86Dic241—42no—
87C2×C241—21no—
88C2×C241—21no—
89C2×C241#39211yescharacteristic
90C2×C241#45511yescharacteristic
91C2×C241#45611yescharacteristic
92D241—82no—
93C241#200711yescharacteristic, complemented, Sylow
94#2007—2411nomaximal, Sylow
95C2×#137—2412no—
96#537—2411no—
97C2×#104—2412no—
98#391D24111yescharacteristic, complemented
99#343—2411no—
100C2×#41—2412no—
101C22×Q8C2×D24111yescharacteristic
102#137—4824no—
103#137—4824no—
104C2×Q16—4822no—
105C2×SD16—4822no—
106C2×M16—2412no—
107C22⋊Q8—4822no—
108#121—4822no—
109#121—4822no—
110C2×C4⋊C4C2×D24111yescharacteristic
111C2×C42C2×D24111yescharacteristic
112#104—4824no—
113#95—22no—
114#41—4822no—
115#41—4822no—
116#41—4822no—
117#41—4822no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—2412no—
122C2×Q8D96412yescomplemented
123C2×D4—4822no—
124C2×D4—4822no—
125C2×D4—2412no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—4822no—
129C22×C4C22⋊D24112yes—
130C22×C4C22×D24111yescharacteristic
131Q16—4828no—
132SD16—4828no—
133M16—4822no—
134M16—2414no—
135C2×C8—4822no—
136C4⋊C4—22no—
137C4⋊C4—4822no—
138C22⋊C4—4824no—
139C42—22no—
140C23—4822no—
141C23C2×C22⋊D24111yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—4822no—
145Q8—4822no—
146D4—19282no—
147D4—9642no—
148D4—9642no—
149D4—4822no—
150D4—4822no—
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—9642no—
160C2×C4—9642no—
161C2×C4—4822no—
162C2×C4D4×D24112yes—
163C2×C4D4×D24112yes—
164C2×C4C2×D96411yescharacteristic
165C2×C4#1683877011yescharacteristic
166C8—4824no—
167C22—21no—
168C22—21no—
169C22—9642no—
170C22—9642no—
171C22—9642no—
172C22#2144061011yescharacteristic
173C22#2144061611yescharacteristic
174C22#2144063811yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—9642no—
179C4#2144061212yes—
180C4#2144061512yes—
181C2—21no—
182C2—21no—
183C2—19282no—
184C2#2950762611yescharacteristic
185C2#2950789411yescharacteristic
186C2#2950789911yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#391×C241C2
socleC22×C241#120
prime radical#29508298C2
hypercenter#391D241
hypocenterC241#2007
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#21440673C2semidirect
3. C2×#21440570C2semidirect
4. #29507486C2semidirect
5. #391×C241C2semidirect
32. #16838754D4semidirect
39. C2×Q8×C241D4semidirect
93. C241#2007semidirect
98. #391D241semidirect
122. C2×Q8D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406732
#295082982
C2×#214405702
#295074862
#391×C2412
#2007241