Finite Group Databasebeta

← #44508494

Subgroups — #44508494

Order 30848.

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

normal subgroups only

This group has 370 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
1C2×#21440675C212yesmaximal, complemented
2#29508298C211yesmaximal, characteristic
3C2×#21440568C212yesmaximal, complemented
4#29507622C211yesmaximal, characteristic, complemented
5#343×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7C22×Dic482C2211yescharacteristic
8#21440675—24no—
9#21440675—24no—
10C2×Dic964—22no—
11C2×#16838759—22no—
12#21440622—22no—
13#21440617—22no—
14#21440616—22no—
15C2×C4×Dic241C2211yescharacteristic
16#21440568—24no—
17#21440549—22no—
18C2×M16×C241C2212yes—
19C2×C4⋊C4×C241C2211yescharacteristic
20#16838770—22no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24C2×Dic482—22no—
25C2×Dic482—22no—
26C2×Dic482—21no—
27C2×Dic482D412yes—
28C2×Dic482D412yescomplemented
29C2×D964—22no—
30C2×D964D412yes—
31C2×C22⋊D241—22no—
32C22×Dic241—21no—
33C22×Dic241—21no—
34C2×C4×D241—22no—
35Dic964—28no—
36#16838759—28no—
37C4⋊Dic241—22no—
38#16838747—24no—
39C4×Dic241—22no—
40C22×C4×C241D412yes—
41C22×C4×C241C2311yescharacteristic
42M16×C241—22no—
43M16×C241D414yescomplemented
44C2×C8×C241—22no—
45C4⋊C4×C241—22no—
46C22×D241—22no—
47Dic482—24no—
48Dic482—22no—
49Dic482—22no—
50Dic482—42no—
51D964—22no—
52D964—22no—
53D964—82no—
54C22⋊D241—42no—
55C22⋊D241—42no—
56C2×Dic241—22no—
57C2×Dic241—22no—
58C2×Dic241—22no—
59C2×Dic241—41no—
60C2×Dic241—41no—
61C2×Dic241—41no—
62C2×Dic241—41no—
63C4×D241—42no—
64C4×D241—42no—
65C23×C241C2×D411yescharacteristic
66C2×C4×C241—22no—
67C2×C4×C241—42no—
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D412yes—
70C2×C4×C241C2×D412yes—
71C2×C4×C241#4111yescharacteristic
72C8×C241—24no—
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#12012yes—
83C4×C241#12112yes—
84Dic241—42no—
85Dic241—42no—
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#391—2411no—
99#343D24111yescharacteristic, complemented
100C2×#41—2412no—
101C22×Q8—2411no—
102#137—4824no—
103#137—4824no—
104C2×Q16—4822no—
105C2×SD16—4822no—
106C2×M16C2×D24112yes—
107C22⋊Q8—4822no—
108#121—4822no—
109#121—4822no—
110C2×C4⋊C4C2×D24111yescharacteristic
111C2×C42—2411no—
112#104—4824no—
113#95—4822no—
114#41—4822no—
115#41—4822no—
116#41—4822no—
117#41—4822no—
118C2×Q8—4822no—
119C2×Q8—4822no—
120C2×Q8—4821no—
121C2×Q8—2412no—
122C2×Q8—2412no—
123C2×D4—4822no—
124C2×D4—4822no—
125C2×D4—2412no—
126C22×C4—4821no—
127C22×C4—4821no—
128C22×C4—4822no—
129C22×C4D96412yes—
130C22×C4C22×D24111yescharacteristic
131Q16—4828no—
132SD16—4828no—
133M16—22no—
134M16D96414yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—4822no—
138C22⋊C4—4824no—
139C42—4822no—
140C23—4822no—
141C23C2×D96411yescharacteristic
142Q8—9642no—
143Q8—4824no—
144Q8—4822no—
145Q8—4822no—
146D4—19282no—
147D4—9642no—
148D4—9642no—
149D4—4822no—
150D4—4822no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—9641no—
154C2×C4—9641no—
155C2×C4—9641no—
156C2×C4—9641no—
157C2×C4—9642no—
158C2×C4—9642no—
159C2×C4—4822no—
160C2×C4—4822no—
161C2×C4—4822no—
162C2×C4D4×D24111yescharacteristic
163C2×C4D4×D24112yes—
164C2×C4C2×D96412yes—
165C2×C4#1683877111yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—9642no—
170C22—9642no—
171C22—9642no—
172C22#2144061211yescharacteristic
173C22#2144061711yescharacteristic
174C22#2144063911yescharacteristic
175C4—42no—
176C4—9642no—
177C4—9642no—
178C4—9642no—
179C4#2144061212yes—
180C4#2144061712yes—
181C2—21no—
182C2—21no—
183C2—19282no—
184C2#2950762711yescharacteristic
185C2#2950789711yescharacteristic
186C2#2950790211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#343×C241C2
socleC22×C241#120
prime radical#29508298C2
hypercenter#343D241
hypocenterC241#2007
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#21440675C2semidirect
3. C2×#21440568C2semidirect
4. #29507622C2semidirect
5. #343×C241C2semidirect
28. C2×Dic482D4semidirect
43. M16×C241D4semidirect
93. C241#2007semidirect
99. #343D241semidirect
134. M16D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406752
#295082982
C2×#214405682
#295076222
#343×C2412
#2007241