Finite Group Databasebeta

← #44506632

Subgroups — #44506632

Order 30848.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508453C211yesmaximal, characteristic
2#29508063C211yesmaximal, characteristic
3#29508003C211yesmaximal, characteristic, complemented
4#29507928C211yesmaximal, characteristic, complemented
5#29507447C211yesmaximal, characteristic, complemented
6#29507447C211yesmaximal, characteristic, complemented
7#331×C241C211yesmaximal, characteristic
8C2×Dic964—21no—
9#21440642C2211yescharacteristic
10#21440629—21no—
11#21440629—21no—
12#21440623—22no—
13C4×Dic482C2211yescharacteristic
14C4×Dic482C2211yescharacteristic
15D4×Dic241—21no—
16D4×Dic241—21no—
17#21440574—21no—
18#21440567—21no—
19#21440567—21no—
20#21440563—22no—
21C4×#14515349C2211yescharacteristic
22#127×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482D411yescharacteristic
27C2×Dic482D411yescharacteristic
28C22×Dic241—22no—
29Dic964—42no—
30C2×#14515349—21no—
31C4⋊Dic241—21no—
32C4⋊Dic241—21no—
33C4⋊Dic241D411yescharacteristic
34C4⋊Dic241D411yescharacteristic
35#16838749—21no—
36#16838749—21no—
37C22⋊Dic241—22no—
38C22⋊Dic241—22no—
39C22⋊Dic241—22no—
40C4×Dic241—21no—
41C4×Dic241—21no—
42C2×D4×C241—21no—
43C2×D4×C241—21no—
44C2×D4×C241D412yes—
45C2×C8×C241—21no—
46C2×C8×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—21no—
49Dic482—21no—
50Dic482—21no—
51Dic482—21no—
52Dic482—41no—
53Dic482—41no—
54C2×Dic241—21no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—41no—
59C2×Dic241—82no—
60#14515349—41no—
61C23×C241—22no—
62D4×C241—42no—
63D4×C241—41no—
64D4×C241—41no—
65D4×C241—41no—
66D4×C241—41no—
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C8×C241—41no—
71C8×C241—41no—
72C22×C241—42no—
73C22×C241—42no—
74C22×C241—42no—
75C22×C241#12011yescharacteristic
76C4×C241—21no—
77C4×C241#13511yescharacteristic
78C4×C241#13511yescharacteristic
79C4×C241AGL(1,ℤ/8)11yescharacteristic
80C4×C241#13711yescharacteristic
81Dic241—41no—
82Dic241—41no—
83Dic241—41no—
84Dic241—41no—
85Dic241—81no—
86C2×C241—82no—
87C2×C241#44911yescharacteristic
88C2×C241#45211yescharacteristic
89C2×C241#45511yescharacteristic
90C241#164011yescharacteristic, complemented, Sylow
91#1640—2411nomaximal, Sylow
92#559—2411no—
93#486—2411no—
94#475—2411no—
95#462—2411no—
96#331D24111yescharacteristic
97Q8⋊C8—2411no—
98Q8⋊C8—2411no—
99C2×Q16—4821no—
100C4⋊Q8—2411no—
101#127C2×D24111yescharacteristic
102#124—4821no—
103#124—4821no—
104#123—4822no—
105C4×Q8—2411no—
106C4×Q8—2411no—
107C4×D4—4821no—
108C4×D4—4821no—
109#106—4821no—
110C4⋊C8C2×D24111yescharacteristic
111C4⋊C8C2×D24111yescharacteristic
112#103—4821no—
113#103—4821no—
114#102—4822no—
115C4×C8—2411no—
116C2×Q8—4821no—
117C2×Q8—2411no—
118C2×Q8—2411no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D96412yes—
122C22×C4—4822no—
123Q16—9642no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—4821no—
127C4⋊C4—4821no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4—4821no—
131C4⋊C4—2411no—
132C4⋊C4—2411no—
133C22⋊C4—4822no—
134C22⋊C4—4822no—
135C22⋊C4—4822no—
136C42—4821no—
137C42—4821no—
138C42C22×D24111yescharacteristic
139C23—22no—
140Q8—9641no—
141Q8—9641no—
142Q8—4821no—
143Q8—4821no—
144Q8—4821no—
145Q8—4821no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—19282no—
152C2×C4—9641no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—4821no—
156C2×C4—4821no—
157C2×C4D4×D24111yescharacteristic
158C2×C4D4×D24111yescharacteristic
159C2×C4C2×D96411yescharacteristic
160C8—41no—
161C8—41no—
162C8—9641no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#2144061211yescharacteristic
167C4—21no—
168C4—19281no—
169C4—9641no—
170C4—9641no—
171C4—9641no—
172C4—9641no—
173C4#2144066111yescharacteristic
174C4#2144066311yescharacteristic
175C4#2144066611yescharacteristic
176C4#2144067111yescharacteristic
177C2—82no—
178C2#2950786311yescharacteristic
179C2#2950788011yescharacteristic
180C2#2950789711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#331×C241C2
socleC22×C241#120
prime radical#127×C241C22
hypercenter#331D241
hypocenterC241#1640
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #29508003C2semidirect
4. #29507928C2semidirect
5. #29507447C2semidirect
6. #29507447C2semidirect
90. C241#1640semidirect

Maximal subgroups

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

subgroupindex
#295084532
#295080632
#295080032
#295079282
#295074472
#331×C2412
#1640241