Finite Group Databasebeta

← #44509113

Subgroups — #44509113

Order 30848.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508285C211yesmaximal, characteristic
2#99×D241C212yesmaximal, complemented
3#29507512C211yesmaximal, characteristic, complemented
4#29507509C212yesmaximal, complemented
5#354×C241C211yesmaximal, characteristic, complemented
6C2×#16838771C411yescharacteristic, complemented
7C2×D4×D241C2211yescharacteristic
8#21440639C411yescharacteristic, complemented
9#21440638C2211yescharacteristic
10#21440631C411yescharacteristic, complemented
11#21440615—22no—
12#21440612—22no—
13#21440599C411yescharacteristic, complemented
14C22⋊C4×D241—22no—
15#21440557C2212yes—
16#21440556—22no—
17#124×C241C2211yescharacteristic
18#99×C241C2212yes—
19C23×D241D412yes—
20#16838771—42no—
21C2×D964—21no—
22C2×D964—22no—
23C2×D964C2×C411yescharacteristic
24C2×D964C2×C411yescharacteristic, complemented
25C2×C22⋊D241—22no—
26C2×C22⋊D241D412yes—
27D4×D241—42no—
28C2×C4×D241—21no—
29C2×C4×D241—42no—
30C2×C4×D241C2×C411yescharacteristic
31#16838749—21no—
32C22⋊Dic241—22no—
33#16838747—21no—
34#16838747—22no—
35#16838747—42no—
36C4×Dic241C2×C411yescharacteristic, complemented
37C2×Q8×C241C2×C411yescharacteristic, complemented
38C2×D4×C241C2311yescharacteristic
39C22⋊C4×C241—22no—
40C22⋊C4×C241—22no—
41C42×C241C2×C411yescharacteristic, complemented
42C22×D241—22no—
43C22×D241—22no—
44C22×D241—21no—
45C22×D241—82no—
46C22×D241C22⋊C412yes—
47C22×D241C22⋊C411yescharacteristic
48D964—41no—
49D964—41no—
50D964—42no—
51D964—82no—
52C22⋊D241—42no—
53C22⋊D241—82no—
54C2×Dic241—21no—
55C2×Dic241—42no—
56C2×Dic241C22⋊C411yescharacteristic
57C4×D241—22no—
58C4×D241—42no—
59C4×D241—84no—
60C23×C241C2×D412yes—
61Q8×C241—41no—
62D4×C241—41no—
63C2×C4×C241—21no—
64C2×C4×C241—21no—
65C2×C4×C241—42no—
66C2×C4×C241C22×C411yescharacteristic
67C22×C241—22no—
68C22×C241—42no—
69C22×C241C2×C22⋊C411yescharacteristic
70C2×D241—22no—
71C2×D241—41no—
72C2×D241—44no—
73C2×D241—42no—
74C2×D241—42no—
75C2×D241—41no—
76C2×D241—82no—
77C2×D241#9912yes—
78C4×C241—21no—
79C4×C241—41no—
80C4×C241—41no—
81C4×C241—82no—
82Dic241—21no—
83Dic241—41no—
84Dic241—82no—
85C2×C241—21no—
86C2×C241—42no—
87C2×C241C2×#9911yescharacteristic
88D241—22no—
89D241—42no—
90D241—81no—
91C241#212711yescharacteristic, complemented, Sylow
92#2127—2411nomaximal, Sylow
93#535—2411no—
94C2×#99—2412no—
95#354—2411no—
96#354D24111yescharacteristic, complemented
97#353—2412no—
98C2×#41—2411no—
99C22×D4—2411no—
100#127—2411no—
101#127—2411no—
102#124—2411no—
103#124C2×D24111yescharacteristic
104#121—4822no—
105#120—4822no—
106#117—2411no—
107C2×C22⋊C4—4822no—
108#99—4822no—
109#99—2412no—
110#99C2×D24112yes—
111C24—2412no—
112#41—9642no—
113C2×Q8C4×D24111yescharacteristic, complemented
114C2×D4—9642no—
115C2×D4—4822no—
116C2×D4—4821no—
117C2×D4—4822no—
118C2×D4—2412no—
119C2×D4—2411no—
120C2×D4—2411no—
121C2×D4C22×D24111yescharacteristic
122C22×C4—9642no—
123C22×C4—4821no—
124C22×C4—2411no—
125C4⋊C4—4821no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—9642no—
129C22⋊C4—4821no—
130C22⋊C4—4822no—
131C22⋊C4—4822no—
132C42—2411no—
133C42C4×D24111yescharacteristic, complemented
134C23—19282no—
135C23—4822no—
136C23—4822no—
137C23—4821no—
138C23—2412no—
139C23—2411no—
140C23D4×D24112yes—
141Q8—41no—
142D4—41no—
143D4—19282no—
144D4—19282no—
145D4—9641no—
146D4—9641no—
147D4—9642no—
148D4—9642no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—19284no—
153C2×C4—9642no—
154C2×C4—9642no—
155C2×C4—4822no—
156C2×C4—4821no—
157C2×C4—2411no—
158C2×C4C2×C4×D24111yescharacteristic
159C22—22no—
160C22—42no—
161C22—19282no—
162C22—9642no—
163C22—9642no—
164C22—9641no—
165C22—9644no—
166C22—9641no—
167C22—4822no—
168C22—2412no—
169C22C22⋊C4×D24111yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—19282no—
175C4—9641no—
176C4—4821no—
177C2—21no—
178C2—42no—
179C2—19281no—
180C2—9642no—
181C2—4822no—
182C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#354×C241C2
socleC2×C241C2×#99
prime radical#29508285C2
cosocleC2×D4×C241C23
hypercenter#354D241
hypocenterC241#2127
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D241C2semidirect
3. #29507512C2semidirect
4. #29507509C2semidirect
5. #354×C241C2semidirect
6. C2×#16838771C4semidirect
8. #21440639C4semidirect
10. #21440631C4semidirect
13. #21440599C4semidirect
24. C2×D964C2×C4semidirect
36. C4×Dic241C2×C4semidirect
37. C2×Q8×C241C2×C4semidirect
41. C42×C241C2×C4semidirect
91. C241#2127semidirect
96. #354D241semidirect
113. C2×Q8C4×D241semidirect
133. C42C4×D241semidirect

Maximal subgroups

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

subgroupindex
#295082852
#99×D2412
#295075122
#295075092
#354×C2412
#2127241