Finite Group Databasebeta

← #44509115

Subgroups — #44509115

Order 30848.

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

normal subgroups only

This group has 270 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#29508280C211yesmaximal, characteristic
2#29507689C212yesmaximal, complemented
3#29507510C211yesmaximal, characteristic, complemented
4#29507509C212yesmaximal, complemented
5#353×C241C211yesmaximal, characteristic, complemented
6C2×#16838769C2211yescharacteristic
7C2×D4×D241C411yescharacteristic, complemented
8#21440638C2211yescharacteristic
9#21440630C411yescharacteristic, complemented
10#21440629C411yescharacteristic, complemented
11#21440614—22no—
12#21440610—22no—
13#21440599C411yescharacteristic, complemented
14#21440598—22no—
15#21440557C2212yescomplemented
16#21440556—22no—
17#127×C241C2211yescharacteristic
18#99×C241C2212yescomplemented
19C23×D241—21no—
20#16838769—42no—
21C2×Dic482C2×C411yescharacteristic
22C2×D964C2×C411yescharacteristic
23C2×C22⋊D241—21no—
24C2×C22⋊D241—22no—
25C2×C22⋊D241D412yes—
26D4×D241—42no—
27C22×Dic241D412yes—
28C2×C4×D241C2×C411yescharacteristic
29#16838749—21no—
30#16838749—42no—
31C22⋊Dic241—22no—
32C22⋊Dic241—22no—
33#16838747—21no—
34#16838747—22no—
35C4×Dic241—42no—
36C4×Dic241C2×C411yescharacteristic
37C2×D4×C241—22no—
38C2×D4×C241C2×C411yescharacteristic
39C2×D4×C241C2311yescharacteristic
40C22⋊C4×C241—22no—
41C42×C241C2×C411yescharacteristic
42C22×D241—21no—
43C22×D241—42no—
44C22×D241—82no—
45C22×D241C22⋊C411yescharacteristic
46Dic482—41no—
47D964—41no—
48C22⋊D241—42no—
49C22⋊D241—42no—
50C22⋊D241—82no—
51C2×Dic241—22no—
52C2×Dic241—22no—
53C2×Dic241—21no—
54C2×Dic241—42no—
55C2×Dic241C22⋊C412yes—
56C2×Dic241C22⋊C411yescharacteristic
57C4×D241—22no—
58C23×C241—21no—
59C23×C241C2×D412yes—
60D4×C241—41no—
61D4×C241—41no—
62D4×C241—82no—
63C2×C4×C241—21no—
64C2×C4×C241—42no—
65C2×C4×C241C22×C411yescharacteristic
66C22×C241—22no—
67C22×C241—42no—
68C22×C241—42no—
69C22×C241—41no—
70C22×C241C2×C22⋊C411yescharacteristic
71C2×D241—21no—
72C2×D241—41no—
73C2×D241—42no—
74C2×D241—41no—
75C2×D241—84no—
76C4×C241—21no—
77C4×C241—41no—
78C4×C241—82no—
79Dic241—22no—
80Dic241—41no—
81Dic241—82no—
82Dic241#9912yes—
83C2×C241—21no—
84C2×C241—42no—
85C2×C241—81no—
86C2×C241C2×#9911yescharacteristic
87D241—41no—
88D241—81no—
89C241#212811yescharacteristic, complemented, Sylow
90#2128—2411nomaximal, Sylow
91#535—2411no—
92#410—2412no—
93#353—2411no—
94#353—2412no—
95#353D24111yescharacteristic, complemented
96C2×#41—2411no—
97C22×D4—2411no—
98#127—2411no—
99#127C2×D24111yescharacteristic
100#124—2411no—
101#124—2411no—
102#121—4822no—
103#120—4822no—
104#117—4822no—
105#117—2411no—
106#99—4822no—
107#99—2412no—
108#99C2×D24112yescomplemented
109C24—4821no—
110#41—9642no—
111C2×Q8—2411no—
112C2×D4—22no—
113C2×D4—9642no—
114C2×D4—4822no—
115C2×D4—4821no—
116C2×D4—2412no—
117C2×D4—2411no—
118C2×D4C4×D24111yescharacteristic
119C2×D4C22×D24111yescharacteristic
120C22×C4—2412no—
121C22×C4—2411no—
122C4⋊C4—9642no—
123C4⋊C4—4821no—
124C22⋊C4—22no—
125C22⋊C4—4821no—
126C22⋊C4—4822no—
127C22⋊C4—4822no—
128C22⋊C4—4822no—
129C42—9642no—
130C42—2411no—
131C42C4×D24111yescharacteristic
132C23—21no—
133C23—19282no—
134C23—9642no—
135C23—4821no—
136C23—2411no—
137C23D4×D24112yes—
138Q8—9641no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—19282no—
143D4—9641no—
144D4—9642no—
145D4—9642no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—9642no—
149C2×C4—4822no—
150C2×C4—4821no—
151C2×C4—4822no—
152C2×C4—4822no—
153C2×C4—2412no—
154C2×C4—2411no—
155C2×C4C2×C4×D24111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—19284no—
161C22—9642no—
162C22—9641no—
163C22—9641no—
164C22—4821no—
165C22C22⋊C4×D24111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—19282no—
170C4—9641no—
171C4—4822no—
172C4—2412no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—19281no—
177C2—9641no—
178C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#353×C241C2
socleC2×C241C2×#99
prime radical#29508280C2
cosocleC2×D4×C241C23
hypercenter#353D241
hypocenterC241#2128
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #29507689C2semidirect
3. #29507510C2semidirect
4. #29507509C2semidirect
5. #353×C241C2semidirect
7. C2×D4×D241C4semidirect
9. #21440630C4semidirect
10. #21440629C4semidirect
13. #21440599C4semidirect
15. #21440557C22semidirect
18. #99×C241C22semidirect
89. C241#2128semidirect
95. #353D241semidirect
108. #99C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082802
#295076892
#295075102
#295075092
#353×C2412
#2128241