Finite Group Databasebeta

← #44509119

Subgroups — #44509119

Order 30848.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508288C211yesmaximal, characteristic
2#29507691C211yesmaximal, characteristic
3#29507511C214yesmaximal, complemented
4#410×C241C211yesmaximal, characteristic
5C22×Dic482C411yescharacteristic, complemented
6#21440640C412yescomplemented
7#21440629C2212yes—
8#21440623—21no—
9#21440623—21no—
10#21440621—21no—
11#21440621—21no—
12#21440601—21no—
13#21440601C411yescharacteristic, complemented
14#21440557—21no—
15#21440557C2212yes—
16C2×#41×C241C2211yescharacteristic
17#117×C241—21no—
18#99×C241—21no—
19#99×C241C2212yes—
20C2×Dic482—21no—
21C2×Dic482—41no—
22C2×Dic482—41no—
23C2×Dic482C2×C412yes—
24C22×Dic241—21no—
25C4⋊Dic241—21no—
26C4⋊Dic241—41no—
27#16838749—22no—
28#16838749—22no—
29C22⋊Dic241—21no—
30C22⋊Dic241—22no—
31C22⋊Dic241—22no—
32C22⋊Dic241—22no—
33C4×Dic241—41no—
34C4×Dic241C2×C412yes—
35#41×C241—41no—
36#41×C241—41no—
37C2×Q8×C241C2×C411yescharacteristic
38C2×D4×C241D411yescharacteristic
39C2×D4×C241D411yescharacteristic
40C2×D4×C241C2311yescharacteristic
41C22×C4×C241C2×C411yescharacteristic
42C22×C4×C241D411yescharacteristic
43C22×C4×C241D411yescharacteristic
44C4⋊C4×C241—41no—
45C22⋊C4×C241—22no—
46C42×C241—41no—
47Dic482—41no—
48Dic482—41no—
49Dic482—42no—
50C2×Dic241—22no—
51C2×Dic241—22no—
52C2×Dic241—42no—
53C2×Dic241—42no—
54C23×C241C22⋊C411yescharacteristic
55C23×C241C2×D411yescharacteristic
56C23×C241C2×D411yescharacteristic
57Q8×C241—41no—
58D4×C241—41no—
59D4×C241—41no—
60D4×C241—41no—
61C2×C4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241—21no—
64C2×C4×C241—21no—
65C2×C4×C241—21no—
66C2×C4×C241—21no—
67C2×C4×C241—42no—
68C2×C4×C241C22⋊C411yescharacteristic
69C2×C4×C241C22⋊C411yescharacteristic
70C2×C4×C241C22⋊C411yescharacteristic
71C2×C4×C241C22×C411yescharacteristic
72C22×C241—21no—
73C22×C241—21no—
74C22×C241—21no—
75C22×C241—41no—
76C22×C241—41no—
77C22×C241—41no—
78C22×C241C2×C22⋊C411yescharacteristic
79C4×C241—21no—
80C4×C241—21no—
81C4×C241—21no—
82C4×C241—82no—
83C4×C241#9911yescharacteristic
84C4×C241#9911yescharacteristic
85Dic241—42no—
86Dic241—42no—
87Dic241—82no—
88C2×C241—21no—
89C2×C241—41no—
90C2×C241—41no—
91C2×C241—41no—
92C2×C241C2×#9911yescharacteristic
93C241#212911yescharacteristic, complemented, Sylow
94#2129—2411nomaximal, Sylow
95#536—2411no—
96#410—2411no—
97#410D24111yescharacteristic
98#354—2414no—
99C2×#41C2×D24111yescharacteristic
100C22×Q8—2411no—
101C4⋊Q8—2412no—
102#124—2412no—
103#123—4821no—
104#123—4821no—
105C22⋊Q8—4821no—
106C22⋊Q8—4821no—
107#117—21no—
108#117—4821no—
109#117—2411no—
110#99—21no—
111#99—4821no—
112#99—2412no—
113#99C2×D24112yes—
114#41—41no—
115#41—41no—
116C2×Q8—9641no—
117C2×Q8—9641no—
118C2×Q8—4821no—
119C2×Q8—2412no—
120C2×Q8C4×D24111yescharacteristic
121C2×D4C22⋊D24111yescharacteristic
122C2×D4D96411yescharacteristic
123C2×D4C22×D24111yescharacteristic
124C22×C4—4821no—
125C22×C4C4×D24111yescharacteristic
126C22×C4C22⋊D24111yescharacteristic
127C22×C4D96411yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—9641no—
130C4⋊C4—4822no—
131C4⋊C4—4822no—
132C4⋊C4—4821no—
133C22⋊C4—22no—
134C22⋊C4—4822no—
135C22⋊C4—4821no—
136C22⋊C4—4822no—
137C22⋊C4—4822no—
138C42—41no—
139C42—9641no—
140C42—2412no—
141C23#1683874711yescharacteristic
142C23C2×C22⋊D24111yescharacteristic
143C23C2×D96411yescharacteristic
144Q8—41no—
145Q8—9642no—
146Q8—9641no—
147Q8—9641no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—9642no—
159C2×C4—9642no—
160C2×C4—4822no—
161C2×C4—4822no—
162C2×C4#1683874711yescharacteristic
163C2×C4#1683874711yescharacteristic
164C2×C4#1683874711yescharacteristic
165C2×C4C2×C4×D24111yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×#1683874711yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—19282no—
178C4—9642no—
179C4—9642no—
180C4#2144055611yescharacteristic
181C4#2144055611yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#2144055611yescharacteristic
subgroupG/H
centerC2C2×#21440556
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#410×C241C2
socleC2×C241C2×#99
prime radicalC2×#41×C241C22
cosocleC2×D4×C241C23
hypercenter#410D241
hypocenterC241#2129
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #29507511C2semidirect
5. C22×Dic482C4semidirect
6. #21440640C4semidirect
13. #21440601C4semidirect
93. C241#2129semidirect

Maximal subgroups

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

subgroupindex
#295082882
#295076912
#295075112
#410×C2412
#2129241