Finite Group Databasebeta

← #44509107

Subgroups — #44509107

Order 30848.

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

normal subgroups only

This group has 258 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#29508265C211yesmaximal, characteristic
2#29507689C212yesmaximal, complemented
3#29507511C212yesmaximal, complemented
4#29507510C211yesmaximal, characteristic, complemented
5#353×C241C211yesmaximal, characteristic, complemented
6C2×#16838769C411yescharacteristic, complemented
7C2×#16838769C2211yescharacteristic
8#21440642C411yescharacteristic, complemented
9#21440629C411yescharacteristic, complemented
10#21440629C2211yescharacteristic
11#21440613—22no—
12D4×Dic241—22no—
13#21440598—22no—
14C42×D241C411yescharacteristic, complemented
15#21440557C2212yes—
16#21440556—22no—
17#127×C241C2211yescharacteristic
18#99×C241C2212yes—
19#16838769—41no—
20#16838769—41no—
21#16838769—41no—
22#16838769—41no—
23C2×Dic482C2×C411yescharacteristic
24C2×Dic482C2×C411yescharacteristic
25C2×C22⋊D241—21no—
26C2×C22⋊D241D412yes—
27C22×Dic241—21no—
28C22×Dic241D412yes—
29C2×C4×D241—21no—
30C2×C4×D241C2×C411yescharacteristic
31C4⋊Dic241—22no—
32#16838749—42no—
33C22⋊Dic241—22no—
34C22⋊Dic241—22no—
35C22⋊Dic241—22no—
36C4×Dic241—21no—
37C4×Dic241—42no—
38C4×Dic241C2×C411yescharacteristic
39C2×D4×C241—22no—
40C2×D4×C241C2×C411yescharacteristic
41C2×D4×C241C2311yescharacteristic
42C22⋊C4×C241—22no—
43C42×C241C2×C411yescharacteristic
44C22×D241C22⋊C411yescharacteristic
45Dic482—41no—
46Dic482—41no—
47C22⋊D241—42no—
48C22⋊D241—42no—
49C2×Dic241—22no—
50C2×Dic241—22no—
51C2×Dic241—21no—
52C2×Dic241—21no—
53C2×Dic241—41no—
54C2×Dic241—41no—
55C2×Dic241—42no—
56C2×Dic241C22⋊C412yes—
57C2×Dic241C22⋊C411yescharacteristic
58C4×D241—21no—
59C4×D241—21no—
60C4×D241—42no—
61C23×C241—21no—
62C23×C241C2×D412yes—
63D4×C241—41no—
64D4×C241—41no—
65D4×C241—44no—
66C2×C4×C241—21no—
67C2×C4×C241—42no—
68C2×C4×C241C22×C411yescharacteristic
69C22×C241—22no—
70C22×C241—42no—
71C22×C241—42no—
72C22×C241—41no—
73C22×C241C2×C22⋊C411yescharacteristic
74C2×D241—21no—
75C2×D241—41no—
76C4×C241—22no—
77C4×C241—21no—
78C4×C241—82no—
79Dic241—22no—
80Dic241—41no—
81Dic241—41no—
82Dic241—82no—
83Dic241#9911yescharacteristic
84Dic241#9911yescharacteristic
85C2×C241—21no—
86C2×C241—42no—
87C2×C241—81no—
88C2×C241C2×#9911yescharacteristic
89D241—41no—
90C241#212611yescharacteristic, complemented, Sylow
91#2126—2411nomaximal, Sylow
92#532—2411no—
93#410—2412no—
94#354—2412no—
95#353—2411no—
96#353D24111yescharacteristic, complemented
97C2×#41—2411no—
98C2×#41—2411no—
99C4⋊Q8—2411no—
100#127C2×D24111yescharacteristic
101#124—2411no—
102#124—2411no—
103#121—4822no—
104C4×D4—4822no—
105#117—4822no—
106C2×C42—2411no—
107#99—4822no—
108#99—2412no—
109#99C2×D24112yes—
110#41—9641no—
111#41—9641no—
112#41—9641no—
113#41—9641no—
114C2×Q8—2411no—
115C2×Q8—2411no—
116C2×D4—22no—
117C2×D4—4821no—
118C2×D4—2412no—
119C2×D4C4×D24111yescharacteristic
120C2×D4C22×D24111yescharacteristic
121C22×C4—4821no—
122C22×C4—4821no—
123C22×C4—2412no—
124C22×C4—2411no—
125C4⋊C4—9642no—
126C4⋊C4—4822no—
127C22⋊C4—22no—
128C22⋊C4—4822no—
129C22⋊C4—4822no—
130C22⋊C4—4822no—
131C42—9642no—
132C42—4821no—
133C42—2411no—
134C42C4×D24111yescharacteristic
135C23—21no—
136C23—2411no—
137C23D4×D24112yes—
138Q8—9641no—
139Q8—9641no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—9642no—
144D4—9642no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—9642no—
148C2×C4—9642no—
149C2×C4—9641no—
150C2×C4—9641no—
151C2×C4—4821no—
152C2×C4—4821no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—4822no—
156C2×C4—4822no—
157C2×C4—2412no—
158C2×C4—2411no—
159C2×C4C2×C4×D24111yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—9641no—
165C22—4821no—
166C22C22⋊C4×D24111yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—19282no—
171C4—9641no—
172C4—9641no—
173C4—4822no—
174C4—2411no—
175C4—2411no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—9641no—
180C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#353×C241C2
socleC2×C241C2×#99
prime radical#29508265C2
cosocleC2×D4×C241C23
hypercenter#353D241
hypocenterC241#2126
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. #29507511C2semidirect
4. #29507510C2semidirect
5. #353×C241C2semidirect
6. C2×#16838769C4semidirect
8. #21440642C4semidirect
9. #21440629C4semidirect
14. C42×D241C4semidirect
90. C241#2126semidirect
96. #353D241semidirect

Maximal subgroups

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

subgroupindex
#295082652
#295076892
#295075112
#295075102
#353×C2412
#2126241