Finite Group Databasebeta

← #44509118

Subgroups — #44509118

Order 30848.

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

normal subgroups only

This group has 238 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#29508287C211yesmaximal, characteristic
2#29507689C212yesmaximal
3#29507512C211yesmaximal, characteristic, complemented
4#29507511C212yesmaximal, complemented
5#354×C241C211yesmaximal, characteristic, complemented
6C2×#16838769C2211yescharacteristic
7C2×Q8×D241C411yescharacteristic, complemented
8#21440642C411yescharacteristic, complemented
9#21440640C411yescharacteristic, complemented
10#21440629C2211yescharacteristic
11#21440624—22no—
12#21440619—22no—
13#21440599C411yescharacteristic, complemented
14#21440598—22no—
15#21440557C2212yes—
16#21440556—22no—
17#124×C241C2211yescharacteristic
18#99×C241C2212yes—
19#16838769—42no—
20C2×Dic482—21no—
21C2×Dic482C2×C411yescharacteristic
22C2×Dic482C2×C411yescharacteristic
23Q8×D241—42no—
24C2×C22⋊D241D412yes—
25C22×Dic241D412yes—
26C2×C4×D241—21no—
27C2×C4×D241C2×C411yescharacteristic
28C4⋊Dic241—22no—
29#16838749—21no—
30#16838749—22no—
31#16838749—42no—
32C22⋊Dic241—22no—
33C22⋊Dic241—22no—
34#16838747—21no—
35C4×Dic241—42no—
36C4×Dic241C2×C411yescharacteristic
37C2×Q8×C241C2×C411yescharacteristic
38C2×D4×C241C2311yescharacteristic
39C22⋊C4×C241—22no—
40C22⋊C4×C241—22no—
41C42×C241C2×C411yescharacteristic
42C22×D241C22⋊C411yescharacteristic
43Dic482—41no—
44Dic482—42no—
45Dic482—41no—
46C22⋊D241—42no—
47C2×Dic241—22no—
48C2×Dic241—22no—
49C2×Dic241—21no—
50C2×Dic241—21no—
51C2×Dic241—42no—
52C2×Dic241C22⋊C412yes—
53C2×Dic241C22⋊C411yescharacteristic
54C4×D241—22no—
55C4×D241—42no—
56C23×C241C2×D412yes—
57Q8×C241—41no—
58D4×C241—41no—
59C2×C4×C241—21no—
60C2×C4×C241—21no—
61C2×C4×C241—42no—
62C2×C4×C241C22×C411yescharacteristic
63C22×C241—22no—
64C22×C241—42no—
65C22×C241C2×C22⋊C411yescharacteristic
66C2×D241—21no—
67C2×D241—41no—
68C4×C241—21no—
69C4×C241—41no—
70C4×C241—41no—
71C4×C241—82no—
72Dic241—22no—
73Dic241—41no—
74Dic241—41no—
75Dic241—82no—
76Dic241#9912yes—
77C2×C241—21no—
78C2×C241—42no—
79C2×C241C2×#9911yescharacteristic
80D241—41no—
81C241#212911yescharacteristic, complemented, Sylow
82#2129—2411nomaximal, Sylow
83#536—2411no—
84#410—2412no—
85#354—2411no—
86#354—2412no—
87#354D24111yescharacteristic, complemented
88C2×#41—2411no—
89C22×Q8—2411no—
90C4⋊Q8—2411no—
91C4⋊Q8—2411no—
92#124—2411no—
93#124C2×D24111yescharacteristic
94#123—4822no—
95C22⋊Q8—4822no—
96#117—4822no—
97#117—2411no—
98#99—4822no—
99#99—2412no—
100#99C2×D24112yes—
101#41—9642no—
102C2×Q8—9642no—
103C2×Q8—4821no—
104C2×Q8—2411no—
105C2×Q8—2411no—
106C2×Q8C4×D24111yescharacteristic
107C2×D4—2412no—
108C2×D4C22×D24111yescharacteristic
109C22×C4—4821no—
110C22×C4—2412no—
111C22×C4—2411no—
112C4⋊C4—9642no—
113C4⋊C4—4821no—
114C4⋊C4—4822no—
115C4⋊C4—4822no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—4821no—
119C22⋊C4—4822no—
120C22⋊C4—4822no—
121C42—9642no—
122C42—2411no—
123C42C4×D24111yescharacteristic
124C23—2411no—
125C23D4×D24112yes—
126Q8—41no—
127Q8—9641no—
128Q8—9641no—
129Q8—9642no—
130D4—41no—
131D4—9642no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—9642no—
136C2×C4—9642no—
137C2×C4—4822no—
138C2×C4—4821no—
139C2×C4—4821no—
140C2×C4—4822no—
141C2×C4—4822no—
142C2×C4—2412no—
143C2×C4—2411no—
144C2×C4C2×C4×D24111yescharacteristic
145C22—22no—
146C22—42no—
147C22—9641no—
148C22—4821no—
149C22C22⋊C4×D24111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—19282no—
155C4—9641no—
156C4—9641no—
157C4—4822no—
158C4—2412no—
159C2—21no—
160C2—42no—
161C2—9641no—
162C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#354×C241C2
socleC2×C241C2×#99
prime radicalC2×#16838769C22
cosocleC2×D4×C241C23
hypercenter#354D241
hypocenterC241#2129
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
3. #29507512C2semidirect
4. #29507511C2semidirect
5. #354×C241C2semidirect
7. C2×Q8×D241C4semidirect
8. #21440642C4semidirect
9. #21440640C4semidirect
13. #21440599C4semidirect
81. C241#2129semidirect
87. #354D241semidirect

Maximal subgroups

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

subgroupindex
#295082872
#295076892
#295075122
#295075112
#354×C2412
#2129241