Finite Group Databasebeta

← #44506472

Subgroups — #44506472

Order 30848.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508343C211yesmaximal, characteristic
2#29508053C212yesmaximal, complemented
3#29507653C211yesmaximal, characteristic
4#29507455C212yesmaximal, complemented
5#323×C241C211yesmaximal, characteristic
6#21440621—21no—
7#21440621C2212yes—
8#21440619—22no—
9#21440619—22no—
10C2×C4⋊Dic241C2211yescharacteristic
11C2×#16838749—21no—
12C2×C22⋊Dic241—21no—
13C2×C22⋊Dic241—21no—
14#21440576—22no—
15#21440567—22no—
16#21440549C2211yescharacteristic
17C2×C22⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19C2×Dic482—21no—
20C2×Dic482D412yes—
21C22×Dic241—21no—
22C22×Dic241—21no—
23C22×Dic241—21no—
24C22×Dic241—21no—
25C4⋊Dic241—21no—
26C4⋊Dic241—22no—
27C4⋊Dic241D412yes—
28#16838749—22no—
29#16838749—22no—
30#16838749—42no—
31C22⋊Dic241—22no—
32C22⋊Dic241—22no—
33C22⋊Dic241—42no—
34C24×C241D411yescharacteristic
35C22×C4×C241D411yescharacteristic
36C22×C4×C241C2311yescharacteristic
37C2×C8×C241—22no—
38C22⋊C4×C241—22no—
39Dic482—42no—
40Dic482—81no—
41C2×Dic241—22no—
42C2×Dic241—22no—
43C2×Dic241—22no—
44C2×Dic241—41no—
45C2×Dic241—41no—
46C2×Dic241—41no—
47C2×Dic241—41no—
48C2×Dic241—41no—
49C2×Dic241—81no—
50C2×Dic241—81no—
51C23×C241—21no—
52C23×C241—21no—
53C23×C241—41no—
54C23×C241—41no—
55C23×C241Q1612yes—
56C23×C241C2×D411yescharacteristic
57C2×C4×C241—21no—
58C2×C4×C241—41no—
59C2×C4×C241—41no—
60C2×C4×C241C2×D412yes—
61C8×C241—42no—
62C22×C241—21no—
63C22×C241—21no—
64C22×C241—22no—
65C22×C241—42no—
66C22×C241—41no—
67C22×C241—41no—
68C22×C241—81no—
69C22×C241#12011yescharacteristic
70C22×C241C2×Q1611yescharacteristic
71C22×C241#13711yescharacteristic
72C4×C241—22no—
73C4×C241—41no—
74Dic241—42no—
75Dic241—42no—
76Dic241—42no—
77Dic241—81no—
78C2×C241—21no—
79C2×C241—21no—
80C2×C241—42no—
81C2×C241#45111yescharacteristic
82C2×C241#45311yescharacteristic
83C2×C241#45811yescharacteristic
84C241#161411yescharacteristic, complemented, Sylow
85#1614—2411nomaximal, Sylow
86#543—2411no—
87#484—2412no—
88#399—2411no—
89#328—2412no—
90#323D24111yescharacteristic
91C22⋊Q8—4822no—
92C22⋊Q8—4822no—
93C22⋊Q8—4821no—
94C22⋊Q8—2412no—
95C2×C4⋊C4—4821no—
96C2×C4⋊C4—2411no—
97C2×C22⋊C4—4821no—
98C2×C22⋊C4—4821no—
99C2×C22⋊C4C2×D24111yescharacteristic
100#107—4822no—
101#103—4822no—
102C22⋊C8C2×D24112yes—
103#95—2411no—
104C24D96411yescharacteristic
105C2×Q8—4821no—
106C2×Q8—2412no—
107C22×C4—4821no—
108C22×C4—4821no—
109C22×C4—4821no—
110C22×C4—4821no—
111C22×C4D96411yescharacteristic
112C22×C4C22×D24111yescharacteristic
113C2×C8—22no—
114C4⋊C4—9642no—
115C4⋊C4—4822no—
116C4⋊C4—4821no—
117C4⋊C4—4822no—
118C4⋊C4—4822no—
119C4⋊C4—2412no—
120C22⋊C4—22no—
121C22⋊C4—9642no—
122C22⋊C4—4822no—
123C22⋊C4—4822no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic96412yes—
129C23C2×D96411yescharacteristic
130Q8—19281no—
131Q8—9642no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—19281no—
136C2×C4—19281no—
137C2×C4—9641no—
138C2×C4—9641no—
139C2×C4—9641no—
140C2×C4—9641no—
141C2×C4—9641no—
142C2×C4—4822no—
143C2×C4—4822no—
144C2×C4—4822no—
145C2×C4D4×D24112yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#2144061211yescharacteristic
155C22C2×Dic96411yescharacteristic
156C22#2144067511yescharacteristic
157C4—22no—
158C4—41no—
159C4—19281no—
160C4—9642no—
161C4—9642no—
162C4—9642no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2950787511yescharacteristic
167C2#2950788711yescharacteristic
168C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#323×C241C2
socleC22×C241#120
prime radicalC24×C241D4
hypercenter#323D241
hypocenterC241#1614
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #29508053C2semidirect
4. #29507455C2semidirect
84. C241#1614semidirect

Maximal subgroups

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

subgroupindex
#295083432
#295080532
#295076532
#295074552
#323×C2412
#1614241