Finite Group Databasebeta

← #44509473

Subgroups — #44509473

Order 30848.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#29508433C211yesmaximal, characteristic, complemented
2#29507899C211yesmaximal, characteristic, complemented
3#29507892C212yesmaximal, complemented
4#29507513C212yesmaximal, complemented
5#356×C241C211yesmaximal, characteristic, complemented
6#21440690C2211yescharacteristic
7#21440673—21no—
8#21440670—22no—
9#21440631—21no—
10#21440631C2212yes—
11#21440617—22no—
12C4×D964—21no—
13#21440600—22no—
14#21440570—21no—
15#21440568—22no—
16#21440561C2211yescharacteristic
17C4⋊Q8×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838771—41no—
20#16838770—22no—
21#16838770—21no—
22Q8×D241—41no—
23C2×D964—21no—
24C2×D964—21no—
25C2×D964D412yes—
26C2×C4×D241—22no—
27#16838760—41no—
28#16838759—42no—
29#16838757—41no—
30D1928—42no—
31#16838754—21no—
32C4⋊Dic241—21no—
33#16838747—22no—
34#16838747—22no—
35#16838747—22no—
36C4×Dic241—21no—
37C4×Dic241D412yes—
38C2×Q8×C241D411yescharacteristic
39C2×Q8×C241C2311yescharacteristic
40M16×C241—22no—
41C4⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43C22×D241—22no—
44Dic482—22no—
45Dic482—21no—
46D964—22no—
47D964—21no—
48D964—42no—
49D964—42no—
50D964—81no—
51C22⋊D241—41no—
52C2×Dic241—22no—
53C4×D241—44no—
54C4×D241—42no—
55C4×D241—41no—
56#14515349—41no—
57Q8×C241—41no—
58Q8×C241—41no—
59C2×C4×C241—21no—
60C2×C4×C241—21no—
61C2×C4×C241C2×D412yes—
62C2×C4×C241C2×D411yescharacteristic
63C8×C241—42no—
64C22×C241#12011yescharacteristic
65C2×D241—42no—
66C2×D241—42no—
67C2×D241—41no—
68C2×D241—42no—
69C4×C241—22no—
70C4×C241—22no—
71C4×C241—21no—
72C4×C241—41no—
73Dic241—42no—
74Dic241—41no—
75C2×C241—21no—
76C2×C241B(4,𝔽2)11yescharacteristic
77D241—81no—
78D241—82no—
79C241#220411yescharacteristic, complemented, Sylow
80#2204—2411nomaximal, Sylow
81#555—2411no—
82#456—2411no—
83#454—2412no—
84#356D24111yescharacteristic, complemented
85#355—2412no—
862−1+4—2411no—
87#137—4821no—
88AGL(1,ℤ/8)—4822no—
89C4⋊Q8C2×D24111yescharacteristic
90#124—4821no—
91#124—2412no—
92#121—4822no—
93C4×D4—4821no—
94#117—4822no—
95#104—4822no—
96#104—4821no—
97#101—2411no—
98#101C2×D24112yes—
99#41—9641no—
100#41—4822no—
101#41—4821no—
102C2×Q8—9641no—
103C2×Q8D96411yescharacteristic
104C2×Q8C22×D24111yescharacteristic
105C2×D4—4821no—
106C2×D4—4821no—
107C2×D4—2412no—
108C22×C4—4822no—
109Q16—9641no—
110SD16—9642no—
111SD16—9641no—
112D8—9642no—
113M16—22no—
114M16—4821no—
115C4⋊C4—22no—
116C4⋊C4—4821no—
117C22⋊C4—4822no—
118C22⋊C4—4822no—
119C22⋊C4—4822no—
120C42—4821no—
121C42—2412no—
122C42D96411yescharacteristic
123C23—4822no—
124Q8—41no—
125Q8—41no—
126Q8—4822no—
127Q8—4821no—
128D4—19281no—
129D4—9642no—
130D4—9642no—
131D4—9641no—
132D4—4822no—
133D4—4821no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—9644no—
137C2×C4—9642no—
138C2×C4—9641no—
139C2×C4—4822no—
140C2×C4D4×D24112yes—
141C2×C4C2×D96411yescharacteristic
142C8—42no—
143C8—9641no—
144C22—9642no—
145C22—9642no—
146C22—9641no—
147C22—9642no—
148C22#2144061211yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—9642no—
154C4—9641no—
155C2—21no—
156C2—19282no—
157C2—19281no—
158C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×Q8×C241C23
FrattiniC2×Q8C22×D241
Fitting#356×C241C2
socleC2×C241B(4,𝔽2)
hypercenter#356D241
hypocenterC241#2204
LCSG ▷ C2×Q8×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #29508433C2semidirect
2. #29507899C2semidirect
3. #29507892C2semidirect
4. #29507513C2semidirect
5. #356×C241C2semidirect
79. C241#2204semidirect
84. #356D241semidirect

Maximal subgroups

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

subgroupindex
#295084332
#295078992
#295078922
#295075132
#356×C2412
#2204241