Finite Group Databasebeta

← #44509131

Subgroups — #44509131

Order 30848.

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

normal subgroups only

This group has 230 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#101×D241C212yesmaximal, complemented
3#29507515C212yesmaximal, complemented
4#29507514C211yesmaximal, characteristic, complemented
5#355×C241C211yesmaximal, characteristic, complemented
6C2×#16838769C411yescharacteristic
7C2×Q8×D241C2211yescharacteristic
8M16×D241—22no—
9#21440642C411yescharacteristic
10#21440640C2211yescharacteristic
11#21440629C411yescharacteristic
12#21440624—22no—
13#21440619—22no—
14#21440599C411yescharacteristic
15#21440561C2212yes—
16#21440560—22no—
17#124×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838769—42no—
20C2×Dic482C2×C411yescharacteristic
21C2×Dic482C2×C411yescharacteristic
22C2×Dic482D412yes—
23Q8×D241—42no—
24C2×C22⋊D241—21no—
25C22×Dic241—21no—
26C2×C4×D241C2×C411yescharacteristic
27C2×C4×D241D412yes—
28#16838754—22no—
29#16838753—42no—
30C8×D241—42no—
31C4⋊Dic241—22no—
32#16838749—21no—
33#16838749—22no—
34C22⋊Dic241—22no—
35#16838747—21no—
36C4×Dic241C2×C411yescharacteristic
37C2×Q8×C241C2311yescharacteristic
38C2×D4×C241C2×C411yescharacteristic
39M16×C241—22no—
40C22⋊C4×C241—22no—
41C42×C241C2×C411yescharacteristic
42C22×D241C22⋊C411yescharacteristic
43Dic482—41no—
44Dic482—42no—
45Dic482—41no—
46C22⋊D241—42no—
47C2×Dic241—21no—
48C2×Dic241—21no—
49C2×Dic241—42no—
50C2×Dic241C22⋊C412yes—
51C2×Dic241C22⋊C411yescharacteristic
52C4×D241—22no—
53C4×D241—22no—
54C4×D241—22no—
55#14515349—42no—
56C23×C241—21no—
57Q8×C241—41no—
58D4×C241—41no—
59C2×C4×C241—21no—
60C2×C4×C241C22×C411yescharacteristic
61C2×C4×C241C2×D412yes—
62C8×C241—42no—
63C22×C241—42no—
64C22×C241—41no—
65C22×C241C2×C22⋊C411yescharacteristic
66C2×D241—41no—
67C2×D241#9912yes—
68C4×C241—22no—
69C4×C241—21no—
70C4×C241—41no—
71Dic241—21no—
72Dic241—22no—
73Dic241—41no—
74Dic241—41no—
75C2×C241—21no—
76C2×C241—81no—
77C2×C241C2×#9911yescharacteristic
78D241—22no—
79C241#213311yescharacteristic, complemented, Sylow
80#2133—2411nomaximal, Sylow
81#536—2411no—
82C2×#101—2412no—
83#356—2412no—
84#355—2411no—
85#355D24111yescharacteristic, complemented
86C2×#41—2411no—
87C22×Q8—2411no—
88C2×M16—4822no—
89C4⋊Q8—2411no—
90C4⋊Q8—2411no—
91#124—2411no—
92#124C2×D24111yescharacteristic
93#123—4822no—
94C22⋊Q8—4822no—
95#117—2411no—
96#101—4822no—
97#101—2412no—
98#101C2×D24112yes—
99#41—9642no—
100C2×Q8—9642no—
101C2×Q8—2411no—
102C2×Q8—2411no—
103C2×Q8—2412no—
104C2×Q8C22×D24111yescharacteristic
105C2×D4—4821no—
106C2×D4C4×D24111yescharacteristic
107C22×C4—4821no—
108C22×C4—2411no—
109C22×C4—2412no—
110M16—22no—
111M16—9642no—
112M16—4822no—
113C2×C8—9642no—
114C4⋊C4—4821no—
115C4⋊C4—4822no—
116C4⋊C4—4822no—
117C22⋊C4—22no—
118C22⋊C4—4821no—
119C22⋊C4—4822no—
120C42—2411no—
121C42C4×D24111yescharacteristic
122C23—21no—
123C23—2411no—
124Q8—41no—
125Q8—9641no—
126Q8—9642no—
127Q8—9641no—
128D4—41no—
129D4—9642no—
130C2×C4—21no—
131C2×C4—9642no—
132C2×C4—4822no—
133C2×C4—4822no—
134C2×C4—4822no—
135C2×C4—4821no—
136C2×C4—4821no—
137C2×C4—2412no—
138C2×C4—2411no—
139C2×C4C2×C4×D24111yescharacteristic
140C2×C4D4×D24112yes—
141C8—42no—
142C8—9642no—
143C22—42no—
144C22—41no—
145C22—9641no—
146C22—2412no—
147C22C22⋊C4×D24111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—9641no—
152C4—9641no—
153C4—4821no—
154C4—4822no—
155C2—21no—
156C2—81no—
157C2—4822no—
158C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×Q8C22×D241
Fitting#355×C241C2
socleC2×C241C2×#99
prime radicalC2×#16838769C4
cosocleC2×Q8×C241C23
hypercenter#355D241
hypocenterC241#2133
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D241C2semidirect
3. #29507515C2semidirect
4. #29507514C2semidirect
5. #355×C241C2semidirect
79. C241#2133semidirect
85. #355D241semidirect

Maximal subgroups

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

subgroupindex
#295082872
#101×D2412
#295075152
#295075142
#355×C2412
#2133241