Finite Group Databasebeta

← #44506078

Subgroups — #44506078

Order 30848.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#29508266C211yesmaximal, characteristic
2#29507772C212yesmaximal, complemented
3#29507457C211yesmaximal, characteristic, complemented
4#29507456C212yesmaximal, complemented
5#329×C241C211yesmaximal, characteristic, complemented
6C2×#16838771C411yescharacteristic
7C2×#16838769C411yescharacteristic
8#21440640C411yescharacteristic
9#21440638C411yescharacteristic
10#21440630C2211yescharacteristic
11#21440615—22no—
12#21440602—22no—
13C42×D241C2211yescharacteristic
14#21440571—22no—
15#21440554—22no—
16#21440553C2212yes—
17#124×C241C2211yescharacteristic
18#97×C241C2212yes—
19#16838771—42no—
20#16838769—42no—
21C2×Dic482C2×C411yescharacteristic
22C2×D964—21no—
23C2×D964C2×C411yescharacteristic
24C2×C22⋊D241—21no—
25C2×C22⋊D241—22no—
26C22×Dic241—21no—
27C2×C4×D241—21no—
28C2×C4×D241C2×C411yescharacteristic
29C2×C4×D241D412yes—
30C2×#14515349—22no—
31#16838749—22no—
32#16838747—22no—
33C4×Dic241C2×C411yescharacteristic
34C4×Dic241D412yes—
35C2×Q8×C241C2×C411yescharacteristic
36C2×D4×C241C2×C411yescharacteristic
37C2×C8×C241—22no—
38C22⋊C4×C241—22no—
39C42×C241C2311yescharacteristic
40C22×D241—21no—
41C22×D241C22⋊C411yescharacteristic
42Dic482—41no—
43D964—41no—
44D964—42no—
45C22⋊D241—44no—
46C22⋊D241—42no—
47C2×Dic241—21no—
48C2×Dic241—42no—
49C2×Dic241C22⋊C412yes—
50C2×Dic241C22⋊C411yescharacteristic
51C4×D241—22no—
52C4×D241—42no—
53C4×D241—42no—
54#14515349—42no—
55C23×C241—21no—
56Q8×C241—41no—
57D4×C241—41no—
58C2×C4×C241—21no—
59C2×C4×C241C22×C411yescharacteristic
60C2×C4×C241C2×D412yes—
61C8×C241—42no—
62C22×C241—41no—
63C22×C241—42no—
64C22×C241C2×C22⋊C411yescharacteristic
65C2×D241—21no—
66C2×D241—22no—
67C2×D241—41no—
68C2×D241—42no—
69C4×C241—21no—
70C4×C241—22no—
71C4×C241—41no—
72Dic241—22no—
73Dic241—41no—
74Dic241#10012yes—
75C2×C241—81no—
76C2×C241C2×#10011yescharacteristic
77C2×C241#42112yes—
78D241—41no—
79D241—81no—
80C241#153611yescharacteristic, complemented, Sylow
81#1536—2411nomaximal, Sylow
82#532—2411no—
83#432—2412no—
84#329—2411no—
85#329—2412no—
86#329D24111yescharacteristic, complemented
87C2×#41—2411no—
88C2×#41—2411no—
89C4⋊Q8—2411no—
90#127—2411no—
91#124—2411no—
92#124C2×D24111yescharacteristic
93#121—4822no—
94C4×D4—4822no—
95C2×C42—2411no—
96C4⋊C8—4822no—
97C22⋊C8—4822no—
98#97—2412no—
99#97C2×D24112yes—
100#41—9642no—
101#41—9642no—
102C2×Q8—2411no—
103C2×Q8C4×D24111yescharacteristic
104C2×D4—4821no—
105C2×D4—4821no—
106C2×D4—4822no—
107C2×D4—2411no—
108C2×D4C4×D24111yescharacteristic
109C22×C4—4821no—
110C22×C4—4821no—
111C22×C4—2412no—
112C22×C4—2411no—
113C2×C8—22no—
114C2×C8—4822no—
115C4⋊C4—4822no—
116C22⋊C4—22no—
117C22⋊C4—4822no—
118C42—2411no—
119C42—2412no—
120C42C22×D24111yescharacteristic
121C23—21no—
122C23—4821no—
123C23—2411no—
124Q8—41no—
125Q8—9641no—
126D4—41no—
127D4—9641no—
128D4—9642no—
129D4—9642no—
130D4—9644no—
131C2×C4—21no—
132C2×C4—9642no—
133C2×C4—9642no—
134C2×C4—9642no—
135C2×C4—4822no—
136C2×C4—4821no—
137C2×C4—2412no—
138C2×C4—2411no—
139C2×C4C2×C4×D24111yescharacteristic
140C2×C4D4×D24112yes—
141C8—42no—
142C8—9642no—
143C22—41no—
144C22—42no—
145C22—9641no—
146C22—9642no—
147C22—4821no—
148C22—4822no—
149C22C22⋊C4×D24111yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—9641no—
154C4—4822no—
155C4—2412no—
156C2—81no—
157C2—19281no—
158C2—9641no—
159C2#100×D24111yescharacteristic
160C2#2950773212yes—
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508266C2
cosocleC42×C241C23
hypercenter#329D241
hypocenterC241#1536
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29507772C2semidirect
3. #29507457C2semidirect
4. #29507456C2semidirect
5. #329×C241C2semidirect
80. C241#1536semidirect
86. #329D241semidirect

Maximal subgroups

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

subgroupindex
#295082662
#295077722
#295074572
#295074562
#329×C2412
#1536241