Finite Group Databasebeta

← #44507524

Subgroups — #44507524

Order 30848.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4⋊C4×D241C211yesmaximal, characteristic
2#29507680C212yesmaximal
3#29507486C211yesmaximal, characteristic, complemented
4#29507485C212yesmaximal, complemented
5#343×C241C211yesmaximal, characteristic, complemented
6C22×C4×D241C412yes—
7C22×C4×D241C2211yescharacteristic
8C2×#16838754C2212yes—
9C2×C4⋊Dic241C2211yescharacteristic
10C2×#16838749C412yes—
11C4⋊C4×D241—22no—
12C4⋊C4×D241—22no—
13#21440554—22no—
14#21440554—22no—
15C2×M16×C241C2212yes—
16C2×C4⋊C4×C241C2211yescharacteristic
17C23×D241C2×C411yescharacteristic
18C22×Dic241C2×C411yescharacteristic
19C22×Dic241C2×C412yes—
20C2×C4×D241—22no—
21C2×C4×D241—22no—
22C2×C4×D241—21no—
23C2×C4×D241—22no—
24C2×C4×D241—21no—
25C2×C4×D241—44no—
26C2×C4×D241D412yes—
27C2×C4×D241D412yes—
28#16838754—22no—
29#16838754—22no—
30C2×#14515349—22no—
31C4⋊Dic241—22no—
32#16838749—24no—
33C22×C4×C241C2×C412yes—
34C22×C4×C241C2311yescharacteristic
35M16×C241—22no—
36M16×C241—22no—
37C2×C8×C241—22no—
38C4⋊C4×C241—22no—
39C22×D241—21no—
40C22×D241—21no—
41C22×D241—22no—
42C22×D241—22no—
43C22×D241C22⋊C411yescharacteristic
44C22×D241C22⋊C411yescharacteristic
45C2×Dic241—21no—
46C2×Dic241—21no—
47C2×Dic241—22no—
48C2×Dic241—42no—
49C2×Dic241C22⋊C412yes—
50C4×D241—22no—
51C4×D241—22no—
52C4×D241—22no—
53C4×D241—22no—
54C4×D241—44no—
55C4×D241—44no—
56#14515349—42no—
57C23×C241C22×C411yescharacteristic
58C2×C4×C241—22no—
59C2×C4×C241—42no—
60C2×C4×C241C2×D412yes—
61C2×C4×C241#4111yescharacteristic
62C2×C4×C241#4112yes—
63C2×C4×C241#4111yescharacteristic
64C8×C241—42no—
65C22×C241—21no—
66C22×C241—21no—
67C22×C241C2×C22⋊C411yescharacteristic
68C22×C241#11711yescharacteristic
69C22×C241#11711yescharacteristic
70C2×D241—24no—
71C2×D241—24no—
72C2×D241—21no—
73C2×D241—21no—
74C2×D241—21no—
75C2×D241—21no—
76C2×D241#10012yes—
77C2×D241#10112yes—
78C4×C241—42no—
79C4×C241#12312yes—
80C4×C241#12312yes—
81Dic241—22no—
82Dic241—42no—
83C2×C241—21no—
84C2×C241—21no—
85C2×C241#38111yescharacteristic
86C2×C241C2×#10011yescharacteristic
87C2×C241C2×#10111yescharacteristic
88D241—22no—
89D241—22no—
90C241#182111yescharacteristic, complemented, Sylow
91#1821—2411nomaximal, Sylow
92C22×C4⋊C4—2411no—
93#407—2412no—
94#343—2412no—
95#343—2411no—
96#343D24111yescharacteristic, complemented
97C23×C4—2412no—
98C23×C4—2411no—
99C2×M16—2412no—
100C2×M16C2×D24112yes—
101C2×C4⋊C4—4822no—
102C2×C4⋊C4—4822no—
103C2×C4⋊C4—2412no—
104C2×C4⋊C4—2411no—
105C2×C4⋊C4C2×D24111yescharacteristic
106C22⋊C8—4822no—
107C22⋊C8—4822no—
108C24—2411no—
109C22×C4—9644no—
110C22×C4—4822no—
111C22×C4—4822no—
112C22×C4—4821no—
113C22×C4—4822no—
114C22×C4—4821no—
115C22×C4—2412no—
116C22×C4—2411no—
117C22×C4—2412no—
118C22×C4—2412no—
119C22×C4C4×D24112yes—
120C22×C4C22×D24111yescharacteristic
121M16—22no—
122M16—22no—
123M16—4822no—
124M16—4822no—
125C2×C8—22no—
126C2×C8—4822no—
127C4⋊C4—22no—
128C4⋊C4—4824no—
129C4⋊C4—4822no—
130C23—4822no—
131C23—4822no—
132C23—4821no—
133C23—4821no—
134C23—2411no—
135C23—2411no—
136C23C2×C4×D24111yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—9644no—
140C2×C4—9644no—
141C2×C4—9642no—
142C2×C4—4822no—
143C2×C4—4821no—
144C2×C4—4821no—
145C2×C4—4822no—
146C2×C4—4822no—
147C2×C4—4822no—
148C2×C4—4822no—
149C2×C4—2412no—
150C2×C4D4×D24112yes—
151C2×C4#1683876911yescharacteristic
152C2×C4#1683877012yes—
153C2×C4#1683877111yescharacteristic
154C8—42no—
155C8—9642no—
156C22—21no—
157C22—21no—
158C22—4824no—
159C22—4824no—
160C22—4821no—
161C22—4821no—
162C22—4821no—
163C22—4821no—
164C22—2412no—
165C22—2412no—
166C22C22⋊C4×D24111yescharacteristic
167C22#2144059911yescharacteristic
168C22#2144060011yescharacteristic
169C4—42no—
170C4—9642no—
171C4—4822no—
172C4#2144062412yes—
173C4#2144062712yes—
174C2—21no—
175C2—21no—
176C2—4822no—
177C2—4822no—
178C2#2950757911yescharacteristic
179C2#100×D24111yescharacteristic
180C2#101×D24111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC23×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#343×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC23×D241C2×C4
cosocleC22×C4×C241C23
hypercenter#343D241
hypocenterC241#1821
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #29507486C2semidirect
4. #29507485C2semidirect
5. #343×C241C2semidirect
90. C241#1821semidirect
96. #343D241semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2412
#295076802
#295074862
#295074852
#343×C2412
#1821241