Finite Group Databasebeta

← #44507362

Subgroups — #44507362

Order 30848.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16838770C211yesmaximal, characteristic
2C2×#21440556C214yesmaximal, complemented
3#29507580C211yesmaximal, characteristic, complemented
4#381×C241C211yesmaximal, characteristic, complemented
5C2×#16838770—28no—
6C2×#16838770—22no—
7C2×#16838770—22no—
8C22×Dic482C411yescharacteristic, complemented
9C22×D964C411yescharacteristic, complemented
10C22×C22⋊D241C2212yes—
11C22×C4×D241C412yescomplemented
12C2×C22⋊Dic241C2212yes—
13#21440556—28no—
14#21440549—22no—
15C23×C4×C241C2211yescharacteristic
16C2×C22⋊C4×C241C2212yes—
17#95×C241—22no—
18C23×D241C2×C412yes—
19#16838770—216no—
20#16838770—216no—
21C2×Dic482—24no—
22C2×Dic482—22no—
23C2×D964—24no—
24C2×D964—22no—
25C2×C22⋊D241—24no—
26C2×C22⋊D241—22no—
27C2×C22⋊D241—22no—
28C2×C22⋊D241D418yes—
29C22×Dic241—22no—
30C22×Dic241C2×C412yes—
31C2×C4×D241—24no—
32C2×C4×D241—24no—
33C2×C4×D241—24no—
34C22⋊Dic241—24no—
35C24×C241C2311yescharacteristic
36C22×C4×C241—24no—
37C22×C4×C241—22no—
38C22×C4×C241C2×C411yescharacteristic
39C22×C4×C241C2×C411yescharacteristic
40C22×C4×C241D412yes—
41C22×C4×C241D412yes—
42C22⋊C4×C241—24no—
43C22×D241—22no—
44C22×D241—22no—
45C22×D241—44no—
46C22×D241C22⋊C414yes—
47Dic482—28no—
48D964—28no—
49C22⋊D241—28no—
50C22⋊D241—28no—
51C2×Dic241—22no—
52C2×Dic241—22no—
53C2×Dic241—44no—
54C2×Dic241—42no—
55C2×Dic241C22⋊C414yes—
56C4×D241—216no—
57C23×C241—42no—
58C23×C241C22×C411yescharacteristic
59C23×C241C2×D414yes—
60C23×C241C2×D411yescharacteristic
61C23×C241C2×D411yescharacteristic
62C2×C4×C241—22no—
63C2×C4×C241—22no—
64C2×C4×C241—24no—
65C2×C4×C241—24no—
66C2×C4×C241—44no—
67C2×C4×C241—42no—
68C2×C4×C241C22⋊C412yes—
69C2×C4×C241C22⋊C412yes—
70C22×C241—22no—
71C22×C241—22no—
72C22×C241—22no—
73C22×C241—44no—
74C22×C241C2×C22⋊C412yes—
75C22×C241C2×C22⋊C411yescharacteristic
76C22×C241#12012yes—
77C22×C241#12012yes—
78C2×D241—24no—
79C2×D241—44no—
80C2×D241—44no—
81C2×D241—44no—
82C4×C241—22no—
83C4×C241—22no—
84C4×C241—82no—
85Dic241—24no—
86Dic241—82no—
87C2×C241—22no—
88C2×C241—22no—
89C2×C241—22no—
90C2×C241#37911yescharacteristic
91C2×C241#41012yes—
92D241—44no—
93C241#178211yescharacteristic, complemented, Sylow
94#1782—2411nomaximal, Sylow
95C22×#41—2411no—
96C2×#99—2414no—
97#381—2411no—
98#381D24111yescharacteristic, complemented
99C2×#41—4828no—
100C2×#41—4822no—
101C2×#41—4822no—
102C22×Q8—2411no—
103C22×D4—2412no—
104C22×D4—2411no—
105C23×C4—2412no—
106C23×C4C2×D24111yescharacteristic
107C2×C22⋊C4—2412no—
108C2×C22⋊C4C2×D24112yes—
109#99—4828no—
110#95—22no—
111#95—4822no—
112C24—2412no—
113C24C22×D24111yescharacteristic
114#41—48216no—
115#41—48216no—
116C2×Q8—4824no—
117C2×Q8—4822no—
118C2×D4—4824no—
119C2×D4—4824no—
120C2×D4—4822no—
121C2×D4—4822no—
122C2×D4—4822no—
123C2×D4—2418no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—4824no—
127C22×C4—4824no—
128C22×C4—4822no—
129C22×C4—4824no—
130C22×C4—2412no—
131C22×C4C4×D24111yescharacteristic
132C22×C4C4×D24111yescharacteristic
133C22×C4C22⋊D24112yes—
134C22×C4D96412yes—
135C22⋊C4—24no—
136C22⋊C4—4824no—
137C23—42no—
138C23—9644no—
139C23—4822no—
140C23—4822no—
141C23—2414no—
142C23C2×C4×D24111yescharacteristic
143C23D4×D24114yes—
144C23C2×C22⋊D24111yescharacteristic
145C23C2×D96411yescharacteristic
146Q8—4828no—
147D4—4828no—
148D4—4828no—
149D4—4828no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—9644no—
157C2×C4—9642no—
158C2×C4—48216no—
159C2×C4—4822no—
160C2×C4—4822no—
161C2×C4—2414no—
162C2×C4#1683874712yes—
163C2×C4#1683874712yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—9644no—
169C22—9644no—
170C22—9644no—
171C22—4824no—
172C22C22⋊C4×D24112yes—
173C22C2×#1683874711yescharacteristic
174C22#2144061012yes—
175C22#2144061212yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—19282no—
180C4—4824no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—9644no—
185C2#2950757211yescharacteristic
186C2#2950769012yes—
subgroupG/H
centerC22C2×#16838747
commutatorC23×C241C22×C4
FrattiniC24C22×D241
Fitting#381×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×#16838770C2
cosocleC24×C241C23
hypercenter#381D241
hypocenterC241#1782
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#21440556C2semidirect
3. #29507580C2semidirect
4. #381×C241C2semidirect
8. C22×Dic482C4semidirect
9. C22×D964C4semidirect
11. C22×C4×D241C4semidirect
93. C241#1782semidirect
98. #381D241semidirect

Maximal subgroups

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

subgroupindex
C22×#168387702
C2×#214405562
#295075802
#381×C2412
#1782241