Finite Group Databasebeta

← #44506464

Subgroups — #44506464

Order 30848.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508279C211yesmaximal, characteristic
2#29508035C212yesmaximal, complemented
3#29507450C212yesmaximal, complemented
4#29507441C211yesmaximal, characteristic, complemented
5#399×C241C211yesmaximal, characteristic, complemented
6C22×C22⋊D241—21no—
7#21440626—22no—
8#21440616—21no—
9#21440616C2212yes—
10#21440612—22no—
11#21440573—22no—
12#21440562—22no—
13C22⋊#14515349C2212yescomplemented
14C2×C4⋊C4×C241—21no—
15C2×C4⋊C4×C241C2211yescharacteristic, complemented
16C2×C22⋊C4×C241—21no—
17C2×C22⋊C4×C241C2211yescharacteristic
18#95×C241C2211yescharacteristic, complemented
19C23×D241—21no—
20C2×D964—21no—
21C2×D964D412yes—
22C2×C22⋊D241—22no—
23C2×C22⋊D241—22no—
24C2×C22⋊D241—42no—
25C2×C22⋊D241—42no—
26C22×Dic241—21no—
27C2×#14515349—22no—
28C4⋊Dic241—21no—
29C4⋊Dic241D412yes—
30#16838747—22no—
31#16838747—22no—
32C24×C241D411yescharacteristic
33C22×C4×C241—21no—
34C22×C4×C241—21no—
35C22×C4×C241D411yescharacteristic
36C22×C4×C241C2311yescharacteristic
37C4⋊C4×C241—22no—
38C4⋊C4×C241—42no—
39C22⋊C4×C241—22no—
40C22⋊C4×C241—42no—
41C22×D241—22no—
42C22×D241—42no—
43C22×D241—81no—
44C22×D241—81no—
45D964—42no—
46D964—81no—
47C22⋊D241—44no—
48C22⋊D241—42no—
49C22⋊D241—42no—
50C2×Dic241—22no—
51C2×Dic241—42no—
52#14515349—42no—
53C23×C241—21no—
54C23×C241—21no—
55C23×C241—41no—
56C23×C241—41no—
57C23×C241SD1612yes—
58C23×C241C2×D411yescharacteristic
59C2×C4×C241—22no—
60C2×C4×C241—21no—
61C2×C4×C241—41no—
62C2×C4×C241—41no—
63C2×C4×C241—41no—
64C2×C4×C241—41no—
65C2×C4×C241—41no—
66C2×C4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241C2×D412yes—
69C22×C241—21no—
70C22×C241—21no—
71C22×C241—22no—
72C22×C241—42no—
73C22×C241—41no—
74C22×C241—41no—
75C22×C241—81no—
76C22×C241#12011yescharacteristic
77C22×C241C2×SD1611yescharacteristic
78C22×C241AGL(1,ℤ/8)11yescharacteristic
79C2×D241—42no—
80C2×D241—42no—
81C2×D241—42no—
82C2×D241—84no—
83C4×C241—22no—
84C4×C241—42no—
85C4×C241—41no—
86C4×C241—81no—
87Dic241—42no—
88C2×C241—21no—
89C2×C241—21no—
90C2×C241—42no—
91C2×C241#45011yescharacteristic
92C2×C241#45311yescharacteristic
93C2×C241#45811yescharacteristic
94D241—82no—
95C241#161311yescharacteristic, complemented, Sylow
96#1613—2411nomaximal, Sylow
97#534—2411no—
98#481—2412no—
99#399D24111yescharacteristic, complemented
100#327—2412no—
101#323—2411no—
102C22×D4—4821no—
103#123—4822no—
104#121—4821no—
105#121—2412no—
106#120—4822no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D24111yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D24111yescharacteristic
111#106—4822no—
112#102—4822no—
113C22⋊C8—2412no—
114#95C2×D24111yescharacteristic, complemented
115C24—4821no—
116C24C22⋊D24111yescharacteristic
117C2×D4—9642no—
118C2×D4—9642no—
119C2×D4—4821no—
120C2×D4—4822no—
121C2×D4—4822no—
122C2×D4—2412no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—4821no—
126C22×C4C22⋊D24111yescharacteristic
127C22×C4C22×D24111yescharacteristic
128C2×C8—4822no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—4821no—
132C4⋊C4—2412no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—4822no—
136C22⋊C4—4822no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—19281no—
142C23—19281no—
143C23—9642no—
144C23—4822no—
145C23#1683875712yes—
146C23C2×C22⋊D24111yescharacteristic
147D4—19281no—
148D4—9642no—
149D4—9644no—
150D4—9642no—
151D4—9642no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—9642no—
162C2×C4—4822no—
163C2×C4D4×D24112yes—
164C8—9642no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—19284no—
173C22—9642no—
174C22—9642no—
175C22—9642no—
176C22#2144061011yescharacteristic
177C22C2×#1683875711yescharacteristic
178C22#2144066711yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—9642no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—19282no—
188C2#2950786711yescharacteristic
189C2#2950788411yescharacteristic
190C2#2950790611yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#399×C241C2
socleC22×C241#120
prime radical#29508279C2
hypercenter#399D241
hypocenterC241#1613
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #29508035C2semidirect
3. #29507450C2semidirect
4. #29507441C2semidirect
5. #399×C241C2semidirect
13. C22⋊#14515349C22semidirect
15. C2×C4⋊C4×C241C22semidirect
18. #95×C241C22semidirect
95. C241#1613semidirect
99. #399D241semidirect
108. C2×C4⋊C4C2×D241semidirect
114. #95C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082792
#295080352
#295074502
#295074412
#399×C2412
#1613241