Finite Group Databasebeta

← #44507893

Subgroups — #44507893

Order 30848.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#29508228C211yesmaximal, characteristic
2C2×#21440570C212yesmaximal, complemented
3#29507681C211yesmaximal, characteristic, complemented
4#29507477C212yesmaximal, complemented
5C2×#117×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2211yescharacteristic
7C2×#16838754C2212yes—
8#21440625—21no—
9#21440621C412yescomplemented
10#21440616C412yescomplemented
11#21440611—21no—
12C4×C22⋊D241—22no—
13#21440601C2211yescharacteristic
14#21440570—24no—
15C22⋊#14515349—22no—
16C23×C4×C241C2211yescharacteristic
17#117×C241—24no—
18C2×C4⋊C4×C241—21no—
19C2×C22⋊C4×C241—21no—
20C2×C42×C241C2212yes—
21#16838770—22no—
22#16838770—22no—
23C2×Dic482C2×C411yescharacteristic
24C2×D964C2×C411yescharacteristic
25C2×C22⋊D241—22no—
26C2×C22⋊D241—21no—
27C2×C4×D241—21no—
28#16838754—22no—
29#16838754—22no—
30C2×#14515349—22no—
31C4⋊Dic241C2×C412yes—
32#16838749—22no—
33C22⋊Dic241—22no—
34C22⋊Dic241—21no—
35#16838747—22no—
36C4×Dic241—21no—
37C24×C241D411yescharacteristic
38C22×C4×C241—22no—
39C22×C4×C241—22no—
40C22×C4×C241—22no—
41C22×C4×C241C2×C412yes—
42C22×C4×C241D411yescharacteristic
43C22×C4×C241D412yes—
44C22×C4×C241C2311yescharacteristic
45C4⋊C4×C241—24no—
46C22⋊C4×C241—24no—
47C42×C241—22no—
48C42×C241D414yescomplemented
49C22×D241—21no—
50Dic482—22no—
51D964—22no—
52C22⋊D241—44no—
53C22⋊D241—41no—
54C22⋊D241—41no—
55C2×Dic241—22no—
56C2×Dic241—21no—
57C4×D241—42no—
58#14515349—42no—
59C23×C241—21no—
60C23×C241—21no—
61C23×C241—42no—
62C23×C241C22⋊C412yes—
63C23×C241C2×D411yescharacteristic
64C2×C4×C241—21no—
65C2×C4×C241—21no—
66C2×C4×C241—24no—
67C2×C4×C241—24no—
68C2×C4×C241—24no—
69C2×C4×C241—44no—
70C2×C4×C241C22⋊C412yes—
71C2×C4×C241C22×C411yescharacteristic
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241#4112yes—
75C22×C241—22no—
76C22×C241—22no—
77C22×C241—22no—
78C22×C241—22no—
79C22×C241—42no—
80C22×C241—42no—
81C22×C241C2×C22⋊C411yescharacteristic
82C22×C241#12011yescharacteristic
83C22×C241#12311yescharacteristic
84C2×D241—41no—
85C2×D241—42no—
86C4×C241—22no—
87C4×C241—44no—
88C4×C241C4×D412yes—
89C4×C241#12112yes—
90Dic241—41no—
91Dic241—42no—
92C2×C241—21no—
93C2×C241—21no—
94C2×C241—42no—
95C2×C241#38611yescharacteristic
96C2×C241#42112yes—
97D241—81no—
98C241#189711yescharacteristic, complemented, Sylow
99#1897—2411nomaximal, Sylow
100#525—2411no—
101C2×#117D24111yescharacteristic, complemented
102C2×#104—2412no—
103#407—2411no—
104#339—2412no—
105C2×#41—2411no—
106C23×C4C2×D24111yescharacteristic
107C2×M16—2412no—
108#123—4821no—
109C22⋊Q8—2412no—
110#121—2412no—
111#120—4821no—
112C4×D4—4822no—
113#117—24no—
114#117—2411no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D24112yes—
118#104—4824no—
119C22⋊C8—4822no—
120C24C22⋊D24111yescharacteristic
121#41—4822no—
122#41—4822no—
123C2×Q8—2411no—
124C2×D4—4822no—
125C2×D4—4821no—
126C2×D4—2411no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—4821no—
131C22×C4C4×D24112yes—
132C22×C4C22⋊D24111yescharacteristic
133C22×C4D96412yes—
134C22×C4C22×D24111yescharacteristic
135M16—4822no—
136M16—4822no—
137C2×C8—4822no—
138C4⋊C4—24no—
139C4⋊C4—4822no—
140C4⋊C4—2412no—
141C22⋊C4—24no—
142C22⋊C4—4822no—
143C22⋊C4—4821no—
144C22⋊C4—4822no—
145C42—22no—
146C42—4821no—
147C42C22⋊D24114yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—4821no—
152C23#1683874712yes—
153C23C2×C22⋊D24111yescharacteristic
154Q8—4822no—
155D4—9644no—
156D4—9641no—
157D4—9641no—
158D4—4822no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—9642no—
166C2×C4—4822no—
167C2×C4—4821no—
168C2×C4#1683874712yes—
169C2×C4C2×C4×D24111yescharacteristic
170C2×C4C2×C22⋊D24112yes—
171C2×C4C2×D96411yescharacteristic
172C2×C4#1683877012yes—
173C8—9642no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—9641no—
181C22—9642no—
182C22C2×#1683874711yescharacteristic
183C22#2144061111yescharacteristic
184C22#2144062511yescharacteristic
185C4—22no—
186C4—44no—
187C4—9641no—
188C4—9642no—
189C4C4×C22⋊D24112yes—
190C4#2144061612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—19281no—
195C2#2950759611yescharacteristic
196C2#2950773512yes—
subgroupG/H
centerC2×C4C2×D964
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC2×#117×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508228C2
cosocleC22×C4×C241C23
hypercenterC2×#117D241
hypocenterC241#1897
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#21440570C2semidirect
3. #29507681C2semidirect
4. #29507477C2semidirect
5. C2×#117×C241C2semidirect
9. #21440621C4semidirect
10. #21440616C4semidirect
48. C42×C241D4semidirect
98. C241#1897semidirect
101. C2×#117D241semidirect
147. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082282
C2×#214405702
#295076812
#295074772
C2×#117×C2412
#1897241