Finite Group Databasebeta

← #44507835

Subgroups — #44507835

Order 30848.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#21440640C211yesmaximal, characteristic
2#29508194C211yesmaximal, characteristic
3#29507726C211yesmaximal, characteristic
4C2×#21440560C211yesmaximal, characteristic
5#29507478C211yesmaximal, characteristic
6#29507476C211yesmaximal, characteristic
7#419×C241C211yesmaximal, characteristic
8C22×Dic482C2211yescharacteristic
9C2×#16838754C2211yescharacteristic
10#21440640—22no—
11#21440640C414yescomplemented
12C4×Dic482—22no—
13#21440607—22no—
14#21440601C2211yescharacteristic
15#21440598—22no—
16C2×#16838749—22no—
17C2×C4×Dic241C2211yescharacteristic
18#21440566—22no—
19#21440560—22no—
20C22×Q8×C241C2211yescharacteristic
21C2×M16×C241C2211yescharacteristic
22#117×C241C2211yescharacteristic
23#103×C241—22no—
24C2×Dic482—21no—
25C2×Dic482—21no—
26C2×Dic482—21no—
27C2×Dic482—21no—
28C2×Dic482C2×C412yes—
29C2×Dic482D412yes—
30C22×Dic241—21no—
31C22×Dic241D412yes—
32#16838754—21no—
33#16838754—21no—
34C2×#14515349—21no—
35C4⋊Dic241D412yes—
36#16838749—24no—
37#16838749—28no—
38C22⋊Dic241—21no—
39C4×Dic241—24no—
40C4×Dic241—21no—
41C4×Dic241—21no—
42C4×Dic241C2×C412yes—
43C2×Q8×C241—21no—
44C2×Q8×C241—21no—
45C2×Q8×C241—21no—
46C2×Q8×C241—21no—
47C2×Q8×C241—21no—
48C2×Q8×C241C2×C412yes—
49C22×C4×C241—21no—
50C22×C4×C241C2311yescharacteristic
51M16×C241—21no—
52M16×C241—21no—
53C2×C8×C241—21no—
54C4⋊C4×C241D412yes—
55C22⋊C4×C241—21no—
56C42×C241—21no—
57Dic482—22no—
58Dic482—22no—
59Dic482—22no—
60Dic482—22no—
61C2×Dic241—24no—
62C2×Dic241—22no—
63C2×Dic241—22no—
64C2×Dic241—22no—
65C2×Dic241—22no—
66C2×Dic241C22⋊C414yes—
67#14515349—41no—
68C23×C241C2×D411yescharacteristic
69Q8×C241—22no—
70Q8×C241—22no—
71Q8×C241—41no—
72Q8×C241—41no—
73C2×C4×C241—22no—
74C2×C4×C241—22no—
75C2×C4×C241—41no—
76C2×C4×C241—41no—
77C2×C4×C241C22×C411yescharacteristic
78C2×C4×C241C2×D411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C2×C4×C241#4111yescharacteristic
82C2×C4×C241#4111yescharacteristic
83C8×C241—41no—
84C22×C241—22no—
85C22×C241C2×C22⋊C411yescharacteristic
86C22×C241#12011yescharacteristic
87C22×C241#12311yescharacteristic
88C4×C241—42no—
89C4×C241—42no—
90C4×C241C4×D411yescharacteristic
91C4×C241C4×D411yescharacteristic
92C4×C241#12111yescharacteristic
93C4×C241#12111yescharacteristic
94Dic241—24no—
95Dic241—24no—
96Dic241—42no—
97C2×C241—21no—
98C2×C241—21no—
99C2×C241#38611yescharacteristic
100C2×C241#45612yes—
101C241#188611yescharacteristic, complemented, Sylow
102#1886—2411nomaximal, Sylow
103C2×C4⋊Q8—2411no—
104#519—2411no—
105#419—2411no—
106#419D24111yescharacteristic
107C2×#101—2411no—
108#339—2411no—
109#339—2411no—
110C22×Q8—2411no—
111C22×Q8C2×D24111yescharacteristic
112C2×M16—2411no—
113C2×M16C2×D24111yescharacteristic
114C4⋊Q8—4822no—
115C4⋊Q8—2414no—
116C4×Q8—4822no—
117C4×Q8—4822no—
118#117—4822no—
119#117—2411no—
120#117C2×D24111yescharacteristic
121C2×C4⋊C4—4822no—
122C2×C42—2411no—
123#103—22no—
124#103—4822no—
125#101—4822no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—4821no—
132C2×Q8—4821no—
133C2×Q8—4821no—
134C2×Q8—4821no—
135C2×Q8—2412no—
136C2×Q8—2412no—
137C2×Q8C4×D24112yes—
138C22×C4—21no—
139C22×C4—4821no—
140C22×C4—2412no—
141C22×C4C22×D24111yescharacteristic
142M16—21no—
143M16—21no—
144M16—4821no—
145M16—4821no—
146C2×C8—21no—
147C2×C8—4821no—
148C4⋊C4—4824no—
149C4⋊C4—4828no—
150C4⋊C4—2412no—
151C4⋊C4C22⋊D24112yes—
152C22⋊C4—21no—
153C22⋊C4—4821no—
154C42—21no—
155C42—4824no—
156C42—4821no—
157C42—4821no—
158C42—2412no—
159C23D4×D24111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—4822no—
165Q8—4822no—
166Q8—4822no—
167Q8—4822no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—4822no—
173C2×C4—4824no—
174C2×C4—4822no—
175C2×C4—4822no—
176C2×C4—4822no—
177C2×C4—2414no—
178C2×C4C2×C4×D24111yescharacteristic
179C2×C4D4×D24111yescharacteristic
180C2×C4D4×D24111yescharacteristic
181C2×C4C2×C22⋊D24111yescharacteristic
182C2×C4#1683876911yescharacteristic
183C2×C4#1683877011yescharacteristic
184C8—41no—
185C8—9641no—
186C22—22no—
187C22C22⋊C4×D24111yescharacteristic
188C22#2144061011yescharacteristic
189C22#2144062411yescharacteristic
190C4—42no—
191C4—42no—
192C4—9642no—
193C4—4824no—
194C4—4824no—
195C4#2144060211yescharacteristic
196C4C4×C22⋊D24111yescharacteristic
197C4#2144061311yescharacteristic
198C4#2144061511yescharacteristic
199C2—21no—
200C2—21no—
201C2#2950759311yescharacteristic
202C2#2950789812yes—
subgroupG/H
centerC22#21440610
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#419×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
cosocleC22×C4×C241C23
hypercenter#419D241
hypocenterC241#1886
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #21440640C4semidirect
101. C241#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#214406402
#295081942
#295077262
C2×#214405602
#295074782
#295074762
#419×C2412
#1886241