Finite Group Databasebeta

← #37572478

Subgroups — #37572478

Order 24448.

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

normal subgroups only

This group has 552 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
1C2×#20259370C211yesmaximal, characteristic
2C2×#20259250C212yesmaximal, complemented
3#27132662C212yesmaximal, complemented
4C2×#20259241C211yesmaximal, characteristic, complemented
5#391×C191C211yesmaximal, characteristic, complemented
6#20259370—24no—
7#20259370—22no—
8#20259370C414yescomplemented
9C2×#15690288—22no—
10C2×#15690287—22no—
11C2×#15690287C2212yes—
12C2×Q8×D191—22no—
13C2×#15690271C2212yes—
14#20259250—24no—
15#20259245—22no—
16#20259242—22no—
17#20259241—22no—
18C22×Q8×C191C2211yescharacteristic
19C2×C4⋊C4×C191C2211yescharacteristic
20C2×C42×C191C2211yescharacteristic
21#95×C191—22no—
22#15690288—28no—
23#15690288—28no—
24#15690287—28no—
25#15690287—28no—
26#15690287—22no—
27#15690287—22no—
28#15690287C2×C414yes—
29#15690287D414yes—
30C2×Dic382—22no—
31C2×Dic382D412yes—
32Q8×D191—28no—
33Q8×D191—28no—
34C2×D764—22no—
35C2×D764D412yes—
36C2×C22⋊D191—22no—
37C2×C4×D191—24no—
38C2×C4×D191—22no—
39#15690271—22no—
40#15690271—22no—
41C2×C191⋊C8—22no—
42C2×Q8×C191—22no—
43C2×Q8×C191—22no—
44C2×Q8×C191C2×C412yes—
45C2×Q8×C191D412yes—
46C22×C4×C191—21no—
47C22×C4×C191—21no—
48C22×C4×C191D412yes—
49C22×C4×C191C2311yescharacteristic
50C4⋊C4×C191—22no—
51C42×C191—22no—
52C22×D191—22no—
53Dic382—28no—
54Dic382—22no—
55Dic382C22⋊C414yes—
56D764—28no—
57D764—22no—
58D764C22⋊C414yes—
59C22⋊D191—24no—
60C22⋊D191—24no—
61C2×Dic191—22no—
62C4×D191—216no—
63C4×D191—24no—
64C4×D191—24no—
65C191⋊C8—42no—
66C23×C191C2×D411yescharacteristic
67Q8×C191—24no—
68Q8×C191—24no—
69C2×C4×C191—22no—
70C2×C4×C191—22no—
71C2×C4×C191—22no—
72C2×C4×C191—41no—
73C2×C4×C191—41no—
74C2×C4×C191—42no—
75C2×C4×C191—41no—
76C2×C4×C191C22⋊C414yes—
77C2×C4×C191C22×C411yescharacteristic
78C2×C4×C191C2×D412yes—
79C2×C4×C191C2×D412yes—
80C2×C4×C191C2×D411yescharacteristic
81C22×C191—21no—
82C22×C191—21no—
83C22×C191C2×C22⋊C411yescharacteristic
84C22×C191#12011yescharacteristic
85C22×C191#12011yescharacteristic
86C2×D191—24no—
87C2×D191—42no—
88C2×D191—42no—
89C4×C191—24no—
90C4×C191—42no—
91C4×C191—81no—
92C4×C191C2×C22⋊C412yes—
93C4×C191#12012yes—
94Dic191—24no—
95C2×C191—21no—
96C2×C191—21no—
97C2×C191#37911yescharacteristic
98C2×C191#45411yescharacteristic
99C2×C191#45611yescharacteristic
100D191—44no—
101C191#179311yescharacteristic, complemented, Sylow
102#1793—1911nomaximal, Sylow
103C2×2−1+4—1911no—
104C2×#104—1912no—
105#417—1912no—
106C2×#101—1911no—
107#391D19111yescharacteristic, complemented
1082−1+4—3824no—
1092−1+4—3822no—
1102−1+4—1914no—
111C2×#41—3822no—
112C2×#41—3822no—
113C2×#41—1912no—
114C22×Q8—3822no—
115C22×Q8C2×D19111yescharacteristic
116C2×M16—1912no—
117C2×C4⋊C4C2×D19111yescharacteristic
118C2×C42C2×D19111yescharacteristic
119#104—3824no—
120#103—3822no—
121#102—3822no—
122#101—3822no—
123#95—22no—
124#41—3828no—
125#41—3828no—
126#41—3828no—
127#41—3828no—
128#41—3822no—
129#41—3822no—
130#41—1914no—
131#41—1914no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—3822no—
135C2×Q8—3828no—
136C2×Q8—3828no—
137C2×Q8—1912no—
138C2×Q8C4×D19112yes—
139C2×Q8D76412yes—
140C2×D4—3822no—
141C2×D4—3822no—
142C2×D4—1912no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3824no—
146C22×C4—3822no—
147C22×C4C22⋊D19112yes—
148C22×C4C22×D19111yescharacteristic
149M16—3822no—
150M16—3822no—
151C2×C8—3822no—
152C4⋊C4—22no—
153C42—22no—
154C23—3822no—
155C23C2×C22⋊D19111yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—3828no—
159Q8—3822no—
160Q8—1914no—
161D4—3828no—
162D4—3824no—
163D4—3824no—
164D4—3822no—
165D4—1914no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—38216no—
174C2×C4—3822no—
175C2×C4—3824no—
176C2×C4—3824no—
177C2×C4(C2×D191)⋊C414yes—
178C2×C4C2×C4×D19111yescharacteristic
179C2×C4D4×D19112yes—
180C2×C4D4×D19112yes—
181C2×C4C2×D76411yescharacteristic
182C8—7642no—
183C22—21no—
184C22—21no—
185C22—3824no—
186C22—7642no—
187C22—7642no—
188C22C2×(C2×D191)⋊C411yescharacteristic
189C22#2025929011yescharacteristic
190C22#2025929011yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—3824no—
195C4C22⋊C4×D19112yes—
196C4#2025929212yes—
197C2—21no—
198C2—21no—
199C2—7644no—
200C2#2713251811yescharacteristic
201C2#2713283511yescharacteristic
202C2#2713284511yescharacteristic
subgroupG/H
centerC22#20259290
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#391×C191C2
socleC22×C191#120
prime radicalC2×#20259370C2
cosocleC22×C4×C191C23
hypercenter#391D191
hypocenterC191#1793
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#20259250C2semidirect
3. #27132662C2semidirect
4. C2×#20259241C2semidirect
5. #391×C191C2semidirect
8. #20259370C4semidirect
101. C191#1793semidirect
107. #391D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593702
C2×#202592502
#271326622
C2×#202592412
#391×C1912
#1793191