Finite Group Databasebeta

← #37572481

Subgroups — #37572481

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×#20259248C212yesmaximal, complemented
3#27132665C212yesmaximal, complemented
4#27132570C211yesmaximal, characteristic, complemented
5C2×#101×C191C211yesmaximal, characteristic, complemented
6#20259370—24no—
7#20259370—22no—
8#20259370C414yescomplemented
9C2×#15690288—22no—
10C2×#15690287—22no—
11C2×#15690287C2212yes—
12C2×Q8×D191—22no—
13C2×C4⋊Dic191C2211yescharacteristic
14C2×C4×Dic191C2211yescharacteristic
15#20259248—24no—
16#20259247—22no—
17#20259244—22no—
18C191⋊#95—22no—
19C22×Q8×C191C2211yescharacteristic
20C2×M16×C191C2212yes—
21#101×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—
37C22×Dic191—21no—
38C22×Dic191—21no—
39C2×C4×D191—24no—
40C2×C4×D191—22no—
41C4⋊Dic191—22no—
42C4×Dic191—22no—
43C2×Q8×C191—22no—
44C2×Q8×C191—22no—
45C2×Q8×C191C2×C412yes—
46C2×Q8×C191D412yes—
47C22×C4×C191D412yes—
48C22×C4×C191C2311yescharacteristic
49M16×C191—22no—
50M16×C191—22no—
51C2×C8×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—
62C2×Dic191—22no—
63C2×Dic191—41no—
64C2×Dic191—41no—
65C2×Dic191—42no—
66C2×Dic191—41no—
67C4×D191—216no—
68C4×D191—24no—
69C4×D191—24no—
70C23×C191C2×D411yescharacteristic
71Q8×C191—24no—
72Q8×C191—24no—
73C2×C4×C191—22no—
74C2×C4×C191—22no—
75C2×C4×C191C22⋊C414yes—
76C2×C4×C191C22×C411yescharacteristic
77C2×C4×C191C2×D412yes—
78C2×C4×C191C2×D412yes—
79C2×C4×C191C2×D411yescharacteristic
80C8×C191—42no—
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×C191C2×C22⋊C412yes—
91C4×C191#12012yes—
92Dic191—24no—
93Dic191—42no—
94Dic191—81no—
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×#101D19111yescharacteristic, complemented
107#391—1911no—
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×M16C2×D19112yes—
117C2×C4⋊C4—1911no—
118C2×C42—1911no—
119#104—3824no—
120#103—3822no—
121#102—3822no—
122#101—22no—
123#95—3822no—
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×Q8C22⋊D19112yes—
140C2×D4—3822no—
141C2×D4—3822no—
142C2×D4—1912no—
143C22×C4—3824no—
144C22×C4—3822no—
145C22×C4—3821no—
146C22×C4—3821no—
147C22×C4D76412yes—
148C22×C4C22×D19111yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—3822no—
153C42—3822no—
154C23—3822no—
155C23C2×D76411yescharacteristic
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—38216no—
169C2×C4—3822no—
170C2×C4—3824no—
171C2×C4—3824no—
172C2×C4—3822no—
173C2×C4—7642no—
174C2×C4—7641no—
175C2×C4—7641no—
176C2×C4—7641no—
177C2×C4(C2×D191)⋊C414yes—
178C2×C4C2×C4×D19111yescharacteristic
179C2×C4D4×D19112yes—
180C2×C4D4×D19112yes—
181C2×C4C2×C22⋊D19111yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—3824no—
186C22—7642no—
187C22—7642no—
188C22C2×(C2×D191)⋊C411yescharacteristic
189C22#2025929211yescharacteristic
190C22#2025929211yescharacteristic
191C4—24no—
192C4—3824no—
193C4—15281no—
194C4—7642no—
195C4C22⋊C4×D19112yes—
196C4#2025929012yes—
197C2—21no—
198C2—21no—
199C2—7644no—
200C2#2713251811yescharacteristic
201C2#2713283811yescharacteristic
202C2#2713284811yescharacteristic
subgroupG/H
centerC22#20259292
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
FittingC2×#101×C191C2
socleC22×C191#120
prime radicalC2×#20259370C2
cosocleC22×C4×C191C23
hypercenterC2×#101D191
hypocenterC191#1793
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#20259248C2semidirect
3. #27132665C2semidirect
4. #27132570C2semidirect
5. C2×#101×C191C2semidirect
8. #20259370C4semidirect
101. C191#1793semidirect
106. C2×#101D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593702
C2×#202592482
#271326652
#271325702
C2×#101×C1912
#1793191