Finite Group Databasebeta

← #37582806

Subgroups — #37582806

Order 24448.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#27133140C211yesmaximal, characteristic, complemented
2#27132984C212yesmaximal, complemented
3#27132967C212yesmaximal, complemented
4#27132860C212yesmaximal, complemented
5#27132801C212yesmaximal, complemented
6#27132763C212yesmaximal, complemented
7C4×#15690275C212yesmaximal, complemented
8#27132724C211yesmaximal, characteristic, complemented
9#540×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11C2×#15690275C2212yes—
12C2×#15690275C2212yes—
13C4×Dic382C2212yes—
14C4×Dic382C2212yes—
15#20259287—22no—
16#20259281C2211yescharacteristic
17#20259278—22no—
18#20259255C2212yes—
19#20259253C2212yes—
20C4⋊(C191⋊C8)C2212yes—
21#20259245C2212yes—
22#20259245C2212yes—
23#20259243C2212yes—
24#20259243C2212yes—
25C22⋊(C191⋊C8)C2212yes—
26#20259233C2211yescharacteristic
27C4×C191⋊C8C2211yescharacteristic
28#127×C191C2211yescharacteristic
29#125×C191C2211yescharacteristic
30#123×C191—22no—
31#121×C191—22no—
32#121×C191C2212yes—
33C4×D4×C191C2212yes—
34#117×C191C2211yescharacteristic
35C2×Dic382—24no—
36C2×Dic382—21no—
37C2×Dic382C2312yes—
38C22×Dic191—21no—
39#15690275—24no—
40#15690275—24no—
41C2×C191⋊C8C2312yes—
42C2×C191⋊C8C2312yes—
43C4⋊Dic191C2312yes—
44Dic191⋊C4—22no—
45Dic191⋊C4—22no—
46C22⋊Dic191—21no—
47C4×Dic191—22no—
48C4×Dic191—22no—
49C4×Dic191—21no—
50C2×D4×C191—22no—
51C2×D4×C191—22no—
52C2×D4×C191C2312yes—
53C22×C4×C191—22no—
54C22×C4×C191C2311yescharacteristic
55C4⋊C4×C191—22no—
56C4⋊C4×C191D412yes—
57C4⋊C4×C191C2312yes—
58C22⋊C4×C191—22no—
59C22⋊C4×C191—22no—
60C22⋊C4×C191D412yes—
61C42×C191C2311yescharacteristic
62C42×C191C2311yescharacteristic
63Dic382—24no—
64Dic382—22no—
65Dic382#4114yes—
66C2×Dic191—24no—
67C2×Dic191—22no—
68C2×Dic191—22no—
69C191⋊C8—22no—
70C191⋊C8—22no—
71C23×C191—22no—
72C23×C191C2×D411yescharacteristic
73D4×C191—22no—
74D4×C191—22no—
75D4×C191—82no—
76D4×C191—82no—
77C2×C4×C191—22no—
78C2×C4×C191—22no—
79C2×C4×C191—82no—
80C2×C4×C191C2×D412yes—
81C2×C4×C191C2×D412yes—
82C2×C4×C191C2×D411yescharacteristic
83C2×C4×C191C2411yescharacteristic
84C22×C191—21no—
85C22×C191—22no—
86C22×C191—42no—
87C22×C191—42no—
88C22×C191—42no—
89C22×C191C22×D411yescharacteristic
90C4×C191—21no—
91C4×C191—22no—
92C4×C191—22no—
93C4×C191—42no—
94C4×C191C2×#4112yes—
95Dic191—24no—
96Dic191—42no—
97C2×C191—41no—
98C2×C191—82no—
99C2×C191#52511yescharacteristic
100C2×C191#57712yes—
101C191#312611yescharacteristic, complemented, Sylow
102#3126—1911nomaximal, Sylow
103#540D19111yescharacteristic
104#519—1911no—
105#482—1912no—
106#479—1912no—
107#460—1912no—
108#448—1912no—
109#440—1912no—
110C4×SD16—1912no—
111#433—1911no—
112C22×Q8—1911no—
113C2×SD16—1912no—
114C2×SD16—1912no—
115#127C2×D19111yescharacteristic
116#125C2×D19111yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D19112yes—
120C4×Q8—3822no—
121C4×Q8—1912no—
122C4×Q8—1912no—
123C4×D4C2×D19112yes—
124#117—3822no—
125#117—1911no—
126#117C2×D19111yescharacteristic
127#107—1912no—
128#106—1912no—
129C4⋊C8—1912no—
130#103—1912no—
131#103—1912no—
132#102—1912no—
133#102—1912no—
134C22⋊C8—1912no—
135#97—1911no—
136C4×C8—1911no—
137C2×Q8—3824no—
138C2×Q8—3821no—
139C2×Q8—1912no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D19112yes—
143C22×C4—22no—
144C22×C4—3821no—
145C22×C4C22×D19111yescharacteristic
146SD16—3824no—
147SD16—3824no—
148C2×C8—1912no—
149C2×C8—1912no—
150C4⋊C4—22no—
151C4⋊C4—3822no—
152C4⋊C4—3822no—
153C4⋊C4—1912no—
154C4⋊C4C22⋊D19112yes—
155C4⋊C4C22×D19112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—3821no—
159C22⋊C4C22⋊D19112yes—
160C42—3822no—
161C42—3822no—
162C42—3821no—
163C42C22×D19111yescharacteristic
164C42C22×D19111yescharacteristic
165C23—22no—
166C23C2×C22⋊D19111yescharacteristic
167Q8—3824no—
168Q8—3822no—
169Q8—1914no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—3824no—
178C2×C4—3822no—
179C2×C4—3822no—
180C2×C4C2×C22⋊D19112yes—
181C2×C4C2×C22⋊D19112yes—
182C2×C4C2×C22⋊D19111yescharacteristic
183C2×C4C23×D19111yescharacteristic
184C8—3822no—
185C8—3822no—
186C22—22no—
187C22—21no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D19111yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—42no—
196C4—3824no—
197C4—7642no—
198C4#41×D19112yes—
199C2—41no—
200C2—82no—
201C2#2713317011yescharacteristic
202C2#2713347412yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting, prime radical#540×C191C2
socleC22×C191C22×D4
hypercenter#540D191
hypocenterC191#3126
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #27133140C2semidirect
2. #27132984C2semidirect
3. #27132967C2semidirect
4. #27132860C2semidirect
5. #27132801C2semidirect
6. #27132763C2semidirect
7. C4×#15690275C2semidirect
8. #27132724C2semidirect
101. C191#3126semidirect

Maximal subgroups

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

subgroupindex
#271331402
#271329842
#271329672
#271328602
#271328012
#271327632
C4×#156902752
#271327242
#540×C1912
#3126191