Finite Group Databasebeta

← #37573745

Subgroups — #37573745

Order 24448.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#27133244C211yesmaximal, characteristic
2C2×#20259248C212yesmaximal, complemented
3#27132665C212yesmaximal, complemented
4#27132532C211yesmaximal, characteristic, complemented
5#343×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7#20259302—22no—
8#20259297—22no—
9#20259296—22no—
10C2×C4⋊Dic191C2211yescharacteristic
11C2×Dic191⋊C4—22no—
12C2×C4×Dic191C2211yescharacteristic
13#20259248—24no—
14#20259247—22no—
15#20259244—22no—
16C2×M16×C191C2212yes—
17C2×C4⋊C4×C191C2211yescharacteristic
18#15690287—22no—
19#15690287—22no—
20#15690287—22no—
21#15690287—22no—
22C2×Dic382D412yes—
23C2×D764—22no—
24C2×D764D412yes—
25C2×C22⋊D191—22no—
26C22×Dic191—21no—
27C22×Dic191—21no—
28C2×C4×D191—22no—
29C4⋊Dic191—22no—
30C4⋊Dic191—22no—
31Dic191⋊C4—44no—
32(C2×D191)⋊C4—24no—
33C4×Dic191—21no—
34C4×Dic191D412yescomplemented
35C22×C4×C191D412yes—
36C22×C4×C191C2311yescharacteristic
37M16×C191—22no—
38M16×C191—22no—
39C2×C8×C191—22no—
40C4⋊C4×C191—22no—
41C22×D191—22no—
42Dic382—22no—
43Dic382—22no—
44D764—22no—
45D764—22no—
46D764—82no—
47C22⋊D191—42no—
48C22⋊D191—42no—
49C2×Dic191—22no—
50C2×Dic191—22no—
51C2×Dic191—22no—
52C2×Dic191—22no—
53C2×Dic191—42no—
54C2×Dic191—41no—
55C4×D191—42no—
56C4×D191—42no—
57C23×C191C2×D411yescharacteristic
58C2×C4×C191—22no—
59C2×C4×C191—42no—
60C2×C4×C191C2×D411yescharacteristic
61C2×C4×C191C2×D412yes—
62C2×C4×C191#4112yes—
63C2×C4×C191#4111yescharacteristic
64C8×C191—42no—
65C22×C191—21no—
66C22×C191—21no—
67C22×C191#12011yescharacteristic
68C22×C191#12111yescharacteristic
69C22×C191#12411yescharacteristic
70C2×D191—42no—
71C2×D191—42no—
72C2×D191—42no—
73C4×C191—42no—
74C4×C191#12112yes—
75C4×C191#12312yes—
76Dic191—24no—
77Dic191—42no—
78Dic191—81no—
79C2×C191—21no—
80C2×C191—21no—
81C2×C191#39411yescharacteristic
82C2×C191#45311yescharacteristic
83C2×C191#45611yescharacteristic
84D191—82no—
85C191#203911yescharacteristic, complemented, Sylow
86#2039—1911nomaximal, Sylow
87#537—1911no—
88C2×#104—1912no—
89#417—1912no—
90#384—1911no—
91#343D19111yescharacteristic, complemented
92C2×#41—1912no—
93C2×M16C2×D19112yes—
94C22⋊Q8—3822no—
95#121—3822no—
96#121—3822no—
97C2×C4⋊C4—3822no—
98C2×C4⋊C4—1911no—
99C2×C4⋊C4C2×D19111yescharacteristic
100C2×C42—1911no—
101#104—3824no—
102#103—3822no—
103#102—3822no—
104#41—3822no—
105#41—3822no—
106#41—3822no—
107#41—3822no—
108C2×Q8—1912no—
109C2×D4—3822no—
110C2×D4—3822no—
111C2×D4—1912no—
112C22×C4—3821no—
113C22×C4—3822no—
114C22×C4—3821no—
115C22×C4D76412yes—
116C22×C4C22×D19111yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—3822no—
122C4⋊C4—3822no—
123C4⋊C4—7644no—
124C22⋊C4—3824no—
125C42—3821no—
126C42—1912no—
127C23—3822no—
128C23C2×D76411yescharacteristic
129Q8—3822no—
130Q8—3822no—
131D4—3822no—
132D4—3822no—
133D4—15282no—
134D4—7642no—
135D4—7642no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—3822no—
139C2×C4—3822no—
140C2×C4—3822no—
141C2×C4—3822no—
142C2×C4—7642no—
143C2×C4—7641no—
144C2×C4—7642no—
145C2×C4—7642no—
146C2×C4D4×D19111yescharacteristic
147C2×C4D4×D19112yes—
148C2×C4#1569028712yes—
149C2×C4#1569028811yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—7642no—
154C22—7642no—
155C22—7642no—
156C22#2025929211yescharacteristic
157C22#2025929711yescharacteristic
158C22#2025931011yescharacteristic
159C4—42no—
160C4—3824no—
161C4—15281no—
162C4—7642no—
163C4#2025929512yes—
164C4#2025930712yes—
165C2—21no—
166C2—21no—
167C2—15282no—
168C2#2713258111yescharacteristic
169C2#2713283311yescharacteristic
170C2#2713284811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#343×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#343D191
hypocenterC191#2039
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#20259248C2semidirect
3. #27132665C2semidirect
4. #27132532C2semidirect
5. #343×C191C2semidirect
34. C4×Dic191D4semidirect
85. C191#2039semidirect
91. #343D191semidirect

Maximal subgroups

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

subgroupindex
#271332442
C2×#202592482
#271326652
#271325322
#343×C1912
#2039191