Finite Group Databasebeta

← #37572621

Subgroups — #37572621

Order 24448.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic191C211yesmaximal, characteristic
2#27132647C211yesmaximal, characteristic
3#27132422C212yesmaximal, complemented
4#27132419C212yesmaximal, complemented
5#410×C191C211yesmaximal, characteristic
6C2×#15690271C2212yes—
7Q8×Dic191—21no—
8D4×Dic191—22no—
9D4×Dic191—21no—
10#20259281C412yescomplemented
11#20259281C2211yescharacteristic
12C2×C4×Dic191C412yescomplemented
13C2×C4×Dic191C2211yescharacteristic
14#20259241—21no—
15#20259239—21no—
16C2×#41×C191C2211yescharacteristic
17#117×C191C2212yes—
18#99×C191—22no—
19C22×Dic191—22no—
20C22×Dic191—21no—
21#15690271—22no—
22#15690271—22no—
23C2×C191⋊C8—22no—
24C4⋊Dic191—22no—
25C4⋊Dic191—21no—
26C22⋊Dic191—22no—
27C22⋊Dic191—21no—
28C4×Dic191—22no—
29C4×Dic191—21no—
30C4×Dic191C2×C411yescharacteristic
31C4×Dic191C2×C412yes—
32C4×Dic191C2×C411yescharacteristic
33#41×C191—22no—
34#41×C191—22no—
35C2×Q8×C191D411yescharacteristic
36C2×D4×C191D412yes—
37C2×D4×C191D411yescharacteristic
38C22×C4×C191C2×C412yes—
39C22×C4×C191C2311yescharacteristic
40C4⋊C4×C191—22no—
41C22⋊C4×C191—22no—
42C42×C191—22no—
43C2×Dic191—21no—
44C2×Dic191—22no—
45C2×Dic191—21no—
46C2×Dic191—42no—
47C2×Dic191—44no—
48C191⋊C8—42no—
49C23×C191C22⋊C412yes—
50C23×C191C2×D411yescharacteristic
51Q8×C191—22no—
52D4×C191—24no—
53D4×C191—22no—
54C2×C4×C191—22no—
55C2×C4×C191—22no—
56C2×C4×C191—42no—
57C2×C4×C191C22⋊C412yes—
58C2×C4×C191C22×C411yescharacteristic
59C2×C4×C191C2×D411yescharacteristic
60C2×C4×C191#4112yes—
61C2×C4×C191#4112yes—
62C22×C191—22no—
63C22×C191—41no—
64C22×C191—42no—
65C22×C191C2×C22⋊C411yescharacteristic
66C22×C191#12312yes—
67C4×C191—22no—
68C4×C191—82no—
69C4×C191#11711yescharacteristic
70C4×C191#11711yescharacteristic
71C4×C191#12312yes—
72Dic191—22no—
73Dic191—42no—
74Dic191—41no—
75C2×C191—21no—
76C2×C191—22no—
77C2×C191—42no—
78C2×C191#38111yescharacteristic
79C191#182711yescharacteristic, complemented, Sylow
80#1827—1911nomaximal, Sylow
81C4×#41—1911no—
82#413—1911no—
83#410D19111yescharacteristic
84#339—1912no—
85H(3,ℤ/4)—1912no—
86C2×#41C2×D19111yescharacteristic
87C2×M16—1912no—
88C4×Q8—3821no—
89C4×D4—3822no—
90C4×D4—3821no—
91#117—1912no—
92#117—1911no—
93#117C2×D19112yes—
94C2×C42—1912no—
95C2×C42—1911no—
96#101—3821no—
97#100—3821no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D76411yescharacteristic
102C2×D4C22⋊D19112yes—
103C2×D4D76411yescharacteristic
104C22×C4—3822no—
105C22×C4—3821no—
106C22×C4C4×D19112yes—
107C22×C4C22×D19111yescharacteristic
108M16—3822no—
109M16—3822no—
110C2×C8—3822no—
111C4⋊C4—22no—
112C4⋊C4—3822no—
113C4⋊C4—3821no—
114C22⋊C4—22no—
115C22⋊C4—3822no—
116C22⋊C4—3821no—
117C42—22no—
118C42—3822no—
119C42—3821no—
120C42—1911no—
121C42—1912no—
122C42—1911no—
123C23(C2×D191)⋊C412yes—
124C23C2×C22⋊D19111yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—3821no—
132C2×C4—3822no—
133C2×C4—3821no—
134C2×C4—7642no—
135C2×C4—7644no—
136C2×C4(C2×D191)⋊C412yes—
137C2×C4C2×C4×D19111yescharacteristic
138C2×C4C2×D76411yescharacteristic
139C2×C4#1569028612yes—
140C2×C4#1569028612yes—
141C8—7642no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D191)⋊C411yescharacteristic
146C22#2025930312yes—
147C4—22no—
148C4—82no—
149C4—3822no—
150C4—7642no—
151C4—7641no—
152C4#2025927811yescharacteristic
153C4#2025927811yescharacteristic
154C4#2025930612yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2713252411yescharacteristic
subgroupG/H
centerC4#20259278
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#410×C191C2
socleC2×C191#381
prime radicalC2×#41×C191C22
cosocleC22×C4×C191C23
hypercenter#410D191
hypocenterC191#1827
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #27132422C2semidirect
4. #27132419C2semidirect
10. #20259281C4semidirect
12. C2×C4×Dic191C4semidirect
79. C191#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1912
#271326472
#271324222
#271324192
#410×C1912
#1827191