Finite Group Databasebeta

← #37574208

Subgroups — #37574208

Order 24448.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133238C211yesmaximal, characteristic
2#101×D191C212yesmaximal, complemented
3#27132462C211yesmaximal, characteristic, complemented
4#27132459C212yesmaximal, complemented
5#356×C191C211yesmaximal, characteristic, complemented
6C2×#15690288C411yescharacteristic
7C2×Q8×D191C2211yescharacteristic
8M16×D191—22no—
9#20259320C411yescharacteristic
10#20259311C2211yescharacteristic
11#20259310C411yescharacteristic
12#20259307—22no—
13#20259300—22no—
14#20259279C411yescharacteristic
15#20259241C2212yes—
16#20259240—22no—
17C4⋊Q8×C191C2211yescharacteristic
18#101×C191C2212yes—
19#15690288—42no—
20C2×Dic382C2×C411yescharacteristic
21C2×Dic382D412yes—
22Q8×D191—42no—
23C2×D764—21no—
24C2×D764C2×C411yescharacteristic
25C2×C4×D191—21no—
26C2×C4×D191C2×C411yescharacteristic
27C2×C4×D191D412yes—
28#15690271—22no—
29#15690270—42no—
30C8×D191—42no—
31Dic191⋊C4—21no—
32Dic191⋊C4—22no—
33(C2×D191)⋊C4—21no—
34(C2×D191)⋊C4—22no—
35(C2×D191)⋊C4—22no—
36C4×Dic191C2×C411yescharacteristic
37C2×Q8×C191C2×C411yescharacteristic
38C2×Q8×C191C2311yescharacteristic
39M16×C191—22no—
40C4⋊C4×C191—22no—
41C42×C191C2×C411yescharacteristic
42C22×D191—21no—
43C22×D191C22⋊C411yescharacteristic
44Dic382—41no—
45Dic382—42no—
46D764—41no—
47D764—42no—
48C2×Dic191—21no—
49C2×Dic191C22⋊C412yes—
50C2×Dic191C22⋊C411yescharacteristic
51C4×D191—22no—
52C4×D191—22no—
53C4×D191—22no—
54C4×D191—42no—
55C191⋊C8—42no—
56Q8×C191—41no—
57Q8×C191—41no—
58C2×C4×C191—21no—
59C2×C4×C191—21no—
60C2×C4×C191C22×C411yescharacteristic
61C2×C4×C191C2×D412yes—
62C8×C191—42no—
63C22×C191C2×C22⋊C411yescharacteristic
64C2×D191—41no—
65C2×D191—42no—
66C2×D191—41no—
67C2×D191#9912yes—
68C4×C191—22no—
69C4×C191—21no—
70C4×C191—41no—
71C4×C191—41no—
72Dic191—21no—
73Dic191—22no—
74Dic191—41no—
75C2×C191—21no—
76C2×C191C2×#9911yescharacteristic
77D191—22no—
78D191—81no—
79C191#213311yescharacteristic, complemented, Sylow
80#2133—1911nomaximal, Sylow
81#536—1911no—
82C2×#101—1912no—
83#356—1911no—
84#356D19111yescharacteristic, complemented
85#355—1912no—
86C2×#41—1911no—
87C22×Q8—1911no—
88C2×M16—3822no—
89C4⋊Q8—1911no—
90C4⋊Q8C2×D19111yescharacteristic
91#124—1911no—
92#124—1911no—
93#123—3822no—
94C22⋊Q8—3822no—
95#117—1911no—
96#101—3822no—
97#101—1912no—
98#101C2×D19112yes—
99#41—7642no—
100C2×Q8—1911no—
101C2×Q8—1912no—
102C2×Q8—7642no—
103C2×Q8C4×D19111yescharacteristic
104C2×Q8C22×D19111yescharacteristic
105C2×D4—3821no—
106C2×D4—1911no—
107C22×C4—3821no—
108C22×C4—1911no—
109C22×C4—1912no—
110M16—22no—
111M16—3822no—
112M16—7642no—
113C2×C8—7642no—
114C4⋊C4—22no—
115C4⋊C4—3821no—
116C4⋊C4—3822no—
117C22⋊C4—3821no—
118C22⋊C4—3822no—
119C22⋊C4—3822no—
120C42—1911no—
121C42C4×D19111yescharacteristic
122C23—3821no—
123C23—1911no—
124Q8—41no—
125Q8—41no—
126Q8—7642no—
127Q8—7641no—
128D4—7641no—
129D4—7642no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3822no—
133C2×C4—3822no—
134C2×C4—3822no—
135C2×C4—3821no—
136C2×C4—1912no—
137C2×C4—1911no—
138C2×C4—7642no—
139C2×C4C2×C4×D19111yescharacteristic
140C2×C4D4×D19112yes—
141C8—42no—
142C8—7642no—
143C22—1912no—
144C22—7641no—
145C22—7642no—
146C22—7641no—
147C22C22⋊C4×D19111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—3821no—
153C4—3822no—
154C4—7641no—
155C2—21no—
156C2—3822no—
157C2—15281no—
158C2#99×D19111yescharacteristic
subgroupG/H
centerC2#99×D191
commutatorC2×C4×C191C22×C4
FrattiniC2×Q8C22×D191
Fitting#356×C191C2
socleC2×C191C2×#99
prime radicalC2×#15690288C4
cosocleC2×Q8×C191C23
hypercenter#356D191
hypocenterC191#2133
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D191C2semidirect
3. #27132462C2semidirect
4. #27132459C2semidirect
5. #356×C191C2semidirect
79. C191#2133semidirect
84. #356D191semidirect

Maximal subgroups

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

subgroupindex
#271332382
#101×D1912
#271324622
#271324592
#356×C1912
#2133191