Finite Group Databasebeta

← #37574202

Subgroups — #37574202

Order 24448.

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

normal subgroups only

This group has 250 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#27133212C211yesmaximal, characteristic
2#27132646C212yesmaximal, complemented
3#27132461C212yesmaximal, complemented
4#27132460C211yesmaximal, characteristic, complemented
5#355×C191C211yesmaximal, characteristic, complemented
6C2×#15690288C2211yescharacteristic
7C2×#15690286C411yescharacteristic
8M16×D191—22no—
9#20259320C2211yescharacteristic
10#20259318C411yescharacteristic
11#20259310C411yescharacteristic
12#20259295—22no—
13(C22⋊D191)⋊C4—22no—
14C42×D191C411yescharacteristic
15#20259241C2212yes—
16#20259238—22no—
17#124×C191C2211yescharacteristic
18#101×C191C2212yes—
19#15690288—41no—
20#15690288—41no—
21#15690286—41no—
22#15690286—41no—
23C2×Dic382C2×C411yescharacteristic
24C2×D764C2×C411yescharacteristic
25C2×D764D412yes—
26C2×C22⋊D191—21no—
27C2×C22⋊D191—22no—
28C22×Dic191—21no—
29C2×C4×D191—21no—
30C2×C4×D191C2×C411yescharacteristic
31C2×C4×D191D412yes—
32#15690271—22no—
33#15690270—42no—
34C8×D191—42no—
35Dic191⋊C4—22no—
36(C2×D191)⋊C4—22no—
37C4×Dic191—21no—
38C4×Dic191C2×C411yescharacteristic
39C2×Q8×C191C2311yescharacteristic
40C2×D4×C191C2×C411yescharacteristic
41M16×C191—22no—
42C22⋊C4×C191—22no—
43C42×C191C2×C411yescharacteristic
44C22×D191C22⋊C412yes—
45C22×D191C22⋊C411yescharacteristic
46Dic382—41no—
47D764—41no—
48D764—42no—
49C22⋊D191—44no—
50C22⋊D191—42no—
51C2×Dic191—21no—
52C2×Dic191—21no—
53C2×Dic191—41no—
54C2×Dic191—41no—
55C2×Dic191C22⋊C411yescharacteristic
56C4×D191—22no—
57C4×D191—22no—
58C4×D191—21no—
59C4×D191—21no—
60C4×D191—42no—
61C191⋊C8—42no—
62C23×C191—21no—
63Q8×C191—41no—
64D4×C191—41no—
65C2×C4×C191—21no—
66C2×C4×C191C22×C411yescharacteristic
67C2×C4×C191C2×D412yes—
68C8×C191—42no—
69C22×C191—42no—
70C22×C191—41no—
71C22×C191C2×C22⋊C411yescharacteristic
72C2×D191—21no—
73C2×D191—22no—
74C2×D191—41no—
75C2×D191—42no—
76C4×C191—22no—
77C4×C191—21no—
78C4×C191—41no—
79Dic191—22no—
80Dic191—41no—
81Dic191#9911yescharacteristic
82Dic191#9911yescharacteristic
83C2×C191—21no—
84C2×C191—81no—
85C2×C191C2×#9911yescharacteristic
86D191—41no—
87D191—42no—
88C191#213211yescharacteristic, complemented, Sylow
89#2132—1911nomaximal, Sylow
90#532—1911no—
91#413—1912no—
92#356—1912no—
93#355—1911no—
94#355D19111yescharacteristic, complemented
95C2×#41—1911no—
96C2×#41—1911no—
97C2×M16—3822no—
98C4⋊Q8—1911no—
99#127—1911no—
100#124—1911no—
101#124C2×D19111yescharacteristic
102#121—3822no—
103C4×D4—3822no—
104C2×C42—1911no—
105#101—1912no—
106#101C2×D19112yes—
107#100—3822no—
108#41—7641no—
109#41—7641no—
110#41—7641no—
111#41—7641no—
112C2×Q8—1911no—
113C2×Q8C22×D19111yescharacteristic
114C2×D4—3822no—
115C2×D4—3821no—
116C2×D4—1911no—
117C2×D4—1912no—
118C2×D4C4×D19111yescharacteristic
119C22×C4—3821no—
120C22×C4—3821no—
121C22×C4—1911no—
122C22×C4—1912no—
123M16—22no—
124M16—3822no—
125M16—7642no—
126C2×C8—7642no—
127C4⋊C4—3822no—
128C22⋊C4—22no—
129C22⋊C4—3822no—
130C42—3821no—
131C42—1911no—
132C42C4×D19111yescharacteristic
133C23—21no—
134C23—1912no—
135C23—1911no—
136Q8—41no—
137Q8—7641no—
138D4—41no—
139D4—7642no—
140D4—7641no—
141D4—7644no—
142D4—7642no—
143C2×C4—21no—
144C2×C4—3822no—
145C2×C4—3822no—
146C2×C4—3821no—
147C2×C4—3821no—
148C2×C4—3821no—
149C2×C4—3821no—
150C2×C4—1911no—
151C2×C4—7642no—
152C2×C4—7641no—
153C2×C4—7641no—
154C2×C4C2×C4×D19111yescharacteristic
155C2×C4D4×D19112yes—
156C8—42no—
157C8—7642no—
158C22—42no—
159C22—41no—
160C22—3821no—
161C22—3822no—
162C22—7641no—
163C22—7642no—
164C22C22⋊C4×D19111yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—3822no—
169C4—1911no—
170C4—1911no—
171C4—7641no—
172C2—21no—
173C2—81no—
174C2—7641no—
175C2—7642no—
176C2#99×D19111yescharacteristic
subgroupG/H
centerC2#99×D191
commutatorC2×C4×C191C22×C4
FrattiniC2×Q8C22×D191
Fitting#355×C191C2
socleC2×C191C2×#99
prime radical#27133212C2
cosocleC2×Q8×C191C23
hypercenter#355D191
hypocenterC191#2132
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #27132646C2semidirect
3. #27132461C2semidirect
4. #27132460C2semidirect
5. #355×C191C2semidirect
88. C191#2132semidirect
94. #355D191semidirect

Maximal subgroups

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

subgroupindex
#271332122
#271326462
#271324612
#271324602
#355×C1912
#2132191