Finite Group Databasebeta

← #1343×C191 #37568085

Subgroups — #1343×C191 #37568085

Order 24448.

222 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 40 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#392×C191C211yesmaximal, characteristic
2#342×C191C211yesmaximal, characteristic, complemented
3#323×C191C211yesmaximal, characteristic, complemented
4C22×D4×C191—21no—
5C22×D4×C191C411yescharacteristic, complemented
6C2×C22⋊C4×C191—21no—
7C2×C22⋊C4×C191—21no—
8C2×C22⋊C4×C191C2211yescharacteristic
9C22⋊C8×C191—21no—
10#95×C191C411yescharacteristic, complemented
11C24×C191—21no—
12C24×C191D411yescharacteristic
13C2×D4×C191—41no—
14C2×D4×C191—42no—
15C2×D4×C191—42no—
16C2×D4×C191—41no—
17C2×D4×C191—41no—
18C2×D4×C191—42no—
19C22×C4×C191—21no—
20C22×C4×C191—41no—
21C22×C4×C191C2×C411yescharacteristic
22C22×C4×C191D411yescharacteristic
23C2×C8×C191—41no—
24C22⋊C4×C191—22no—
25C22⋊C4×C191—41no—
26C22⋊C4×C191—42no—
27C22⋊C4×C191—41no—
28C23×C191—21no—
29C23×C191—21no—
30C23×C191—22no—
31C23×C191—41no—
32C23×C191—41no—
33C23×C191—41no—
34C23×C191—41no—
35C23×C191—41no—
36C23×C191—41no—
37C23×C191—41no—
38C23×C191—41no—
39C23×C191C22⋊C411yescharacteristic
40C23×C191D811yescharacteristic
41C23×C191SD1611yescharacteristic
42D4×C191—42no—
43D4×C191—44no—
44D4×C191—44no—
45D4×C191—42no—
46C2×C4×C191—22no—
47C2×C4×C191—21no—
48C2×C4×C191—21no—
49C2×C4×C191—41no—
50C2×C4×C191—41no—
51C2×C4×C191—41no—
52C2×C4×C191—41no—
53C2×C4×C191—42no—
54C2×C4×C191—81no—
55C2×C4×C191—81no—
56C8×C191—81no—
57C22×C191—21no—
58C22×C191—21no—
59C22×C191—21no—
60C22×C191—21no—
61C22×C191—41no—
62C22×C191—41no—
63C22×C191—42no—
64C22×C191—42no—
65C22×C191—41no—
66C22×C191—41no—
67C22×C191—42no—
68C22×C191—81no—
69C22×C191—81no—
70C22×C191—81no—
71C22×C191—81no—
72C22×C191—81no—
73C22×C191#9911yescharacteristic
74C22×C191#10211yescharacteristic
75C22×C191#10411yescharacteristic
76C4×C191—42no—
77C4×C191—41no—
78C4×C191—41no—
79C4×C191—82no—
80C2×C191—21no—
81C2×C191—21no—
82C2×C191—41no—
83C2×C191—41no—
84C2×C191—82no—
85C2×C191#32711yescharacteristic
86C2×C191AΣL(1,𝔽16)11yescharacteristic
87C2×C191#35311yescharacteristic
88C191#134311yescharacteristic, direct product factor, Sylow
89#1343C19111yesmaximal, characteristic, direct product factor, Sylow
90#392C2×C19111yescharacteristic
91#342C2×C19111yescharacteristic, complemented
92#323C2×C19111yescharacteristic, complemented
93C22×D4—21no—
94C22×D4C4×C19111yescharacteristic, complemented
95C2×C22⋊C4—21no—
96C2×C22⋊C4—21no—
97C2×C22⋊C4C22×C19111yescharacteristic
98C22⋊C8—21no—
99#95C4×C19111yescharacteristic, complemented
100C24—21no—
101C24D4×C19111yescharacteristic
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—42no—
105C2×D4—41no—
106C2×D4—41no—
107C2×D4—42no—
108C22×C4—21no—
109C22×C4—41no—
110C22×C4C2×C4×C19111yescharacteristic
111C22×C4D4×C19111yescharacteristic
112C2×C8—41no—
113C22⋊C4—22no—
114C22⋊C4—41no—
115C22⋊C4—42no—
116C22⋊C4—41no—
117C23—21no—
118C23—21no—
119C23—22no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23—41no—
127C23—41no—
128C23C22⋊C4×C19111yescharacteristic
129C23D8×C19111yescharacteristic
130C23SD16×C19111yescharacteristic
131D4—42no—
132D4—44no—
133D4—44no—
134D4—42no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—81no—
144C2×C4—81no—
145C8—81no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22—41no—
151C22—41no—
152C22—42no—
153C22—42no—
154C22—41no—
155C22—41no—
156C22—42no—
157C22—81no—
158C22—81no—
159C22—81no—
160C22—81no—
161C22—81no—
162C22#99×C19111yescharacteristic
163C22#102×C19111yescharacteristic
164C22#104×C19111yescharacteristic
165C4—42no—
166C4—41no—
167C4—41no—
168C4—82no—
169C2—21no—
170C2—21no—
171C2—41no—
172C2—41no—
173C2—82no—
174C2#327×C19111yescharacteristic
175C2AΣL(1,𝔽16)×C19111yescharacteristic
176C2#353×C19111yescharacteristic
subgroupG/H
center, socleC22×C191#99
commutatorC22×C4C2×C4×C191
Frattini, cosocleC2×C22⋊C4C22×C191
prime radical#392×C191C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C191 ◁ C23×C191 ◁ C2×C22⋊C4×C191 ◁ G

Complements

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

NH ≅ G/Ntype
2. #342×C191C2semidirect
3. #323×C191C2semidirect
5. C22×D4×C191C4semidirect
10. #95×C191C4semidirect
88. C191#1343direct (N × H)
89. #1343C191direct (N × H)
91. #342C2×C191semidirect
92. #323C2×C191semidirect
94. C22×D4C4×C191semidirect
99. #95C4×C191semidirect

Maximal subgroups

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

subgroupindex
#392×C1912
#342×C1912
#323×C1912
#1343191