Finite Group Databasebeta

← #355×D191 #37574196

Subgroups — #355×D191 #37574196

Order 24448.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D191C211yesmaximal, characteristic
2#101×D191C212yesmaximal, complemented
3#27132460C211yesmaximal, characteristic, complemented
4#27132459C212yesmaximal, complemented
5#355×C191C211yesmaximal, characteristic, complemented
6C2×Q8×D191C2211yescharacteristic
7C2×D4×D191C411yescharacteristic
8M16×D191—22no—
9#20259311C2211yescharacteristic
10#20259310C411yescharacteristic
11#20259309C411yescharacteristic
12#20259308—22no—
13C22⋊C4×D191—22no—
14C42×D191C411yescharacteristic
15#20259241C2212yescomplemented
16#20259240—22no—
17#124×C191C2211yescharacteristic
18#101×C191C2212yescomplemented
19C23×D191—21no—
20C2×Dic382C2×C411yescharacteristic
21C2×Dic382D412yes—
22Q8×D191—41no—
23Q8×D191—41no—
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—21no—
26D4×D191—41no—
27D4×D191—41no—
28C2×C4×D191—21no—
29C2×C4×D191C2×C411yescharacteristic
30C2×C4×D191D412yes—
31#15690271—22no—
32#15690270—42no—
33C8×D191—42no—
34C22⋊Dic191—22no—
35(C2×D191)⋊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×D191—21no—
45C22×D191—44no—
46C22×D191—41no—
47C22×D191—41no—
48C22×D191C22⋊C411yescharacteristic
49Dic382—41no—
50Dic382—42no—
51D764—41no—
52C22⋊D191—42no—
53C2×Dic191—21no—
54C2×Dic191C22⋊C411yescharacteristic
55C2×Dic191C22⋊C412yes—
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—22no—
73C2×D191—42no—
74C2×D191—41no—
75C2×D191—82no—
76C2×D191—82no—
77C2×D191#9911yescharacteristic
78C2×D191#9911yescharacteristic
79C4×C191—22no—
80C4×C191—21no—
81C4×C191—41no—
82Dic191—21no—
83Dic191—22no—
84Dic191—41no—
85C2×C191—21no—
86C2×C191—81no—
87C2×C191C2×#9911yescharacteristic
88D191—21no—
89D191—81no—
90D191#35512yesdirect product factor
91C191C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—1911nomaximal, Sylow
93C2×#124—1911no—
94C2×#101—1912no—
95#355—1911no—
96#355—1912no—
97#355D19111yescharacteristic, direct product factor
98C22×Q8—1911no—
99C22×D4—1911no—
100C2×M16—3822no—
101#124—3822no—
102#124—1911no—
103#124—1911no—
104#124—1911no—
105#124C2×D19111yescharacteristic
106C2×C22⋊C4—3822no—
107C2×C42—1911no—
108#101—3822no—
109#101—1912no—
110#101C2×D19112yescomplemented
111C24—3821no—
112C2×Q8—1911no—
113C2×Q8—1912no—
114C2×Q8—7641no—
115C2×Q8—7641no—
116C2×Q8C22×D19111yescharacteristic
117C2×D4—3821no—
118C2×D4—1911no—
119C2×D4—7641no—
120C2×D4—7641no—
121C2×D4C4×D19111yescharacteristic
122C22×C4—3821no—
123C22×C4—1911no—
124C22×C4—1912no—
125M16—22no—
126M16—3822no—
127M16—7642no—
128C2×C8—7642no—
129C22⋊C4—22no—
130C22⋊C4—3822no—
131C22⋊C4—3822no—
132C22⋊C4—3822no—
133C42—3821no—
134C42—1911no—
135C42C4×D19111yescharacteristic
136C23—21no—
137C23—3821no—
138C23—1911no—
139C23—7644no—
140C23—7641no—
141C23—7641no—
142Q8—41no—
143Q8—7642no—
144Q8—7641no—
145D4—41no—
146D4—7641no—
147D4—7642no—
148C2×C4—21no—
149C2×C4—3822no—
150C2×C4—3822no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—1911no—
155C2×C4—1912no—
156C2×C4—7642no—
157C2×C4C2×C4×D19111yescharacteristic
158C2×C4D4×D19112yes—
159C8—42no—
160C8—7642no—
161C22—42no—
162C22—41no—
163C22—3822no—
164C22—1911no—
165C22—1911no—
166C22—15282no—
167C22—15282no—
168C22—7642no—
169C22—7641no—
170C22C22⋊C4×D19111yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—3821no—
175C4—3822no—
176C4—7641no—
177C2—21no—
178C2—81no—
179C2—3821no—
180C2—1912no—
181C2—15281no—
182C2#99×D19111yescharacteristic
subgroupG/H
centerC2#99×D191
commutatorC2×C4×C191C22×C4
FrattiniC2×Q8C22×D191
Fitting#355×C191C2
socleC2×C191C2×#99
prime radicalC2×D4×D191C4
cosocleC2×Q8×C191C23
hypercenter#355D191
hypocenterC191C2×#355
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. #101×D191C2semidirect
3. #27132460C2semidirect
4. #27132459C2semidirect
5. #355×C191C2semidirect
15. #20259241C22semidirect
18. #101×C191C22semidirect
90. D191#355direct (N × H)
91. C191C2×#355semidirect
97. #355D191direct (N × H)
110. #101C2×D191semidirect

Maximal subgroups

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

subgroupindex
#124×D1912
#101×D1912
#271324602
#271324592
#355×C1912
C2×#355191