Finite Group Databasebeta

← #37571842

Subgroups — #37571842

Order 24448.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#27133407C211yesmaximal, characteristic
2#27133031C211yesmaximal, characteristic, complemented
3#27133025C211yesmaximal, characteristic, complemented
4#27132404C211yesmaximal, characteristic, complemented
5#27132403C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic, complemented
7#489×C191C211yesmaximal, characteristic, complemented
8#20259314C2211yescharacteristic
9#20259310C2211yescharacteristic
10#20259306—21no—
11#20259304—21no—
12#20259299—21no—
13#20259298—21no—
14#20259295—21no—
15#20259294—21no—
16#20259246—21no—
17#20259246—21no—
18#20259245—21no—
19#20259242—21no—
20#20259233C2211yescharacteristic
21#20259233C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#124×C191C2211yescharacteristic
24#103×C191—21no—
25#102×C191—21no—
26#97×C191C2211yescharacteristic
27C2×Dic382D411yescharacteristic
28C2×D764D411yescharacteristic
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C22×Dic191—21no—
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37C4⋊Dic191D411yescharacteristic
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41C22⋊Dic191—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45C2×Q8×C191—21no—
46C2×Q8×C191D411yescharacteristic
47C2×D4×C191D411yescharacteristic
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C22⋊C4×C191—21no—
52C22⋊C4×C191—21no—
53C42×C191C2311yescharacteristic
54C22×D191—21no—
55Dic382—41no—
56D764—41no—
57C22⋊D191—81no—
58C22⋊D191—81no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—81no—
63C4×D191—81no—
64C191⋊C8—41no—
65C191⋊C8—41no—
66C23×C191—21no—
67Q8×C191—41no—
68Q8×C191—42no—
69D4×C191—41no—
70C2×C4×C191—21no—
71C2×C4×C191—41no—
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191C2×D411yescharacteristic
75C8×C191—41no—
76C22×C191—41no—
77C22×C191—41no—
78C22×C191—41no—
79C22×C191#12011yescharacteristic
80C2×D191—41no—
81C2×D191—41no—
82C2×D191—41no—
83C4×C191—21no—
84C4×C191—21no—
85C4×C191—21no—
86C4×C191—41no—
87C4×C191—81no—
88Dic191—41no—
89Dic191—41no—
90Dic191—41no—
91C2×C191—81no—
92C2×C191#45411yescharacteristic
93C2×C191#45511yescharacteristic
94C2×C191#45511yescharacteristic
95D191—81no—
96C191#166211yescharacteristic, complemented, Sylow
97#1662—1911nomaximal, Sylow
98#562—1911no—
99#491—1911no—
100#489—1911no—
101#489D19111yescharacteristic, complemented
102#330—1911no—
103#329—1911no—
104#329—1911no—
105C4⋊Q8C2×D19111yescharacteristic
106#125—1911no—
107#124—1911no—
108#124C2×D19111yescharacteristic
109#123—3821no—
110#123—3821no—
111C22⋊Q8—3821no—
112C22⋊Q8—3821no—
113#121—3821no—
114#121—3821no—
115#103—21no—
116#103—3821no—
117#103—3821no—
118#103—3821no—
119#102—21no—
120#102—3821no—
121#97—1911no—
122#97—1911no—
123#97C2×D19111yescharacteristic
124C2×Q8—21no—
125C2×Q8—1911no—
126C2×Q8C22⋊D19111yescharacteristic
127C2×D4—3821no—
128C2×D4—3821no—
129C2×D4—1911no—
130C2×D4C22⋊D19111yescharacteristic
131C22×C4—3821no—
132C22×C4—3821no—
133C2×C8—21no—
134C2×C8—3821no—
135C2×C8—3821no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3821no—
139C4⋊C4—3821no—
140C4⋊C4—3821no—
141C4⋊C4—3821no—
142C4⋊C4—1911no—
143C4⋊C4—1911no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—3821no—
147C22⋊C4—3821no—
148C22⋊C4—3821no—
149C22⋊C4—3821no—
150C42C22×D19111yescharacteristic
151C23—21no—
152C23—3821no—
153Q8—41no—
154Q8—42no—
155Q8—7641no—
156D4—41no—
157D4—15281no—
158D4—15281no—
159D4—7641no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—3821no—
163C2×C4—3821no—
164C2×C4—3821no—
165C2×C4—15281no—
166C2×C4—15281no—
167C2×C4D4×D19111yescharacteristic
168C2×C4D4×D19111yescharacteristic
169C2×C4C2×C22⋊D19111yescharacteristic
170C8—41no—
171C8—7641no—
172C8—7641no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—7641no—
177C22—7641no—
178C22—7641no—
179C22#2025929011yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—7641no—
186C4—7641no—
187C4—7641no—
188C2—81no—
189C2—15281no—
190C2#2713283411yescharacteristic
191C2#2713283911yescharacteristic
192C2#2713284011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#489×C191C2
socleC22×C191#120
prime radical#27133407C2
hypercenter#489D191
hypocenterC191#1662
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #27133031C2semidirect
3. #27133025C2semidirect
4. #27132404C2semidirect
5. #27132403C2semidirect
6. #27132402C2semidirect
7. #489×C191C2semidirect
96. C191#1662semidirect
101. #489D191semidirect

Maximal subgroups

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

subgroupindex
#271334072
#271330312
#271330252
#271324042
#271324032
#271324022
#489×C1912
#1662191