Finite Group Databasebeta

← #37571610

Subgroups — #37571610

Order 24448.

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

normal subgroups only

This group has 256 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#27133316C211yesmaximal, characteristic, complemented
2#27133011C211yesmaximal, characteristic, complemented
3#27132859C211yesmaximal, characteristic, complemented
4#27132859C211yesmaximal, characteristic, complemented
5#27132390C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic, complemented
7#332×C191C211yesmaximal, characteristic, complemented
8C2×#15690288—21no—
9C2×D1528—21no—
10C2×D1528—21no—
11#20259319C2211yescharacteristic
12#20259307—22no—
13#20259298—21no—
14#20259297—21no—
15C4×D764C2211yescharacteristic
16C4×D764C2211yescharacteristic
17C4⋊C4×D191—21no—
18#20259244—21no—
19#20259244—21no—
20#20259242—22no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25#15690288—42no—
26#15690288—42no—
27C2×D764—22no—
28C2×D764—21no—
29C2×D764—21no—
30C2×D764—21no—
31C2×D764D411yescharacteristic
32C2×D764D411yescharacteristic
33C2×C4×D191—22no—
34C2×C4×D191—21no—
35C2×C4×D191—21no—
36D1528—42no—
37D1528—42no—
38C2×C191⋊C8—21no—
39C4⋊Dic191D411yescharacteristic
40C4⋊Dic191D411yescharacteristic
41Dic191⋊C4—22no—
42(C2×D191)⋊C4—22no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45C2×Q8×C191—21no—
46C2×C8×C191—21no—
47C2×C8×C191—21no—
48C4⋊C4×C191—21no—
49C4⋊C4×C191D412yes—
50C42×C191C2311yescharacteristic
51C22×D191—21no—
52C22×D191—21no—
53C22×D191—41no—
54D764—21no—
55D764—21no—
56D764—21no—
57D764—42no—
58D764—44no—
59D764—41no—
60D764—41no—
61D764—41no—
62D764—41no—
63D764D812yescomplemented
64C2×Dic191—21no—
65C2×Dic191—21no—
66C4×D191—44no—
67C4×D191—41no—
68C4×D191—41no—
69C4×D191—41no—
70C4×D191—41no—
71C191⋊C8—41no—
72Q8×C191—41no—
73Q8×C191—41no—
74C2×C4×C191—22no—
75C2×C4×C191C2×D411yescharacteristic
76C2×C4×C191C2×D411yescharacteristic
77C2×C4×C191C2×D411yescharacteristic
78C8×C191—41no—
79C8×C191—41no—
80C22×C191#12011yescharacteristic
81C2×D191—22no—
82C2×D191—41no—
83C2×D191—41no—
84C2×D191—41no—
85C2×D191—41no—
86C2×D191—41no—
87C2×D191—81no—
88C2×D191—81no—
89C2×D191—81no—
90C4×C191—21no—
91C4×C191—42no—
92C4×C191C2×D811yescharacteristic
93C4×C191#13511yescharacteristic
94C4×C191AGL(1,ℤ/8)11yescharacteristic
95C4×C191AGL(1,ℤ/8)11yescharacteristic
96Dic191—41no—
97Dic191—41no—
98C2×C191#44711yescharacteristic
99C2×C191#44911yescharacteristic
100C2×C191#45411yescharacteristic
101D191—42no—
102D191—81no—
103D191—161no—
104C191#162511yescharacteristic, complemented, Sylow
105#1625—1911nomaximal, Sylow
106#547—1911no—
107#486—1911no—
108#459—1911no—
109#459—1911no—
110#332D19111yescharacteristic, complemented
111D4⋊C8—1911no—
112D4⋊C8—1911no—
113C2×#41—3821no—
114C2×D8—3821no—
115C2×D8—3821no—
116C4⋊Q8C2×D19111yescharacteristic
117#127—1911no—
118#123—3822no—
119C22⋊Q8—3821no—
120#121—3821no—
121C4×D4—1911no—
122C4×D4—1911no—
123C2×C4⋊C4—3821no—
124C4⋊C8C2×D19111yescharacteristic
125C4⋊C8C2×D19111yescharacteristic
126#102—3821no—
127#102—3821no—
128#102—3822no—
129C4×C8—1911no—
130#41—7642no—
131#41—7642no—
132C2×Q8—21no—
133C2×D4—3822no—
134C2×D4—3821no—
135C2×D4—3821no—
136C2×D4—3821no—
137C2×D4—1911no—
138C2×D4—1911no—
139C22×C4—3822no—
140C22×C4—3821no—
141C22×C4—3821no—
142D8—7642no—
143D8—7642no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—3821no—
147C4⋊C4—21no—
148C4⋊C4—3822no—
149C4⋊C4—1911no—
150C4⋊C4—1911no—
151C4⋊C4D76412yes—
152C22⋊C4—3822no—
153C22⋊C4—3821no—
154C22⋊C4—3821no—
155C42C22×D19111yescharacteristic
156C23—3821no—
157C23—3821no—
158C23—7641no—
159Q8—41no—
160Q8—41no—
161D4—3821no—
162D4—3821no—
163D4—3821no—
164D4—1912no—
165D4—7642no—
166D4—7644no—
167D4—7641no—
168D4—7641no—
169D4—7641no—
170D4—7641no—
171C2×C4—22no—
172C2×C4—3821no—
173C2×C4—3821no—
174C2×C4—7644no—
175C2×C4—7641no—
176C2×C4—7641no—
177C2×C4—7641no—
178C2×C4—7641no—
179C2×C4D4×D19111yescharacteristic
180C2×C4D4×D19111yescharacteristic
181C2×C4C2×D76411yescharacteristic
182C8—41no—
183C8—41no—
184C8—7641no—
185C22—3822no—
186C22—15281no—
187C22—15281no—
188C22—15281no—
189C22—7641no—
190C22—7641no—
191C22—7641no—
192C22—7641no—
193C22—7641no—
194C22#2025929211yescharacteristic
195C4—21no—
196C4—42no—
197C4—7641no—
198C4—7641no—
199C4D8×D19111yescharacteristic
200C4#2025934511yescharacteristic
201C4#2025934911yescharacteristic
202C4#2025934911yescharacteristic
203C2—30561no—
204C2—15281no—
205C2—7642no—
206C2#2713279811yescharacteristic
207C2#2713281111yescharacteristic
208C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#332×C191C2
socleC22×C191#120
hypercenter#332D191
hypocenterC191#1625
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #27133316C2semidirect
2. #27133011C2semidirect
3. #27132859C2semidirect
4. #27132859C2semidirect
5. #27132390C2semidirect
6. #27132390C2semidirect
7. #332×C191C2semidirect
63. D764D8semidirect
104. C191#1625semidirect
110. #332D191semidirect

Maximal subgroups

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

subgroupindex
#271333162
#271330112
#271328592
#271323902
#332×C1912
#1625191