Finite Group Databasebeta

← #37571620

Subgroups — #37571620

Order 24448.

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

normal subgroups only

This group has 250 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#27133328C211yesmaximal, characteristic, complemented
2#27132860C211yesmaximal, characteristic, complemented
3#27132855C211yesmaximal, characteristic
4#27132409C211yesmaximal, characteristic, complemented
5#27132395C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7#486×C191C211yesmaximal, characteristic, complemented
8C2×Q8×D191—21no—
9C2×#15690275—21no—
10C2×#15690272—21no—
11#20259321—21no—
12#20259300—22no—
13#20259298—21no—
14C4×Dic382C2211yescharacteristic
15C4×D764C2211yescharacteristic
16#20259284—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259243—21no—
20#20259243—21no—
21C4⋊Q8×C191C2211yescharacteristic
22#127×C191C2211yescharacteristic
23#102×C191—22no—
24C4×C8×C191C2211yescharacteristic
25C2×Dic382—22no—
26C2×Dic382D411yescharacteristic
27Q8×D191—42no—
28Q8×D191—42no—
29C2×D764D411yescharacteristic
30C2×C4×D191—22no—
31C2×C4×D191—21no—
32#15690275—42no—
33#15690272—42no—
34C2×C191⋊C8—21no—
35C2×C191⋊C8—21no—
36C4⋊Dic191D411yescharacteristic
37C4⋊Dic191D411yescharacteristic
38Dic191⋊C4—22no—
39Dic191⋊C4—21no—
40(C2×D191)⋊C4—22no—
41(C2×D191)⋊C4—21no—
42C4×Dic191—21no—
43C2×Q8×C191—21no—
44C2×D4×C191—21no—
45C2×D4×C191—21no—
46C2×D4×C191—21no—
47C2×C8×C191—21no—
48C4⋊C4×C191—21no—
49C4⋊C4×C191D412yes—
50C42×C191C2311yescharacteristic
51C22×D191—21no—
52Dic382—21no—
53Dic382—44no—
54Dic382D812yescomplemented
55D764—21no—
56D764SD1612yescomplemented
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C4×D191—44no—
61C4×D191—41no—
62C4×D191—41no—
63C191⋊C8—41no—
64C191⋊C8—41no—
65C23×C191—41no—
66Q8×C191—41no—
67Q8×C191—41no—
68D4×C191—42no—
69D4×C191—41no—
70D4×C191—41no—
71D4×C191—41no—
72D4×C191—41no—
73C2×C4×C191—22no—
74C2×C4×C191C2×D411yescharacteristic
75C2×C4×C191C2×D411yescharacteristic
76C2×C4×C191C2×D411yescharacteristic
77C8×C191—41no—
78C22×C191—81no—
79C22×C191—81no—
80C22×C191—81no—
81C22×C191#12011yescharacteristic
82C2×D191—22no—
83C2×D191—41no—
84C2×D191—41no—
85C4×C191—21no—
86C4×C191—42no—
87C4×C191C2×D811yescharacteristic
88C4×C191C2×SD1611yescharacteristic
89C4×C191AGL(1,ℤ/8)11yescharacteristic
90C4×C191#13711yescharacteristic
91Dic191—22no—
92Dic191—41no—
93Dic191—41no—
94C2×C191—161no—
95C2×C191#44711yescharacteristic
96C2×C191#44811yescharacteristic
97C2×C191#45411yescharacteristic
98D191—42no—
99C191#162711yescharacteristic, complemented, Sylow
100#1627—1911nomaximal, Sylow
101D4×Q8—1911no—
102#486D19111yescharacteristic, complemented
103#460—1911no—
104#459—1911no—
105#332—1911no—
106Q8⋊C8—1911no—
107D4⋊C8—1911no—
108C22×Q8—3821no—
109C2×SD16—3821no—
110C2×D8—3821no—
111C4⋊Q8—3821no—
112C4⋊Q8C2×D19111yescharacteristic
113#127C2×D19111yescharacteristic
114C22⋊Q8—3821no—
115C22⋊Q8—3822no—
116C4×Q8—1911no—
117C4×D4—3821no—
118C4×D4—1911no—
119C4⋊C8—1911no—
120C4⋊C8—1911no—
121#102—22no—
122#102—3821no—
123#102—3821no—
124C4×C8C2×D19111yescharacteristic
125C2×Q8—21no—
126C2×Q8—3822no—
127C2×Q8—1911no—
128C2×Q8—7642no—
129C2×Q8—7642no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—1911no—
134C22×C4—3822no—
135C22×C4—3821no—
136SD16—7642no—
137D8—7642no—
138C2×C8—21no—
139C2×C8—3821no—
140C2×C8—3821no—
141C4⋊C4—21no—
142C4⋊C4—3822no—
143C4⋊C4—3821no—
144C4⋊C4—1911no—
145C4⋊C4—1911no—
146C4⋊C4C22⋊D19112yes—
147C22⋊C4—3822no—
148C22⋊C4—3821no—
149C42—3821no—
150C42C22×D19111yescharacteristic
151C23—41no—
152C23—3821no—
153Q8—41no—
154Q8—41no—
155Q8—3821no—
156Q8—1912no—
157Q8—7644no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3821no—
164D4—1912no—
165C2×C4—22no—
166C2×C4—3821no—
167C2×C4—3821no—
168C2×C4—3821no—
169C2×C4—7644no—
170C2×C4—7641no—
171C2×C4—7641no—
172C2×C4D4×D19111yescharacteristic
173C2×C4D4×D19111yescharacteristic
174C2×C4C2×C22⋊D19111yescharacteristic
175C8—41no—
176C8—7641no—
177C8—7641no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—3822no—
182C22—7641no—
183C22—7641no—
184C22#2025929011yescharacteristic
185C4—21no—
186C4—42no—
187C4—3822no—
188C4—7641no—
189C4—7641no—
190C4D8×D19111yescharacteristic
191C4SD16×D19111yescharacteristic
192C4#2025934611yescharacteristic
193C4#2025935111yescharacteristic
194C2—161no—
195C2—7642no—
196C2#2713279511yescharacteristic
197C2#2713280011yescharacteristic
198C2#2713283511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#486×C191C2
socleC22×C191#120
prime radical#27132855C2
hypercenter#486D191
hypocenterC191#1627
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #27133328C2semidirect
2. #27132860C2semidirect
4. #27132409C2semidirect
5. #27132395C2semidirect
6. #27132392C2semidirect
7. #486×C191C2semidirect
54. Dic382D8semidirect
56. D764SD16semidirect
99. C191#1627semidirect
102. #486D191semidirect

Maximal subgroups

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

subgroupindex
#271333282
#271328602
#271328552
#271324092
#271323952
#271323922
#486×C1912
#1627191