Finite Group Databasebeta

← #37572736

Subgroups — #37572736

Order 24448.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#27133140C211yesmaximal, characteristic
2#27132706C211yesmaximal, characteristic
3#27132705C211yesmaximal, characteristic
4C2×#20259240C211yesmaximal, characteristic
5#27132569C211yesmaximal, characteristic
6#27132423C211yesmaximal, characteristic
7#339×C191C211yesmaximal, characteristic
8C22×Dic382C2211yescharacteristic
9C2×#15690271C2211yescharacteristic
10C4×Dic382—21no—
11C4×Dic382—21no—
12#20259287—21no—
13#20259287—21no—
14#20259281C2211yescharacteristic
15#20259278—22no—
16C2×C4⋊Dic191C2211yescharacteristic
17#20259256—21no—
18#20259255—21no—
19#20259254—21no—
20#20259253—21no—
21#20259240C414yescomplemented
22C191⋊#95—22no—
23C2×M16×C191C2211yescharacteristic
24#117×C191C2211yescharacteristic
25C2×C42×C191C2211yescharacteristic
26C2×Dic382—21no—
27C2×Dic382—21no—
28C2×Dic382—21no—
29C2×Dic382—21no—
30C2×Dic382C2×C412yes—
31C2×Dic382Q812yes—
32C22×Dic191—21no—
33C22×Dic191D412yes—
34#15690271—21no—
35#15690271C2×C412yes—
36C2×C191⋊C8—21no—
37C4⋊Dic191—21no—
38C4⋊Dic191—21no—
39C4⋊Dic191D411yescharacteristic
40C4⋊Dic191D411yescharacteristic
41Dic191⋊C4—22no—
42Dic191⋊C4—22no—
43C22⋊Dic191—21no—
44C4×Dic191—22no—
45C4×Dic191—22no—
46C4×Dic191—21no—
47C22×C4×C191—21no—
48C22×C4×C191C2311yescharacteristic
49M16×C191—21no—
50M16×C191C2×C412yes—
51C2×C8×C191—21no—
52C4⋊C4×C191D411yescharacteristic
53C4⋊C4×C191D411yescharacteristic
54C22⋊C4×C191—21no—
55C42×C191—21no—
56C42×C191—21no—
57C42×C191—21no—
58Dic382—22no—
59Dic382—22no—
60Dic382—22no—
61Dic382—22no—
62C2×Dic191—22no—
63C2×Dic191—22no—
64C2×Dic191—21no—
65C2×Dic191—21no—
66C2×Dic191—42no—
67C2×Dic191—41no—
68C2×Dic191C4⋊C414yes—
69C191⋊C8—22no—
70C23×C191C2×D411yescharacteristic
71C2×C4×C191—22no—
72C2×C4×C191—21no—
73C2×C4×C191—21no—
74C2×C4×C191—41no—
75C2×C4×C191—41no—
76C2×C4×C191C22×C411yescharacteristic
77C2×C4×C191C2×D411yescharacteristic
78C2×C4×C191C2×D411yescharacteristic
79C2×C4×C191C2×Q811yescharacteristic
80C2×C4×C191#4111yescharacteristic
81C2×C4×C191#4111yescharacteristic
82C8×C191—22no—
83C22×C191—21no—
84C22×C191—21no—
85C22×C191C2×C4⋊C411yescharacteristic
86C22×C191#12011yescharacteristic
87C22×C191#12311yescharacteristic
88C4×C191—42no—
89C4×C191—41no—
90C4×C191—41no—
91C4×C191C4×D411yescharacteristic
92C4×C191C4×D411yescharacteristic
93C4×C191C22⋊Q811yescharacteristic
94C4×C191C22⋊Q811yescharacteristic
95Dic191—24no—
96Dic191—41no—
97Dic191—41no—
98Dic191—81no—
99C2×C191—21no—
100C2×C191—21no—
101C2×C191#38511yescharacteristic
102C2×C191#45411yescharacteristic
103C2×C191#45611yescharacteristic
104C191#185711yescharacteristic, complemented, Sylow
105#1857—1911nomaximal, Sylow
106#519—1911no—
107#428—1911no—
108#428—1911no—
109C2×#101—1911no—
110#391—1911no—
111#339—1911no—
112#339D19111yescharacteristic
113C22×Q8—1911no—
114C2×M16—1911no—
115C2×M16C2×D19111yescharacteristic
116C4×Q8—3821no—
117C4×Q8—3821no—
118C4×Q8—3821no—
119C4×Q8—3821no—
120#117—3822no—
121#117—1911no—
122#117C2×D19111yescharacteristic
123C2×C4⋊C4—1911no—
124C2×C42C2×D19111yescharacteristic
125#107—3821no—
126#107—3821no—
127#106—3821no—
128#106—3821no—
129#101—1914no—
130#95—3822no—
131C2×Q8—3821no—
132C2×Q8—3821no—
133C2×Q8—3821no—
134C2×Q8—3821no—
135C2×Q8—1912no—
136C2×Q8—1912no—
137C22×C4—21no—
138C22×C4—3821no—
139C22×C4—1912no—
140C22×C4C22×D19111yescharacteristic
141M16—21no—
142M16—3821no—
143M16—1912no—
144M16C4×D19112yes—
145C2×C8—21no—
146C2×C8—3821no—
147C4⋊C4—3822no—
148C4⋊C4—3822no—
149C4⋊C4—3821no—
150C4⋊C4—3821no—
151C4⋊C4—1911no—
152C4⋊C4—1911no—
153C4⋊C4D76411yescharacteristic
154C4⋊C4D76411yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—3821no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—3822no—
161C42—3822no—
162C42—3821no—
163C23D4×D19111yescharacteristic
164Q8—3822no—
165Q8—3822no—
166Q8—3822no—
167Q8—3822no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3822no—
174C2×C4—3822no—
175C2×C4—3821no—
176C2×C4—3821no—
177C2×C4—1914no—
178C2×C4—7642no—
179C2×C4—7641no—
180C2×C4C2×C4×D19111yescharacteristic
181C2×C4D4×D19111yescharacteristic
182C2×C4C2×D76411yescharacteristic
183C2×C4Q8×D19111yescharacteristic
184C2×C4#1569028611yescharacteristic
185C2×C4#1569028711yescharacteristic
186C8—22no—
187C8—3822no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D19111yescharacteristic
191C22#2025929211yescharacteristic
192C22#2025930411yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—3824no—
197C4—15281no—
198C4—7641no—
199C4—7641no—
200C4(C22⋊D191)⋊C411yescharacteristic
201C4C4×D76411yescharacteristic
202C4#2025930011yescharacteristic
203C4#2025930211yescharacteristic
204C2—21no—
205C2—21no—
206C2#2713253711yescharacteristic
207C2#2713283711yescharacteristic
208C2#2713284711yescharacteristic
subgroupG/H
centerC22#20259292
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#339×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
cosocleC22×C4×C191C23
hypercenter#339D191
hypocenterC191#1857
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #20259240C4semidirect
104. C191#1857semidirect

Maximal subgroups

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

subgroupindex
#271331402
#271327062
#271327052
C2×#202592402
#271325692
#271324232
#339×C1912
#1857191