Finite Group Databasebeta

← #37533934

Subgroups — #37533934

Order 23168.

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#26041756C211yesmaximal, characteristic
2#26041319C211yesmaximal, characteristic
3C2×#19153734C211yesmaximal, characteristic
4#26041184C211yesmaximal, characteristic
5#26041040C211yesmaximal, characteristic
6#26041038C211yesmaximal, characteristic
7#428×C181C211yesmaximal, characteristic
8C22×Dic362C2211yescharacteristic
9C2×#15668433C2211yescharacteristic
10C4×Dic362—21no—
11C4×Dic362—21no—
12#19153781—21no—
13#19153781—21no—
14#19153775C2211yescharacteristic
15#19153772—22no—
16C2×C4×Dic181C2211yescharacteristic
17#19153749—21no—
18#19153747—21no—
19#19153734C414yescomplemented
20#19153723—22no—
21C2×M16×C181C2211yescharacteristic
22#117×C181C2211yescharacteristic
23C2×C4⋊C4×C181C2211yescharacteristic
24#107×C181—21no—
25#106×C181—21no—
26C2×Dic362—21no—
27C2×Dic362—21no—
28C2×Dic362—21no—
29C2×Dic362—21no—
30C2×Dic362C2×C412yes—
31C2×Dic362Q812yes—
32C22×Dic181—21no—
33C22×Dic181D412yes—
34#15668433—21no—
35#15668433C2×C412yes—
36C2×#13089678—21no—
37C4⋊Dic181D411yescharacteristic
38C4⋊Dic181D411yescharacteristic
39#15668428—22no—
40#15668428—22no—
41C22⋊Dic181—21no—
42C4×Dic181—22no—
43C4×Dic181—22no—
44C4×Dic181—21no—
45C4×Dic181—21no—
46C4×Dic181—21no—
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49M16×C181—21no—
50M16×C181C2×C412yes—
51C2×C8×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181—21no—
54C4⋊C4×C181D411yescharacteristic
55C4⋊C4×C181D411yescharacteristic
56C22⋊C4×C181—21no—
57C42×C181—21no—
58Dic362—22no—
59Dic362—22no—
60Dic362—22no—
61Dic362—22no—
62C2×Dic181—22no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65C2×Dic181—21no—
66C2×Dic181—21no—
67C2×Dic181—41no—
68C2×Dic181—41no—
69C2×Dic181C4⋊C414yes—
70#13089678—22no—
71C23×C181C2×D411yescharacteristic
72C2×C4×C181—21no—
73C2×C4×C181—21no—
74C2×C4×C181—42no—
75C2×C4×C181—41no—
76C2×C4×C181C22×C411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2×Q811yescharacteristic
80C2×C4×C181#4111yescharacteristic
81C2×C4×C181#4111yescharacteristic
82C8×C181—22no—
83C22×C181—21no—
84C22×C181—21no—
85C22×C181C2×C4⋊C411yescharacteristic
86C22×C181#12011yescharacteristic
87C22×C181#12311yescharacteristic
88C4×C181—41no—
89C4×C181—41no—
90C4×C181—81no—
91C4×C181C4×D411yescharacteristic
92C4×C181C4×D411yescharacteristic
93C4×C181C22⋊Q811yescharacteristic
94C4×C181C22⋊Q811yescharacteristic
95Dic181—24no—
96Dic181—42no—
97Dic181—41no—
98Dic181—41no—
99C2×C181—21no—
100C2×C181—21no—
101C2×C181#38511yescharacteristic
102C2×C181#45411yescharacteristic
103C2×C181#45611yescharacteristic
104C181#185711yescharacteristic, complemented, Sylow
105#1857—1811nomaximal, Sylow
106#519—1811no—
107#428—1811no—
108#428D18111yescharacteristic
109C2×#101—1811no—
110#391—1811no—
111#339—1811no—
112#339—1811no—
113C22×Q8—1811no—
114C2×M16—1811no—
115C2×M16C2×D18111yescharacteristic
116C4×Q8—3621no—
117C4×Q8—3621no—
118C4×Q8—3621no—
119C4×Q8—3621no—
120#117—3622no—
121#117—1811no—
122#117C2×D18111yescharacteristic
123C2×C4⋊C4C2×D18111yescharacteristic
124C2×C42—1811no—
125#107—21no—
126#107—3621no—
127#106—21no—
128#106—3621no—
129#101—1814no—
130#95—3622no—
131C2×Q8—3621no—
132C2×Q8—3621no—
133C2×Q8—3621no—
134C2×Q8—3621no—
135C2×Q8—1812no—
136C2×Q8—1812no—
137C22×C4—21no—
138C22×C4—3621no—
139C22×C4—1812no—
140C22×C4C22×D18111yescharacteristic
141M16—21no—
142M16—3621no—
143M16—1812no—
144M16C4×D18112yes—
145C2×C8—21no—
146C2×C8—3621no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—3622no—
150C4⋊C4—3622no—
151C4⋊C4—1811no—
152C4⋊C4—1811no—
153C4⋊C4C22⋊D18111yescharacteristic
154C4⋊C4C22⋊D18111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—3621no—
157C42—21no—
158C42—3622no—
159C42—3622no—
160C42—3621no—
161C42—3621no—
162C42—3621no—
163C23D4×D18111yescharacteristic
164Q8—3622no—
165Q8—3622no—
166Q8—3622no—
167Q8—3622no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—3622no—
173C2×C4—3622no—
174C2×C4—3622no—
175C2×C4—3621no—
176C2×C4—3621no—
177C2×C4—1814no—
178C2×C4—7241no—
179C2×C4—7241no—
180C2×C4C2×C4×D18111yescharacteristic
181C2×C4D4×D18111yescharacteristic
182C2×C4C2×C22⋊D18111yescharacteristic
183C2×C4Q8×D18111yescharacteristic
184C2×C4#1566844911yescharacteristic
185C2×C4#1566845011yescharacteristic
186C8—22no—
187C8—3622no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D18111yescharacteristic
191C22#1915378411yescharacteristic
192C22#1915380111yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—3624no—
197C4—7242no—
198C4—7241no—
199C4—7241no—
200C4C4×C22⋊D18111yescharacteristic
201C4#1915377811yescharacteristic
202C4#1915379211yescharacteristic
203C4#1915379411yescharacteristic
204C2—21no—
205C2—21no—
206C2#2604115011yescharacteristic
207C2#2604145011yescharacteristic
208C2#2604146011yescharacteristic
subgroupG/H
centerC22#19153784
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#428×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
cosocleC22×C4×C181C23
hypercenter#428D181
hypocenterC181#1857
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
19. #19153734C4semidirect
104. C181#1857semidirect

Maximal subgroups

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

subgroupindex
#260417562
#260413192
C2×#191537342
#260411842
#260410402
#260410382
#428×C1812
#1857181