Finite Group Databasebeta

← #37534825

Subgroups — #37534825

Order 23168.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#26042079C211yesmaximal, characteristic, complemented
2#26042077C212yesmaximal, complemented
3#26041245C212yesmaximal, complemented
4#26041037C211yesmaximal, characteristic, complemented
5#408×C181C211yesmaximal, characteristic, complemented
6C2×#15668449C2212yes—
7#19153849—22no—
8#19153847—22no—
9#19153846—22no—
10#19153844—22no—
11#19153842—22no—
12#19153841—22no—
13#19153838—22no—
14#19153836—24no—
15C2×#15668433C2212yes—
16#19153728—24no—
17C2×#41×C181C2211yescharacteristic
18C2×M16×C181C2211yescharacteristic
19C22×C8×C181C2211yescharacteristic
20C22⋊C8×C181—22no—
21#15668449—22no—
22#15668449—22no—
23#15668449—22no—
24#15668449—22no—
25C2×Dic362D412yes—
26C2×D724D412yes—
27C2×C22⋊D181—22no—
28C2×C4×D181—22no—
29Dic724—22no—
30#15668439—24no—
31#15668438—24no—
32#15668437—24no—
33#15668436—24no—
34D1448—22no—
35#15668434—24no—
36#15668433—22no—
37#15668433—22no—
38C2×#13089678D414yes—
39#41×C181—22no—
40#41×C181—22no—
41C2×Q8×C181D411yescharacteristic
42C2×D4×C181—21no—
43C2×D4×C181D411yescharacteristic
44C22×C4×C181—21no—
45C22×C4×C181C2311yescharacteristic
46M16×C181—22no—
47C2×C8×C181—21no—
48C2×C8×C181—22no—
49C2×C8×C181D412yes—
50C22×D181—22no—
51Dic362—22no—
52Dic362—22no—
53D724—22no—
54D724—22no—
55C22⋊D181—42no—
56C22⋊D181—42no—
57C2×Dic181—22no—
58C4×D181—42no—
59C4×D181—42no—
60#13089678—24no—
61C23×C181—21no—
62C23×C181#4111yescharacteristic
63Q8×C181—22no—
64D4×C181—22no—
65D4×C181—42no—
66C2×C4×C181—21no—
67C2×C4×C181—41no—
68C2×C4×C181—41no—
69C2×C4×C181C2×D412yes—
70C2×C4×C181C2×D412yes—
71C2×C4×C181C2×D411yescharacteristic
72C2×C4×C181C2×D411yescharacteristic
73C8×C181—22no—
74C8×C181—41no—
75C22×C181—41no—
76C22×C181—42no—
77C22×C181—41no—
78C22×C181#12112yes—
79C22×C181#12111yescharacteristic
80C2×D181—44no—
81C2×D181—42no—
82C4×C181—41no—
83C4×C181#12011yescharacteristic
84C4×C181#12012yes—
85C4×C181#12711yescharacteristic
86Dic181—42no—
87C2×C181—22no—
88C2×C181—21no—
89C2×C181—81no—
90C2×C181#39211yescharacteristic
91D181—82no—
92C181#201711yescharacteristic, complemented, Sylow
93#2017—1811nomaximal, Sylow
94#575—1812no—
95#575—1811no—
96#408—1812no—
97#408D18111yescharacteristic, complemented
98#338—1811no—
99C2×#41—1812no—
100C2×#41C2×D18111yescharacteristic
101#137—3622no—
102#137—3622no—
103#137—3622no—
104AGL(1,ℤ/8)—3622no—
105AGL(1,ℤ/8)—3622no—
106AGL(1,ℤ/8)—3622no—
107#135—3624no—
108#135—3622no—
109C2×M16—1812no—
110C2×M16C2×D18111yescharacteristic
111C22×C8C2×D18111yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—3624no—
114#41—22no—
115#41—22no—
116#41—3622no—
117#41—3622no—
118#41—3622no—
119#41—3622no—
120C2×Q8—1812no—
121C2×Q8D72411yescharacteristic
122C2×D4—21no—
123C2×D4—3622no—
124C2×D4—1812no—
125C2×D4D72411yescharacteristic
126C22×C4—21no—
127C22×C4—3622no—
128C22×C4C22×D18111yescharacteristic
129Q16—3622no—
130Q16—3624no—
131SD16—3624no—
132SD16—3624no—
133SD16—3624no—
134D8—3622no—
135D8—3624no—
136M16—22no—
137M16—3622no—
138M16—3622no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—1814no—
142C2×C8C22⋊D18112yes—
143C23—21no—
144C23—3622no—
145C23#1566844911yescharacteristic
146Q8—22no—
147Q8—3622no—
148Q8—3622no—
149D4—22no—
150D4—42no—
151D4—3622no—
152D4—3622no—
153D4—7242no—
154D4—7242no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3622no—
159C2×C4—7242no—
160C2×C4—7242no—
161C2×C4D4×D18112yes—
162C2×C4D4×D18112yes—
163C2×C4C2×C22⋊D18111yescharacteristic
164C2×C4C2×D72411yescharacteristic
165C8—22no—
166C8—41no—
167C8—3624no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—7244no—
172C22—7242no—
173C22#1915378912yes—
174C22#1915379011yescharacteristic
175C4—41no—
176C4—7242no—
177C4#1915378411yescharacteristic
178C4#1915378612yes—
179C4#1915381211yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—14482no—
184C2#2604118811yescharacteristic
subgroupG/H
centerC4#19153812
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#408×C181C2
socleC2×C181#392
hypercenter#408D181
hypocenterC181#2017
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #26042079C2semidirect
2. #26042077C2semidirect
3. #26041245C2semidirect
4. #26041037C2semidirect
5. #408×C181C2semidirect
92. C181#2017semidirect
97. #408D181semidirect

Maximal subgroups

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

subgroupindex
#260420792
#260420772
#260412452
#260410372
#408×C1812
#2017181