Finite Group Databasebeta

← C22×#22627595 #49172004

Subgroups — C22×#22627595 #49172004

Order 37504.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×C22⋊D293C212yesmaximal, complemented
2C23×C4×D293C211yesmaximal, characteristic, complemented
3C2×#22627595C2124yesmaximal, direct product factor
4C22×C4⋊Dic293C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic293C212yesmaximal, complemented
6C23×D4×C293C211yesmaximal, characteristic, complemented
7C24×D293C2211yescharacteristic
8C22×C22⋊D293—216no—
9C22×C22⋊D293C22124yescomplemented
10C23×Dic293C2211yescharacteristic
11C23×Dic293C2212yes—
12C22×C4×D293—28no—
13C22×C4×D293C22112yescomplemented
14#22627595C22164yesdirect product factor
15C2×C4⋊Dic293C22112yescomplemented
16C2×C22⋊Dic293C22124yescomplemented
17C25×C293C2212yes—
18C22×D4×C293—28no—
19C22×D4×C293C22112yescomplemented
20C23×C4×C293C2211yescharacteristic
21C23×D293—24no—
22C23×D293—24no—
23C23×D293D418yescomplemented
24C23×D293C2316yes—
25C2×C22⋊D293—296no—
26C2×C22⋊D293C23132yescomplemented
27C22×Dic293—24no—
28C22×Dic293—28no—
29C22×Dic293C2316yes—
30C22×Dic293C23112yes—
31C2×C4×D293—248no—
32C2×C4×D293C23116yescomplemented
33C4⋊Dic293C23116yescomplemented
34C22⋊Dic293C23132yescomplemented
35C24×C293—28no—
36C24×C293—28no—
37C24×C293—28no—
38C24×C293C23112yes—
39C24×C293C2311yescharacteristic
40C2×D4×C293—248no—
41C2×D4×C293C23116yescomplemented
42C22×C4×C293D418yescomplemented
43C22×C4×C293C2316yes—
44C22×D293—232no—
45C22×D293—212no—
46C22×D293—212no—
47C22×D293C2×D4124yescomplemented
48C22×D293C2414yes—
49C22⋊D293—264no—
50C2×Dic293—212no—
51C2×Dic293—224no—
52C2×Dic293C2414yes—
53C2×Dic293C2418yes—
54C4×D293—232no—
55C23×C293—224no—
56C23×C293—224no—
57C23×C293—224no—
58C23×C293—432no—
59C23×C293C2×D414yes—
60C23×C293C2×D414yes—
61C23×C293#4114yes—
62C23×C293C2418yes—
63C23×C293C2413yes—
64D4×C293—232no—
65C2×C4×C293C2×D4124yescomplemented
66C2×C4×C293C2414yes—
67C22×C293—28no—
68C22×C293—28no—
69C22×C293—28no—
70C22×C293—448no—
71C22×C293#121116yescomplemented
72C22×C293C22×D416yes—
73C22×C293C22×D416yes—
74C22×C293C2×#4116yes—
75C22×C293C2511yescharacteristic
76C2×D293—248no—
77C2×D293—24no—
78C2×D293—24no—
79C2×D293C22×D418yescomplemented
80C4×C293C22×D418yescomplemented
81Dic293—24no—
82Dic293—28no—
83C2×C293—48no—
84C2×C293C2×#121112yescomplemented
85C2×C293C23×D411yescharacteristic
86C2×C293C23×D411yescharacteristic
87C2×C293C22×#4111yescharacteristic
88D293—28no—
89C293C22×#12111yescharacteristic, complemented, Sylow
90C22×#121—2931nomaximal, Sylow
91C23×D4—2932no—
92C23×D4D29311yescharacteristic, complemented
93C24×C4—2931no—
94C2×#121—29324no—
95C22×C4⋊C4—2931no—
96C22×C22⋊C4—2932no—
97C25—2931no—
98C25C2×D29312yes—
99C22×D4—28no—
100C22×D4—29324no—
101C22×D4—58616no—
102C22×D4C2×D293112yescomplemented
103C23×C4—2931no—
104C23×C4—2932no—
105C23×C4—29312no—
106C23×C4—5868no—
107C23×C4C2×D29311yescharacteristic
108#121—29364no—
109C2×C4⋊C4—29312no—
110C2×C22⋊C4—29324no—
111C24—28no—
112C24—28no—
113C24—28no—
114C24—2938no—
115C24—2936no—
116C24—5864no—
117C24—5864no—
118C24C22×D293112yes—
119C24C22×D29311yescharacteristic
120C2×D4—248no—
121C2×D4—29332no—
122C2×D4—58696no—
123C2×D4C22×D293116yescomplemented
124C22×C4—2936no—
125C22×C4—29312no—
126C22×C4—29316no—
127C22×C4—5868no—
128C22×C4—5864no—
129C22×C4—58648no—
130C22×C4C22⋊D29318yescomplemented
131C22×C4C22×D29316yes—
132C4⋊C4—29316no—
133C22⋊C4—29332no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—29324no—
139C23—2934no—
140C23—58632no—
141C23—58612no—
142C23—58612no—
143C23D4×D29314yes—
144C23C2×C22⋊D29314yes—
145C23#1798980114yes—
146C23C23×D29318yes—
147C23C23×D29313yes—
148D4—232no—
149D4—58664no—
150C2×C4—2934no—
151C2×C4—2938no—
152C2×C4—58624no—
153C2×C4—58612no—
154C2×C4—58632no—
155C2×C4C2×C22⋊D293124yescomplemented
156C2×C4C23×D29314yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—2938no—
162C22—58648no—
163C22—5864no—
164C22—5864no—
165C22#22627595116yesdirect product factor
166C22C2×D4×D29316yes—
167C22C22×C22⋊D29316yes—
168C22C2×#1798980116yes—
169C22C24×D29311yescharacteristic
170C4—5868no—
171C4—5864no—
172C4C22×C22⋊D29318yescomplemented
173C2—48no—
174C2—5868no—
175C2C2×#22627595112yesdirect product factor
176C2C22×D4×D29311yescharacteristic
177C2C23×C22⋊D29311yescharacteristic
178C2C22×#1798980111yescharacteristic
subgroupG/H
centerC24C22×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC23×D4×C293C2
socleC24×C293C23
hypercenterC23×D4D293
hypocenterC293C22×#121
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D293C2semidirect
2. C23×C4×D293C2semidirect
3. C2×#22627595C2direct (N × H)
4. C22×C4⋊Dic293C2semidirect
5. C22×C22⋊Dic293C2semidirect
6. C23×D4×C293C2semidirect
9. C22×C22⋊D293C22semidirect
13. C22×C4×D293C22semidirect
14. #22627595C22direct (N × H)
15. C2×C4⋊Dic293C22semidirect
16. C2×C22⋊Dic293C22semidirect
19. C22×D4×C293C22semidirect
23. C23×D293D4semidirect
26. C2×C22⋊D293C23semidirect
32. C2×C4×D293C23semidirect
33. C4⋊Dic293C23semidirect
34. C22⋊Dic293C23semidirect
41. C2×D4×C293C23semidirect
42. C22×C4×C293D4semidirect
47. C22×D293C2×D4semidirect
65. C2×C4×C293C2×D4semidirect
71. C22×C293#121semidirect
79. C2×D293C22×D4semidirect
80. C4×C293C22×D4semidirect
84. C2×C293C2×#121semidirect
89. C293C22×#121semidirect
92. C23×D4D293semidirect
102. C22×D4C2×D293semidirect
123. C2×D4C22×D293semidirect
130. C22×C4C22⋊D293semidirect
155. C2×C4C2×C22⋊D293semidirect
165. C22#22627595direct (N × H)
172. C4C22×C22⋊D293semidirect
175. C2C2×#22627595direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D2932
C23×C4×D2932
C2×#226275952
C22×C4⋊Dic2932
C22×C22⋊Dic2932
C23×D4×C2932
C22×#121293