Finite Group Databasebeta

← #49174765

Subgroups — #49174765

Order 37504.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C22×#17989812C211yesmaximal, characteristic, complemented
2C2×#22627681C212yesmaximal, complemented
3C2×#22627681C211yesmaximal, characteristic, complemented
4#34036995C212yesmaximal, complemented
5C2×#22627586C211yesmaximal, characteristic
6C2×#17989812—24no—
7C2×#17989812—22no—
8C22×#14556880C2212yes—
9C22×#14556880C2212yes—
10#22627681—24no—
11#22627681—22no—
12C22×D1172C411yescharacteristic
13C22×C4×D293C2211yescharacteristic
14C22×C4×D293C2211yescharacteristic
15#22627586—22no—
16#22627586—22no—
17C2×#17989779C411yescharacteristic
18C2×#17989779C411yescharacteristic
19C2×C4×Dic293C2211yescharacteristic
20C2×C4⋊C4×C293C411yescharacteristic
21#17989812—28no—
22C2×#14556880—22no—
23C2×#14556880—22no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C2×#14556880—22no—
27C2×#14556880D414yescomplemented
28C23×D293C2×C411yescharacteristic
29C23×D293C2×C411yescharacteristic
30C2×D1172—22no—
31C2×D1172—22no—
32C2×D1172—22no—
33C22×Dic293C2×C411yescharacteristic
34C22×Dic293C2311yescharacteristic
35C2×C4×D293—22no—
36C2×C4×D293—22no—
37C2×C4×D293—21no—
38C2×C4×D293—21no—
39C2×C4×D293—22no—
40C2×C4×D293—22no—
41C2×C4×D293D412yes—
42C2×C4×D293D412yes—
43#17989779—22no—
44#17989779—22no—
45C4×Dic293—21no—
46C4×Dic293—21no—
47C22×C4×C293C2×C411yescharacteristic
48C22×C4×C293C2×C411yescharacteristic
49C22×C4×C293C2×C411yescharacteristic
50C4⋊C4×C293—22no—
51#14556880—24no—
52#14556880—42no—
53C22×D293—21no—
54C22×D293—22no—
55C22×D293—22no—
56C22×D293—21no—
57C22×D293—21no—
58C22×D293—21no—
59C22×D293—22no—
60C22×D293—22no—
61C22×D293C22⋊C412yes—
62C22×D293M1612yescomplemented
63D1172—28no—
64C2×Dic293—21no—
65C2×Dic293—22no—
66C2×Dic293C2×D412yes—
67C2×Dic293C2×D411yescharacteristic
68C2×Dic293C2×D411yescharacteristic
69C2×Dic293#4112yes—
70C4×D293—22no—
71C4×D293—24no—
72C4×D293—22no—
73C4×D293—41no—
74C4×D293—42no—
75C4×D293—41no—
76C23×C293C22×C411yescharacteristic
77C2×C4×C293—21no—
78C2×C4×C293—22no—
79C2×C4×C293—21no—
80C2×C4×C293—21no—
81C2×C4×C293—22no—
82C2×C4×C293C22⋊C412yes—
83C2×C4×C293M1612yescomplemented
84C22×C293C2×C22⋊C411yescharacteristic
85C22×C293C4×D412yes—
86C22×C293C2×M1611yescharacteristic
87C22×C293C2×M1611yescharacteristic
88C22×C293#13112yes—
89C2×D293—22no—
90C2×D293—22no—
91C2×D293—22no—
92C2×D293—22no—
93C2×D293—24no—
94C2×D293—41no—
95C2×D293—41no—
96C2×D293—42no—
97C2×D293—42no—
98C2×D293—42no—
99C4×C293—22no—
100C4×C293—22no—
101C4×C293—41no—
102Dic293—41no—
103Dic293#12011yescharacteristic
104Dic293#12112yes—
105Dic293#12311yescharacteristic
106C2×C293#38611yescharacteristic
107C2×C293#40711yescharacteristic
108C2×C293#40811yescharacteristic
109C2×C293#43512yes—
110C2×C293#43612yes—
111D293—42no—
112D293—42no—
113C293#187011yescharacteristic, complemented, Sylow
114#1870—2931nomaximal, Sylow
115C22×M16—2931no—
116C2×C4×D4—2931no—
117C2×C22⋊C8—2932no—
118C2×C22⋊C8—2931no—
119#336—2932no—
120C22×D4—2931no—
121C23×C4—2931no—
122C23×C4—2931no—
123C2×M16—5864no—
124C2×M16—5862no—
125C22×C8—2932no—
126C22×C8—2932no—
127C4×D4—5862no—
128C4×D4—5862no—
129C2×C4⋊C4#1192407811yescharacteristic
130C2×C22⋊C4—2931no—
131C2×C22⋊C4—2931no—
132C2×C42—2931no—
133C22⋊C8—5864no—
134C22⋊C8—5862no—
135C24—2931no—
136C24—2931no—
137C2×D4—5862no—
138C2×D4—5862no—
139C2×D4—5862no—
140C22×C4—2931no—
141C22×C4—2932no—
142C22×C4—2932no—
143C22×C4—2931no—
144C22×C4—5862no—
145C22×C4—5862no—
146C22×C4—5862no—
147C22×C4—5861no—
148C22×C4—5861no—
149C22×C4—5862no—
150C22×C4C2×#1192407811yescharacteristic
151C22×C4C2×#1192407811yescharacteristic
152C22×C4C2×#1192407811yescharacteristic
153M16—5868no—
154C2×C8—2934no—
155C2×C8—5862no—
156C2×C8—5862no—
157C2×C8—5862no—
158C2×C8—5862no—
159C2×C8—5862no—
160C4⋊C4—22no—
161C22⋊C4—5862no—
162C22⋊C4—5862no—
163C42—5861no—
164C42—5861no—
165C23—2932no—
166C23—2932no—
167C23—5861no—
168C23—5862no—
169C23—5862no—
170C23—5861no—
171C23—5861no—
172C23—5861no—
173C23—5862no—
174C23—5862no—
175C23C22×#1192407811yescharacteristic
176D4—5868no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—2931no—
183C2×C4—2931no—
184C2×C4—2932no—
185C2×C4—2932no—
186C2×C4—5862no—
187C2×C4—5864no—
188C2×C4—5862no—
189C2×C4—5861no—
190C2×C4—5862no—
191C2×C4—11721no—
192C2×C4—11722no—
193C2×C4—11721no—
194C2×C4C22⋊#1192407812yes—
195C2×C4#1798981212yescomplemented
196C8—5864no—
197C8—11722no—
198C22—5862no—
199C22—5862no—
200C22—5862no—
201C22—5862no—
202C22—5864no—
203C22—11721no—
204C22—11721no—
205C22—11722no—
206C22—11722no—
207C22—11722no—
208C22C2×C22⋊#1192407811yescharacteristic
209C22D4×#1192407812yes—
210C22D293⋊M1611yescharacteristic
211C22C2×#1798981211yescharacteristic
212C22#2262771212yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—2931no—
217C4—2932no—
218C4—2931no—
219C4—11721no—
220C2—11722no—
221C2—11722no—
222C2#3403707711yescharacteristic
223C2#3403710011yescharacteristic
224C2#3403710411yescharacteristic
225C2#3403715912yes—
226C2#3403716312yes—
subgroupG/H
center, FrattiniC23C22×#11924078
commutator, socleC23×C293C22×C4
FittingC2×C4⋊C4×C293C4
prime radicalC22×D1172C4
cosocleC22×Dic293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293#1870
LCSG ▷ C23×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#17989812C2semidirect
2. C2×#22627681C2semidirect
3. C2×#22627681C2semidirect
4. #34036995C2semidirect
27. C2×#14556880D4semidirect
62. C22×D293M16semidirect
83. C2×C4×C293M16semidirect
113. C293#1870semidirect
195. C2×C4#17989812semidirect

Maximal subgroups

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

subgroupindex
C22×#179898122
C2×#226276812
#340369952
C2×#226275862
#1870293