Finite Group Databasebeta

← #49174222

Subgroups — #49174222

Order 37504.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D293⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#34037071C211yesmaximal, characteristic, complemented
3#34036981C214yesmaximal, complemented
4C2×#22627599C211yesmaximal, characteristic
5C2×D293⋊C8—21no—
6C2×C4⋊#11924078—21no—
7C2×C22⋊#11924078—21no—
8#22627681C2212yescomplemented
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4C2212yescomplemented
11C22×D1172—21no—
12C22×D1172C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627599—21no—
15#22627599—21no—
16#22627599C412yescomplemented
17#22627599C2212yes—
18C2×#17989779—21no—
19C2×C4⋊C4×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21D293⋊C8—42no—
22C2×#14556880—22no—
23C4⋊#11924078—42no—
24C22⋊#11924078—42no—
25C23×D293—21no—
26C23×D293D411yescharacteristic
27C2×D1172—22no—
28C2×D1172—22no—
29C2×D1172—21no—
30C2×D1172—42no—
31C2×D1172—42no—
32C2×D1172—42no—
33C2×D1172C2×C412yes—
34C22×Dic293D411yescharacteristic
35C2×C4×D293—42no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39C2×C4×D293C2311yescharacteristic
40#17989779—22no—
41#17989779—22no—
42C22×C4×C293—21no—
43C22×C4×C293C2×C411yescharacteristic
44C4⋊C4×C293—21no—
45C4⋊C4×C293C2×C412yes—
46C2×#11924078—42no—
47C2×#11924078—42no—
48C2×#11924078—42no—
49#14556880—42no—
50C22×D293—22no—
51C22×D293—41no—
52C22×D293—41no—
53C22×D293—42no—
54C22×D293—42no—
55C22×D293—42no—
56C22×D293C22⋊C411yescharacteristic
57C22×D293D812yes—
58C22×D293SD1612yes—
59C22×D293C2×D411yescharacteristic
60D1172—42no—
61D1172—44no—
62D1172—42no—
63D1172—42no—
64D1172—42no—
65C2×Dic293—41no—
66C2×Dic293C22⋊C411yescharacteristic
67C2×Dic293C2×D411yescharacteristic
68C4×D293—22no—
69C4×D293—22no—
70C4×D293—41no—
71C4×D293—41no—
72C23×C293C22⋊C411yescharacteristic
73C2×C4×C293—22no—
74C2×C4×C293—22no—
75C2×C4×C293—42no—
76C2×C4×C293C22⋊C411yescharacteristic
77C2×C4×C293C22×C411yescharacteristic
78C22×C293—21no—
79C22×C293—21no—
80C22×C293#10212yes—
81C22×C293C2×C22⋊C411yescharacteristic
82C2×D293—21no—
83C2×D293—21no—
84C2×D293—21no—
85C2×D293—21no—
86C2×D293—42no—
87C2×D293—42no—
88C2×D293—42no—
89C2×D293—42no—
90C2×D293—42no—
91C2×D293—84no—
92C2×D293#10212yes—
93C2×D293C2×D811yescharacteristic
94C2×D293C2×SD1611yescharacteristic
95#11924078—82no—
96C4×C293—21no—
97C4×C293—42no—
98C4×C293#9912yes—
99Dic293—21no—
100Dic293—21no—
101C2×C293—22no—
102C2×C293C2×#9911yescharacteristic
103C2×C293C2×#10211yescharacteristic
104C2×C293#42111yescharacteristic
105D293—21no—
106D293—22no—
107D293—21no—
108D293—82no—
109C293#151911yescharacteristic, complemented, Sylow
110#1519—2931nomaximal, Sylow
111C2×#121—2931no—
112C2×C22⋊C8—2931no—
113#380—2931no—
114#327—2934no—
115C22×D4—2931no—
116C22×D4—5861no—
117C23×C4—2931no—
118C22×C8—5861no—
119#121—2932no—
120#121—2932no—
121#121—5861no—
122#121—5861no—
123C2×C4⋊C4—5861no—
124C2×C4⋊C4#1192407811yescharacteristic, complemented
125C2×C22⋊C4—5861no—
126C2×C22⋊C4—5861no—
127C22⋊C8—2932no—
128C22⋊C8—5861no—
129#95—2932no—
130C24—2931no—
131C24—5861no—
132C2×D4—2932no—
133C2×D4—5862no—
134C2×D4—5862no—
135C2×D4—5861no—
136C2×D4—11722no—
137C2×D4—11722no—
138C2×D4—11722no—
139C22×C4—21no—
140C22×C4—2931no—
141C22×C4—2931no—
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—5862no—
146C22×C4—11722no—
147C22×C4C2×#1192407811yescharacteristic
148C2×C8—5862no—
149C2×C8—11722no—
150C4⋊C4—21no—
151C4⋊C4—11722no—
152C4⋊C4C2×#1192407812yes—
153C22⋊C4—5862no—
154C22⋊C4—5862no—
155C22⋊C4—11722no—
156C23—2931no—
157C23—2931no—
158C23—2932no—
159C23—2932no—
160C23—5862no—
161C23—11722no—
162C23—11722no—
163C23—11721no—
164C23—11721no—
165C23—11722no—
166C23C22⋊#1192407811yescharacteristic
167D4—11722no—
168D4—11722no—
169D4—11724no—
170D4—11722no—
171D4—11722no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—2931no—
176C2×C4—2931no—
177C2×C4—5862no—
178C2×C4—5862no—
179C2×C4—11721no—
180C2×C4—11721no—
181C2×C4—11722no—
182C2×C4—11722no—
183C2×C4—11722no—
184C2×C4—11721no—
185C2×C4C22⋊#1192407811yescharacteristic
186C2×C4C22×#1192407811yescharacteristic
187C8—11722no—
188C22—21no—
189C22—21no—
190C22—2931no—
191C22—2932no—
192C22—2931no—
193C22—23444no—
194C22—5861no—
195C22—5861no—
196C22—5861no—
197C22—5861no—
198C22—11722no—
199C22—11722no—
200C22—11722no—
201C22—11722no—
202C22—11722no—
203C22#2262768612yes—
204C22C2×C22⋊#1192407811yescharacteristic
205C4—21no—
206C4—42no—
207C4—23442no—
208C4—5861no—
209C4—5861no—
210C4#2262768312yes—
211C2—22no—
212C2—23442no—
213C2—5861no—
214C2—5862no—
215C2—5861no—
216C2C2×#2262768311yescharacteristic
217C2C2×#2262768611yescharacteristic
218C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×C4⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×#22627599C2
cosocleC2×C4×D293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293#1519
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D293⋊(C22⋊C8)C2semidirect
2. #34037071C2semidirect
3. #34036981C2semidirect
8. #22627681C22semidirect
10. (C2×#11924078)⋊C4C22semidirect
12. C22×D1172C4semidirect
16. #22627599C4semidirect
19. C2×C4⋊C4×C293C4semidirect
109. C293#1519semidirect
124. C2×C4⋊C4#11924078semidirect

Maximal subgroups

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

subgroupindex
D293⋊(C22⋊C8)2
#340370712
#340369812
C2×#226275992
#1519293