Finite Group Databasebeta

← #49174221

Subgroups — #49174221

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#34036980C214yesmaximal, complemented
4C2×#22627595C211yesmaximal, characteristic
5C2×D293⋊C8—21no—
6C2×C4⋊#11924078—21no—
7C2×C22⋊#11924078—21no—
8#22627681C2212yescomplemented
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4C2212yescomplemented
11C22×C22⋊D293—21no—
12C22×C4×D293C2211yescharacteristic
13#22627595—21no—
14#22627595—21no—
15#22627595C412yescomplemented
16#22627595C2212yes—
17C2×C4⋊Dic293C411yescharacteristic, complemented
18C2×C22⋊Dic293—21no—
19C22×D4×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21D293⋊C8—42no—
22C2×#14556880—22no—
23C4⋊#11924078—42no—
24C22⋊#11924078—42no—
25C23×D293D411yescharacteristic
26C2×C22⋊D293—22no—
27C2×C22⋊D293—22no—
28C2×C22⋊D293—42no—
29C2×C22⋊D293—42no—
30C22×Dic293—21no—
31C22×Dic293D411yescharacteristic
32C2×C4×D293—42no—
33C2×C4×D293C2×C411yescharacteristic
34C2×C4×D293D411yescharacteristic
35C2×C4×D293D411yescharacteristic
36C2×C4×D293C2311yescharacteristic
37C4⋊Dic293—21no—
38C4⋊Dic293C2×C412yes—
39C22⋊Dic293—22no—
40C22⋊Dic293—22no—
41C24×C293—21no—
42C2×D4×C293—21no—
43C2×D4×C293—42no—
44C2×D4×C293C2×C412yes—
45C22×C4×C293C2×C411yescharacteristic
46C2×#11924078—42no—
47C2×#11924078—42no—
48C2×#11924078—42no—
49#14556880—42no—
50C22×D293—41no—
51C22×D293—41no—
52C22×D293C22⋊C411yescharacteristic
53C22×D293D812yes—
54C22×D293SD1612yes—
55C22×D293C2×D411yescharacteristic
56C22⋊D293—44no—
57C22⋊D293—42no—
58C22⋊D293—42no—
59C2×Dic293—22no—
60C2×Dic293—41no—
61C2×Dic293—42no—
62C2×Dic293C22⋊C411yescharacteristic
63C2×Dic293C2×D411yescharacteristic
64C4×D293—22no—
65C4×D293—22no—
66C4×D293—41no—
67C4×D293—41no—
68C23×C293—22no—
69C23×C293—42no—
70C23×C293—42no—
71C23×C293—42no—
72C23×C293C22⋊C411yescharacteristic
73D4×C293—42no—
74D4×C293—42no—
75C2×C4×C293—22no—
76C2×C4×C293C22⋊C411yescharacteristic
77C2×C4×C293C22×C411yescharacteristic
78C22×C293—21no—
79C22×C293—21no—
80C22×C293—42no—
81C22×C293—42no—
82C22×C293—42no—
83C22×C293—84no—
84C22×C293#10212yes—
85C22×C293C2×C22⋊C411yescharacteristic
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—21no—
89C2×D293—21no—
90C2×D293—42no—
91C2×D293—42no—
92C2×D293#10212yes—
93C2×D293C2×D811yescharacteristic
94C2×D293C2×SD1611yescharacteristic
95#11924078—82no—
96C4×C293—21no—
97C4×C293#9912yes—
98Dic293—21no—
99Dic293—21no—
100Dic293—42no—
101C2×C293—22no—
102C2×C293—82no—
103C2×C293C2×#9911yescharacteristic
104C2×C293C2×#10211yescharacteristic
105C2×C293#42111yescharacteristic
106D293—21no—
107D293—22no—
108D293—21no—
109C293#151911yescharacteristic, complemented, Sylow
110#1519—2931nomaximal, Sylow
111C2×#121—2931no—
112C2×C22⋊C8—2931no—
113#380—2931no—
114#327—2934no—
115C22×D4—5861no—
116C22×D4#1192407811yescharacteristic, complemented
117C23×C4—2931no—
118C22×C8—5861no—
119#121—2932no—
120#121—2932no—
121#121—5861no—
122#121—5861no—
123C2×C4⋊C4—2931no—
124C2×C4⋊C4—5861no—
125C2×C22⋊C4—5861no—
126C2×C22⋊C4—5861no—
127C22⋊C8—2932no—
128C22⋊C8—5861no—
129#95—2932no—
130C24—21no—
131C24—2931no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—5862no—
135C2×D4—5862no—
136C2×D4—11722no—
137C2×D4—11722no—
138C2×D4C2×#1192407812yes—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—2931no—
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—5861no—
145C22×C4—5862no—
146C22×C4—11722no—
147C22×C4C2×#1192407811yescharacteristic
148C2×C8—5862no—
149C2×C8—11722no—
150C4⋊C4—2932no—
151C4⋊C4—5861no—
152C4⋊C4—11722no—
153C22⋊C4—5862no—
154C22⋊C4—5862no—
155C22⋊C4—11722no—
156C23—22no—
157C23—42no—
158C23—42no—
159C23—42no—
160C23—2931no—
161C23—2931no—
162C23—2932no—
163C23—2932no—
164C23—11721no—
165C23—11721no—
166C23C22⋊#1192407811yescharacteristic
167D4—42no—
168D4—42no—
169D4—11722no—
170D4—11724no—
171D4—11722no—
172C2×C4—22no—
173C2×C4—2931no—
174C2×C4—2931no—
175C2×C4—5862no—
176C2×C4—5862no—
177C2×C4—5862no—
178C2×C4—11721no—
179C2×C4—11721no—
180C2×C4—11722no—
181C2×C4—11722no—
182C2×C4—11722no—
183C2×C4—11721no—
184C2×C4—11722no—
185C2×C4C22⋊#1192407811yescharacteristic
186C2×C4C22×#1192407811yescharacteristic
187C8—11722no—
188C22—21no—
189C22—21no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—84no—
194C22—2931no—
195C22—2932no—
196C22—2931no—
197C22—5861no—
198C22—5861no—
199C22—5861no—
200C22—5861no—
201C22—11722no—
202C22—11722no—
203C22#2262768612yes—
204C22C2×C22⋊#1192407811yescharacteristic
205C4—21no—
206C4—23442no—
207C4—5861no—
208C4—5861no—
209C4—11722no—
210C4#2262768212yes—
211C2—22no—
212C2—82no—
213C2—5861no—
214C2—5862no—
215C2—5861no—
216C2C2×#2262768211yescharacteristic
217C2C2×#2262768611yescharacteristic
218C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×#22627595C2
cosocleC2×C4×D293C23
hypercenterC22×D4#11924078
hypocenterC293#1519
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. D293⋊(C22⋊C8)C2semidirect
2. #34037071C2semidirect
3. #34036980C2semidirect
8. #22627681C22semidirect
10. (C2×#11924078)⋊C4C22semidirect
15. #22627595C4semidirect
17. C2×C4⋊Dic293C4semidirect
19. C22×D4×C293C4semidirect
109. C293#1519semidirect
116. C22×D4#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
#340369802
C2×#226275952
#1519293