Finite Group Databasebeta

← #49183306

Subgroups — #49183306

Order 37952.

218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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#34039280C211yesmaximal, characteristic, complemented
2#34039277C211yesmaximal, characteristic, complemented
3#34039276C211yesmaximal, characteristic, complemented
4#34039270C211yesmaximal, characteristic, complemented
5#34039269C211yesmaximal, characteristic, complemented
6#34039267C211yesmaximal, characteristic, complemented
7#34039267C211yesmaximal, characteristic, complemented
8#34039265C211yesmaximal, characteristic, complemented
9#34039263C211yesmaximal, characteristic, complemented
10#34039262C211yesmaximal, characteristic, complemented
11#34039258C211yesmaximal, characteristic
12C4×D2372C211yesmaximal, characteristic, complemented
13#34039245C211yesmaximal, characteristic, complemented
14C4⋊C4×D593C211yesmaximal, characteristic, complemented
15#126×C593C211yesmaximal, characteristic, complemented
16C2×Dic1186C2211yescharacteristic
17C2×D2372C2211yescharacteristic
18C2×C22⋊D593C2211yescharacteristic
19C2×C22⋊D593C2211yescharacteristic
20C22×Dic593C2211yescharacteristic
21C2×C4×D593C2211yescharacteristic
22C2×C4×D593C2211yescharacteristic
23C2×C4×D593C2211yescharacteristic
24C2×C4×D593C2211yescharacteristic
25C4⋊Dic593C2211yescharacteristic
26C4⋊Dic593C2211yescharacteristic
27C4⋊Dic593C2211yescharacteristic
28C4⋊Dic593C2211yescharacteristic
29C4⋊Dic593C2211yescharacteristic
30#23748712C2211yescharacteristic
31#23748712C2211yescharacteristic
32#23748712C2211yescharacteristic
33#23748712C2211yescharacteristic
34#23748712C2211yescharacteristic
35#23748712C2211yescharacteristic
36C22⋊Dic593C2211yescharacteristic
37#23748710C2211yescharacteristic
38#23748710C2211yescharacteristic
39#23748710C2211yescharacteristic
40#23748710C2211yescharacteristic
41#23748710C2211yescharacteristic
42#23748710C2211yescharacteristic
43C4×Dic593C2211yescharacteristic
44C4⋊C4×C593C2211yescharacteristic
45C4⋊C4×C593C2211yescharacteristic
46C4⋊C4×C593C2211yescharacteristic
47C22⋊C4×C593C2211yescharacteristic
48C22⋊C4×C593C2211yescharacteristic
49C22⋊C4×C593C2211yescharacteristic
50C42×C593C2211yescharacteristic
51C22×D593C2311yescharacteristic
52C22×D593C2311yescharacteristic
53Dic1186—41no—
54D2372—22no—
55C22⋊D593—22no—
56C22⋊D593—41no—
57C2×Dic593—41no—
58C2×Dic593C2311yescharacteristic
59C2×Dic593C2311yescharacteristic
60C2×Dic593C2311yescharacteristic
61C2×Dic593C2311yescharacteristic
62C2×Dic593C2311yescharacteristic
63C2×Dic593C2311yescharacteristic
64C4×D593—22no—
65C4×D593—41no—
66C4×D593—41no—
67C4×D593—41no—
68C23×C593C2311yescharacteristic
69C2×C4×C593C2311yescharacteristic
70C2×C4×C593C2311yescharacteristic
71C2×C4×C593C2311yescharacteristic
72C2×C4×C593C2311yescharacteristic
73C2×C4×C593C2311yescharacteristic
74C2×C4×C593C2311yescharacteristic
75C22×C593—21no—
76C22×C593—21no—
77C22×C593—21no—
78C22×C593C2411yescharacteristic
79C2×D593—21no—
80C2×D593—21no—
81C2×D593—21no—
82C2×D593—21no—
83C2×D593—21no—
84C2×D593#4112yes—
85C4×C593—21no—
86C4×C593—21no—
87C4×C593—21no—
88C4×C593—21no—
89C4×C593—21no—
90C4×C593—21no—
91Dic593—21no—
92Dic593—21no—
93Dic593—21no—
94Dic593—21no—
95Dic593—21no—
96Dic593—21no—
97C2×C593—41no—
98C2×C593C2×#4111yescharacteristic
99C2×C593H(5,𝔽2)11yescharacteristic
100C2×C5932−1+411yescharacteristic
101D593—22no—
102D593—41no—
103C593#53911yescharacteristic, complemented, Sylow
104#539—5931nomaximal, Sylow
105#126—5931no—
106#126D59311yescharacteristic, complemented
107#125—5931no—
108#125—5931no—
109#123—5931no—
110#123—5931no—
111#123—5931no—
112#123—5931no—
113C22⋊Q8—5931no—
114C22⋊Q8—5931no—
115C22⋊Q8—5931no—
116#121—5931no—
117C4×D4—5931no—
118C4×D4—5931no—
119C2×C4⋊C4—5931no—
120C2×Q8—5931no—
121C2×D4—5931no—
122C2×D4—5931no—
123C2×D4—5931no—
124C22×C4—5931no—
125C22×C4—5931no—
126C22×C4—5931no—
127C22×C4—5931no—
128C22×C4—5931no—
129C4⋊C4—5931no—
130C4⋊C4—5931no—
131C4⋊C4—5931no—
132C4⋊C4—5931no—
133C4⋊C4—5931no—
134C4⋊C4—5931no—
135C4⋊C4—5931no—
136C4⋊C4—5931no—
137C4⋊C4—5931no—
138C4⋊C4—5931no—
139C4⋊C4—5931no—
140C4⋊C4C2×D59311yescharacteristic
141C4⋊C4C2×D59311yescharacteristic
142C4⋊C4C2×D59311yescharacteristic
143C22⋊C4—5931no—
144C22⋊C4—5931no—
145C22⋊C4—5931no—
146C22⋊C4—5931no—
147C22⋊C4—5931no—
148C22⋊C4—5931no—
149C22⋊C4—5931no—
150C22⋊C4C2×D59311yescharacteristic
151C22⋊C4C2×D59311yescharacteristic
152C22⋊C4C2×D59311yescharacteristic
153C42—5931no—
154C42C2×D59311yescharacteristic
155C23—5931no—
156C23—5931no—
157C23C22×D59311yescharacteristic
158Q8—23721no—
159D4—23721no—
160D4—11862no—
161D4—11862no—
162C2×C4—23721no—
163C2×C4—23721no—
164C2×C4—23721no—
165C2×C4—23721no—
166C2×C4—5931no—
167C2×C4—5931no—
168C2×C4—5931no—
169C2×C4—5931no—
170C2×C4—5931no—
171C2×C4—5931no—
172C2×C4—11862no—
173C2×C4C22×D59311yescharacteristic
174C2×C4C22×D59311yescharacteristic
175C2×C4C22×D59311yescharacteristic
176C2×C4C22×D59311yescharacteristic
177C2×C4C22×D59311yescharacteristic
178C2×C4C22×D59311yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—5932no—
183C22—11861no—
184C22—11861no—
185C22—11861no—
186C22—11861no—
187C22—11861no—
188C22C23×D59311yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—11861no—
196C4—11861no—
197C4—11861no—
198C4—11861no—
199C4—11861no—
200C4—11861no—
201C2—41no—
202C2—23721no—
203C2—11862no—
204C2#41×D59311yescharacteristic
205C2#3403933111yescharacteristic
206C2#3403933211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D593
commutator, socle, cosocleC22×C593C24
Fitting#126×C593C2
prime radical#34039258C2
hypercenter#126D593
hypocenterC593#539
LCSG ▷ C22×C593 ▷ C593
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #34039280C2semidirect
2. #34039277C2semidirect
3. #34039276C2semidirect
4. #34039270C2semidirect
5. #34039269C2semidirect
6. #34039267C2semidirect
7. #34039267C2semidirect
8. #34039265C2semidirect
9. #34039263C2semidirect
10. #34039262C2semidirect
12. C4×D2372C2semidirect
13. #34039245C2semidirect
14. C4⋊C4×D593C2semidirect
15. #126×C593C2semidirect
103. C593#539semidirect
106. #126D593semidirect

Maximal subgroups

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

subgroupindex
#340392802
#340392772
#340392762
#340392702
#340392692
#340392672
#340392652
#340392632
#340392622
#340392582
C4×D23722
#340392452
C4⋊C4×D5932
#126×C5932
#539593