Finite Group Databasebeta

← #49183315

Subgroups — #49183315

Order 37952.

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

normal subgroups only

This group has 240 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#34039281C211yesmaximal, characteristic, complemented
2#34039275C211yesmaximal, characteristic, complemented
3#34039270C211yesmaximal, characteristic, complemented
4#34039268C211yesmaximal, characteristic, complemented
5#34039267C211yesmaximal, characteristic, complemented
6#34039266C211yesmaximal, characteristic, complemented
7#34039258C211yesmaximal, characteristic, complemented
8#34039257C211yesmaximal, characteristic, complemented
9#34039257C211yesmaximal, characteristic, complemented
10#34039257C211yesmaximal, characteristic, complemented
11#34039256C211yesmaximal, characteristic, complemented
12C4×C22⋊D593C211yesmaximal, characteristic, complemented
13#34039245C211yesmaximal, characteristic, complemented
14#34039241C211yesmaximal, characteristic, complemented
15#121×C593C211yesmaximal, characteristic, complemented
16C2×D2372C2211yescharacteristic
17C2×C22⋊D593C2211yescharacteristic
18C2×C22⋊D593C2211yescharacteristic
19C2×C22⋊D593C2211yescharacteristic
20C2×C22⋊D593C2211yescharacteristic
21C2×C22⋊D593C2211yescharacteristic
22C2×C22⋊D593C2211yescharacteristic
23C22×Dic593C2211yescharacteristic
24C22×Dic593C2211yescharacteristic
25C2×C4×D593C2211yescharacteristic
26C2×C4×D593C2211yescharacteristic
27C4⋊Dic593C2211yescharacteristic
28#23748712C2211yescharacteristic
29#23748712C2211yescharacteristic
30#23748712C2211yescharacteristic
31#23748712C2211yescharacteristic
32#23748712C2211yescharacteristic
33#23748712C2211yescharacteristic
34C22⋊Dic593C2211yescharacteristic
35C22⋊Dic593C2211yescharacteristic
36C22⋊Dic593C2211yescharacteristic
37C22⋊Dic593C2211yescharacteristic
38#23748710C2211yescharacteristic
39#23748710C2211yescharacteristic
40#23748710C2211yescharacteristic
41#23748710C2211yescharacteristic
42C4×Dic593C2211yescharacteristic
43C4×Dic593C2211yescharacteristic
44C2×D4×C593C2211yescharacteristic
45C2×D4×C593C2211yescharacteristic
46C2×D4×C593C2211yescharacteristic
47C22×C4×C593C2211yescharacteristic
48C4⋊C4×C593C2211yescharacteristic
49C22⋊C4×C593C2211yescharacteristic
50C22⋊C4×C593C2211yescharacteristic
51C22×D593C2311yescharacteristic
52C22×D593C2311yescharacteristic
53D2372—41no—
54C22⋊D593—22no—
55C22⋊D593—22no—
56C22⋊D593—41no—
57C22⋊D593—41no—
58C22⋊D593—41no—
59C22⋊D593—41no—
60C2×Dic593—22no—
61C2×Dic593—41no—
62C2×Dic593C2311yescharacteristic
63C2×Dic593C2311yescharacteristic
64C2×Dic593C2311yescharacteristic
65C2×Dic593C2311yescharacteristic
66C2×Dic593C2311yescharacteristic
67C2×Dic593C2311yescharacteristic
68C4×D593—41no—
69C4×D593—41no—
70C23×C593C2311yescharacteristic
71C23×C593C2311yescharacteristic
72C23×C593C2311yescharacteristic
73D4×C593—41no—
74D4×C593—41no—
75D4×C593—41no—
76C2×C4×C593—41no—
77C2×C4×C593C2311yescharacteristic
78C2×C4×C593C2311yescharacteristic
79C2×C4×C593C2311yescharacteristic
80C2×C4×C593C2311yescharacteristic
81C22×C593—21no—
82C22×C593—21no—
83C22×C593—21no—
84C22×C593—21no—
85C22×C593—21no—
86C22×C593—21no—
87C22×C593—21no—
88C22×C593—21no—
89C22×C593—21no—
90C22×C593C2411yescharacteristic
91C2×D593—21no—
92C2×D593—21no—
93C2×D593—21no—
94C2×D593—21no—
95C2×D593—21no—
96C2×D593—21no—
97C4×C593—21no—
98C4×C593—21no—
99C4×C593—21no—
100C4×C593—21no—
101Dic593—21no—
102Dic593—21no—
103Dic593—21no—
104Dic593—21no—
105Dic593—21no—
106Dic593#4112yes—
107C2×C593—41no—
108C2×C593—41no—
109C2×C593—41no—
110C2×C593C2×#4111yescharacteristic
111C2×C593H(5,𝔽2)11yescharacteristic
112C2×C593H(5,𝔽2)11yescharacteristic
113D593—41no—
114D593—41no—
115C593#54011yescharacteristic, complemented, Sylow
116#540—5931nomaximal, Sylow
117#127—5931no—
118#125—5931no—
119#123—5931no—
120#123—5931no—
121#123—5931no—
122#123—5931no—
123#121—5931no—
124#121—5931no—
125#121—5931no—
126#121—5931no—
127#121—5931no—
128#121D59311yescharacteristic, complemented
129C4×D4—5931no—
130C4×D4—5931no—
131#117—5931no—
132C2×D4—5931no—
133C2×D4—5931no—
134C2×D4—5931no—
135C2×D4—5931no—
136C2×D4—5931no—
137C2×D4—5931no—
138C2×D4—5931no—
139C2×D4C2×D59311yescharacteristic
140C2×D4C2×D59311yescharacteristic
141C2×D4C2×D59311yescharacteristic
142C22×C4—5931no—
143C22×C4—5931no—
144C22×C4—5931no—
145C22×C4—5931no—
146C22×C4C2×D59311yescharacteristic
147C4⋊C4—5931no—
148C4⋊C4—5931no—
149C4⋊C4—5931no—
150C4⋊C4—5931no—
151C4⋊C4—5931no—
152C4⋊C4—5931no—
153C4⋊C4—5931no—
154C4⋊C4C2×D59311yescharacteristic
155C22⋊C4—5931no—
156C22⋊C4—5931no—
157C22⋊C4—5931no—
158C22⋊C4—5931no—
159C22⋊C4—5931no—
160C22⋊C4—5931no—
161C22⋊C4—5931no—
162C22⋊C4—5931no—
163C22⋊C4C2×D59311yescharacteristic
164C22⋊C4C2×D59311yescharacteristic
165C42—5931no—
166C42—5931no—
167C23—5931no—
168C23—5931no—
169C23C22×D59311yescharacteristic
170C23C22×D59311yescharacteristic
171C23C22×D59311yescharacteristic
172D4—41no—
173D4—41no—
174D4—41no—
175D4—23721no—
176D4—23721no—
177D4—23721no—
178D4—23721no—
179D4—23721no—
180D4—11862no—
181D4—11862no—
182C2×C4—41no—
183C2×C4—23721no—
184C2×C4—23721no—
185C2×C4—23721no—
186C2×C4—5931no—
187C2×C4—5931no—
188C2×C4—5931no—
189C2×C4—5931no—
190C2×C4—5931no—
191C2×C4—5931no—
192C2×C4—11862no—
193C2×C4C22×D59311yescharacteristic
194C2×C4C22×D59311yescharacteristic
195C2×C4C22×D59311yescharacteristic
196C2×C4C22×D59311yescharacteristic
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—11861no—
207C22—11861no—
208C22—11861no—
209C22—11861no—
210C22—11861no—
211C22—11861no—
212C22C23×D59311yescharacteristic
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—5932no—
218C4—11861no—
219C4—11861no—
220C4—11861no—
221C4—11861no—
222C4—11861no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2—23721no—
227C2—23721no—
228C2#41×D59311yescharacteristic
229C2#3403933011yescharacteristic
230C2#3403933011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D593
commutator, socle, cosocleC22×C593C24
Fitting#121×C593C2
hypercenter#121D593
hypocenterC593#540
LCSG ▷ C22×C593 ▷ C593
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #34039281C2semidirect
2. #34039275C2semidirect
3. #34039270C2semidirect
4. #34039268C2semidirect
5. #34039267C2semidirect
6. #34039266C2semidirect
7. #34039258C2semidirect
8. #34039257C2semidirect
9. #34039257C2semidirect
10. #34039257C2semidirect
11. #34039256C2semidirect
12. C4×C22⋊D593C2semidirect
13. #34039245C2semidirect
14. #34039241C2semidirect
15. #121×C593C2semidirect
115. C593#540semidirect
128. #121D593semidirect

Maximal subgroups

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

subgroupindex
#340392812
#340392752
#340392702
#340392682
#340392672
#340392662
#340392582
#340392572
#340392562
C4×C22⋊D5932
#340392452
#340392412
#121×C5932
#540593