Finite Group Databasebeta

← #21425269

Subgroups — #21425269

Order 7552.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#16837959C211yesmaximal, characteristic, complemented
2#16837418C211yesmaximal, characteristic
3C2×#14273655C211yesmaximal, characteristic
4#16837375C211yesmaximal, characteristic
5#16837173C211yesmaximal, characteristic, complemented
6#16837158C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273727—21no—
11#14273719—21no—
12#14273706—22no—
13C4×Dic118—22no—
14#14273686C2211yescharacteristic
15#14273686C2211yescharacteristic
16#14273655—21no—
17#14273655—21no—
18#14273653—22no—
19#14273641—22no—
20C2×M16×C59C2211yescharacteristic
21#117×C59C2211yescharacteristic
22C2×C42×C59C2211yescharacteristic
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C2×C22⋊D59—21no—
26#11745685—21no—
27#11745685—21no—
28#11745685—21no—
29#11745685—21no—
30C2×D236Q811yescharacteristic, complemented
31C2×C4×D59—21no—
32C2×Dic118—22no—
33C2×Dic118Q811yescharacteristic, complemented
34M16×C59—21no—
35M16×C59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C22⋊C4×C59—21no—
39C42×C59—21no—
40C42×C59—21no—
41C42×C59D411yescharacteristic
42C42×C59D411yescharacteristic
43C22⋊Dic59—21no—
44C22⋊Dic59D412yes—
45C4⋊Dic59—22no—
46C4⋊Dic59—21no—
47C4⋊Dic59—21no—
48Dic59⋊C4—24no—
49C4×Dic59—21no—
50C4×Dic59D412yes—
51#11745664—21no—
52#11745664—21no—
53C2×C59⋊C8—21no—
54C23×C59C2×D411yescharacteristic
55C22×D59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—42no—
59C2×C4×C59—41no—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×Q811yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C22⋊D59—41no—
67C22⋊D59—41no—
68C2×Dic59—22no—
69C2×Dic59—22no—
70C2×Dic59—21no—
71D236—21no—
72D236—21no—
73C4×D59—41no—
74C4×D59—41no—
75Dic118—21no—
76Dic118—21no—
77Dic118—44no—
78C8×C59—41no—
79C59⋊C8—41no—
80C22×C59—41no—
81C22×C59#12011yescharacteristic
82C22×C59C22⋊Q811yescharacteristic
83C22×C59#12411yescharacteristic
84C2×D59—41no—
85C2×D59—81no—
86C4×C59—22no—
87C4×C59—41no—
88C4×C59—81no—
89C4×C59C22⋊Q811yescharacteristic
90C4×C59C22⋊Q811yescharacteristic
91C4×C59#12411yescharacteristic
92C4×C59#12411yescharacteristic
93Dic59—42no—
94Dic59—42no—
95Dic59—41no—
96#2031—591nomaximal, Sylow
97C2×C59—21no—
98C2×C59—21no—
99C2×C59—21no—
100C2×C59#39311yescharacteristic
101D59—81no—
102#533—591no—
103#421—591no—
104C2×#104—591no—
105#410—591no—
106#344—591no—
107#339D5911yescharacteristic, complemented
108H(3,ℤ/4)—591no—
109C59#203111yescharacteristic, complemented, Sylow
110C2×#41—591no—
111C2×M16—591no—
112C2×M16C2×D5911yescharacteristic
113C4⋊Q8—1181no—
114#125—1181no—
115C22⋊Q8—1182no—
116C4×Q8—1182no—
117#117—591no—
118#117—591no—
119#117C2×D5911yescharacteristic
120C2×C42C2×D5911yescharacteristic
121#104—1182no—
122#104—1181no—
123#104—1181no—
124#99—1182no—
125#41—1181no—
126#41—1181no—
127#41—1181no—
128#41—1181no—
129C2×Q8—591no—
130C2×Q8—1182no—
131C2×D4—591no—
132C2×D4—1181no—
133C22×C4—21no—
134C22×C4—1181no—
135C22×C4C22×D5911yescharacteristic
136M16—21no—
137M16—21no—
138M16—1181no—
139M16—1181no—
140C2×C8—21no—
141C2×C8—1181no—
142C4⋊C4—21no—
143C4⋊C4—1184no—
144C4⋊C4—1182no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C22⋊C4—21no—
148C22⋊C4—592no—
149C22⋊C4—1181no—
150C42—21no—
151C42—21no—
152C42—592no—
153C42—1181no—
154C42D23611yescharacteristic
155C42D23611yescharacteristic
156C23—1181no—
157C23D4×D5911yescharacteristic
158Q8—1181no—
159Q8—1181no—
160Q8—2364no—
161D4—1181no—
162D4—1181no—
163D4—2361no—
164D4—2361no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—1182no—
170C2×C4—1182no—
171C2×C4—1181no—
172C2×C4—2361no—
173C2×C4—2361no—
174C2×C4C2×D23611yescharacteristic
175C2×C4#1174568511yescharacteristic
176C2×C4#1174568511yescharacteristic
177C2×C4D4×D5911yescharacteristic
178C2×C4#1174568711yescharacteristic
179C2×C4Q8×D5911yescharacteristic
180C8—41no—
181C8—2361no—
182C22—41no—
183C22—4721no—
184C22—2361no—
185C22#1427369711yescharacteristic
186C22#1427370511yescharacteristic
187C22#1427371311yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—2362no—
192C4—2362no—
193C4—2361no—
194C4#1427370511yescharacteristic
195C4#1427370711yescharacteristic
196C4#1427371311yescharacteristic
197C4#1427371511yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—4721no—
202C2#1683731511yescharacteristic
subgroupG/H
centerC4#14273713
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC2×C59#393
hypercenter#339D59
hypocenterC59#2031
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #16837959C2semidirect
5. #16837173C2semidirect
6. #16837158C2semidirect
7. C59×#339C2semidirect
30. C2×D236Q8semidirect
33. C2×Dic118Q8semidirect
107. #339D59semidirect
109. C59#2031semidirect