Finite Group Databasebeta

← #21425271

Subgroups — #21425271

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#16837955C211yesmaximal, characteristic, complemented
2#16837418C211yesmaximal, characteristic
3C2×#14273653C211yesmaximal, characteristic
4#16837375C211yesmaximal, characteristic
5#16837163C211yesmaximal, characteristic, complemented
6#16837159C211yesmaximal, characteristic, complemented
7C59×#344C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273726—21no—
10#14273718—21no—
11#14273704—22no—
12C4×Dic118—22no—
13#14273686C2211yescharacteristic
14#14273686C2211yescharacteristic
15C2×C4×Dic59C2211yescharacteristic
16#14273653—21no—
17#14273653—21no—
18#14273653—22no—
19#14273641—22no—
20C2×M16×C59C2211yescharacteristic
21C2×M16×C59C2211yescharacteristic
22#117×C59C2211yescharacteristic
23C22×C4×C59C2311yescharacteristic
24C2×C22⋊D59—21no—
25C22×Dic59—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—
36M16×C59—21no—
37M16×C59—21no—
38C2×C8×C59—21no—
39C2×C8×C59—21no—
40C4⋊C4×C59—21no—
41C22⋊C4×C59D412yes—
42C42×C59—21no—
43C22⋊Dic59—21no—
44C22⋊Dic59—21no—
45C4⋊Dic59—22no—
46C4⋊Dic59—21no—
47C4⋊Dic59—21no—
48Dic59⋊C4—22no—
49Dic59⋊C4—22no—
50C4×Dic59—21no—
51C4×Dic59—21no—
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C4×Dic59D412yes—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57C2×C4×C59—22no—
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×Q811yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C22⋊D59—41no—
65C22⋊D59—41no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—22no—
69C2×Dic59—21no—
70C2×Dic59—42no—
71C2×Dic59—41no—
72D236—21no—
73D236—21no—
74C4×D59—41no—
75C4×D59—41no—
76Dic118—21no—
77Dic118—21no—
78Dic118—44no—
79C8×C59—41no—
80C8×C59—41no—
81C22×C59—41no—
82C22×C59#12011yescharacteristic
83C22×C59C22⋊Q811yescharacteristic
84C22×C59#12411yescharacteristic
85C2×D59—41no—
86C2×D59—81no—
87C4×C59—42no—
88C4×C59C22⋊Q811yescharacteristic
89C4×C59C22⋊Q811yescharacteristic
90C4×C59#12411yescharacteristic
91C4×C59#12411yescharacteristic
92Dic59—22no—
93Dic59—42no—
94Dic59—41no—
95Dic59—41no—
96Dic59—81no—
97#2031—591nomaximal, Sylow
98C2×C59—21no—
99C2×C59—21no—
100C2×C59—21no—
101C2×C59#39311yescharacteristic
102D59—81no—
103#533—591no—
104#421—591no—
105C2×#104—591no—
106#410—591no—
107#344D5911yescharacteristic, complemented
108#339—591no—
109H(3,ℤ/4)—591no—
110C59#203111yescharacteristic, complemented, Sylow
111C2×#41—591no—
112C2×M16C2×D5911yescharacteristic
113C2×M16C2×D5911yescharacteristic
114C4⋊Q8—1181no—
115#125—1181no—
116C22⋊Q8—1182no—
117C4×Q8—1182no—
118#117—591no—
119#117—591no—
120#117C2×D5911yescharacteristic
121C2×C42—591no—
122#104—1181no—
123#104—1181no—
124#104—1182no—
125#99—1182no—
126#41—1181no—
127#41—1181no—
128#41—1181no—
129#41—1181no—
130C2×Q8—591no—
131C2×Q8—1182no—
132C2×D4—591no—
133C2×D4—1181no—
134C22×C4—1181no—
135C22×C4—1181no—
136C22×C4C22×D5911yescharacteristic
137M16—21no—
138M16—21no—
139M16—21no—
140M16—21no—
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—1182no—
145C4⋊C4—1182no—
146C4⋊C4—1182no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C22⋊C4—1181no—
150C22⋊C4—1181no—
151C22⋊C4D23612yes—
152C42—21no—
153C42—591no—
154C42—591no—
155C42—592no—
156C42—1181no—
157C42—1181no—
158C23—1181no—
159C23C2×D23611yescharacteristic
160Q8—1181no—
161Q8—1181no—
162Q8—2364no—
163D4—1181no—
164D4—1181no—
165D4—2361no—
166D4—2361no—
167C2×C4—22no—
168C2×C4—1181no—
169C2×C4—1181no—
170C2×C4—1182no—
171C2×C4—1181no—
172C2×C4—2362no—
173C2×C4—2361no—
174C2×C4—2361no—
175C2×C4—2361no—
176C2×C4#1174568511yescharacteristic
177C2×C4#1174568511yescharacteristic
178C2×C4D4×D5911yescharacteristic
179C2×C4D4×D5911yescharacteristic
180C2×C4#1174568711yescharacteristic
181C2×C4Q8×D5911yescharacteristic
182C8—41no—
183C8—41no—
184C22—41no—
185C22—4721no—
186C22—2361no—
187C22#1427369711yescharacteristic
188C22#1427370711yescharacteristic
189C22#1427371511yescharacteristic
190C4—42no—
191C4—1182no—
192C4—4721no—
193C4—2361no—
194C4—2362no—
195C4—2361no—
196C4#1427370511yescharacteristic
197C4#1427370511yescharacteristic
198C4#1427371311yescharacteristic
199C4#1427371311yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4721no—
204C2#1683731511yescharacteristic
subgroupG/H
centerC4#14273713
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#344C2
socleC2×C59#393
hypercenter#344D59
hypocenterC59#2031
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #16837955C2semidirect
5. #16837163C2semidirect
6. #16837159C2semidirect
7. C59×#344C2semidirect
30. C2×D236Q8semidirect
33. C2×Dic118Q8semidirect
107. #344D59semidirect
110. C59#2031semidirect