Finite Group Databasebeta

← #21435233

Subgroups — #21435233

Order 7552.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837957C211yesmaximal, characteristic, complemented
2#16837953C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837750C211yesmaximal, characteristic, complemented
5#16837749C211yesmaximal, characteristic, complemented
6#16837728C214yesmaximal, complemented
7#16837701C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic, complemented
9C59×#498C211yesmaximal, characteristic, complemented
10C2×#11745689—21no—
11#14273727C2211yescharacteristic
12#14273724C2211yescharacteristic
13#14273718C2212yes—
14#14273716—21no—
15#14273707—21no—
16#14273703—21no—
17#14273702—21no—
18#14273702C2212yes—
19Q8×Dic59—21no—
20#14273692—21no—
21#14273689—21no—
22#14273689C2212yes—
23#14273685C2212yes—
24C42×D59C2211yescharacteristic
25#14273660C2214yes—
26Dic59⋊C8C2212yes—
27#14273649C2214yes—
28#14273647C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#106×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59—21no—
37#11745689—44no—
38C2×D236—22no—
39C2×D236—21no—
40C2×D236—21no—
41C2×D236C2312yes—
42C2×C4×D59—22no—
43C2×C4×D59D411yescharacteristic
44C2×C4×D59D411yescharacteristic
45C2×C4×D59C2311yescharacteristic
46C2×Dic118—21no—
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59C2312yes—
51C4⋊C4×C59C2312yes—
52C42×C59C2311yescharacteristic
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56C4⋊Dic59—21no—
57C4⋊Dic59—22no—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60C4×Dic59—22no—
61C4×Dic59D411yescharacteristic
62C4×Dic59D411yescharacteristic
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2312yes—
65C22×D59—22no—
66C22×D59C2×D411yescharacteristic
67Q8×C59—42no—
68Q8×C59—42no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2411yescharacteristic
74C2×Dic59—22no—
75C2×Dic59C2×D411yescharacteristic
76C2×Dic59C2×D411yescharacteristic
77C2×Dic59C2×D411yescharacteristic
78D236—24no—
79D236—44no—
80D236—42no—
81D236—42no—
82C4×D59—22no—
83C4×D59—22no—
84C4×D59—22no—
85C4×D59—44no—
86Dic118—42no—
87C8×C59—22no—
88C59⋊C8—22no—
89C22×C59C22×D411yescharacteristic
90C2×D59—21no—
91C2×D59—21no—
92C2×D59—21no—
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—42no—
96C4×C59—42no—
97C4×C59—42no—
98C4×C59#13512yes—
99C4×C59AGL(1,ℤ/8)12yes—
100C4×C592−1+412yes—
101Dic59—21no—
102Dic59—21no—
103Dic59—21no—
104Dic59—42no—
105#3228—591nomaximal, Sylow
106C2×C59#53611yescharacteristic
107C2×C59C2×#13511yescharacteristic
108C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
109D59—41no—
110D59—82no—
111#533—591no—
112#532—591no—
113#500—591no—
114#498D5911yescharacteristic, complemented
115#486—591no—
116#486—591no—
117#482—594no—
118#478—594no—
119#431—591no—
120C59#322811yescharacteristic, complemented, Sylow
121C2×#41—1181no—
122C4⋊Q8—591no—
123C4⋊Q8C2×D5911yescharacteristic
124C4⋊Q8C2×D5911yescharacteristic
125#127—591no—
126#125—592no—
127#124—1181no—
128C22⋊Q8—1181no—
129C22⋊Q8—1181no—
130#121—592no—
131#121—1181no—
132C4×Q8—1181no—
133C4×Q8—1181no—
134C4×D4—592no—
135C4×D4—1181no—
136#117—592no—
137C2×C42—591no—
138#107—594no—
139#106C2×D5914yes—
140C4⋊C8—592no—
141#102—594no—
142#102—594no—
143C22⋊C8—592no—
144C4×C8—591no—
145C4×C8C2×D5911yescharacteristic
146#41—2364no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—1181no—
150C2×D4—592no—
151C2×D4—1182no—
152C2×D4—1181no—
153C2×D4—1181no—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4—1182no—
158C2×C8—592no—
159C2×C8C22×D5912yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—592no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—1181no—
166C4⋊C4C22×D5912yes—
167C4⋊C4C22×D5912yes—
168C22⋊C4—1182no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C42—591no—
172C42—591no—
173C42—591no—
174C42—1182no—
175C42C22×D5911yescharacteristic
176C23—591no—
177C23—1182no—
178Q8—42no—
179Q8—42no—
180Q8—2362no—
181D4—1184no—
182D4—2364no—
183D4—2362no—
184D4—2362no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—591no—
188C2×C4—591no—
189C2×C4—591no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—2364no—
195C2×C4D4×D5911yescharacteristic
196C2×C4D4×D5911yescharacteristic
197C2×C4C23×D5911yescharacteristic
198C8—22no—
199C8—1182no—
200C22—1181no—
201C22—1181no—
202C22—1181no—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22C2×D4×D5911yescharacteristic
207C4—42no—
208C4—42no—
209C4—1181no—
210C4—1181no—
211C4—1181no—
212C4—2362no—
213C4#1427374812yes—
214C4#1427375412yes—
215C4#1427377512yes—
216C2—4722no—
217C2—2361no—
218C2#1683797711yescharacteristic
219C2C2×#1427374811yescharacteristic
220C2C2×#1427375411yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#498C2
socleC22×C59C22×D4
hypercenter#498D59
hypocenterC59#3228
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837805C2semidirect
4. #16837750C2semidirect
5. #16837749C2semidirect
6. #16837728C2semidirect
7. #16837701C2semidirect
8. #16837453C2semidirect
9. C59×#498C2semidirect
114. #498D59semidirect
120. C59#3228semidirect