Finite Group Databasebeta

← #21429048

Subgroups — #21429048

Order 7552.

676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#14273726C211yesmaximal, characteristic, complemented
2C2×#14273705C214yesmaximal, complemented
3C2×#14273689C211yesmaximal, characteristic
4#16837337C214yesmaximal, complemented
5#16837304C211yesmaximal, characteristic
6#16837303C211yesmaximal, characteristic
7#16837271C211yesmaximal, characteristic, complemented
8C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
9C59×#384C211yesmaximal, characteristic, complemented
10C22×Dic118C2212yes—
11C22×D236C2211yescharacteristic
12C22×C4×D59C2212yes—
13#14273726—24no—
14#14273705—216no—
15#14273689—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2214yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2214yes—
21C2×(C2×D59)⋊C4C2214yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×C4×Dic59C2211yescharacteristic
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2212yes—
26C2×C4⋊C4×C59C2214yes—
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C42×C59C2211yescharacteristic
30C23×D59C2312yes—
31C22×C4×C59C2312yes—
32C22×C4×C59C2312yes—
33C22×C4×C59C2312yes—
34C22×C4×C59C2311yescharacteristic
35C22×Dic59C2312yes—
36C22×Dic59C2311yescharacteristic
37C22×Dic59C2312yes—
38C22×Dic59C2311yescharacteristic
39C2×D236—22no—
40C2×D236—22no—
41C2×D236Q814yescomplemented
42C2×C4×D59—24no—
43C2×C4×D59—28no—
44C2×Dic118—28no—
45C2×Dic118—24no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—28no—
48C4⋊C4×C59—22no—
49C42×C59—22no—
50(C2×D59)⋊C4—28no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—28no—
53C4⋊Dic59—22no—
54Dic59⋊C4—28no—
55Dic59⋊C4—24no—
56Dic59⋊C4D418yescomplemented
57C4×Dic59—22no—
58C4×Dic59D414yes—
59C23×C59C2411yescharacteristic
60C22×D59—24no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—24no—
64C22×D59C2×Q814yes—
65C2×C4×C59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—24no—
69C2×C4×C59—24no—
70C2×C4×C59—22no—
71C2×C4×C59C2×D414yes—
72C2×C4×C59C2×D412yes—
73C2×C4×C59C2×Q812yes—
74C2×C4×C59#4112yes—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—24no—
80C2×Dic59C2×D412yes—
81C2×Dic59C2×D414yes—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D414yes—
84D236—28no—
85C4×D59—48no—
86Dic118—48no—
87C22×C59C22×D411yescharacteristic
88C22×C59C22×D412yes—
89C22×C59C22×Q811yescharacteristic
90C22×C59C2×#4111yescharacteristic
91C22×C592−1+412yes—
92C2×D59—24no—
93C2×D59—28no—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—44no—
97C4×C59—24no—
98C4×C59—42no—
99C4×C59—42no—
100C4×C59C22⋊Q814yescomplemented
101Dic59—22no—
102Dic59—24no—
103Dic59—42no—
104Dic59#12714yes—
105#2542—591nomaximal, Sylow
106C2×C59C2×C22⋊Q811yescharacteristic
107C2×C59C2×#12711yescharacteristic
108C2×C59#53611yescharacteristic
109C2×C59#54712yes—
110C2×C59D4×Q812yes—
111D59—44no—
112C2×C4⋊Q8—591no—
113C2×C22⋊Q8—594no—
114C2×C4×D4—591no—
115#399—594no—
116#390—591no—
117#390—591no—
118#384—591no—
119#384D5911yescharacteristic, complemented
120C4×C4⋊C4—591no—
121C59#254211yescharacteristic, complemented, Sylow
122C22×Q8—592no—
123C22×D4—591no—
124C23×C4—592no—
125C4⋊Q8—1184no—
126C22⋊Q8—11816no—
127C4×D4—1184no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—594no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4—592no—
132C2×C4⋊C4C2×D5911yescharacteristic
133C2×C4⋊C4C2×D5914yes—
134C2×C4⋊C4C2×D5911yescharacteristic
135C2×C22⋊C4—592no—
136C2×C22⋊C4—594no—
137C2×C22⋊C4—594no—
138C2×C42—591no—
139C2×C42—591no—
140C2×C42C2×D5911yescharacteristic
141#95—592no—
142C24—592no—
143C2×Q8—1188no—
144C2×Q8—1184no—
145C2×D4—594no—
146C2×D4—1182no—
147C2×D4—1182no—
148C22×C4—591no—
149C22×C4—591no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4—1184no—
153C22×C4—1188no—
154C22×C4C22×D5912yes—
155C22×C4C22×D5912yes—
156C22×C4C22×D5912yes—
157C22×C4C22×D5911yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—28no—
160C4⋊C4—22no—
161C4⋊C4—598no—
162C4⋊C4—1188no—
163C4⋊C4—1184no—
164C4⋊C4—1182no—
165C22⋊C4—1184no—
166C22⋊C4—1188no—
167C22⋊C4—1188no—
168C42—22no—
169C42—594no—
170C42—1182no—
171C23—594no—
172C23—1184no—
173C23—1182no—
174C23—1182no—
175C23—1184no—
176C23C23×D5911yescharacteristic
177Q8—2368no—
178D4—1188no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—592no—
186C2×C4—594no—
187C2×C4—592no—
188C2×C4—594no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1184no—
193C2×C4—1182no—
194C2×C4—2368no—
195C2×C4#1174568512yes—
196C2×C4D4×D5914yes—
197C2×C4D4×D5912yes—
198C2×C4Q8×D5912yes—
199C22—1184no—
200C22—1188no—
201C22—2362no—
202C22—2362no—
203C22—2364no—
204C22C2×D4×D5911yescharacteristic
205C22C2×D4×D5912yes—
206C22C2×Q8×D5911yescharacteristic
207C22C2×#1174568511yescharacteristic
208C22#1427377512yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—594no—
213C4—1182no—
214C4—1184no—
215C4—2362no—
216C4#1427370514yescomplemented
217C2—2364no—
218C2C2×#1427370511yescharacteristic
219C2#127×D5911yescharacteristic
220C2#1683797711yescharacteristic
221C2#1683805312yes—
222C2#1683806712yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#384C2
hypercenter#384D59
hypocenterC59#2542
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#14273726C2semidirect
2. C2×#14273705C2semidirect
4. #16837337C2semidirect
7. #16837271C2semidirect
8. C4×Dic59⋊C4C2semidirect
9. C59×#384C2semidirect
41. C2×D236Q8semidirect
56. Dic59⋊C4D4semidirect
100. C4×C59C22⋊Q8semidirect
119. #384D59semidirect
121. C59#2542semidirect
216. C4#14273705semidirect