Finite Group Databasebeta

← #21431065

Subgroups — #21431065

Order 7552.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14273703C212yesmaximal, complemented
2#16837342C212yesmaximal, complemented
3#16837332C211yesmaximal, characteristic, complemented
4#16837329C212yesmaximal, complemented
5#16837319C211yesmaximal, characteristic
6#16837293C212yesmaximal, complemented
7#16837280C212yesmaximal
8#16837276C212yesmaximal, complemented
9C59×#391C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12#14273703—28no—
13C2×C4⋊Dic59C2212yes—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2211yescharacteristic
27C22×Q8×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C42×C59C2211yescharacteristic
30#95×C59C2212yes—
31#95×C59C2212yes—
32C23×D59C2312yes—
33C2×Q8×C59—41no—
34C2×Q8×C59—41no—
35C2×Q8×C59D414yescomplemented
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C2×D236—24no—
45C2×D236—41no—
46C2×C4×D59—24no—
47C2×C4×D59—42no—
48C2×C4×D59—42no—
49C4⋊C4×C59—41no—
50C42×C59—41no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—42no—
56C4⋊Dic59—24no—
57C4⋊Dic59—41no—
58Dic59⋊C4—24no—
59Dic59⋊C4—24no—
60C23×C59C2411yescharacteristic
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59—22no—
67C22×D59#4114yes—
68Q8×C59—44no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D412yes—
81C2×C4×C59C2×D414yes—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91D236—44no—
92C4×D59—48no—
93C22×C59C22×D411yescharacteristic
94C22×C59C2×#4112yes—
95C22×C59H(5,𝔽2)11yescharacteristic
96C22×C59H(5,𝔽2)11yescharacteristic
97C22×C592−1+412yes—
98C2×D59—24no—
99C2×D59—24no—
100C2×D59—24no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C4×C59—24no—
106C4×C59—22no—
107C4×C59—42no—
108C4×C59—41no—
109C4×C59—41no—
110Dic59—42no—
111Dic59—42no—
112Dic59—42no—
113#2728—591nomaximal, Sylow
114C2×C59#53411yescharacteristic
115C2×C59#53912yes—
116C2×C59#54812yes—
117C2×C59#55111yescharacteristic
118C2×C59#56311yescharacteristic
119D59—44no—
120C2×C22⋊Q8—592no—
121#400—592no—
122#398—591no—
123#397—592no—
124#394—591no—
125#391D5911yescharacteristic, complemented
126#388—592no—
127#386—592no—
128#385—592no—
129C59#272811yescharacteristic, complemented, Sylow
130C22×Q8C2×D5911yescharacteristic
131C22×D4—591no—
132C23×C4—592no—
133C22⋊Q8—1188no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—592no—
137C2×C4⋊C4—591no—
138C2×C4⋊C4C2×D5911yescharacteristic
139C2×C22⋊C4—592no—
140C2×C22⋊C4—592no—
141C2×C22⋊C4—592no—
142C2×C22⋊C4—592no—
143C2×C22⋊C4—592no—
144C2×C42C2×D5911yescharacteristic
145#95—592no—
146#95—592no—
147#95—592no—
148#95—591no—
149#95—591no—
150#95C2×D5912yes—
151#95C2×D5912yes—
152C24—592no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8D23614yescomplemented
156C2×D4—1184no—
157C2×D4—2361no—
158C22×C4—592no—
159C22×C4—592no—
160C22×C4—592no—
161C22×C4—1184no—
162C22×C4—2362no—
163C22×C4—2362no—
164C22×C4C22×D5911yescharacteristic
165C22×C4C22×D5912yes—
166C22×C4C22×D5911yescharacteristic
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—1184no—
171C4⋊C4—1184no—
172C4⋊C4—1184no—
173C4⋊C4—2361no—
174C22⋊C4—1184no—
175C22⋊C4—1184no—
176C22⋊C4—1184no—
177C22⋊C4—1184no—
178C22⋊C4—2362no—
179C42—41no—
180C23—594no—
181C23—1182no—
182C23—1182no—
183C23—1182no—
184C23—1182no—
185C23—1182no—
186C23—1182no—
187C23C23×D5911yescharacteristic
188Q8—44no—
189D4—2364no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—2368no—
211C2×C4C2×D23612yes—
212C2×C4C2×D23614yes—
213C22—1184no—
214C22—1184no—
215C22—1184no—
216C22—2362no—
217C22—2362no—
218C22—2362no—
219C22—2362no—
220C22C22×D23611yescharacteristic
221C22#41×D5912yes—
222C22#1427377211yescharacteristic
223C22#1427377211yescharacteristic
224C22#1427377512yes—
225C4—24no—
226C4—22no—
227C4—42no—
228C4—41no—
229C4—41no—
230C4—2362no—
231C4—2362no—
232C4—2362no—
233C2—2364no—
234C2#1683796411yescharacteristic
235C2#1683799812yes—
236C2#1683806412yes—
237C2#1683808211yescharacteristic
238C2#1683815111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#391C2
hypercenter#391D59
hypocenterC59#2728
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14273703C2semidirect
2. #16837342C2semidirect
3. #16837332C2semidirect
4. #16837329C2semidirect
6. #16837293C2semidirect
8. #16837276C2semidirect
9. C59×#391C2semidirect
35. C2×Q8×C59D4semidirect
125. #391D59semidirect
129. C59#2728semidirect
155. C2×Q8D236semidirect