Finite Group Databasebeta

← #21429047

Subgroups — #21429047

Order 7552.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14273704C214yesmaximal, complemented
3C2×D4×Dic59C211yesmaximal, characteristic
4#16837338C214yesmaximal, complemented
5#16837305C211yesmaximal, characteristic
6#16837272C211yesmaximal, characteristic, complemented
7#16837271C211yesmaximal, characteristic, complemented
8C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
9C59×#390C211yesmaximal, characteristic
10C22×Dic118C2212yes—
11C23×Dic59C2212yes—
12#14273726—24no—
13#14273704—216no—
14D4×Dic59—24no—
15C2×C4⋊Dic59C2214yes—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2211yescharacteristic
18C2×Dic59⋊C4C2214yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×C22⋊Dic59C2214yes—
22C2×C22⋊Dic59C2212yes—
23C2×C4×Dic59C2211yescharacteristic
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2212yes—
26C22×D4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C22⋊C4×C59C2214yes—
29C2×C42×C59C2211yescharacteristic
30C24×C59C2312yes—
31C2×D4×C59—22no—
32C2×D4×C59—22no—
33C2×D4×C59Q814yescomplemented
34C22×C4×C59C2312yes—
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×Dic59—24no—
38C22×Dic59—28no—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2311yescharacteristic
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C2×Dic118—28no—
45C2×Dic118—24no—
46C4⋊C4×C59—22no—
47C22⋊C4×C59—28no—
48C42×C59—22no—
49C22⋊Dic59—24no—
50C22⋊Dic59—28no—
51C4⋊Dic59—22no—
52C4⋊Dic59—28no—
53C4⋊Dic59—22no—
54Dic59⋊C4—28no—
55Dic59⋊C4—24no—
56Dic59⋊C4D418yescomplemented
57C4×Dic59—22no—
58C4×Dic59D414yes—
59C23×C59—24no—
60C23×C59—22no—
61C23×C59—22no—
62C23×C59—24no—
63C23×C59C2×Q814yes—
64C23×C59C2411yescharacteristic
65D4×C59—28no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—24no—
69C2×C4×C59—22no—
70C2×C4×C59C2×D414yes—
71C2×C4×C59C2×D412yes—
72C2×C4×C59C2×Q812yes—
73C2×C4×C59#4112yes—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—24no—
79C2×Dic59—24no—
80C2×Dic59—22no—
81C2×Dic59—48no—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D414yes—
84C2×Dic59C2×D412yes—
85C2×Dic59C2×D414yes—
86Dic118—48no—
87C22×C59—24no—
88C22×C59—28no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—44no—
92C22×C59C22×D411yescharacteristic
93C22×C59C22×D412yes—
94C22×C59C22×Q811yescharacteristic
95C22×C59C2×#4111yescharacteristic
96C22×C592−1+412yes—
97C4×C59—24no—
98C4×C59—42no—
99C4×C59C22⋊Q814yescomplemented
100Dic59—22no—
101Dic59—24no—
102Dic59—42no—
103Dic59—42no—
104Dic59#12714yes—
105#2542—591nomaximal, Sylow
106C2×C59—44no—
107C2×C59C2×C22⋊Q811yescharacteristic
108C2×C59C2×#12711yescharacteristic
109C2×C59#53611yescharacteristic
110C2×C59#54712yes—
111C2×C59D4×Q812yes—
112C2×C4⋊Q8—591no—
113C2×C22⋊Q8—594no—
114C2×C4×D4—591no—
115#399—594no—
116#390—591no—
117#390D5911yescharacteristic
118#384—591no—
119#384—591no—
120C4×C4⋊C4—591no—
121C59#254211yescharacteristic, complemented, Sylow
122C22×Q8—592no—
123C22×D4C2×D5911yescharacteristic
124C23×C4—592no—
125C4⋊Q8—1184no—
126C22⋊Q8—11816no—
127C4×D4—1184no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—591no—
130C2×C4⋊C4—594no—
131C2×C4⋊C4—594no—
132C2×C4⋊C4—591no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4C2×D5911yescharacteristic
135C2×C22⋊C4—592no—
136C2×C22⋊C4—594no—
137C2×C22⋊C4C2×D5914yes—
138C2×C42—591no—
139C2×C42—591no—
140C2×C42C2×D5911yescharacteristic
141#95—592no—
142C24C22×D5912yes—
143C2×Q8—1188no—
144C2×Q8—1184no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4Dic11814yescomplemented
148C22×C4—591no—
149C22×C4—591no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4—592no—
153C22×C4—1184no—
154C22×C4—1188no—
155C22×C4C22×D5912yes—
156C22×C4C22×D5912yes—
157C22×C4C22×D5911yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—598no—
160C4⋊C4—1188no—
161C4⋊C4—1184no—
162C4⋊C4—1182no—
163C4⋊C4—1188no—
164C4⋊C4—1182no—
165C22⋊C4—28no—
166C22⋊C4—1184no—
167C22⋊C4—1188no—
168C42—22no—
169C42—594no—
170C42—1182no—
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic11814yes—
176C23C23×D5911yescharacteristic
177Q8—2368no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—592no—
184C2×C4—594no—
185C2×C4—592no—
186C2×C4—594no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—1184no—
192C2×C4—1184no—
193C2×C4—1182no—
194C2×C4—2368no—
195C2×C4C2×Dic11812yes—
196C2×C4D4×D5914yes—
197C2×C4D4×D5912yes—
198C2×C4#1174568712yes—
199C22—24no—
200C22—28no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22C2×D4×D5911yescharacteristic
205C22C2×D4×D5912yes—
206C22C22×Dic11811yescharacteristic
207C22C2×#1174568711yescharacteristic
208C22#1427377412yes—
209C4—24no—
210C4—42no—
211C4—594no—
212C4—1182no—
213C4—1184no—
214C4—2362no—
215C4—2362no—
216C4#1427370414yescomplemented
217C2—44no—
218C2C2×#1427370411yescharacteristic
219C2#127×D5911yescharacteristic
220C2#1683797211yescharacteristic
221C2#1683805212yes—
222C2D4×Dic11812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#390C2
hypercenter#390D59
hypocenterC59#2542
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14273726C2semidirect
2. C2×#14273704C2semidirect
4. #16837338C2semidirect
6. #16837272C2semidirect
7. #16837271C2semidirect
8. C4×Dic59⋊C4C2semidirect
33. C2×D4×C59Q8semidirect
56. Dic59⋊C4D4semidirect
99. C4×C59C22⋊Q8semidirect
121. C59#2542semidirect
147. C2×D4Dic118semidirect
216. C4#14273704semidirect