Finite Group Databasebeta

← #21429080

Subgroups — #21429080

Order 7552.

540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14273726C212yesmaximal
2C2×#14273726C211yesmaximal, characteristic
3C2×#14273692C211yesmaximal, characteristic
4#16837334C211yesmaximal, characteristic
5#16837333C211yesmaximal, characteristic
6#16837332C211yesmaximal, characteristic
7#16837306C212yesmaximal
8#16837299C212yesmaximal
9#16837297C212yesmaximal
10#16837253C211yesmaximal, characteristic
11C59×#398C211yesmaximal, characteristic
12C22×Dic118C2212yes—
13C22×Dic118C2211yescharacteristic
14#14273726—28no—
15#14273726—24no—
16#14273692—24no—
17C2×C4⋊Dic59C2212yes—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×Dic59⋊C4C2212yes—
25C2×C4×Dic59C2212yes—
26C2×C4×Dic59C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2211yescharacteristic
29C59⋊#95C2211yescharacteristic
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2212yes—
33C2×C4⋊C4×C59C2212yes—
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C4⋊C4×C59C2211yescharacteristic
36#95×C59C2211yescharacteristic
37#95×C59C2212yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2311yescharacteristic
49C2×Dic118—22no—
50C2×Dic118—22no—
51C2×Dic118—24no—
52C2×Dic118—24no—
53C2×Dic118—24no—
54C2×Dic118D414yes—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—24no—
57C4⋊C4×C59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—24no—
60Dic59⋊C4—22no—
61Dic59⋊C4—24no—
62Dic59⋊C4—22no—
63Dic59⋊C4—24no—
64Dic59⋊C4—24no—
65Dic59⋊C4Q818yescomplemented
66C4×Dic59—22no—
67C4×Dic59—22no—
68C4×Dic59—24no—
69C4×Dic59D414yes—
70C23×C59C2411yescharacteristic
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D412yes—
83C2×C4×C59C2×Q814yes—
84C2×Dic59—22no—
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93C2×Dic59C2×D412yes—
94C2×Dic59C2×D412yes—
95C2×Dic59C2×D412yes—
96C2×Dic59C2×D412yes—
97C2×Dic59C2×Q814yes—
98C2×Dic59C2×Q814yes—
99C2×Dic59#4112yes—
100Dic118—28no—
101Dic118—48no—
102C22×C59C22×D411yescharacteristic
103C22×C59C22×D411yescharacteristic
104C22×C59C22×Q812yes—
105C22×C59C2×#4111yescharacteristic
106C22×C592−1+412yes—
107C4×C59—22no—
108C4×C59—22no—
109C4×C59—24no—
110C4×C59—42no—
111C4×C59—41no—
112Dic59—22no—
113Dic59—24no—
114Dic59—42no—
115Dic59—41no—
116Dic59#12114yes—
117Dic59C4⋊Q814yescomplemented
118#2546—591nomaximal, Sylow
119C2×C59C2×#12111yescharacteristic
120C2×C59C2×C4⋊Q811yescharacteristic
121C2×C59#53611yescharacteristic
122C2×C59D4×Q812yes—
123C2×C59#55712yes—
124C2×C4⋊Q8—591no—
125C2×C4⋊Q8—592no—
126C2×C4×Q8—591no—
127#398—591no—
128#398—591no—
129#398—591no—
130#398D5911yescharacteristic
131#391—592no—
132#389—592no—
133#389—592no—
134C4×C4⋊C4—591no—
135C59#254611yescharacteristic, complemented, Sylow
136C22×Q8—591no—
137C22×Q8—592no—
138C4⋊Q8—1184no—
139C4⋊Q8—1188no—
140C4×Q8—1184no—
141C2×C4⋊C4—592no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—592no—
145C2×C4⋊C4—592no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4C2×D5911yescharacteristic
150C2×C4⋊C4C2×D5912yes—
151C2×C4⋊C4C2×D5911yescharacteristic
152C2×C42—591no—
153C2×C42—591no—
154C2×C42—591no—
155C2×C42—592no—
156#95—591no—
157#95—592no—
158#95—592no—
159#95—592no—
160#95C2×D5911yescharacteristic
161#95C2×D5912yes—
162C2×Q8—594no—
163C2×Q8—1182no—
164C2×Q8—1182no—
165C2×Q8—1184no—
166C2×Q8—1184no—
167C2×Q8—1184no—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4—592no—
171C22×C4—591no—
172C22×C4—591no—
173C22×C4—592no—
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5912yes—
176C22×C4C22×D5911yescharacteristic
177C22×C4C22×D5911yescharacteristic
178C22×C4C22×D5912yes—
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—598no—
183C4⋊C4—1182no—
184C4⋊C4—1184no—
185C4⋊C4—1184no—
186C4⋊C4—1184no—
187C4⋊C4—1182no—
188C4⋊C4—1184no—
189C4⋊C4—1182no—
190C42—594no—
191C42—1182no—
192C42—1182no—
193C42—1184no—
194C23C23×D5911yescharacteristic
195Q8—1188no—
196Q8—2368no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—592no—
208C2×C4—592no—
209C2×C4—592no—
210C2×C4—594no—
211C2×C4—592no—
212C2×C4—592no—
213C2×C4—594no—
214C2×C4—1182no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—1182no—
218C2×C4—1181no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4D4×D5912yes—
224C2×C4D4×D5912yes—
225C2×C4Q8×D5914yes—
226C22C2×D4×D5911yescharacteristic
227C22C2×D4×D5911yescharacteristic
228C22C2×Q8×D5912yes—
229C22#41×D5911yescharacteristic
230C22#1427377412yes—
231C4—22no—
232C4—22no—
233C4—24no—
234C4—42no—
235C4—41no—
236C4—594no—
237C4—594no—
238C4—1182no—
239C4—1184no—
240C4—2362no—
241C4—2361no—
242C2#121×D5911yescharacteristic
243C2C4⋊Q8×D5911yescharacteristic
244C2#1683797411yescharacteristic
245C2#1683806512yes—
246C2#1683812912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2546
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. Dic59⋊C4Q8semidirect
117. Dic59C4⋊Q8semidirect
135. C59#2546semidirect