Finite Group Databasebeta

← #21432060

Subgroups — #21432060

Order 7552.

392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 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#16837335C212yesmaximal
2#16837334C212yesmaximal
3#16837323C212yesmaximal
4#16837309C212yesmaximal
5#16837308C211yesmaximal, characteristic
6#16837300C211yesmaximal, characteristic
7#16837299C212yesmaximal
8#16837285C212yesmaximal
9C59×#391C211yesmaximal, characteristic
10C22×Dic118C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2212yes—
14C2×C4⋊Dic59C2212yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×C4×Dic59C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C22×Q8×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28C2×C42×C59C2211yescharacteristic
29#95×C59C2212yes—
30#95×C59C2212yes—
31C2×Q8×C59—41no—
32C2×Q8×C59—41no—
33C2×Q8×C59Q814yescomplemented
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C2×Dic118—22no—
44C2×Dic118—41no—
45C2×Dic118—41no—
46C4⋊C4×C59—41no—
47C42×C59—41no—
48C4⋊Dic59—41no—
49C4⋊Dic59—42no—
50C4⋊Dic59—41no—
51C4⋊Dic59—42no—
52C4⋊Dic59Q814yescomplemented
53Dic59⋊C4—24no—
54Dic59⋊C4—42no—
55Dic59⋊C4—42no—
56C4×Dic59—42no—
57C23×C59C2411yescharacteristic
58Q8×C59—44no—
59C2×C4×C59—22no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—22no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59C2×Q814yes—
71C2×C4×C59C2×Q812yes—
72C2×C4×C59C2×Q812yes—
73C2×C4×C59#4112yes—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59C2×Q814yes—
86Dic118—44no—
87C22×C59C22×Q811yescharacteristic
88C22×C59C22×Q811yescharacteristic
89C22×C59C2×#4111yescharacteristic
90C22×C59H(5,𝔽2)11yescharacteristic
91C22×C59H(5,𝔽2)11yescharacteristic
92C22×C59H(5,𝔽2)11yescharacteristic
93C22×C592−1+411yescharacteristic
94C4×C59—22no—
95C4×C59—24no—
96C4×C59—22no—
97C4×C59—22no—
98C4×C59—42no—
99Dic59—24no—
100Dic59—42no—
101Dic59—42no—
102Dic59—42no—
103#2806—591nomaximal, Sylow
104C2×C59#53811yescharacteristic
105C2×C59#54311yescharacteristic
106C2×C59#54411yescharacteristic
107C2×C59#55411yescharacteristic
108C2×C59#55711yescharacteristic
109C2×C59Q8211yescharacteristic
110C2×C59#56211yescharacteristic
111#398—592no—
112#398—592no—
113#395—592no—
114#391—592no—
115#391—591no—
116#391D5911yescharacteristic
117#389—591no—
118#389—592no—
119#387—592no—
120C59#280611yescharacteristic, complemented, Sylow
121C22×Q8—591no—
122C22×Q8C2×D5911yescharacteristic
123C2×C4⋊C4—591no—
124C2×C4⋊C4—592no—
125C2×C4⋊C4—592no—
126C2×C4⋊C4—591no—
127C2×C4⋊C4—592no—
128C2×C4⋊C4—591no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4—592no—
131C2×C4⋊C4C2×D5911yescharacteristic
132C2×C42—592no—
133C2×C42C2×D5911yescharacteristic
134#95—592no—
135#95—592no—
136#95—592no—
137#95—592no—
138#95—592no—
139#95—592no—
140#95C2×D5912yes—
141#95C2×D5912yes—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—1182no—
145C2×Q8—2361no—
146C2×Q8—2361no—
147C2×Q8Dic11814yescomplemented
148C22×C4—592no—
149C22×C4—592no—
150C22×C4—592no—
151C22×C4—592no—
152C22×C4C22×D5912yes—
153C22×C4C22×D5911yescharacteristic
154C22×C4C22×D5912yes—
155C22×C4C22×D5911yescharacteristic
156C22×C4C22×D5911yescharacteristic
157C4⋊C4—41no—
158C4⋊C4—594no—
159C4⋊C4—1184no—
160C4⋊C4—2362no—
161C4⋊C4—2362no—
162C4⋊C4—2361no—
163C4⋊C4—2362no—
164C4⋊C4—2361no—
165C4⋊C4—2362no—
166C42—41no—
167C42—2362no—
168C23C23×D5911yescharacteristic
169Q8—44no—
170Q8—2364no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—594no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4C2×Dic11812yes—
195C2×C4C2×Dic11814yes—
196C2×C4Q8×D5912yes—
197C2×C4#1174568912yes—
198C22C2×Q8×D5911yescharacteristic
199C22C22×Dic11811yescharacteristic
200C22C2×#1174568911yescharacteristic
201C22#1427377211yescharacteristic
202C22#1427377211yescharacteristic
203C22#1427377311yescharacteristic
204C22#1427377411yescharacteristic
205C4—22no—
206C4—22no—
207C4—24no—
208C4—22no—
209C4—42no—
210C4—1184no—
211C4—2362no—
212C4—2362no—
213C4—2362no—
214C2#1683799211yescharacteristic
215C2#1683802811yescharacteristic
216C2#1683803111yescharacteristic
217C2#1683811311yescharacteristic
218C2#1683813111yescharacteristic
219C2Q8×Dic11811yescharacteristic
220C2#1683814611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#391C2
hypercenter#391D59
hypocenterC59#2806
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
33. C2×Q8×C59Q8semidirect
52. C4⋊Dic59Q8semidirect
120. C59#2806semidirect
147. C2×Q8Dic118semidirect