Finite Group Databasebeta

← #21429307

Subgroups — #21429307

Order 7552.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C2×#14273692C211yesmaximal, characteristic
3#16837342C211yesmaximal, characteristic
4#16837341C211yesmaximal, characteristic
5#16837340C211yesmaximal, characteristic
6#16837306C212yesmaximal
7#16837306C212yesmaximal
8#16837306C212yesmaximal
9#16837266C212yesmaximal
10#16837253C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic
12C22×Dic118C2212yes—
13C22×Dic118C2211yescharacteristic
14#14273726—24no—
15#14273692—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×C4×Dic59C2212yes—
22C2×C4×Dic59C2211yescharacteristic
23C2×C4×Dic59C2211yescharacteristic
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2211yescharacteristic
35#95×C59C2212yes—
36#95×C59C2212yes—
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×Dic118—22no—
49C2×Dic118—22no—
50C2×Dic118—24no—
51C2×Dic118—28no—
52C2×Dic118Q814yescomplemented
53C4⋊C4×C59—22no—
54C4⋊C4×C59—22no—
55C4⋊Dic59—22no—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58Dic59⋊C4—24no—
59Dic59⋊C4—24no—
60C4×Dic59—22no—
61C4×Dic59—22no—
62C4×Dic59—24no—
63C4×Dic59D414yes—
64C23×C59C2411yescharacteristic
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—24no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D412yes—
76C2×C4×C59C2×Q812yes—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—24no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87C2×Dic59C2×D412yes—
88C2×Dic59C2×Q812yes—
89C2×Dic59C2×Q812yes—
90C2×Dic59#4112yes—
91C2×Dic59#4114yes—
92Dic118—28no—
93Dic118—48no—
94C22×C59C22×D411yescharacteristic
95C22×C59C22×Q811yescharacteristic
96C22×C59C2×#4111yescharacteristic
97C22×C59C2×#4112yes—
98C22×C592−1+412yes—
99C4×C59—22no—
100C4×C59—22no—
101C4×C59—42no—
102C4×C59—41no—
103C4×C59—42no—
104Dic59—22no—
105Dic59—42no—
106Dic59—41no—
107Dic59—42no—
108Dic59C22⋊Q814yes—
109Dic59#12414yes—
110#2568—591nomaximal, Sylow
111C2×C59C2×C22⋊Q811yescharacteristic
112C2×C59C2×#12411yescharacteristic
113C2×C59#53611yescharacteristic
114C2×C59#55612yes—
115C2×C59#55712yes—
116C2×C4⋊Q8—591no—
117C2×C4×Q8—591no—
118#400—591no—
119#400—591no—
120#400—591no—
121#400D5911yescharacteristic
122#391—592no—
123#391—592no—
124#391—592no—
125#382—592no—
126C4×C4⋊C4—591no—
127C59#256811yescharacteristic, complemented, Sylow
128C22×Q8—591no—
129C22×Q8—592no—
130C4⋊Q8—1184no—
131C4×Q8—1184no—
132C2×C4⋊C4—591no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—591no—
136C2×C4⋊C4—592no—
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C4⋊C4C2×D5911yescharacteristic
139C2×C42—591no—
140C2×C42—591no—
141C2×C42—591no—
142C2×C42—592no—
143#95—591no—
144#95—592no—
145#95—592no—
146#95—592no—
147#95—592no—
148#95—592no—
149#95—592no—
150#95C2×D5911yescharacteristic
151#95C2×D5912yes—
152#95C2×D5912yes—
153C2×Q8—594no—
154C2×Q8—1182no—
155C2×Q8—1182no—
156C2×Q8—1184no—
157C2×Q8—1188no—
158C22×C4—591no—
159C22×C4—591no—
160C22×C4—591no—
161C22×C4—592no—
162C22×C4—591no—
163C22×C4—592no—
164C22×C4C22×D5912yes—
165C22×C4C22×D5911yescharacteristic
166C22×C4C22×D5912yes—
167C22×C4C22×D5911yescharacteristic
168C22×C4C22×D5911yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1182no—
172C4⋊C4—1184no—
173C4⋊C4—1184no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C42—594no—
177C42—1182no—
178C42—1182no—
179C42—1184no—
180C23C23×D5911yescharacteristic
181Q8—1188no—
182Q8—2368no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—592no—
194C2×C4—592no—
195C2×C4—592no—
196C2×C4—592no—
197C2×C4—594no—
198C2×C4—592no—
199C2×C4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1184no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4D4×D5912yes—
209C2×C4Q8×D5912yes—
210C22C2×D4×D5911yescharacteristic
211C22C2×Q8×D5911yescharacteristic
212C22#41×D5911yescharacteristic
213C22#41×D5912yes—
214C22#1427377412yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—41no—
219C4—42no—
220C4—594no—
221C4—594no—
222C4—1182no—
223C4—2362no—
224C4—2361no—
225C4—2362no—
226C2C22⋊Q8×D5911yescharacteristic
227C2#124×D5911yescharacteristic
228C2#1683797411yescharacteristic
229C2#1683811912yes—
230C2#1683812912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2568
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic118Q8semidirect
127. C59#2568semidirect