Finite Group Databasebeta

← #21428578

Subgroups — #21428578

Order 7552.

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

normal subgroups only

This group has 512 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
1C2×#14273707C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic
3#16837344C214yesmaximal, complemented
4#16837308C211yesmaximal, characteristic, complemented
5#16837307C211yesmaximal, characteristic, complemented
6#16837267C211yesmaximal, characteristic, complemented
7#16837264C214yesmaximal
8C4×(C2×D59)⋊C4C211yesmaximal, characteristic
9C59×#382C211yesmaximal, characteristic, complemented
10C22×Dic118C2211yescharacteristic
11C22×C4×D59C2212yes—
12C22×C4×D59C2211yescharacteristic
13#14273707—24no—
14C2×C4⋊Dic59C2212yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C2212yes—
17C4⋊C4×D59—24no—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×C4×Dic59C2211yescharacteristic
21C59⋊#95C2212yes—
22C59⋊#95C2214yes—
23C59⋊#95C2214yes—
24C59⋊#95C2214yes—
25C2×C4⋊C4×C59C2211yescharacteristic
26C2×C4⋊C4×C59C2211yescharacteristic
27C2×C42×C59C2211yescharacteristic
28#95×C59C2214yes—
29C23×D59C2311yescharacteristic
30C22×C4×C59C2312yes—
31C22×C4×C59C2312yes—
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×Dic59C2312yes—
35C22×Dic59C2312yes—
36C22×Dic59C2312yes—
37C22×Dic59C2311yescharacteristic
38C2×C4×D59—22no—
39C2×C4×D59—22no—
40C2×C4×D59—24no—
41C2×C4×D59—28no—
42C2×C4×D59D414yes—
43C2×Dic118—22no—
44C2×Dic118—22no—
45C2×Dic118—22no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—22no—
48C42×C59—22no—
49(C2×D59)⋊C4—24no—
50(C2×D59)⋊C4—24no—
51C4⋊Dic59—22no—
52C4⋊Dic59—24no—
53Dic59⋊C4—24no—
54C4×Dic59—22no—
55C23×C59C2411yescharacteristic
56C22×D59—21no—
57C22×D59—21no—
58C22×D59—22no—
59C22×D59C2×D412yes—
60C22×D59#4114yes—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—24no—
66C2×C4×C59—24no—
67C2×C4×C59—22no—
68C2×C4×C59C2×D412yes—
69C2×C4×C59#4112yes—
70C2×C4×C59#4112yes—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—24no—
80C2×Dic59—22no—
81C2×Dic59C2×D412yes—
82C4×D59—28no—
83C4×D59—48no—
84Dic118—44no—
85C22×C59C22×D411yescharacteristic
86C22×C59C2×#4112yes—
87C22×C59C2×#4111yescharacteristic
88C22×C59C2×#4111yescharacteristic
89C22×C592−1+412yes—
90C2×D59—22no—
91C2×D59—22no—
92C2×D59—24no—
93C2×D59—24no—
94C2×D59#12414yes—
95C4×C59—42no—
96C4×C59—42no—
97C4×C59—42no—
98C4×C59#12314yes—
99Dic59—22no—
100Dic59—42no—
101Dic59—42no—
102Dic59—42no—
103#2503—591nomaximal, Sylow
104C2×C59C2×#12311yescharacteristic
105C2×C59C2×#12411yescharacteristic
106C2×C59#53611yescharacteristic
107C2×C59#55212yes—
108C2×C59#55212yes—
109D59—24no—
110C2×C22⋊Q8—591no—
111C22×C4⋊C4—591no—
112#400—594no—
113#391—591no—
114#391—591no—
115#382—591no—
116#382D5911yescharacteristic, complemented
117#381—594no—
118C4×C22⋊C4—591no—
119C59#250311yescharacteristic, complemented, Sylow
120C22×Q8—591no—
121C23×C4—591no—
122C23×C4—592no—
123C22⋊Q8—1184no—
124C2×C4⋊C4—591no—
125C2×C4⋊C4—592no—
126C2×C4⋊C4—592no—
127C2×C4⋊C4—1184no—
128C2×C4⋊C4C2×D5911yescharacteristic
129C2×C4⋊C4C2×D5911yescharacteristic
130C2×C22⋊C4—592no—
131C2×C22⋊C4—592no—
132C2×C42—591no—
133C2×C42C2×D5911yescharacteristic
134#95—592no—
135#95—594no—
136#95—594no—
137#95—594no—
138#95C2×D5914yes—
139C24—591no—
140C2×Q8—1182no—
141C2×Q8—1182no—
142C2×Q8—1182no—
143C22×C4—591no—
144C22×C4—594no—
145C22×C4—592no—
146C22×C4—592no—
147C22×C4—592no—
148C22×C4—1184no—
149C22×C4—1188no—
150C22×C4—1182no—
151C22×C4—1182no—
152C22×C4C22×D5912yes—
153C22×C4C22×D5912yes—
154C22×C4C22×D5912yes—
155C22×C4C22×D5911yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—1184no—
159C4⋊C4—1184no—
160C4⋊C4—1182no—
161C22⋊C4—1184no—
162C22⋊C4—1184no—
163C42—22no—
164C42—1182no—
165C23—592no—
166C23—594no—
167C23—1181no—
168C23—1181no—
169C23—1182no—
170C23C23×D5911yescharacteristic
171Q8—2364no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—592no—
180C2×C4—1181no—
181C2×C4—1181no—
182C2×C4—1188no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1184no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—2368no—
192C2×C4#1174568512yes—
193C2×C4D4×D5912yes—
194C2×C4#1174568912yes—
195C22—594no—
196C22—1182no—
197C22—1182no—
198C22—1184no—
199C22—1184no—
200C22C2×D4×D5911yescharacteristic
201C22#41×D5912yes—
202C22C2×#1174568511yescharacteristic
203C22C2×#1174568911yescharacteristic
204C22#1427377412yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—1182no—
209C4—2362no—
210C4—2362no—
211C4—2362no—
212C4#1427371214yes—
213C2—1184no—
214C2C2×#1427371211yescharacteristic
215C2#124×D5911yescharacteristic
216C2#1683797211yescharacteristic
217C2#1683809012yes—
218C2#1683809112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#382C2
hypercenter#382D59
hypocenterC59#2503
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #16837344C2semidirect
4. #16837308C2semidirect
5. #16837307C2semidirect
6. #16837267C2semidirect
9. C59×#382C2semidirect
116. #382D59semidirect
119. C59#2503semidirect