Finite Group Databasebeta

← #21434840

Subgroups — #21434840

Order 7552.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837957C211yesmaximal, characteristic
2#16837957C211yesmaximal, characteristic
3#16837798C211yesmaximal, characteristic, complemented
4#16837781C211yesmaximal, characteristic, complemented
5#16837753C211yesmaximal, characteristic, complemented
6#16837659C214yesmaximal
7#16837506C214yesmaximal, complemented
8C4×#11745659C211yesmaximal, characteristic
9C59×#487C211yesmaximal, characteristic, complemented
10C2×#11745672C2214yes—
11C2×#11745659C2212yes—
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273718—21no—
15#14273718—21no—
16#14273707—21no—
17#14273707C2212yes—
18#14273703—21no—
19#14273703C2212yes—
20Q8×Dic59—21no—
21Q8×Dic59C2212yes—
22#14273692—21no—
23#14273692C2212yes—
24#14273685—21no—
25#14273685—21no—
26C42×D59C2211yescharacteristic
27#14273658C2214yes—
28#14273652C2214yes—
29#14273637C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37C2×C4×D59D411yescharacteristic
38C2×C4×D59D411yescharacteristic
39C2×C4×D59C2311yescharacteristic
40C2×Dic118—21no—
41C2×Dic118C2312yes—
42C2×C8×C59C2312yes—
43C4⋊C4×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59C2312yes—
47C42×C59C2311yescharacteristic
48#11745672—28no—
49(C2×D59)⋊C4—22no—
50(C2×D59)⋊C4—22no—
51C4⋊Dic59—21no—
52C4⋊Dic59—21no—
53C4⋊Dic59—21no—
54C4⋊Dic59—22no—
55C4⋊Dic59—22no—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59C4×Dic59—22no—
60C4×Dic59—22no—
61C4×Dic59D411yescharacteristic
62C4×Dic59D411yescharacteristic
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2312yes—
65#11745659—24no—
66C22×D59C2×D411yescharacteristic
67Q8×C59—24no—
68Q8×C59—42no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2411yescharacteristic
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59C2×D411yescharacteristic
77C2×Dic59C2×D411yescharacteristic
78C2×Dic59C2×D411yescharacteristic
79C4×D59—22no—
80C4×D59—22no—
81C4×D59—22no—
82Dic118—24no—
83Dic118—42no—
84C8×C59—22no—
85C59⋊C8#4114yes—
86C22×C59C22×D411yescharacteristic
87C2×D59—21no—
88C2×D59—21no—
89C2×D59—21no—
90C4×C59—42no—
91C4×C59—42no—
92C4×C59#13712yes—
93C4×C59#13712yes—
94C4×C59C2×#4112yes—
95Dic59—21no—
96Dic59—21no—
97Dic59—21no—
98Dic59—42no—
99Dic59—42no—
100#3185—591nomaximal, Sylow
101C2×C59#53211yescharacteristic
102C2×C59C2×#13711yescharacteristic
103C2×C59C2×#13711yescharacteristic
104D59—41no—
105#533—591no—
106#533—591no—
107#498—591no—
108#494—591no—
109#487—591no—
110#487D5911yescharacteristic, complemented
111#470—594no—
112#441—594no—
113C4×M16—591no—
114C59#318511yescharacteristic, complemented, Sylow
115C2×Q16—594no—
116C2×M16—592no—
117C4⋊Q8—591no—
118C4⋊Q8—591no—
119C4⋊Q8C2×D5911yescharacteristic
120C4⋊Q8C2×D5911yescharacteristic
121#125—1181no—
122#125—1181no—
123C22⋊Q8—592no—
124C22⋊Q8—592no—
125C22⋊Q8—1181no—
126C22⋊Q8—1181no—
127C4×Q8—592no—
128C4×Q8—592no—
129C4×Q8—1181no—
130C4×Q8—1181no—
131#117—1181no—
132#117—1181no—
133C2×C42—591no—
134#106—594no—
135#103—594no—
136#103C2×D5914yes—
137#97—592no—
138C4×C8—591no—
139C4×C8C2×D5911yescharacteristic
140C2×Q8—21no—
141C2×Q8—592no—
142C2×Q8—1181no—
143C2×Q8C22×D5912yes—
144C22×C4—591no—
145C22×C4—591no—
146C22×C4—591no—
147Q16—1188no—
148M16—1184no—
149C2×C8—592no—
150C2×C8C22×D5912yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—592no—
155C4⋊C4—1182no—
156C4⋊C4—1182no—
157C4⋊C4—1182no—
158C4⋊C4—1182no—
159C4⋊C4—1181no—
160C4⋊C4—1181no—
161C4⋊C4—1181no—
162C4⋊C4C22×D5912yes—
163C22⋊C4—1182no—
164C22⋊C4—1182no—
165C42—591no—
166C42—591no—
167C42—591no—
168C42—1182no—
169C42—1182no—
170C42C22×D5911yescharacteristic
171C23—591no—
172Q8—24no—
173Q8—42no—
174Q8—1184no—
175Q8—2362no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—591no—
179C2×C4—591no—
180C2×C4—591no—
181C2×C4—1182no—
182C2×C4—1182no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4D4×D5911yescharacteristic
187C2×C4D4×D5911yescharacteristic
188C2×C4C23×D5911yescharacteristic
189C8—22no—
190C8—594no—
191C22—1181no—
192C22—1181no—
193C22—1181no—
194C22C2×D4×D5911yescharacteristic
195C4—42no—
196C4—42no—
197C4—1181no—
198C4—1181no—
199C4—1181no—
200C4—2362no—
201C4—2362no—
202C4#1427375612yes—
203C4#1427375912yes—
204C4#41×D5912yes—
205C2—2361no—
206C2#1683795111yescharacteristic
207C2C2×#1427375611yescharacteristic
208C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3185
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16837798C2semidirect
4. #16837781C2semidirect
5. #16837753C2semidirect
7. #16837506C2semidirect
9. C59×#487C2semidirect
110. #487D59semidirect
114. C59#3185semidirect