Finite Group Databasebeta

← #21422563

Subgroups — #21422563

Order 7552.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#16837949C211yesmaximal, characteristic
2#16837458C211yesmaximal, characteristic, complemented
3#16837453C211yesmaximal, characteristic, complemented
4#16837131C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745685—21no—
9#14273726C411yescharacteristic
10#14273723C411yescharacteristic
11#14273713—21no—
12#14273702C411yescharacteristic
13#14273700—21no—
14#14273698C411yescharacteristic
15C4×D236C2211yescharacteristic
16C4×C22⋊D59—21no—
17C42×D59C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21(C2×D59)⋊C8—21no—
22#14273637—21no—
23C4×C59⋊C8C2211yescharacteristic
24C4×D4×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic
26C4×C8×C59C2211yescharacteristic
27C2×D4×C59C2×C411yescharacteristic
28C22×C4×C59—21no—
29C2×C22⋊D59—21no—
30C2×C22⋊D59—21no—
31C2×C22⋊D59—21no—
32#11745685—42no—
33#11745685—42no—
34C2×D236—21no—
35C2×D236C2×C411yescharacteristic
36C2×C4×D59—21no—
37C2×C4×D59C2×C411yescharacteristic
38C2×C4×D59D411yescharacteristic
39C2×C4×D59D411yescharacteristic
40C2×Dic118—21no—
41C2×C8×C59—21no—
42C2×C8×C59—21no—
43C4⋊C4×C59C2×C411yescharacteristic
44C22⋊C4×C59—21no—
45C42×C59C2311yescharacteristic
46C22⋊Dic59—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49C4⋊Dic59C2×C411yescharacteristic
50Dic59⋊C4—21no—
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59D411yescharacteristic
53C4×Dic59D411yescharacteristic
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56C23×C59—21no—
57C22×D59—21no—
58C22×D59C22⋊C411yescharacteristic
59D4×C59—21no—
60D4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C22⋊D59—42no—
68C22⋊D59—42no—
69C22⋊D59—42no—
70C2×Dic59—21no—
71C2×Dic59C22⋊C411yescharacteristic
72C2×Dic59C22⋊C411yescharacteristic
73C2×Dic59C22⋊C411yescharacteristic
74D236—21no—
75D236—21no—
76D236—42no—
77C4×D59—21no—
78C4×D59—21no—
79C4×D59—21no—
80C4×D59—21no—
81C4×D59—41no—
82C4×D59—41no—
83C4×D59—41no—
84Dic118—42no—
85C8×C59—41no—
86C8×C59—41no—
87C59⋊C8—41no—
88C59⋊C8—41no—
89C22×C59—41no—
90C22×C59—41no—
91C22×C59—41no—
92C22×C59C2×C22⋊C411yescharacteristic
93C2×D59—21no—
94C2×D59—21no—
95C2×D59—21no—
96C2×D59—41no—
97C2×D59—41no—
98C2×D59—41no—
99C4×C59—21no—
100C4×C59—41no—
101C4×C59#13111yescharacteristic
102C4×C59#13111yescharacteristic
103C4×C59AGL(1,ℤ/8)11yescharacteristic
104C4×C59AGL(1,ℤ/8)11yescharacteristic
105Dic59—21no—
106Dic59—21no—
107Dic59—21no—
108Dic59—41no—
109#1496—591nomaximal, Sylow
110C2×C59—81no—
111C2×C59#40811yescharacteristic
112C2×C59#41811yescharacteristic
113C2×C59#42111yescharacteristic
114D59—41no—
115D59—81no—
116#532—591no—
117#432—591no—
118#431—591no—
119D4⋊C8—591no—
120D4⋊C8—591no—
121D4⋊C8—591no—
122D4⋊C8D5911yescharacteristic, complemented
123C59#149611yescharacteristic, complemented, Sylow
124C2×#41—1181no—
125C4⋊Q8—591no—
126#127—591no—
127#124—1181no—
128#121—591no—
129#121—591no—
130#121—1181no—
131C4×D4—591no—
132C4×D4—1181no—
133C4×D4C2×D5911yescharacteristic
134C2×C42—591no—
135C4⋊C8—591no—
136C4⋊C8—1181no—
137C4⋊C8C2×D5911yescharacteristic
138C22⋊C8—1181no—
139C22⋊C8—1181no—
140#97—1181no—
141C4×C8—591no—
142C4×C8C2×D5911yescharacteristic
143#41—2362no—
144#41—2362no—
145C2×Q8—1181no—
146C2×D4—591no—
147C2×D4—1181no—
148C2×D4—1181no—
149C2×D4—1181no—
150C2×D4—1181no—
151C2×D4C4×D5911yescharacteristic
152C22×C4—21no—
153C22×C4—591no—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—1181no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—1181no—
160C2×C8—1181no—
161C4⋊C4—591no—
162C4⋊C4—1181no—
163C4⋊C4C4×D5911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—1181no—
166C22⋊C4—1181no—
167C22⋊C4—1181no—
168C42—591no—
169C42—591no—
170C42—591no—
171C42C22×D5911yescharacteristic
172C23—21no—
173C23—591no—
174C23—1181no—
175Q8—2362no—
176D4—21no—
177D4—21no—
178D4—1181no—
179D4—1181no—
180D4—2362no—
181D4—2362no—
182D4—2362no—
183D4—2362no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—591no—
188C2×C4—591no—
189C2×C4—591no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1181no—
194C2×C4—1181no—
195C2×C4—2361no—
196C2×C4—2361no—
197C2×C4—2361no—
198C2×C4C2×C4×D5911yescharacteristic
199C2×C4D4×D5911yescharacteristic
200C2×C4D4×D5911yescharacteristic
201C8—41no—
202C8—41no—
203C8—2361no—
204C8—2361no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—1181no—
209C22—1181no—
210C22—1181no—
211C22—2361no—
212C22—2361no—
213C22—2361no—
214C22C22⋊C4×D5911yescharacteristic
215C4—21no—
216C4—41no—
217C4—1181no—
218C4—1181no—
219C4—1181no—
220C4—2361no—
221C4#1427373311yescharacteristic
222C4#1427373511yescharacteristic
223C4#1427375111yescharacteristic
224C4#1427375411yescharacteristic
225C2—81no—
226C2—4721no—
227C2—2361no—
228C2#1683736711yescharacteristic
229C2#1683740511yescharacteristic
230C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×D4⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterD4⋊C8D59
hypocenterC59#1496
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837458C2semidirect
3. #16837453C2semidirect
4. #16837131C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×D4⋊C8C2semidirect
122. D4⋊C8D59semidirect
123. C59#1496semidirect