Finite Group Databasebeta

← #21422653

Subgroups — #21422653

Order 7552.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#16837913C211yesmaximal, characteristic
2#16837265C211yesmaximal, characteristic, complemented
3#16837140C212yesmaximal, complemented
4#16837137C212yesmaximal, complemented
5C2×C22⋊C8×C59C211yesmaximal, characteristic, complemented
6C2×#11745685C411yescharacteristic, complemented
7#14273710—21no—
8#14273706C411yescharacteristic, complemented
9#14273706C2211yescharacteristic
10#14273701C411yescharacteristic, complemented
11#14273701C2211yescharacteristic
12#14273696—21no—
13C4×C22⋊D59—21no—
14C4×C22⋊D59—21no—
15#14273686C411yescharacteristic, complemented
16C2×C22⋊Dic59—21no—
17C59⋊#95—21no—
18C59⋊#95C2212yes—
19C23×C4×C59C2211yescharacteristic
20C22×C8×C59—21no—
21C22⋊C8×C59—21no—
22C22⋊C8×C59C2212yes—
23C24×C59D411yescharacteristic
24C22×C4×C59—42no—
25C22×C4×C59C2×C411yescharacteristic
26C22×C4×C59C2×C411yescharacteristic
27C22×C4×C59D411yescharacteristic
28C22×C4×C59D411yescharacteristic
29C22×C4×C59D411yescharacteristic
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—22no—
35#11745685—42no—
36C2×D236C2×C411yescharacteristic
37C2×C4×D59—21no—
38C2×Dic118C2×C411yescharacteristic
39C2×C8×C59—22no—
40C2×C8×C59—42no—
41C22⋊Dic59—21no—
42C22⋊Dic59—21no—
43C22⋊Dic59—21no—
44C22⋊Dic59—42no—
45(C2×D59)⋊C4—21no—
46(C2×D59)⋊C4—21no—
47C4⋊Dic59C2×C411yescharacteristic
48C4⋊Dic59C2×C411yescharacteristic
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51C4×Dic59—21no—
52C23×C59—22no—
53C23×C59—22no—
54C23×C59—41no—
55C23×C59C22⋊C411yescharacteristic
56C23×C59C22⋊C411yescharacteristic
57C23×C59C2×D411yescharacteristic
58C22×D59—21no—
59C2×C4×C59—22no—
60C2×C4×C59—22no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59C22⋊C411yescharacteristic
66C2×C4×C59C22⋊C411yescharacteristic
67C2×C4×C59C22×C411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C22⋊D59—42no—
70C22⋊D59—42no—
71C22⋊D59—42no—
72C2×Dic59—21no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—42no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78D236—41no—
79C4×D59—42no—
80Dic118—41no—
81C8×C59—42no—
82C22×C59—21no—
83C22×C59—21no—
84C22×C59—21no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59—44no—
90C22×C59#9912yes—
91C22×C59C2×C22⋊C411yescharacteristic
92C22×C59#13512yes—
93C2×D59—41no—
94C2×D59—41no—
95C2×D59—41no—
96C4×C59—21no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—21no—
100Dic59—41no—
101Dic59—41no—
102Dic59—41no—
103Dic59—82no—
104#1516—591nomaximal, Sylow
105C2×C59—22no—
106C2×C59—22no—
107C2×C59—41no—
108C2×C59C2×#9911yescharacteristic
109C2×C59#41611yescharacteristic
110C2×C59#42111yescharacteristic
111D59—81no—
112#525—591no—
113C2×C22⋊C8D5911yescharacteristic, complemented
114#381—591no—
115#328—592no—
116#327—592no—
117C59#151611yescharacteristic, complemented, Sylow
118C2×#41—591no—
119C23×C4C2×D5911yescharacteristic
120C22×C8—21no—
121#123—1181no—
122C22⋊Q8—591no—
123C22⋊Q8—591no—
124#121—591no—
125#121—591no—
126#120—1181no—
127C4×D4—1181no—
128C4×D4—1181no—
129#117—591no—
130C2×C22⋊C4—1181no—
131C22⋊C8—21no—
132C22⋊C8C2×D5912yes—
133#95—592no—
134#95—1181no—
135C24D23611yescharacteristic
136#41—2362no—
137C2×Q8—591no—
138C2×D4—591no—
139C2×D4—1181no—
140C2×D4—1181no—
141C2×D4—1181no—
142C22×C4—42no—
143C22×C4—1181no—
144C22×C4—1182no—
145C22×C4C4×D5911yescharacteristic
146C22×C4C4×D5911yescharacteristic
147C22×C4D23611yescharacteristic
148C22×C4C22⋊D5911yescharacteristic
149C22×C4C22⋊D5911yescharacteristic
150C22×C4C22×D5911yescharacteristic
151C2×C8—22no—
152C2×C8—42no—
153C4⋊C4—591no—
154C4⋊C4—591no—
155C4⋊C4—1181no—
156C4⋊C4—1181no—
157C22⋊C4—1181no—
158C22⋊C4—1181no—
159C22⋊C4—1181no—
160C22⋊C4—1181no—
161C22⋊C4—1181no—
162C22⋊C4—2362no—
163C42—1181no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—1181no—
168C23(C2×D59)⋊C411yescharacteristic
169C23(C2×D59)⋊C411yescharacteristic
170C23C2×D23611yescharacteristic
171Q8—2361no—
172D4—2361no—
173D4—2362no—
174D4—2362no—
175D4—2362no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1181no—
183C2×C4—1181no—
184C2×C4—1181no—
185C2×C4—2362no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4—2362no—
189C2×C4(C2×D59)⋊C411yescharacteristic
190C2×C4(C2×D59)⋊C411yescharacteristic
191C2×C4C2×C4×D5911yescharacteristic
192C2×C4C2×C22⋊D5911yescharacteristic
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—2361no—
203C22—2361no—
204C22—2361no—
205C22#1427364112yes—
206C22C2×(C2×D59)⋊C411yescharacteristic
207C22#1427374912yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—4722no—
213C4—2361no—
214C4—2361no—
215C4—2361no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—4721no—
220C2C2×#1427364111yescharacteristic
221C2#1683739911yescharacteristic
222C2#1683741811yescharacteristic
subgroupG/H
centerC22C2×(C2×D59)⋊C4
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×C22⋊C8×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC2×C22⋊C8D59
hypocenterC59#1516
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837265C2semidirect
3. #16837140C2semidirect
4. #16837137C2semidirect
5. C2×C22⋊C8×C59C2semidirect
6. C2×#11745685C4semidirect
8. #14273706C4semidirect
10. #14273701C4semidirect
15. #14273686C4semidirect
113. C2×C22⋊C8D59semidirect
117. C59#1516semidirect