Finite Group Databasebeta

← #21424620

Subgroups — #21424620

Order 7552.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#16838168C211yesmaximal, characteristic, complemented
2#16837969C211yesmaximal, characteristic
3#16837407C211yesmaximal, characteristic, complemented
4#16837375C211yesmaximal, characteristic, complemented
5#16837159C211yesmaximal, characteristic, complemented
6#16837158C211yesmaximal, characteristic, complemented
7C59×#418C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273735—22no—
10#14273733—22no—
11C2×#11745664C2211yescharacteristic
12M16×D59—22no—
13#14273723C412yescomplemented
14#14273714C412yescomplemented
15#14273698—22no—
16#14273696—22no—
17#14273686C2211yescharacteristic
18#14273686C2211yescharacteristic
19#14273648—22no—
20#14273641—22no—
21C22×D4×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24#102×C59—22no—
25C24×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59—21no—
29C2×D4×C59—21no—
30C2×D4×C59—21no—
31C2×D4×C59C2×C412yes—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—24no—
34C2×C22⋊D59D412yes—
35#11745685—21no—
36#11745685—21no—
37#11745685—21no—
38#11745685—21no—
39C2×D236C2×C411yescharacteristic
40C2×C4×D59D412yes—
41C2×Dic118C2×C411yescharacteristic
42M16×C59—21no—
43M16×C59—21no—
44C2×C8×C59D412yescomplemented
45C4⋊C4×C59—21no—
46C22⋊C4×C59—21no—
47C42×C59—21no—
48C22⋊Dic59—21no—
49C22⋊Dic59—24no—
50C22⋊Dic59—21no—
51C4⋊Dic59—21no—
52C4⋊Dic59—21no—
53C4×Dic59—21no—
54C4×Dic59C2×C412yes—
55#11745664—21no—
56#11745664—21no—
57C2×C59⋊C8D412yescomplemented
58#11745659—24no—
59C8×D59—24no—
60C23×C59—22no—
61C23×C59—41no—
62C23×C59—41no—
63C23×C59—82no—
64C23×C59C2×D411yescharacteristic
65C22×D59C22⋊C412yes—
66D4×C59—22no—
67D4×C59—22no—
68D4×C59—41no—
69D4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59C22×C411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59#4111yescharacteristic
76C2×C4×C59#4111yescharacteristic
77C22⋊D59—22no—
78C22⋊D59—22no—
79C22⋊D59—84no—
80C2×Dic59—22no—
81C2×Dic59—41no—
82C2×Dic59C22⋊C412yes—
83D236—21no—
84D236—21no—
85C4×D59—22no—
86C4×D59—22no—
87Dic118—21no—
88Dic118—21no—
89C8×C59—22no—
90C59⋊C8—22no—
91C22×C59—41no—
92C22×C59—44no—
93C22×C59—42no—
94C22×C59—82no—
95C22×C59—82no—
96C22×C59C2×C22⋊C411yescharacteristic
97C22×C59#12111yescharacteristic
98C22×C59#12111yescharacteristic
99C2×D59—22no—
100C2×D59—42no—
101C4×C59—81no—
102C4×C59C4×D411yescharacteristic
103C4×C59C4×D411yescharacteristic
104C4×C59#12011yescharacteristic
105C4×C59#12311yescharacteristic
106Dic59—22no—
107Dic59—42no—
108Dic59—81no—
109#1910—591nomaximal, Sylow
110C2×C59—21no—
111C2×C59—21no—
112C2×C59—21no—
113C2×C59—82no—
114C2×C59#38611yescharacteristic
115D59—42no—
116#568—591no—
117#535—591no—
118#418—591no—
119#418D5911yescharacteristic, complemented
120#410—591no—
121H(3,ℤ/4)—591no—
122H(3,ℤ/4)—591no—
123C59#191011yescharacteristic, complemented, Sylow
124C2×#41—591no—
125C22×D4C2×D5911yescharacteristic
126#131—1182no—
127#131—1182no—
128C2×M16—591no—
129C2×M16—1182no—
130C2×M16C2×D5911yescharacteristic
131#127—592no—
132#124—592no—
133#121—1182no—
134#120—1182no—
135#117—591no—
136#117—591no—
137#117C2×D5911yescharacteristic
138#102—22no—
139#102—1182no—
140#99—1182no—
141C24—21no—
142#41—1181no—
143#41—1181no—
144#41—1181no—
145#41—1181no—
146C2×Q8—591no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—592no—
153C2×D4—591no—
154C2×D4—1184no—
155C2×D4C4×D5912yes—
156C22×C4—592no—
157C22×C4C22×D5911yescharacteristic
158M16—21no—
159M16—21no—
160M16—1184no—
161M16—1181no—
162M16—1181no—
163C2×C8—592no—
164C2×C8—1184no—
165C2×C8C22⋊D5912yescomplemented
166C4⋊C4—21no—
167C4⋊C4—1181no—
168C4⋊C4—1181no—
169C22⋊C4—21no—
170C22⋊C4—1184no—
171C22⋊C4—1181no—
172C22⋊C4—1181no—
173C42—21no—
174C42—592no—
175C42—1181no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—82no—
180C23—592no—
181C23D4×D5911yescharacteristic
182Q8—1181no—
183Q8—1181no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—1182no—
189D4—1182no—
190D4—1181no—
191D4—1181no—
192D4—4724no—
193C2×C4—41no—
194C2×C4—592no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—2361no—
199C2×C4C2×C4×D5911yescharacteristic
200C2×C4#1174568511yescharacteristic
201C2×C4D4×D5911yescharacteristic
202C2×C4D4×D5911yescharacteristic
203C2×C4#1174568711yescharacteristic
204C2×C4C2×C22⋊D5911yescharacteristic
205C8—22no—
206C8—1182no—
207C22—41no—
208C22—44no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—1182no—
213C22—2362no—
214C22C22⋊C4×D5911yescharacteristic
215C22#1427369811yescharacteristic
216C22#1427370011yescharacteristic
217C4—81no—
218C4—1182no—
219C4—4721no—
220C4—2362no—
221C4(C22⋊D59)⋊C411yescharacteristic
222C4C4×C22⋊D5911yescharacteristic
223C4#1427369511yescharacteristic
224C4#1427370911yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—82no—
229C2—2362no—
230C2#1683727811yescharacteristic
subgroupG/H
centerC2#16837278
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#418C2
socleC2×C59#386
hypercenter#418D59
hypocenterC59#1910
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16838168C2semidirect
3. #16837407C2semidirect
4. #16837375C2semidirect
5. #16837159C2semidirect
6. #16837158C2semidirect
7. C59×#418C2semidirect
13. #14273723C4semidirect
14. #14273714C4semidirect
44. C2×C8×C59D4semidirect
57. C2×C59⋊C8D4semidirect
119. #418D59semidirect
123. C59#1910semidirect
165. C2×C8C22⋊D59semidirect