Finite Group Databasebeta

← #21424476

Subgroups — #21424476

Order 7552.

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

normal subgroups only

This group has 332 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#16837948C211yesmaximal, characteristic
3#16837419C211yesmaximal, characteristic, complemented
4#16837375C211yesmaximal, characteristic, complemented
5#16837163C211yesmaximal, characteristic, complemented
6#16837161C211yesmaximal, characteristic, complemented
7C59×#421C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273735—22no—
10#14273733—22no—
11C2×#11745664C2211yescharacteristic
12M16×D59—22no—
13#14273725C411yescharacteristic, complemented
14#14273723C411yescharacteristic, complemented
15#14273716C411yescharacteristic, complemented
16#14273714C411yescharacteristic, complemented
17#14273699—22no—
18C4×C22⋊D59—22no—
19#14273686C2211yescharacteristic
20C2×C4×Dic59C2211yescharacteristic
21#14273654—22no—
22#14273641—22no—
23C2×#41×C59C2211yescharacteristic
24C2×M16×C59C2211yescharacteristic
25#117×C59C2211yescharacteristic
26#104×C59—22no—
27#41×C59—21no—
28#41×C59—21no—
29#41×C59—21no—
30#41×C59—21no—
31C2×Q8×C59C2×C411yescharacteristic
32C2×D4×C59—21no—
33C2×D4×C59C2×C411yescharacteristic
34C22×C4×C59—21no—
35C22×C4×C59C2311yescharacteristic
36C2×C22⋊D59—22no—
37C2×C22⋊D59D412yes—
38C22×Dic59—21no—
39#11745685—21no—
40#11745685—21no—
41#11745685—21no—
42#11745685—21no—
43C2×D236C2×C411yescharacteristic
44C2×C4×D59D412yes—
45C2×Dic118C2×C411yescharacteristic
46M16×C59—21no—
47M16×C59D412yescomplemented
48C2×C8×C59—21no—
49C4⋊C4×C59—21no—
50C22⋊C4×C59—21no—
51C42×C59—21no—
52C22⋊Dic59—22no—
53C22⋊Dic59—21no—
54(C2×D59)⋊C4—22no—
55C4⋊Dic59—21no—
56Dic59⋊C4—22no—
57C4×Dic59—21no—
58C4×Dic59—21no—
59C4×Dic59C2×C411yescharacteristic
60C4×Dic59C2×C411yescharacteristic
61#11745664—21no—
62#11745664D412yescomplemented
63C2×C59⋊C8—21no—
64#11745659—24no—
65C8×D59—24no—
66C23×C59—21no—
67C23×C59C2×D411yescharacteristic
68C22×D59C22⋊C412yes—
69Q8×C59—21no—
70Q8×C59—21no—
71D4×C59—21no—
72D4×C59—21no—
73D4×C59—41no—
74D4×C59—41no—
75C2×C4×C59—21no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59—41no—
79C2×C4×C59C22×C411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59#4111yescharacteristic
84C2×C4×C59#4111yescharacteristic
85C22⋊D59—22no—
86C22⋊D59—22no—
87C22⋊D59—44no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—42no—
91C2×Dic59—41no—
92C2×Dic59C22⋊C412yes—
93D236—21no—
94D236—21no—
95C4×D59—22no—
96C4×D59—22no—
97Dic118—21no—
98Dic118—21no—
99C8×C59—22no—
100C59⋊C8—22no—
101C22×C59—41no—
102C22×C59—42no—
103C22×C59—41no—
104C22×C59C2×C22⋊C411yescharacteristic
105C22×C59#12111yescharacteristic
106C22×C59#12111yescharacteristic
107C2×D59—22no—
108C2×D59—42no—
109C4×C59—41no—
110C4×C59—81no—
111C4×C59C4×D411yescharacteristic
112C4×C59C4×D411yescharacteristic
113C4×C59#12011yescharacteristic
114C4×C59#12311yescharacteristic
115Dic59—22no—
116Dic59—22no—
117Dic59—41no—
118Dic59—81no—
119#1884—591nomaximal, Sylow
120C2×C59—21no—
121C2×C59—21no—
122C2×C59—21no—
123C2×C59—81no—
124C2×C59#38611yescharacteristic
125D59—42no—
126#568—591no—
127#532—591no—
128#421—591no—
129#421D5911yescharacteristic, complemented
130#410—591no—
131#339—591no—
132#339—591no—
133C59#188411yescharacteristic, complemented, Sylow
134C2×#41—591no—
135C2×#41C2×D5911yescharacteristic
136#131—1182no—
137#131—1182no—
138C2×M16—591no—
139C2×M16—1182no—
140C2×M16C2×D5911yescharacteristic
141C4⋊Q8—591no—
142#127—591no—
143#124—591no—
144#124—591no—
145#121—1182no—
146C4×D4—1182no—
147#117—591no—
148#117C2×D5911yescharacteristic
149C2×C42—591no—
150#104—22no—
151#104—1182no—
152#99—1182no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—1181no—
158#41—1181no—
159#41—1181no—
160#41—1181no—
161C2×Q8—591no—
162C2×Q8C4×D5911yescharacteristic
163C2×D4—21no—
164C2×D4—592no—
165C2×D4—591no—
166C2×D4—1182no—
167C2×D4C4×D5911yescharacteristic
168C22×C4—21no—
169C22×C4—592no—
170C22×C4—1181no—
171C22×C4C22×D5911yescharacteristic
172M16—21no—
173M16—592no—
174M16—1184no—
175M16—1181no—
176M16C22⋊D5912yescomplemented
177C2×C8—21no—
178C2×C8—1184no—
179C2×C8—1181no—
180C4⋊C4—21no—
181C4⋊C4—1182no—
182C4⋊C4—1181no—
183C22⋊C4—21no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—1181no—
187C42—21no—
188C42—591no—
189C42—591no—
190C42—1181no—
191C42—1181no—
192C23—21no—
193C23—592no—
194C23D4×D5911yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—1181no—
198Q8—1181no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—1182no—
204D4—1182no—
205D4—1181no—
206D4—1181no—
207D4—2364no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—592no—
213C2×C4—1181no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1181no—
217C2×C4—2362no—
218C2×C4—2361no—
219C2×C4C2×C4×D5911yescharacteristic
220C2×C4#1174568511yescharacteristic
221C2×C4D4×D5911yescharacteristic
222C2×C4D4×D5911yescharacteristic
223C2×C4#1174568711yescharacteristic
224C2×C4C2×C22⋊D5911yescharacteristic
225C8—22no—
226C8—1182no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—1182no—
231C22—2362no—
232C22C22⋊C4×D5911yescharacteristic
233C22#1427369811yescharacteristic
234C22#1427370011yescharacteristic
235C4—41no—
236C4—81no—
237C4—1182no—
238C4—1182no—
239C4—4721no—
240C4—2361no—
241C4(C22⋊D59)⋊C411yescharacteristic
242C4C4×C22⋊D5911yescharacteristic
243C4#1427369511yescharacteristic
244C4#1427370911yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—81no—
249C2—2362no—
250C2#1683727811yescharacteristic
subgroupG/H
centerC4#14273695
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#421C2
socleC2×C59#386
hypercenter#421D59
hypocenterC59#1884
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #16838168C2semidirect
3. #16837419C2semidirect
4. #16837375C2semidirect
5. #16837163C2semidirect
6. #16837161C2semidirect
7. C59×#421C2semidirect
13. #14273725C4semidirect
14. #14273723C4semidirect
15. #14273716C4semidirect
16. #14273714C4semidirect
47. M16×C59D4semidirect
62. #11745664D4semidirect
129. #421D59semidirect
133. C59#1884semidirect
176. M16C22⋊D59semidirect