Finite Group Databasebeta

← #21434647

Subgroups — #21434647

Order 7552.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#125×D59C211yesmaximal, characteristic
3#16837812C211yesmaximal, characteristic, complemented
4#16837811C211yesmaximal, characteristic, complemented
5#16837808C211yesmaximal, characteristic, complemented
6#16837803C212yesmaximal, complemented
7#16837802C212yesmaximal, complemented
8#16837443C212yesmaximal
9#16837441C212yesmaximal
10#16837354C211yesmaximal, characteristic
11C59×#501C211yesmaximal, characteristic, complemented
12C2×#11745659C2212yes—
13#14273727C2211yescharacteristic
14#14273719C2211yescharacteristic
15#14273718C2211yescharacteristic
16#14273718C2211yescharacteristic
17#14273718C2212yes—
18#14273717—21no—
19#14273717—21no—
20#14273707—21no—
21#14273703—21no—
22Q8×Dic59—21no—
23#14273692—21no—
24#14273685C2212yes—
25C4⋊C4×D59—21no—
26C4⋊C4×D59—21no—
27C4⋊C4×D59C2211yescharacteristic
28C4⋊C4×D59C2211yescharacteristic
29C42×D59C2211yescharacteristic
30#14273661C2212yes—
31#14273660C2212yes—
32#14273660C2212yes—
33#14273659C2212yes—
34#14273658C2212yes—
35#14273658C2212yes—
36#14273638C2211yescharacteristic
37C8×Dic59C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic
40#107×C59C2212yes—
41#106×C59C2212yes—
42#97×C59C2211yescharacteristic
43C2×Q8×C59—21no—
44C2×C4×D59—21no—
45C2×C4×D59—21no—
46C2×C4×D59D411yescharacteristic
47C2×C4×D59D411yescharacteristic
48C2×C4×D59C2311yescharacteristic
49C2×Dic118—21no—
50C2×C8×C59C2312yes—
51C4⋊C4×C59—21no—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2311yescharacteristic
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C42×C59C2311yescharacteristic
58(C2×D59)⋊C4—22no—
59C4⋊Dic59—21no—
60C4⋊Dic59—21no—
61C4⋊Dic59—21no—
62C4⋊Dic59—22no—
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2312yes—
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—21no—
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73C4×Dic59—22no—
74C4×Dic59D411yescharacteristic
75C4×Dic59D411yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78#11745659Q818yescomplemented
79C22×D59C2×D411yescharacteristic
80Q8×C59—42no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59C2×D411yescharacteristic
91C2×Dic59C2×D411yescharacteristic
92C2×Dic59C2×D411yescharacteristic
93C4×D59—41no—
94C4×D59—41no—
95C4×D59—42no—
96C4×D59—42no—
97C4×D59C2×Q814yes—
98Dic118—42no—
99C8×C59C2×Q814yes—
100C59⋊C8C2×Q814yes—
101C22×C59C22×D411yescharacteristic
102C2×D59—21no—
103C2×D59—21no—
104C2×D59C4⋊Q812yes—
105C4×C59—21no—
106C4×C59—21no—
107C4×C59—41no—
108C4×C59—41no—
109C4×C59—42no—
110C4×C59C22×Q812yes—
111Dic59—21no—
112Dic59—21no—
113Dic59—42no—
114Dic59—41no—
115Dic59—41no—
116Dic59C4⋊Q812yes—
117#3166—591nomaximal, Sylow
118C2×C59C2×C4⋊Q811yescharacteristic
119C2×C59#57511yescharacteristic
120C2×C59#57511yescharacteristic
121D59—22no—
122#533—591no—
123C2×#125—591no—
124#501—591no—
125#501—591no—
126#501—591no—
127#501D5911yescharacteristic, complemented
128#499—592no—
129#499—592no—
130#428—592no—
131#428—592no—
132C4×M16—591no—
133C59#316611yescharacteristic, complemented, Sylow
134C2×M16—592no—
135C4⋊Q8—591no—
136C4⋊Q8C2×D5911yescharacteristic
137#125—591no—
138#125—591no—
139#125—592no—
140#125—591no—
141#125—1181no—
142#125—1181no—
143#125C2×D5911yescharacteristic
144C22⋊Q8—1181no—
145C22⋊Q8—1181no—
146C4×Q8—1181no—
147C4×Q8—1181no—
148#117—592no—
149C2×C4⋊C4—591no—
150C2×C4⋊C4—591no—
151C2×C4⋊C4—1181no—
152C2×C4⋊C4—1181no—
153C2×C42—591no—
154#107—592no—
155#107—592no—
156#107—592no—
157#107C2×D5912yes—
158#106—592no—
159#106—592no—
160#106—592no—
161#106C2×D5912yes—
162#97—591no—
163#97C2×D5911yescharacteristic
164C4×C8—592no—
165C2×Q8—21no—
166C2×Q8—1181no—
167C22×C4—591no—
168C22×C4—591no—
169C22×C4—591no—
170C22×C4—1181no—
171C22×C4—1181no—
172M16—598no—
173C2×C8—592no—
174C2×C8C22×D5912yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—591no—
179C4⋊C4—591no—
180C4⋊C4—592no—
181C4⋊C4—1181no—
182C4⋊C4—1181no—
183C4⋊C4—1181no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1181no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4C22×D5911yescharacteristic
193C4⋊C4C22×D5912yes—
194C4⋊C4C22×D5911yescharacteristic
195C22⋊C4—1182no—
196C42—591no—
197C42—591no—
198C42—591no—
199C42—1182no—
200C42C22×D5911yescharacteristic
201C23—591no—
202Q8—42no—
203Q8—2362no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—591no—
208C2×C4—594no—
209C2×C4—591no—
210C2×C4—591no—
211C2×C4—1182no—
212C2×C4—1181no—
213C2×C4—1181no—
214C2×C4—2361no—
215C2×C4—2361no—
216C2×C4—2362no—
217C2×C4—2362no—
218C2×C4D4×D5911yescharacteristic
219C2×C4D4×D5911yescharacteristic
220C2×C4C23×D5911yescharacteristic
221C8—594no—
222C8Q8×D5914yes—
223C22—592no—
224C22—1181no—
225C22—1181no—
226C22C2×D4×D5911yescharacteristic
227C4—21no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—41no—
232C4—592no—
233C4—1181no—
234C4—1181no—
235C4—2361no—
236C4—2361no—
237C4—2362no—
238C4C2×Q8×D5912yes—
239C2—1182no—
240C2C4⋊Q8×D5911yescharacteristic
241C2#1683819811yescharacteristic
242C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3166
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #16837812C2semidirect
4. #16837811C2semidirect
5. #16837808C2semidirect
6. #16837803C2semidirect
7. #16837802C2semidirect
11. C59×#501C2semidirect
78. #11745659Q8semidirect
127. #501D59semidirect
133. C59#3166semidirect