Finite Group Databasebeta

← #21436780

Subgroups — #21436780

Order 7552.

336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838127C211yesmaximal, characteristic, complemented
2#16838122C211yesmaximal, characteristic
3#16837755C212yesmaximal
4#16837754C211yesmaximal, characteristic, complemented
5#16837708C212yesmaximal, complemented
6#16837623C212yesmaximal
7#16837613C211yesmaximal, characteristic, complemented
8#16837526C211yesmaximal, characteristic, complemented
9#16837496C212yesmaximal, complemented
10C4×#11745670C211yesmaximal, characteristic
11C59×#474C211yesmaximal, characteristic
12C2×Dic236C2212yes—
13C2×#11745670C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273725—21no—
16#14273720—22no—
17#14273718C2212yes—
18#14273717—22no—
19#14273714C2212yes—
20#14273706—21no—
21Q8×Dic59—21no—
22C4×Dic118C2211yescharacteristic
23C4×Dic118C2211yescharacteristic
24#14273692C2212yes—
25#14273692C2212yes—
26#14273686—21no—
27#14273658C2211yescharacteristic
28Dic59⋊C8C2212yes—
29#14273652C2212yes—
30#14273650C2212yes—
31#14273650C2211yescharacteristic
32#14273650C2212yes—
33#14273648C2211yescharacteristic
34C4×C59⋊C8C2211yescharacteristic
35C8×Dic59C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4×D4×C59C2211yescharacteristic
38#107×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#102×C59C2212yes—
41C2×Q8×C59—21no—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C2×Dic118D411yescharacteristic
45C2×Dic118C2312yes—
46C2×Dic118C2311yescharacteristic
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C4⋊C4×C59C2311yescharacteristic
51C22⋊C4×C59—21no—
52C42×C59C2311yescharacteristic
53C22⋊Dic59—22no—
54C22⋊Dic59—22no—
55#11745670—22no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59—22no—
59C4⋊Dic59D411yescharacteristic
60C4⋊Dic59C2311yescharacteristic
61Dic59⋊C4—21no—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4D412yes—
66C4×Dic59—21no—
67C4×Dic59—22no—
68C4×Dic59—22no—
69C4×Dic59C2312yes—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72Dic236—24no—
73C23×C59—21no—
74Q8×C59—42no—
75D4×C59—21no—
76D4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—42no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87C2×Dic59C2×D412yes—
88Dic118—22no—
89Dic118—21no—
90Dic118—22no—
91Dic118—22no—
92Dic118#4112yes—
93C8×C59—22no—
94C59⋊C8—21no—
95C59⋊C8—21no—
96C22×C59—41no—
97C22×C59—41no—
98C22×C59—41no—
99C22×C59C22×D411yescharacteristic
100C4×C59—21no—
101C4×C59—41no—
102C4×C59—42no—
103C4×C59#13512yes—
104C4×C59C2×#4111yescharacteristic
105C4×C592−1+411yescharacteristic
106Dic59—22no—
107Dic59—22no—
108Dic59—22no—
109Dic59—42no—
110Dic59—41no—
111#3364—591nomaximal, Sylow
112C2×C59—81no—
113C2×C59#54811yescharacteristic
114C2×C59C2×#13511yescharacteristic
115C2×C59#57811yescharacteristic
116#557—591no—
117#556—591no—
118#488—592no—
119#487—591no—
120#479—592no—
121#474D5911yescharacteristic
122#464—592no—
123#462—591no—
124C8×Q8—591no—
125C4×Q16—592no—
126C4×SD16—591no—
127C59#336411yescharacteristic, complemented, Sylow
128C2×Q16—592no—
129C2×SD16—591no—
130C4⋊Q8—591no—
131C4⋊Q8—1181no—
132C4⋊Q8C2×D5911yescharacteristic
133#126—1182no—
134#125—592no—
135#125—1182no—
136#124—592no—
137C22⋊Q8—1181no—
138C4×Q8—591no—
139C4×Q8—592no—
140C4×Q8—592no—
141C4×Q8—591no—
142C4×Q8—1181no—
143C4×D4C2×D5911yescharacteristic
144#117—1181no—
145#107C2×D5912yes—
146#106—591no—
147C4⋊C8—592no—
148C4⋊C8C2×D5911yescharacteristic
149#103—592no—
150#103—591no—
151#103—592no—
152#103—592no—
153#102—591no—
154#102C2×D5912yes—
155C4×C8—592no—
156C4×C8—591no—
157C2×Q8—21no—
158C2×Q8—591no—
159C2×Q8—591no—
160C2×Q8—592no—
161C2×D4C22×D5911yescharacteristic
162C22×C4—21no—
163Q16—1184no—
164SD16—1182no—
165C2×C8—591no—
166C2×C8—591no—
167C2×C8C22×D5912yes—
168C4⋊C4—21no—
169C4⋊C4—591no—
170C4⋊C4—592no—
171C4⋊C4—591no—
172C4⋊C4—1182no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1181no—
177C4⋊C4—1181no—
178C4⋊C4—1181no—
179C4⋊C4C22×D5912yes—
180C4⋊C4C22×D5911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C42—592no—
185C42—1182no—
186C42—1182no—
187C42—1181no—
188C42C22×D5911yescharacteristic
189C23—21no—
190Q8—42no—
191Q8—592no—
192Q8—1182no—
193Q8—1181no—
194Q8—1182no—
195Q8—1182no—
196D4—21no—
197D4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—592no—
202C2×C4—592no—
203C2×C4—1181no—
204C2×C4—1182no—
205C2×C4—1181no—
206C2×C4D4×D5911yescharacteristic
207C2×C4D4×D5911yescharacteristic
208C2×C4C23×D5911yescharacteristic
209C8—22no—
210C8—1181no—
211C8—1181no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22C2×D4×D5911yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—1182no—
220C4—1182no—
221C4—1182no—
222C4—2361no—
223C4—2362no—
224C4#1427374612yes—
225C4#41×D5911yescharacteristic
226C4#1427377511yescharacteristic
227C2—81no—
228C2#1683806211yescharacteristic
229C2C2×#1427374611yescharacteristic
230C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3364
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16838127C2semidirect
4. #16837754C2semidirect
5. #16837708C2semidirect
7. #16837613C2semidirect
8. #16837526C2semidirect
9. #16837496C2semidirect
127. C59#3364semidirect