Finite Group Databasebeta

← #21436409

Subgroups — #21436409

Order 7552.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#16838113C211yesmaximal, characteristic, complemented
2#16838056C211yesmaximal, characteristic
3#16837754C211yesmaximal, characteristic, complemented
4#16837734C212yesmaximal, complemented
5#16837661C212yesmaximal, complemented
6#16837613C211yesmaximal, characteristic, complemented
7#16837565C212yesmaximal, complemented
8C4×#11745670C211yesmaximal, characteristic, complemented
9#16837479C211yesmaximal, characteristic, complemented
10#16837400C212yesmaximal, complemented
11C59×#476C211yesmaximal, characteristic, complemented
12C2×#11745687C2212yes—
13C2×Dic236C2212yes—
14C2×#11745670C2211yescharacteristic
15C2×#11745659C2212yes—
16#14273727C2211yescharacteristic
17#14273718—21no—
18#14273711—22no—
19#14273707C2212yes—
20#14273707C2212yes—
21#14273703—22no—
22#14273701—21no—
23C4×Dic118C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273689—21no—
26C2×C4⋊Dic59—21no—
27C4⋊C4×D59C2212yes—
28#14273658C2211yescharacteristic
29#14273652C2212yes—
30#14273650C2212yes—
31#14273650C2211yescharacteristic
32#14273650C2212yes—
33#14273648C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C4⋊Q8×C59C2211yescharacteristic
37C4×D4×C59C2211yescharacteristic
38#106×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#102×C59C2212yes—
41C2×Q8×C59—21no—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C2×C22⋊D59—22no—
45C22×Dic59—22no—
46#11745687—24no—
47#11745687—42no—
48C2×D236D411yescharacteristic
49C2×C4×D59—22no—
50C2×C4×D59C2312yes—
51C2×Dic118C2312yes—
52C2×Dic118C2311yescharacteristic
53C2×C8×C59C2312yes—
54C4⋊C4×C59—21no—
55C4⋊C4×C59C2312yes—
56C4⋊C4×C59C2311yescharacteristic
57C22⋊C4×C59—21no—
58C42×C59C2311yescharacteristic
59#11745670—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4D412yes—
63C4⋊Dic59—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59—22no—
66C4⋊Dic59—22no—
67C4⋊Dic59D411yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—21no—
70Dic59⋊C4—22no—
71C4×Dic59—21no—
72C2×C59⋊C8C2311yescharacteristic
73C2×C59⋊C8C2311yescharacteristic
74Dic236—42no—
75#11745659—42no—
76C23×C59—21no—
77C22×D59C2×D412yes—
78Q8×C59—81no—
79D4×C59—21no—
80D4×C59#4112yes—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—42no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C22⋊D59—44no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—44no—
92C2×Dic59C2×D412yes—
93D236—22no—
94C4×D59—22no—
95C4×D59—22no—
96C4×D59—82no—
97Dic118—21no—
98Dic118—22no—
99Dic118—21no—
100Dic118—22no—
101C8×C59—22no—
102C59⋊C8—21no—
103C59⋊C8—21no—
104C22×C59—22no—
105C22×C59—41no—
106C22×C59—41no—
107C22×C59C22×D411yescharacteristic
108C2×D59—22no—
109C2×D59—22no—
110C2×D59—22no—
111C4×C59—21no—
112C4×C59—41no—
113C4×C59—42no—
114C4×C59#13712yes—
115C4×C59C2×#4111yescharacteristic
116C4×C59H(5,𝔽2)11yescharacteristic
117Dic59—22no—
118Dic59—41no—
119Dic59—42no—
120Dic59—41no—
121#3331—591nomaximal, Sylow
122C2×C59—42no—
123C2×C59#54611yescharacteristic
124C2×C59C2×#13711yescharacteristic
125C2×C59#57711yescharacteristic
126D59—42no—
127#554—591no—
128#547—591no—
129#487—591no—
130#483—592no—
131#476D5911yescharacteristic, complemented
132#470—592no—
133#462—591no—
134#452—592no—
135C4×SD16—591no—
136#436—591no—
137#417—592no—
138C59#333111yescharacteristic, complemented, Sylow
139C2×#41—592no—
140C2×Q16—592no—
141C2×SD16—591no—
142C2×M16—592no—
143C4⋊Q8—591no—
144C4⋊Q8C2×D5911yescharacteristic
145#125—1181no—
146#123—1182no—
147C22⋊Q8—592no—
148C22⋊Q8—592no—
149C22⋊Q8—1182no—
150#121—1181no—
151C4×Q8—591no—
152C4×D4—591no—
153C4×D4—1181no—
154C4×D4C2×D5911yescharacteristic
155C2×C4⋊C4—592no—
156C2×C4⋊C4—1181no—
157#106—591no—
158#106C2×D5912yes—
159C4⋊C8C2×D5911yescharacteristic
160#103—592no—
161#103—592no—
162#103—591no—
163#103—592no—
164#102—591no—
165#102C2×D5912yes—
166C22⋊C8—592no—
167C4×C8—591no—
168#41—1184no—
169#41—2362no—
170C2×Q8—21no—
171C2×Q8—592no—
172C2×Q8—591no—
173C2×D4—591no—
174C2×D4—1182no—
175C2×D4C22×D5911yescharacteristic
176C22×C4—21no—
177C22×C4—592no—
178C22×C4—1182no—
179C22×C4—1182no—
180Q16—2362no—
181SD16—1182no—
182M16—2362no—
183C2×C8—591no—
184C2×C8—591no—
185C2×C8C22×D5912yes—
186C4⋊C4—21no—
187C4⋊C4—591no—
188C4⋊C4—591no—
189C4⋊C4—1182no—
190C4⋊C4—1182no—
191C4⋊C4—1182no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4—1181no—
195C4⋊C4C22×D5912yes—
196C4⋊C4C22×D5911yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—592no—
199C22⋊C4—1182no—
200C22⋊C4—1182no—
201C42—1181no—
202C42C22×D5911yescharacteristic
203C23—21no—
204C23—592no—
205Q8—81no—
206Q8—1181no—
207Q8—1182no—
208Q8—1181no—
209Q8—1182no—
210D4—21no—
211D4—1182no—
212D4—2364no—
213D4#1174568912yes—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—592no—
218C2×C4—1182no—
219C2×C4—1182no—
220C2×C4—1181no—
221C2×C4—1181no—
222C2×C4—1182no—
223C2×C4—4722no—
224C2×C4—2364no—
225C2×C4D4×D5911yescharacteristic
226C2×C4D4×D5911yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—22no—
229C8—1181no—
230C8—1181no—
231C22—22no—
232C22—41no—
233C22—41no—
234C22—1182no—
235C22—1182no—
236C22—1182no—
237C22C2×D4×D5911yescharacteristic
238C4—21no—
239C4—41no—
240C4—42no—
241C4—1182no—
242C4—2361no—
243C4—2362no—
244C4—2361no—
245C4#1427375612yes—
246C4C2×#1174568911yescharacteristic
247C4#1427377311yescharacteristic
248C2—42no—
249C2—2362no—
250C2#1683804311yescharacteristic
251C2C2×#1427375611yescharacteristic
252C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#476C2
socleC22×C59C22×D4
hypercenter#476D59
hypocenterC59#3331
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16838113C2semidirect
3. #16837754C2semidirect
4. #16837734C2semidirect
5. #16837661C2semidirect
6. #16837613C2semidirect
7. #16837565C2semidirect
8. C4×#11745670C2semidirect
9. #16837479C2semidirect
10. #16837400C2semidirect
11. C59×#476C2semidirect
131. #476D59semidirect
138. C59#3331semidirect