Finite Group Databasebeta

← #21435008

Subgroups — #21435008

Order 7552.

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

normal subgroups only

This group has 402 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#16837980C212yesmaximal, complemented
2#16837733C212yesmaximal, complemented
3#16837721C212yesmaximal, complemented
4#16837660C211yesmaximal, characteristic, complemented
5#16837655C211yesmaximal, characteristic, complemented
6#16837631C212yesmaximal, complemented
7#16837566C212yesmaximal, complemented
8#16837549C212yesmaximal, complemented
9C59×#408C211yesmaximal, characteristic, complemented
10C2×#11745685C2212yes—
11C2×Dic236C2211yescharacteristic
12C2×#11745660C2212yes—
13C2×D472C2211yescharacteristic
14#14273706C2212yes—
15#14273706C2212yes—
16#14273703—22no—
17#14273701C2212yes—
18#14273701C2212yes—
19#14273699—22no—
20#14273699—22no—
21#14273698—22no—
22C2×C4⋊Dic59C2212yes—
23#14273659C2211yescharacteristic
24#14273659C2211yescharacteristic
25#14273659C2212yes—
26#14273652C2212yes—
27#14273652C2212yes—
28#14273649C2212yes—
29#14273649C2212yes—
30C2×#41×C59C2211yescharacteristic
31C2×M16×C59C2211yescharacteristic
32C22×C8×C59C2211yescharacteristic
33C22⋊C8×C59C2212yes—
34C22⋊C8×C59C2212yes—
35#41×C59—41no—
36#41×C59—41no—
37C2×Q8×C59D411yescharacteristic
38C2×D4×C59D412yes—
39C2×D4×C59D411yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C2×C22⋊D59—22no—
43C2×C22⋊D59—22no—
44C2×C22⋊D59—22no—
45C22×Dic59—22no—
46#11745685—42no—
47#11745685—42no—
48C2×D236C2312yes—
49C2×C4×D59—22no—
50C2×Dic118C2312yes—
51M16×C59—41no—
52C2×C8×C59—41no—
53C2×C8×C59C2312yes—
54C2×C8×C59C2311yescharacteristic
55C2×C8×C59C2311yescharacteristic
56C22⋊Dic59—22no—
57C22⋊Dic59—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60C4⋊Dic59—22no—
61C4⋊Dic59C2312yes—
62C4⋊Dic59C2312yes—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic236—41no—
66D472—41no—
67#11745660—42no—
68C23×C59C2×D411yescharacteristic
69C23×C59C2×D412yes—
70C22×D59—22no—
71Q8×C59—41no—
72D4×C59—42no—
73D4×C59—41no—
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D412yes—
80C2×C4×C59C2411yescharacteristic
81C22⋊D59—44no—
82C22⋊D59—82no—
83C22⋊D59—82no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—82no—
88D236—22no—
89D236—22no—
90C4×D59—44no—
91Dic118—22no—
92Dic118—22no—
93C8×C59—22no—
94C8×C59—21no—
95C8×C59—21no—
96C22×C59—22no—
97C22×C59—21no—
98C22×C59—22no—
99C22×C59—22no—
100C22×C59—22no—
101C22×C59C22×D411yescharacteristic
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C4×C59—22no—
106C4×C59—21no—
107C4×C59H(5,𝔽2)11yescharacteristic
108C4×C59H(5,𝔽2)11yescharacteristic
109Dic59—42no—
110Dic59—42no—
111Dic59—42no—
112#3204—591nomaximal, Sylow
113C2×C59—42no—
114C2×C59—41no—
115C2×C59#53411yescharacteristic
116C2×C59#57712yes—
117D59—82no—
118#537—592no—
119#483—592no—
120#481—592no—
121#470—591no—
122#469—591no—
123#465—592no—
124#452—592no—
125#449—592no—
126#408D5911yescharacteristic, complemented
127C59#320411yescharacteristic, complemented, Sylow
128C2×#41—592no—
129C2×#41C2×D5911yescharacteristic
130C2×Q16—591no—
131C2×SD16—592no—
132C2×D8—591no—
133C2×M16C2×D5911yescharacteristic
134C22×C8C2×D5911yescharacteristic
135C22⋊Q8—592no—
136C22⋊Q8—592no—
137C22⋊Q8—1182no—
138#121—592no—
139#121—592no—
140#121—1182no—
141#121—1182no—
142#121—1182no—
143C2×C4⋊C4—592no—
144#106—592no—
145#106—591no—
146#106—591no—
147#103—592no—
148#103—592no—
149#102—592no—
150#102—592no—
151C22⋊C8C2×D5912yes—
152C22⋊C8C2×D5912yes—
153#41—41no—
154#41—41no—
155#41—2362no—
156#41—2362no—
157C2×Q8—592no—
158C2×Q8D23611yescharacteristic
159C2×D4—592no—
160C2×D4—1182no—
161C2×D4—1182no—
162C2×D4—1182no—
163C2×D4D23611yescharacteristic
164C2×D4D23612yes—
165C22×C4—1182no—
166C22×C4—1182no—
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169Q16—2361no—
170SD16—2362no—
171D8—2361no—
172M16—41no—
173C2×C8—41no—
174C2×C8C22×D5911yescharacteristic
175C2×C8C22×D5912yes—
176C2×C8C22×D5911yescharacteristic
177C4⋊C4—592no—
178C4⋊C4—592no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C23—1182no—
187C23C2×D23611yescharacteristic
188C23C2×D23612yes—
189Q8—41no—
190Q8—1182no—
191Q8—1182no—
192D4—42no—
193D4—41no—
194D4—1182no—
195D4—1182no—
196D4—4722no—
197D4—4722no—
198D4—2364no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—4722no—
207C2×C4—2364no—
208C2×C4C2×D23611yescharacteristic
209C2×C4C2×D23612yes—
210C2×C4C23×D5911yescharacteristic
211C8—22no—
212C8—21no—
213C8—21no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—21no—
219C22—2362no—
220C22—2362no—
221C22—2362no—
222C22C22×D23611yescharacteristic
223C4—22no—
224C4—21no—
225C4—2362no—
226C4—2362no—
227C4—2362no—
228C4#1427377211yescharacteristic
229C4#1427377211yescharacteristic
230C2—42no—
231C2—41no—
232C2—4722no—
233C2#1683796411yescharacteristic
234C2#1683821412yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#408C2
socleC22×C59C22×D4
hypercenter#408D59
hypocenterC59#3204
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16837980C2semidirect
2. #16837733C2semidirect
3. #16837721C2semidirect
4. #16837660C2semidirect
5. #16837655C2semidirect
6. #16837631C2semidirect
7. #16837566C2semidirect
8. #16837549C2semidirect
9. C59×#408C2semidirect
126. #408D59semidirect
127. C59#3204semidirect