Finite Group Databasebeta

← #21436824

Subgroups — #21436824

Order 7552.

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

normal subgroups only

This group has 382 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#16838073C211yesmaximal, characteristic
3#16837765C212yesmaximal, complemented
4#16837750C211yesmaximal, characteristic, complemented
5#16837705C212yesmaximal, complemented
6#16837603C211yesmaximal, characteristic, complemented
7#16837601C212yesmaximal, complemented
8#16837529C211yesmaximal, characteristic, complemented
9#16837501C212yesmaximal, complemented
10C4×#11745670C211yesmaximal, characteristic, complemented
11C59×#474C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×#11745660C2212yes—
14C2×#11745670C2211yescharacteristic
15#14273725—21no—
16#14273724C2211yescharacteristic
17#14273723C2212yes—
18#14273718C2212yes—
19#14273717—22no—
20#14273701—21no—
21#14273700—22no—
22Q8×Dic59—21no—
23C4×Dic118C2211yescharacteristic
24C4×Dic118C2211yescharacteristic
25#14273692C2212yes—
26#14273689C2212yes—
27#14273658C2211yescharacteristic
28Dic59⋊C8C2212yes—
29#14273650C2211yescharacteristic
30#14273649C2212yes—
31#14273648C2211yescharacteristic
32#14273647C2212yes—
33#14273647C2212yes—
34#14273637C2212yes—
35C4×C59⋊C8C2211yescharacteristic
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×C22⋊D59—22no—
45C2×C22⋊D59—22no—
46#11745685—44no—
47C2×D236—21no—
48C2×D236—21no—
49C2×D236C2312yes—
50C2×C4×D59—22no—
51C2×Dic118D411yescharacteristic
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—
61C4⋊Dic59—22no—
62C4⋊Dic59D411yescharacteristic
63C4⋊Dic59C2311yescharacteristic
64Dic59⋊C4—21no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4D412yes—
68C4×Dic59—21no—
69C4×Dic59—22no—
70C4×Dic59C2312yes—
71C2×C59⋊C8C2311yescharacteristic
72C2×C59⋊C8C2311yescharacteristic
73#11745660—24no—
74C23×C59—21no—
75C22×D59—22no—
76Q8×C59—42no—
77D4×C59—21no—
78D4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—21no—
81C2×C4×C59—42no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—44no—
86C22⋊D59—82no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91D236—22no—
92D236—22no—
93D236—42no—
94D236—81no—
95C4×D59—44no—
96Dic118—22no—
97Dic118—21no—
98Dic118#4112yescomplemented
99C8×C59—22no—
100C59⋊C8—21no—
101C59⋊C8—21no—
102C22×C59—41no—
103C22×C59—41no—
104C22×C59—41no—
105C22×C59C22×D411yescharacteristic
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—42no—
109C4×C59—21no—
110C4×C59—41no—
111C4×C59—42no—
112C4×C59AGL(1,ℤ/8)12yes—
113C4×C59C2×#4111yescharacteristic
114C4×C592−1+411yescharacteristic
115Dic59—22no—
116Dic59—22no—
117Dic59—22no—
118Dic59—41no—
119#3368—591nomaximal, Sylow
120C2×C59—81no—
121C2×C59#54811yescharacteristic
122C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C59#57711yescharacteristic
124D59—82no—
125#557—591no—
126#550—591no—
127#490—592no—
128#486—591no—
129#478—592no—
130#474D5911yescharacteristic, complemented
131#460—591no—
132#460—592no—
133#446—591no—
134#440—592no—
135C4×SD16—591no—
136C59#336811yescharacteristic, complemented, Sylow
137C2×#41—1181no—
138C2×SD16—591no—
139C2×SD16—592no—
140C4⋊Q8—1181no—
141C4⋊Q8C2×D5911yescharacteristic
142#127—592no—
143#127—591no—
144#125—592no—
145#125—1182no—
146#121—1182no—
147#121—1181no—
148C4×Q8—591no—
149C4×Q8—592no—
150C4×Q8—591no—
151C4×Q8—1181no—
152C4×D4—592no—
153C4×D4C2×D5911yescharacteristic
154#107C2×D5912yes—
155#106—591no—
156C4⋊C8—592no—
157C4⋊C8C2×D5911yescharacteristic
158#103—591no—
159#102—591no—
160#102—592no—
161#102—592no—
162#102—592no—
163#102C2×D5912yes—
164#97—592no—
165C4×C8—591no—
166#41—2364no—
167C2×Q8—21no—
168C2×Q8—591no—
169C2×Q8—591no—
170C2×D4—592no—
171C2×D4—1182no—
172C2×D4—1182no—
173C2×D4—1181no—
174C2×D4—1181no—
175C2×D4C22×D5911yescharacteristic
176C22×C4—21no—
177C22×C4—1182no—
178SD16—1184no—
179SD16—1182no—
180C2×C8—591no—
181C2×C8—591no—
182C2×C8C22×D5912yes—
183C4⋊C4—21no—
184C4⋊C4—591no—
185C4⋊C4—592no—
186C4⋊C4—591no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—1182no—
190C4⋊C4—1181no—
191C4⋊C4C22×D5912yes—
192C4⋊C4C22×D5911yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—1182no—
195C42—592no—
196C42—1182no—
197C42—1181no—
198C42C22×D5911yescharacteristic
199C23—21no—
200C23—1182no—
201Q8—42no—
202Q8—592no—
203Q8—1182no—
204Q8—1181no—
205D4—21no—
206D4—21no—
207D4—1182no—
208D4—1182no—
209D4—4721no—
210D4—4722no—
211D4—2364no—
212D4—2362no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—592no—
217C2×C4—592no—
218C2×C4—1181no—
219C2×C4—1181no—
220C2×C4—2364no—
221C2×C4D4×D5911yescharacteristic
222C2×C4D4×D5911yescharacteristic
223C2×C4C23×D5911yescharacteristic
224C8—22no—
225C8—1181no—
226C8—1181no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—2362no—
231C22—2362no—
232C22—2362no—
233C22C2×D4×D5911yescharacteristic
234C4—21no—
235C4—41no—
236C4—42no—
237C4—1182no—
238C4—1182no—
239C4—1182no—
240C4—2361no—
241C4#1427375112yes—
242C4#41×D5911yescharacteristic
243C4#1427377511yescharacteristic
244C2—81no—
245C2—4722no—
246C2#1683806211yescharacteristic
247C2C2×#1427375111yescharacteristic
248C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3368
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
3. #16837765C2semidirect
4. #16837750C2semidirect
5. #16837705C2semidirect
6. #16837603C2semidirect
7. #16837601C2semidirect
8. #16837529C2semidirect
9. #16837501C2semidirect
10. C4×#11745670C2semidirect
11. C59×#474C2semidirect
98. Dic118#41semidirect
130. #474D59semidirect
136. C59#3368semidirect