Finite Group Databasebeta

← #21437148

Subgroups — #21437148

Order 7552.

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

normal subgroups only

This group has 362 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#16838138C211yesmaximal, characteristic
2#16838130C211yesmaximal, characteristic, complemented
3#16837793C212yesmaximal, complemented
4#16837774C211yesmaximal, characteristic
5#16837623C212yesmaximal, complemented
6#16837613C211yesmaximal, characteristic, complemented
7#16837605C212yesmaximal, complemented
8#16837529C211yesmaximal, characteristic, complemented
9#16837499C212yesmaximal, complemented
10C4×#11745672C211yesmaximal, characteristic, complemented
11C59×#460C211yesmaximal, characteristic
12C2×Dic236C2212yes—
13C2×#11745672C2211yescharacteristic
14C2×#11745670C2212yes—
15C2×#11745670C2212yes—
16#14273727C2211yescharacteristic
17#14273725C2212yes—
18#14273719—21no—
19#14273717—22no—
20#14273714—21no—
21#14273714C2212yes—
22#14273708—22no—
23C4×Dic118—21no—
24C4×Dic118C2211yescharacteristic
25C4×Dic118C2211yescharacteristic
26#14273692C2212yes—
27D4×Dic59—21no—
28D4×Dic59C2212yes—
29#14273660C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273652C2212yes—
32#14273651C2211yescharacteristic
33#14273650C2211yescharacteristic
34#14273637C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C2×SD16×C59C2212yes—
37#127×C59C2211yescharacteristic
38C4×Q8×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic
40#102×C59C2212yes—
41C2×Q8×C59C2311yescharacteristic
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C22×Dic59—22no—
46C2×Dic118D411yescharacteristic
47C2×Dic118C2311yescharacteristic
48C2×Dic118C2312yes—
49SD16×C59—42no—
50C2×C8×C59C2312yes—
51C4⋊C4×C59—21no—
52C4⋊C4×C59C2311yescharacteristic
53C42×C59—21no—
54C42×C59C2311yescharacteristic
55C22⋊Dic59—22no—
56C22⋊Dic59—22no—
57C22⋊Dic59—22no—
58#11745672—22no—
59#11745670—24no—
60#11745670—42no—
61C4⋊Dic59—21no—
62C4⋊Dic59—21no—
63C4⋊Dic59D411yescharacteristic
64C4⋊Dic59C2311yescharacteristic
65Dic59⋊C4—21no—
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4D412yes—
70C4×Dic59—21no—
71C4×Dic59—22no—
72C4×Dic59C2312yes—
73C2×C59⋊C8C2311yescharacteristic
74C2×C59⋊C8C2311yescharacteristic
75Dic236—42no—
76C23×C59—22no—
77Q8×C59—21no—
78Q8×C59—21no—
79D4×C59—22no—
80D4×C59—22no—
81D4×C59—42no—
82D4×C59—81no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2411yescharacteristic
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59—82no—
92C2×Dic59C2×D412yes—
93C2×Dic59C2×D412yes—
94Dic118—22no—
95Dic118—22no—
96Dic118—21no—
97Dic118—21no—
98Dic118—22no—
99C8×C59—22no—
100C59⋊C8—21no—
101C59⋊C8#4112yes—
102C22×C59—42no—
103C22×C59—42no—
104C22×C59—42no—
105C22×C59C22×D411yescharacteristic
106C4×C59—21no—
107C4×C59—41no—
108C4×C59—41no—
109C4×C59#13712yes—
110C4×C59C2×#4111yescharacteristic
111C4×C59H(5,𝔽2)11yescharacteristic
112Dic59—22no—
113Dic59—22no—
114Dic59—42no—
115Dic59—41no—
116Dic59—41no—
117#3400—591nomaximal, Sylow
118C2×C59—82no—
119C2×C59#55011yescharacteristic
120C2×C59C2×#13711yescharacteristic
121C2×C59#57711yescharacteristic
122#559—591no—
123#557—591no—
124#497—592no—
125#492—591no—
126#464—592no—
127#462—591no—
128#461—592no—
129#460D5911yescharacteristic
130#446—591no—
131#440—592no—
132C4×Q16—591no—
133C59#340011yescharacteristic, complemented, Sylow
134C2×Q16—591no—
135C2×Q16—592no—
136C2×SD16—592no—
137C2×SD16—592no—
138C2×SD16C2×D5912yes—
139C4⋊Q8—592no—
140C4⋊Q8—591no—
141#127C2×D5911yescharacteristic
142#125—1181no—
143#125—1182no—
144#124—592no—
145#124—1181no—
146#123—1182no—
147C4×Q8—591no—
148C4×Q8—592no—
149C4×Q8—591no—
150C4×Q8—1181no—
151C4×Q8C2×D5911yescharacteristic
152C4×D4—592no—
153C4×D4—1181no—
154#107—591no—
155C4⋊C8—592no—
156C4⋊C8C2×D5911yescharacteristic
157#103—591no—
158#103—592no—
159#103—591no—
160#102C2×D5912yes—
161#97—592no—
162C4×C8—591no—
163C2×Q8—591no—
164C2×Q8—591no—
165C2×Q8—592no—
166C2×Q8C22×D5911yescharacteristic
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D5912yes—
170C22×C4—1182no—
171Q16—1182no—
172Q16—2362no—
173SD16—42no—
174SD16—1184no—
175SD16—2362no—
176C2×C8—591no—
177C2×C8—591no—
178C2×C8C22×D5912yes—
179C4⋊C4—21no—
180C4⋊C4—591no—
181C4⋊C4—592no—
182C4⋊C4—591no—
183C4⋊C4—1182no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C4⋊C4—1181no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C4⋊C4C22×D5911yescharacteristic
190C22⋊C4—1182no—
191C22⋊C4—1182no—
192C22⋊C4—1182no—
193C42—21no—
194C42—592no—
195C42—1182no—
196C42—1181no—
197C42C22×D5911yescharacteristic
198C23—22no—
199Q8—21no—
200Q8—21no—
201Q8—1182no—
202Q8—1182no—
203Q8—1181no—
204Q8—1182no—
205Q8—1181no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—592no—
213C2×C4—592no—
214C2×C4—1181no—
215C2×C4—1181no—
216C2×C4—1182no—
217C2×C4—4722no—
218C2×C4D4×D5911yescharacteristic
219C2×C4D4×D5911yescharacteristic
220C2×C4C23×D5911yescharacteristic
221C8—22no—
222C8—592no—
223C8—1181no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C2×D4×D5911yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—1182no—
232C4—1182no—
233C4—2361no—
234C4—2361no—
235C4—2362no—
236C4#1427375612yes—
237C4#41×D5911yescharacteristic
238C4#1427377211yescharacteristic
239C2—82no—
240C2#1683807011yescharacteristic
241C2C2×#1427375611yescharacteristic
242C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#460C2
socleC22×C59C22×D4
hypercenter#460D59
hypocenterC59#3400
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #16838130C2semidirect
3. #16837793C2semidirect
5. #16837623C2semidirect
6. #16837613C2semidirect
7. #16837605C2semidirect
8. #16837529C2semidirect
9. #16837499C2semidirect
10. C4×#11745672C2semidirect
133. C59#3400semidirect