Finite Group Databasebeta

← #21437153

Subgroups — #21437153

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#16838137C211yesmaximal, characteristic
2#16838127C211yesmaximal, characteristic, complemented
3#16837795C212yesmaximal, complemented
4#16837776C211yesmaximal, characteristic
5#16837626C212yesmaximal, complemented
6#16837606C212yesmaximal, complemented
7#16837603C211yesmaximal, characteristic
8#16837529C211yesmaximal, characteristic, complemented
9#16837505C212yesmaximal, complemented
10C4×#11745672C211yesmaximal, characteristic, complemented
11C59×#462C211yesmaximal, characteristic, complemented
12C2×#11745672C2211yescharacteristic
13C2×#11745660C2212yes—
14C2×#11745671C2212yes—
15C2×#11745671C2212yes—
16#14273725C2212yes—
17#14273724C2211yescharacteristic
18#14273718—21no—
19#14273717—22no—
20#14273716C2212yes—
21#14273715—21no—
22#14273712—22no—
23Q8×Dic59C2212yes—
24C4×Dic118C2211yescharacteristic
25C4×Dic118C2211yescharacteristic
26#14273692—21no—
27C4×D236—21no—
28#14273689C2212yes—
29#14273660C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273651C2211yescharacteristic
32#14273650C2211yescharacteristic
33#14273649C2212yes—
34#14273637C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C2×Q16×C59C2212yes—
37C4⋊Q8×C59C2211yescharacteristic
38C4×Q8×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59C2312yes—
42C2×Q8×C59C2311yescharacteristic
43C2×D236—21no—
44C2×D236—21no—
45C2×D236C2312yes—
46C2×C4×D59—22no—
47C2×Dic118D411yescharacteristic
48C2×Dic118C2311yescharacteristic
49Q16×C59—42no—
50C2×C8×C59C2312yes—
51C4⋊C4×C59—21no—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2311yescharacteristic
55C42×C59—21no—
56C42×C59C2311yescharacteristic
57#11745672—22no—
58#11745671—24no—
59#11745671—42no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63C4⋊Dic59—22no—
64C4⋊Dic59D411yescharacteristic
65C4⋊Dic59C2311yescharacteristic
66Dic59⋊C4—21no—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4D412yes—
70C4×Dic59—21no—
71C4×Dic59—22no—
72C4×Dic59C2312yes—
73C2×C59⋊C8C2311yescharacteristic
74C2×C59⋊C8C2311yescharacteristic
75#11745660—42no—
76C22×D59—22no—
77Q8×C59—22no—
78Q8×C59—21no—
79Q8×C59—22no—
80Q8×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91D236—22no—
92D236—22no—
93D236—42no—
94D236—81no—
95C4×D59—82no—
96Dic118—22no—
97Dic118—21no—
98Dic118—21no—
99C8×C59—22no—
100C59⋊C8—21no—
101C59⋊C8#4112yes—
102C22×C59C22×D411yescharacteristic
103C2×D59—42no—
104C2×D59—42no—
105C2×D59—42no—
106C4×C59—21no—
107C4×C59—42no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59#13712yes—
111C4×C59C2×#4111yescharacteristic
112C4×C59H(5,𝔽2)11yescharacteristic
113Dic59—22no—
114Dic59—22no—
115Dic59—41no—
116Dic59—41no—
117#3400—591nomaximal, Sylow
118C2×C59#55011yescharacteristic
119C2×C59C2×#13711yescharacteristic
120C2×C59#57711yescharacteristic
121D59—82no—
122#559—591no—
123#557—591no—
124#497—592no—
125#492—591no—
126#464—592no—
127#462D5911yescharacteristic, complemented
128#461—592no—
129#460—591no—
130#446—591no—
131#440—592no—
132C4×Q16—591no—
133C59#340011yescharacteristic, complemented, Sylow
134C2×Q16—591no—
135C2×Q16C2×D5912yes—
136C2×SD16—592no—
137C2×SD16—592no—
138C2×SD16—592no—
139C4⋊Q8—592no—
140C4⋊Q8C2×D5911yescharacteristic
141#127—591no—
142#125—1182no—
143#125—1181no—
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—591no—
159#103C2×D5912yes—
160#102—592no—
161#97—592no—
162C4×C8—591no—
163C2×Q8—591no—
164C2×Q8—591no—
165C2×Q8C22×D5911yescharacteristic
166C2×Q8C22×D5912yes—
167C2×D4—592no—
168C2×D4—1181no—
169C2×D4—1181no—
170C22×C4—1182no—
171Q16—42no—
172Q16—1182no—
173SD16—1184no—
174SD16—2362no—
175SD16—2362no—
176C2×C8—591no—
177C2×C8—591no—
178C2×C8C22×D5912yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—591no—
183C4⋊C4—592no—
184C4⋊C4—591no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
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—1182no—
199Q8—22no—
200Q8—21no—
201Q8—22no—
202Q8—21no—
203Q8—1182no—
204Q8—1181no—
205Q8—1181no—
206D4—1182no—
207D4—1182no—
208D4—4721no—
209D4—2362no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—592no—
214C2×C4—592no—
215C2×C4—1181no—
216C2×C4—1181no—
217C2×C4—4722no—
218C2×C4D4×D5911yescharacteristic
219C2×C4D4×D5911yescharacteristic
220C2×C4C23×D5911yescharacteristic
221C8—22no—
222C8—592no—
223C8—1181no—
224C22—2362no—
225C22—2362no—
226C22—2362no—
227C22C2×D4×D5911yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—42no—
232C4—1182no—
233C4—1182no—
234C4—2361no—
235C4—2361no—
236C4#1427375912yes—
237C4#41×D5911yescharacteristic
238C4#1427377211yescharacteristic
239C2—4722no—
240C2#1683807011yescharacteristic
241C2C2×#1427375911yescharacteristic
242C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#462C2
socleC22×C59C22×D4
hypercenter#462D59
hypocenterC59#3400
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #16838127C2semidirect
3. #16837795C2semidirect
5. #16837626C2semidirect
6. #16837606C2semidirect
8. #16837529C2semidirect
9. #16837505C2semidirect
10. C4×#11745672C2semidirect
11. C59×#462C2semidirect
127. #462D59semidirect
133. C59#3400semidirect