Finite Group Databasebeta

← #21436525

Subgroups — #21436525

Order 7552.

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

normal subgroups only

This group has 340 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#16838126C211yesmaximal, characteristic
2#16838125C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837746C212yesmaximal, complemented
5#16837741C212yesmaximal, complemented
6#16837688C211yesmaximal, characteristic, complemented
7#16837642C212yesmaximal, complemented
8C4×#11745672C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic
10#16837437C212yesmaximal, complemented
11C59×#475C211yesmaximal, characteristic, complemented
12C2×#11745672C2211yescharacteristic
13C2×C8×D59C2212yes—
14#14273727C2211yescharacteristic
15#14273722—22no—
16#14273722—22no—
17#14273716—21no—
18#14273715—21no—
19#14273707C2212yes—
20#14273703C2212yes—
21Q8×Dic59—21no—
22C4×Dic118—21no—
23C4×Dic118C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273685C2212yes—
26#14273685C2212yes—
27#14273660C2212yes—
28#14273660C2211yescharacteristic
29#14273660C2212yes—
30#14273659C2212yes—
31#14273652C2212yes—
32#14273651C2211yescharacteristic
33#14273650C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C4⋊Q8×C59C2211yescharacteristic
37C4×Q8×C59C2211yescharacteristic
38#106×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59—21no—
42C2×Q8×C59C2311yescharacteristic
43C2×D236D411yescharacteristic
44C2×C4×D59C2312yes—
45C2×Dic118—21no—
46C2×Dic118C2311yescharacteristic
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59C2312yes—
51C4⋊C4×C59C2311yescharacteristic
52C42×C59—21no—
53C42×C59C2311yescharacteristic
54#11745672—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4D412yes—
60C4⋊Dic59—21no—
61C4⋊Dic59—22no—
62C4⋊Dic59D411yescharacteristic
63C4⋊Dic59C2311yescharacteristic
64C4⋊Dic59C2312yes—
65Dic59⋊C4—21no—
66Dic59⋊C4—22no—
67C4×Dic59—21no—
68C4×Dic59—22no—
69C4×Dic59—22no—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72C8×D59—24no—
73C22×D59C2×D412yes—
74Q8×C59—21no—
75Q8×C59—21no—
76Q8×C59—42no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—21no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2411yescharacteristic
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87D236—22no—
88C4×D59—22no—
89C4×D59—22no—
90Dic118—21no—
91Dic118—21no—
92Dic118—42no—
93C8×C59—22no—
94C59⋊C8—21no—
95C59⋊C8#4112yes—
96C22×C59C22×D411yescharacteristic
97C2×D59—22no—
98C2×D59—22no—
99C2×D59—22no—
100C4×C59—21no—
101C4×C59—41no—
102C4×C59—42no—
103C4×C59—41no—
104C4×C59#13512yes—
105C4×C59C2×#4111yescharacteristic
106C4×C592−1+411yescharacteristic
107Dic59—22no—
108Dic59—41no—
109Dic59—42no—
110Dic59—41no—
111#3342—591nomaximal, Sylow
112C2×C59#54711yescharacteristic
113C2×C59C2×#13511yescharacteristic
114C2×C59#57811yescharacteristic
115D59—42no—
116#556—591no—
117#556—591no—
118#500—591no—
119#485—592no—
120#485—592no—
121#475—591no—
122#475D5911yescharacteristic, complemented
123#467—592no—
124C4×Q16—591no—
125C8×D4—591no—
126#427—592no—
127C59#334211yescharacteristic, complemented, Sylow
128C2×Q16—591no—
129C22×C8—592no—
130C4⋊Q8—591no—
131C4⋊Q8C2×D5911yescharacteristic
132#126—1182no—
133#126—1182no—
134#124—1181no—
135#124—1181no—
136C22⋊Q8—592no—
137C22⋊Q8—592no—
138C4×Q8—591no—
139C4×Q8—1181no—
140C4×Q8—1181no—
141C4×Q8C2×D5911yescharacteristic
142C4×D4—591no—
143#117—592no—
144#117—592no—
145#107—591no—
146#107—592no—
147#107—592no—
148#106—592no—
149#106C2×D5912yes—
150C4⋊C8C2×D5911yescharacteristic
151#103—591no—
152#103—592no—
153#103—591no—
154#103C2×D5912yes—
155C22⋊C8—592no—
156C4×C8—591no—
157C2×Q8—21no—
158C2×Q8—591no—
159C2×Q8—1181no—
160C2×Q8C22×D5911yescharacteristic
161C2×D4—591no—
162C22×C4—592no—
163Q16—1182no—
164C2×C8—591no—
165C2×C8—591no—
166C2×C8—1184no—
167C2×C8C22×D5912yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—591no—
171C4⋊C4—591no—
172C4⋊C4—592no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1181no—
176C4⋊C4—1181no—
177C4⋊C4C22×D5911yescharacteristic
178C4⋊C4C22×D5912yes—
179C22⋊C4—592no—
180C22⋊C4—1182no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4—1182no—
184C42—21no—
185C42—1182no—
186C42—1182no—
187C42—1181no—
188C42C22×D5911yescharacteristic
189C23—592no—
190Q8—21no—
191Q8—21no—
192Q8—42no—
193Q8—1181no—
194Q8—1181no—
195Q8—2362no—
196D4—1182no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—592no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1181no—
204C2×C4—1182no—
205C2×C4—1181no—
206C2×C4D4×D5911yescharacteristic
207C2×C4D4×D5911yescharacteristic
208C2×C4C23×D5911yescharacteristic
209C8—22no—
210C8—592no—
211C8—1181no—
212C22—1182no—
213C22—1182no—
214C22—1182no—
215C22C2×D4×D5911yescharacteristic
216C4—21no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—1182no—
221C4—2362no—
222C4—2361no—
223C4—2361no—
224C4#1427374812yes—
225C4#41×D5911yescharacteristic
226C4#1427377511yescharacteristic
227C2—2362no—
228C2#1683805411yescharacteristic
229C2C2×#1427374811yescharacteristic
230C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#475C2
socleC22×C59C22×D4
hypercenter#475D59
hypocenterC59#3342
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #16837805C2semidirect
4. #16837746C2semidirect
5. #16837741C2semidirect
6. #16837688C2semidirect
7. #16837642C2semidirect
8. C4×#11745672C2semidirect
10. #16837437C2semidirect
11. C59×#475C2semidirect
122. #475D59semidirect
127. C59#3342semidirect