Finite Group Databasebeta

← #21435440

Subgroups — #21435440

Order 7552.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837957C211yesmaximal, characteristic
2#16837956C211yesmaximal, characteristic
3#16837696C212yesmaximal, complemented
4#16837694C211yesmaximal, characteristic, complemented
5#16837644C212yesmaximal
6#16837642C212yesmaximal
7#16837613C211yesmaximal, characteristic, complemented
8#16837612C211yesmaximal, characteristic, complemented
9#16837611C212yesmaximal, complemented
10C4⋊C8×D59C211yesmaximal, characteristic
11C59×#477C211yesmaximal, characteristic, complemented
12C2×Dic236C2212yes—
13C2×#11745672C2212yes—
14C2×C8×D59C2212yes—
15#14273727C2211yescharacteristic
16#14273726C2211yescharacteristic
17#14273725C2211yescharacteristic
18#14273718—21no—
19#14273717—21no—
20#14273707C2212yes—
21#14273707C2211yescharacteristic
22#14273705—21no—
23#14273703—21no—
24#14273703C2211yescharacteristic
25Q8×Dic59—21no—
26C4×Dic118—21no—
27C4×Dic118C2211yescharacteristic
28#14273692C2212yes—
29#14273685—21no—
30#14273684—21no—
31C42×D59C2211yescharacteristic
32#14273660C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273652C2212yes—
36#14273650C2212yes—
37#14273650C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×Q8×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59—21no—
44C2×Q8×C59C2311yescharacteristic
45C2×C4×D59D411yescharacteristic
46C2×C4×D59D411yescharacteristic
47C2×C4×D59C2311yescharacteristic
48C2×Dic118—21no—
49C2×Dic118C2311yescharacteristic
50C2×Dic118C2312yes—
51C2×C8×C59C2312yes—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2312yes—
55C4⋊C4×C59C2311yescharacteristic
56C42×C59—21no—
57C42×C59C2311yescharacteristic
58#11745672—42no—
59(C2×D59)⋊C4—21no—
60(C2×D59)⋊C4—21no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59—21no—
63C4⋊Dic59—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59—22no—
66C4⋊Dic59C2311yescharacteristic
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—21no—
70Dic59⋊C4—22no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73C4×Dic59—21no—
74C4×Dic59—22no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79Dic236—42no—
80C8×D59—42no—
81C22×D59C2×D411yescharacteristic
82Q8×C59—21no—
83Q8×C59—21no—
84Q8×C59—42no—
85C2×C4×C59—22no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2411yescharacteristic
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C4×D59—21no—
98C4×D59—21no—
99C4×D59—41no—
100C4×D59Q1614yescomplemented
101Dic118—21no—
102Dic118—22no—
103Dic118—21no—
104Dic118—22no—
105Dic118—42no—
106C8×C59—22no—
107C59⋊C8—22no—
108C22×C59C22×D411yescharacteristic
109C2×D59—21no—
110C2×D59—21no—
111C2×D59C2×Q1612yes—
112C4×C59—21no—
113C4×C59—41no—
114C4×C59—41no—
115C4×C59—42no—
116C4×C59C2×Q1612yes—
117C4×C59H(5,𝔽2)11yescharacteristic
118C4×C592−1+411yescharacteristic
119Dic59—21no—
120Dic59—21no—
121Dic59—41no—
122Dic59—42no—
123Dic59—41no—
124Dic59C2×Q1612yes—
125#3249—591nomaximal, Sylow
126C2×C59#53711yescharacteristic
127C2×C59C22×Q1611yescharacteristic
128C2×C59#57511yescharacteristic
129D59—22no—
130#533—591no—
131#533—591no—
132#477—591no—
133#477—592no—
134#477D5911yescharacteristic, complemented
135#467—592no—
136#467—592no—
137#462—591no—
138#462—591no—
139#462—592no—
140C2×C4⋊C8—591no—
141C59#324911yescharacteristic, complemented, Sylow
142C2×Q16—592no—
143C2×Q16—592no—
144C22×C8—592no—
145C4⋊Q8—591no—
146C4⋊Q8—591no—
147C4⋊Q8—591no—
148C4⋊Q8C2×D5911yescharacteristic
149#125—1181no—
150#125—1181no—
151C22⋊Q8—591no—
152C22⋊Q8—591no—
153C22⋊Q8—592no—
154C22⋊Q8—1181no—
155C22⋊Q8—1181no—
156C4×Q8—592no—
157C4×Q8—591no—
158C4×Q8—1181no—
159C4×Q8—1181no—
160C4×Q8C2×D5911yescharacteristic
161#117—1181no—
162#117—1181no—
163C2×C42—591no—
164#107—592no—
165#107C2×D5912yes—
166C4⋊C8—592no—
167C4⋊C8—591no—
168C4⋊C8C2×D5911yescharacteristic
169#103—592no—
170#103—592no—
171#103—592no—
172#103C2×D5912yes—
173C2×Q8—21no—
174C2×Q8—592no—
175C2×Q8—591no—
176C2×Q8—1181no—
177C2×Q8C22×D5911yescharacteristic
178C22×C4—591no—
179C22×C4—591no—
180C22×C4—591no—
181Q16—2362no—
182Q16—2362no—
183C2×C8—592no—
184C2×C8—2362no—
185C2×C8C22×D5912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—591no—
189C4⋊C4—1181no—
190C4⋊C4—1181no—
191C4⋊C4—1182no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4—1182no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4C22×D5911yescharacteristic
200C4⋊C4C22×D5912yes—
201C22⋊C4—1181no—
202C22⋊C4—1181no—
203C22⋊C4—1182no—
204C42—21no—
205C42—591no—
206C42—591no—
207C42—591no—
208C42—1182no—
209C42—1181no—
210C42C22×D5911yescharacteristic
211C23—591no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—1181no—
216Q8—1182no—
217Q8—1181no—
218Q8—1182no—
219Q8—2362no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—591no—
224C2×C4—594no—
225C2×C4—591no—
226C2×C4—591no—
227C2×C4—1181no—
228C2×C4—1181no—
229C2×C4—1181no—
230C2×C4—1181no—
231C2×C4—1182no—
232C2×C4—2361no—
233C2×C4D4×D5911yescharacteristic
234C2×C4D4×D5911yescharacteristic
235C2×C4C23×D5911yescharacteristic
236C8—22no—
237C8—1182no—
238C22—592no—
239C22—1181no—
240C22—1181no—
241C22C2×D4×D5911yescharacteristic
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—592no—
247C4—1181no—
248C4—1181no—
249C4—2361no—
250C4—2361no—
251C4—2362no—
252C4Q16×D5912yes—
253C4#1427377311yescharacteristic
254C4#1427377511yescharacteristic
255C2—1182no—
256C2#1683798211yescharacteristic
257C2C2×Q16×D5911yescharacteristic
258C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#477C2
socleC22×C59C22×D4
hypercenter#477D59
hypocenterC59#3249
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16837696C2semidirect
4. #16837694C2semidirect
7. #16837613C2semidirect
8. #16837612C2semidirect
9. #16837611C2semidirect
11. C59×#477C2semidirect
100. C4×D59Q16semidirect
134. #477D59semidirect
141. C59#3249semidirect