Finite Group Databasebeta

← #21434802

Subgroups — #21434802

Order 7552.

366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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, complemented
2#16837931C211yesmaximal, characteristic
3#16837811C211yesmaximal, characteristic, complemented
4#16837770C211yesmaximal, characteristic, complemented
5#16837761C211yesmaximal, characteristic, complemented
6#16837640C212yesmaximal, complemented
7#16837628C212yesmaximal
8#16837509C212yesmaximal, complemented
9#16837503C212yesmaximal, complemented
10#97×D59C211yesmaximal, characteristic, complemented
11C59×#497C211yesmaximal, characteristic, complemented
12C2×C8×D59C2212yes—
13#14273727C2211yescharacteristic
14#14273720—21no—
15#14273719C2211yescharacteristic
16#14273718—21no—
17#14273709—21no—
18#14273707—21no—
19#14273703C2211yescharacteristic
20#14273703C2212yes—
21#14273698C2211yescharacteristic
22Q8×Dic59C2211yescharacteristic
23Q8×Dic59C2212yes—
24#14273692—21no—
25D4×Dic59C2211yescharacteristic
26(C22⋊D59)⋊C4—21no—
27#14273685—21no—
28#14273683—21no—
29C42×D59C2211yescharacteristic
30#14273661C2212yes—
31#14273659C2212yes—
32#14273651C2212yes—
33#14273651C2212yes—
34#14273651C2212yes—
35#14273648C2212yes—
36#14273638C2211yescharacteristic
37#14273637C2212yes—
38C2×Q16×C59C2212yes—
39C2×SD16×C59C2212yes—
40C4⋊Q8×C59C2211yescharacteristic
41#124×C59C2211yescharacteristic
42#97×C59C2211yescharacteristic
43C2×Q8×C59C2311yescharacteristic
44C2×Q8×C59C2312yes—
45C2×D4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C22×Dic59—21no—
48C2×C4×D59D411yescharacteristic
49C2×C4×D59D411yescharacteristic
50C2×C4×D59C2311yescharacteristic
51C2×Dic118—21no—
52Q16×C59—24no—
53SD16×C59—24no—
54C2×C8×C59C2312yes—
55C4⋊C4×C59—21no—
56C4⋊C4×C59—21no—
57C22⋊C4×C59—21no—
58C22⋊C4×C59—21no—
59C42×C59C2311yescharacteristic
60C22⋊Dic59—21no—
61C22⋊Dic59—21no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59—22no—
66C4⋊Dic59—21no—
67C4⋊Dic59C2312yes—
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—21no—
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74C4×Dic59—21no—
75C4×Dic59—22no—
76C4×Dic59D411yescharacteristic
77C4×Dic59D411yescharacteristic
78C4×Dic59C2311yescharacteristic
79C2×C59⋊C8C2312yes—
80C8×D59—24no—
81C23×C59—21no—
82C22×D59C2×D411yescharacteristic
83Q8×C59—22no—
84Q8×C59—22no—
85Q8×C59—22no—
86D4×C59—22no—
87C2×C4×C59—21no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2411yescharacteristic
92C22⋊D59—42no—
93C2×Dic59—21no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96C2×Dic59—42no—
97C2×Dic59C2×D411yescharacteristic
98C2×Dic59C2×D411yescharacteristic
99C2×Dic59C2×D411yescharacteristic
100C4×D59—22no—
101C4×D59—22no—
102C4×D59—41no—
103Dic118—42no—
104C8×C59#4114yes—
105C59⋊C8—22no—
106C22×C59—41no—
107C22×C59—41no—
108C22×C59—41no—
109C22×C59C22×D411yescharacteristic
110C2×D59—21no—
111C2×D59—21no—
112C2×D59#13712yes—
113C4×C59—21no—
114C4×C59—21no—
115C4×C59—41no—
116C4×C59—42no—
117C4×C59C2×#4112yes—
118Dic59—21no—
119Dic59—21no—
120Dic59—21no—
121Dic59—41no—
122Dic59—42no—
123Dic59—41no—
124#3181—591nomaximal, Sylow
125C2×C59—81no—
126C2×C59#53211yescharacteristic
127C2×C59C2×#13711yescharacteristic
128C2×C59#57511yescharacteristic
129D59—22no—
130#533—591no—
131#529—591no—
132#501—591no—
133#497D5911yescharacteristic, complemented
134#491—591no—
135#489—591no—
136#467—592no—
137#465—592no—
138#441—592no—
139#440—592no—
140C2×#97—591no—
141C59#318111yescharacteristic, complemented, Sylow
142C2×Q16C2×D5912yes—
143C2×SD16C2×D5912yes—
144C22×C8—592no—
145C4⋊Q8—591no—
146C4⋊Q8C2×D5911yescharacteristic
147#126—1181no—
148#125—591no—
149#125—1181no—
150#124C2×D5911yescharacteristic
151#123—1181no—
152C22⋊Q8—591no—
153C22⋊Q8—592no—
154C22⋊Q8—1181no—
155#121—591no—
156C4×Q8—591no—
157C4×Q8—592no—
158C4×Q8—1181no—
159C4×D4—591no—
160C4×D4—1181no—
161#117—1181no—
162#117—1181no—
163C2×C42—591no—
164#107—592no—
165#106—592no—
166#103—592no—
167#103—592no—
168#103—592no—
169#102—592no—
170#97—592no—
171#97—591no—
172#97C2×D5911yescharacteristic
173C2×Q8—1181no—
174C2×Q8C22×D5911yescharacteristic
175C2×Q8C22×D5912yes—
176C2×D4—1181no—
177C2×D4C22×D5911yescharacteristic
178C22×C4—591no—
179C22×C4—591no—
180C22×C4—591no—
181C22×C4—1181no—
182Q16—24no—
183SD16—24no—
184C2×C8—592no—
185C2×C8—1184no—
186C2×C8C22×D5912yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—592no—
190C4⋊C4—591no—
191C4⋊C4—591no—
192C4⋊C4—1181no—
193C4⋊C4—1182no—
194C4⋊C4—1181no—
195C4⋊C4—1182no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—1182no—
202C22⋊C4—1181no—
203C22⋊C4—1181no—
204C22⋊C4—1181no—
205C42—591no—
206C42—591no—
207C42—591no—
208C42—1181no—
209C42—1182no—
210C42C22×D5911yescharacteristic
211C23—21no—
212C23—591no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—2362no—
217D4—22no—
218D4—2362no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—591no—
222C2×C4—591no—
223C2×C4—591no—
224C2×C4—1182no—
225C2×C4—1182no—
226C2×C4—1181no—
227C2×C4—1182no—
228C2×C4—1181no—
229C2×C4—2361no—
230C2×C4—2362no—
231C2×C4D4×D5911yescharacteristic
232C2×C4D4×D5911yescharacteristic
233C2×C4C23×D5911yescharacteristic
234C8—1182no—
235C8#1174568714yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—592no—
240C22—1181no—
241C22—1181no—
242C22C2×D4×D5911yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—1181no—
248C4—1181no—
249C4—1181no—
250C4—2361no—
251C4—2361no—
252C4—2362no—
253C4C2×#1174568712yes—
254C2—81no—
255C2—1182no—
256C2#1683795011yescharacteristic
257C2#137×D5911yescharacteristic
258C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#497C2
socleC22×C59C22×D4
hypercenter#497D59
hypocenterC59#3181
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837811C2semidirect
4. #16837770C2semidirect
5. #16837761C2semidirect
6. #16837640C2semidirect
8. #16837509C2semidirect
9. #16837503C2semidirect
10. #97×D59C2semidirect
11. C59×#497C2semidirect
133. #497D59semidirect
141. C59#3181semidirect