Finite Group Databasebeta

← #21434721

Subgroups — #21434721

Order 7552.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#16838013C211yesmaximal, characteristic, complemented
2#16838006C211yesmaximal, characteristic
3#16837804C211yesmaximal, characteristic, complemented
4#16837770C211yesmaximal, characteristic, complemented
5#16837766C211yesmaximal, characteristic, complemented
6#16837645C212yesmaximal, complemented
7#16837628C212yesmaximal, complemented
8#16837503C212yesmaximal, complemented
9SD16×Dic59C212yesmaximal, complemented
10#16837356C211yesmaximal, characteristic, complemented
11C59×#492C211yesmaximal, characteristic, complemented
12C2×#11745659C2211yescharacteristic
13C2×C8×D59C2211yescharacteristic
14#14273722—22no—
15#14273719C2211yescharacteristic
16#14273719C2211yescharacteristic
17#14273717—22no—
18#14273708—22no—
19#14273703C2212yes—
20#14273699—22no—
21#14273698C2212yes—
22Q8×Dic59C2212yes—
23D4×Dic59C2212yes—
24#14273684C2211yescharacteristic
25#14273661C2212yes—
26#14273659C2212yes—
27#14273651C2212yes—
28#14273651C2212yes—
29#14273648C2212yes—
30#14273648C2212yes—
31#14273638C2211yescharacteristic
32#14273637C2211yescharacteristic
33C8×Dic59C2211yescharacteristic
34C2×SD16×C59C2212yes—
35C2×SD16×C59C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37#127×C59C2211yescharacteristic
38C4×C8×C59C2211yescharacteristic
39C2×Q8×C59C2312yes—
40C2×D4×C59—22no—
41C2×D4×C59C2312yes—
42C2×C22⋊D59—22no—
43C22×Dic59—22no—
44C2×C4×D59C2311yescharacteristic
45SD16×C59—24no—
46SD16×C59—24no—
47C2×C8×C59C2311yescharacteristic
48C2×C8×C59C2311yescharacteristic
49C4⋊C4×C59—22no—
50C42×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52C22⋊Dic59—22no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4D412yes—
55C4⋊Dic59—22no—
56C4⋊Dic59C2312yes—
57C4⋊Dic59C2312yes—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4D412yes—
62C4×Dic59—22no—
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66#11745659—22no—
67C8×D59—22no—
68C23×C59—22no—
69C22×D59C2×D411yescharacteristic
70Q8×C59—22no—
71Q8×C59—22no—
72D4×C59—22no—
73D4×C59—22no—
74D4×C59—82no—
75C2×C4×C59—22no—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2411yescharacteristic
78C22⋊D59—82no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—82no—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D411yescharacteristic
84C4×D59—21no—
85C4×D59—21no—
86C8×C59#4112yes—
87C8×C59#4112yes—
88C59⋊C8—21no—
89C59⋊C8—21no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59C22×D411yescharacteristic
94C2×D59—21no—
95C2×D59—22no—
96C4×C59—22no—
97C4×C59—42no—
98C4×C59C2×#4111yescharacteristic
99C4×C59C2×#4111yescharacteristic
100Dic59—21no—
101Dic59—22no—
102Dic59—42no—
103Dic59—42no—
104#3174—591nomaximal, Sylow
105C2×C59—82no—
106C2×C59#53211yescharacteristic
107C2×C59#57712yes—
108D59—41no—
109#541—591no—
110#540—591no—
111#499—591no—
112#492D5911yescharacteristic, complemented
113#491—591no—
114#490—591no—
115#468—592no—
116#465—592no—
117#440—592no—
118C4×SD16—592no—
119#405—591no—
120C59#317411yescharacteristic, complemented, Sylow
121C2×SD16C2×D5912yes—
122C2×SD16C2×D5912yes—
123C2×M16—591no—
124C22×C8—591no—
125C4⋊Q8C2×D5911yescharacteristic
126#127C2×D5911yescharacteristic
127#126—1182no—
128#125—591no—
129#125—591no—
130#125—1182no—
131#123—1182no—
132C22⋊Q8—592no—
133#121—592no—
134#121—1182no—
135C4×Q8—592no—
136C4×D4—592no—
137#117—591no—
138#107—592no—
139#106—592no—
140#103—592no—
141#103—592no—
142#102—592no—
143#102—592no—
144#97—591no—
145#97—591no—
146C4×C8—591no—
147C4×C8C2×D5911yescharacteristic
148C2×Q8C22×D5912yes—
149C2×D4—22no—
150C2×D4—1182no—
151C2×D4C22×D5912yes—
152C22×C4—591no—
153C22×C4—1182no—
154SD16—24no—
155SD16—24no—
156M16—1182no—
157C2×C8—591no—
158C2×C8—591no—
159C2×C8—1182no—
160C2×C8C22×D5911yescharacteristic
161C2×C8C22×D5911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—592no—
164C4⋊C4—592no—
165C4⋊C4—592no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C22⋊C4—592no—
171C22⋊C4—1182no—
172C22⋊C4—1182no—
173C22⋊C4—1182no—
174C42—591no—
175C42—1182no—
176C42C22×D5911yescharacteristic
177C23—22no—
178C23—591no—
179Q8—22no—
180Q8—22no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—4722no—
185C2×C4—22no—
186C2×C4—592no—
187C2×C4—591no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—4722no—
193C2×C4D4×D5912yes—
194C2×C4C23×D5911yescharacteristic
195C8—1181no—
196C8—1181no—
197C8#1174568712yes—
198C8#1174568712yes—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—1181no—
203C22—1182no—
204C22C2×D4×D5911yescharacteristic
205C4—22no—
206C4—42no—
207C4—1181no—
208C4—1182no—
209C4—2362no—
210C4—2362no—
211C4C2×#1174568711yescharacteristic
212C4C2×#1174568711yescharacteristic
213C2—82no—
214C2—2361no—
215C2#1683795011yescharacteristic
216C2#1683820812yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#492C2
socleC22×C59C22×D4
hypercenter#492D59
hypocenterC59#3174
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16838013C2semidirect
3. #16837804C2semidirect
4. #16837770C2semidirect
5. #16837766C2semidirect
6. #16837645C2semidirect
7. #16837628C2semidirect
8. #16837503C2semidirect
9. SD16×Dic59C2semidirect
10. #16837356C2semidirect
11. C59×#492C2semidirect
112. #492D59semidirect
120. C59#3174semidirect