Finite Group Databasebeta

← #21434815

Subgroups — #21434815

Order 7552.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#16837952C211yesmaximal, characteristic
2#16837805C211yesmaximal, characteristic, complemented
3#16837776C211yesmaximal, characteristic, complemented
4#16837752C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837650C214yesmaximal, complemented
7#16837500C214yesmaximal, complemented
8C4×#11745664C211yesmaximal, characteristic, complemented
9C59×#533C211yesmaximal, characteristic, complemented
10C2×#11745685—21no—
11C2×#11745671C2214yes—
12C2×#11745664C2212yes—
13#14273727C2211yescharacteristic
14#14273724C2211yescharacteristic
15#14273715—21no—
16#14273701—21no—
17#14273701C2212yes—
18C4×D236—21no—
19C4×D236C2212yes—
20#14273660C2214yes—
21#14273651C2214yes—
22#14273647C2214yes—
23#14273638C2212yes—
24C4×C59⋊C8C2211yescharacteristic
25C4×C59⋊C8C2211yescharacteristic
26C4⋊Q8×C59C2211yescharacteristic
27C4⋊Q8×C59C2211yescharacteristic
28#125×C59—21no—
29C22⋊Q8×C59—21no—
30C22⋊Q8×C59C2212yes—
31C4×Q8×C59—21no—
32C4×Q8×C59C2212yes—
33#117×C59—21no—
34C2×C42×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37C22×C4×C59D411yescharacteristic
38C22×C4×C59D411yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—22no—
41#11745685—44no—
42C2×D236—21no—
43C2×D236—21no—
44C2×D236C2312yes—
45C2×C4×D59—22no—
46C2×Dic118—21no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59C2312yes—
53C22⋊C4×C59—22no—
54C42×C59—22no—
55C42×C59D411yescharacteristic
56C42×C59D411yescharacteristic
57C42×C59C2311yescharacteristic
58C42×C59C2311yescharacteristic
59#11745671—28no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59—21no—
63C4⋊Dic59C2312yes—
64#11745664—24no—
65C2×C59⋊C8C2312yes—
66C2×C59⋊C8C2312yes—
67C23×C59C2×D411yescharacteristic
68C22×D59—22no—
69Q8×C59—24no—
70Q8×C59—42no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C22⋊D59—44no—
83C2×Dic59—22no—
84D236—24no—
85D236—42no—
86D236—42no—
87C4×D59—44no—
88Dic118—42no—
89C59⋊C8—22no—
90C59⋊C8#4114yescomplemented
91C22×C59—21no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59C22×D411yescharacteristic
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C4×C59—21no—
99C4×C59—21no—
100C4×C59—21no—
101C4×C59—42no—
102C4×C59—42no—
103C4×C59AGL(1,ℤ/8)12yes—
104C4×C59#13712yes—
105C4×C59C2×#4112yes—
106Dic59—42no—
107#3182—591nomaximal, Sylow
108C2×C59—41no—
109C2×C59#53211yescharacteristic
110C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C59C2×#13711yescharacteristic
112D59—82no—
113#533D5911yescharacteristic, complemented
114#532—591no—
115#500—591no—
116#492—591no—
117#487—591no—
118#486—591no—
119#468—594no—
120#440—594no—
121C4×M16—591no—
122C59#318211yescharacteristic, complemented, Sylow
123C2×#41—1181no—
124C2×SD16—594no—
125C2×M16—592no—
126C4⋊Q8—591no—
127C4⋊Q8C2×D5911yescharacteristic
128C4⋊Q8C2×D5911yescharacteristic
129#127—591no—
130#125—21no—
131#124—1181no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D5912yes—
134#121—592no—
135#121—1181no—
136C4×Q8—21no—
137C4×Q8C2×D5912yes—
138C4×D4—592no—
139C4×D4—1181no—
140#117—21no—
141C2×C42C2×D5911yescharacteristic
142#107—594no—
143#103—594no—
144#102—594no—
145#97—592no—
146C4×C8—591no—
147C4×C8—591no—
148#41—2364no—
149C2×Q8—21no—
150C2×Q8—1181no—
151C2×Q8C22×D5912yes—
152C2×D4—592no—
153C2×D4—1182no—
154C2×D4—1181no—
155C2×D4—1181no—
156C22×C4—1182no—
157C22×C4C22⋊D5911yescharacteristic
158C22×C4C22⋊D5911yescharacteristic
159C22×C4C22×D5911yescharacteristic
160SD16—1188no—
161M16—1184no—
162C2×C8—592no—
163C2×C8—592no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—592no—
170C4⋊C4—1181no—
171C4⋊C4C22×D5912yes—
172C22⋊C4—22no—
173C22⋊C4—1182no—
174C22⋊C4—1182no—
175C42—22no—
176C42C22⋊D5911yescharacteristic
177C42C22⋊D5911yescharacteristic
178C42C22×D5911yescharacteristic
179C42C22×D5911yescharacteristic
180C23—1182no—
181C23C2×C22⋊D5911yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—2362no—
185D4—1184no—
186D4—2364no—
187D4—2362no—
188D4—2362no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1182no—
195C2×C4—2364no—
196C2×C4C2×C22⋊D5911yescharacteristic
197C2×C4C2×C22⋊D5911yescharacteristic
198C2×C4C2×C22⋊D5911yescharacteristic
199C2×C4C2×C22⋊D5911yescharacteristic
200C2×C4C2×C22⋊D5911yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—594no—
203C8—1182no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22C22×C22⋊D5911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—2362no—
217C4#1427375212yes—
218C4#1427375812yes—
219C4#41×D5912yes—
220C2—41no—
221C2—4722no—
222C2#1683794811yescharacteristic
223C2C2×#1427375211yescharacteristic
224C2C2×#1427375811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#533C2
socleC22×C59C22×D4
hypercenter#533D59
hypocenterC59#3182
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16837805C2semidirect
3. #16837776C2semidirect
4. #16837752C2semidirect
5. #16837750C2semidirect
6. #16837650C2semidirect
7. #16837500C2semidirect
8. C4×#11745664C2semidirect
9. C59×#533C2semidirect
90. C59⋊C8#41semidirect
113. #533D59semidirect
122. C59#3182semidirect