Finite Group Databasebeta

← #21425503

Subgroups — #21425503

Order 7552.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×#14273649C211yesmaximal, characteristic
2C2×#14273647C211yesmaximal, characteristic
3#16837303C211yesmaximal, characteristic
4#16837271C211yesmaximal, characteristic, complemented
5#16837164C211yesmaximal, characteristic, complemented
6#16837156C211yesmaximal, characteristic, complemented
7C59×#340C211yesmaximal, characteristic, complemented
8C22×D236C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×Dic59⋊C4—21no—
12C2×Dic59⋊C4—21no—
13C2×(C2×D59)⋊C4—21no—
14C2×(C2×D59)⋊C4—21no—
15C2×C4×Dic59C2211yescharacteristic
16#14273649—22no—
17#14273647—22no—
18C22×C8×C59C2211yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21C23×D59—21no—
22C22×C4×C59—21no—
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—21no—
26C22×Dic59D411yescharacteristic
27C22×Dic59D411yescharacteristic
28C2×D236—21no—
29C2×D236—21no—
30C2×D236—21no—
31C2×D236—21no—
32C2×D236—21no—
33C2×D236D412yes—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41(C2×D59)⋊C4—42no—
42(C2×D59)⋊C4—42no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45Dic59⋊C4—42no—
46Dic59⋊C4—42no—
47C4×Dic59—21no—
48C4×Dic59—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8—21no—
51C2×C59⋊C8—21no—
52C23×C59C2×D411yescharacteristic
53C22×D59—22no—
54C22×D59—41no—
55C22×D59—41no—
56C22×D59—41no—
57C22×D59—41no—
58C22×D59—41no—
59C22×D59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59C2×D411yescharacteristic
67C2×C4×C59#4111yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C2×C4×C59#4111yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×Dic59—21no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59D812yes—
80C2×Dic59SD1612yes—
81D236—22no—
82D236—22no—
83D236—41no—
84D236—41no—
85C8×C59—41no—
86C59⋊C8—41no—
87C22×C59#12111yescharacteristic
88C22×C59#12311yescharacteristic
89C22×C59#12411yescharacteristic
90C22×C59C2×D811yescharacteristic
91C22×C59C2×SD1611yescharacteristic
92C22×C59AGL(1,ℤ/8)11yescharacteristic
93C22×C59#13711yescharacteristic
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—81no—
98C2×D59—81no—
99C2×D59—81no—
100C2×D59—81no—
101C4×C59—81no—
102C4×C59—81no—
103C4×C59#12311yescharacteristic
104C4×C59#12311yescharacteristic
105C4×C59#12611yescharacteristic
106C4×C59#12611yescharacteristic
107Dic59—22no—
108Dic59—22no—
109Dic59—81no—
110#2071—591nomaximal, Sylow
111C2×C59#39711yescharacteristic
112C2×C59#45911yescharacteristic
113C2×C59#46111yescharacteristic
114C2×C59#48011yescharacteristic
115C2×C59#48111yescharacteristic
116C2×C59#48611yescharacteristic
117C2×C59#48911yescharacteristic
118D59—82no—
119C2×#102—591no—
120C2×#102—591no—
121#390—591no—
122#384—591no—
123#340—591no—
124#340D5911yescharacteristic, complemented
125#336—591no—
126C59#207111yescharacteristic, complemented, Sylow
127C22×D4—591no—
128C22×C8—591no—
129C22×C8C2×D5911yescharacteristic
130C2×C4⋊C4—591no—
131C2×C4⋊C4—1181no—
132C2×C4⋊C4—1181no—
133C2×C4⋊C4C2×D5911yescharacteristic
134C2×C4⋊C4C2×D5911yescharacteristic
135C2×C22⋊C4—1181no—
136C2×C22⋊C4—1181no—
137C2×C42—591no—
138#102—1182no—
139#102—1182no—
140C24—1181no—
141C2×D4—592no—
142C2×D4—1181no—
143C2×D4—1181no—
144C2×D4—1181no—
145C2×D4—1181no—
146C2×D4—1181no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—591no—
150C22×C4—591no—
151C22×C4—1181no—
152C22×C4C22×D5911yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1181no—
157C2×C8—1181no—
158C2×C8—1181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—2362no—
166C4⋊C4—2362no—
167C22⋊C4—2362no—
168C22⋊C4—2362no—
169C42—1181no—
170C42—1181no—
171C23—1182no—
172C23—2361no—
173C23—2361no—
174C23—2361no—
175C23—2361no—
176C23—2361no—
177C23—2361no—
178C23D4×D5911yescharacteristic
179D4—1182no—
180D4—1182no—
181D4—2361no—
182D4—2361no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—592no—
190C2×C4—592no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1181no—
194C2×C4—1181no—
195C2×C4—2361no—
196C2×C4—2361no—
197C2×C4—2361no—
198C2×C4#1174568511yescharacteristic
199C2×C4#1174568511yescharacteristic
200C2×C4#1174568511yescharacteristic
201C2×C4D4×D5911yescharacteristic
202C2×C4#1174568711yescharacteristic
203C2×C4#1174568911yescharacteristic
204C8—41no—
205C8—2361no—
206C22—4721no—
207C22—4721no—
208C22—4721no—
209C22—4721no—
210C22—2362no—
211C22—2362no—
212C22—2362no—
213C22#1427370011yescharacteristic
214C22#1427371211yescharacteristic
215C22#1427371311yescharacteristic
216C22D8×D5911yescharacteristic
217C22SD16×D5911yescharacteristic
218C22#1427375411yescharacteristic
219C22#1427375911yescharacteristic
220C4—81no—
221C4—81no—
222C4—1182no—
223C4—1182no—
224C4—4721no—
225C4#1427370911yescharacteristic
226C4#1427371211yescharacteristic
227C4#1427372111yescharacteristic
228C4#1427372211yescharacteristic
229C2—4722no—
230C2#1683733111yescharacteristic
231C2#1683759611yescharacteristic
232C2#1683760611yescharacteristic
233C2#1683771711yescharacteristic
234C2#1683772211yescharacteristic
235C2#1683774711yescharacteristic
236C2#1683776311yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#2071
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. #16837271C2semidirect
5. #16837164C2semidirect
6. #16837156C2semidirect
7. C59×#340C2semidirect
124. #340D59semidirect
126. C59#2071semidirect