Finite Group Databasebeta

← #21423097

Subgroups — #21423097

Order 7552.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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#16837979C211yesmaximal, characteristic
2#16837715C211yesmaximal, characteristic, complemented
3#16837333C211yesmaximal, characteristic, complemented
4#16837137C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837127C211yesmaximal, characteristic, complemented
7C59×#480C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9#14273705—21no—
10#14273704—21no—
11#14273701C2211yescharacteristic
12#14273700—21no—
13#14273699—21no—
14#14273699—21no—
15C2×Dic59⋊C4—21no—
16C2×Dic59⋊C4C2211yescharacteristic
17#14273660—21no—
18#14273647—21no—
19C22⋊(C59⋊C8)C2211yescharacteristic
20C59⋊#95—21no—
21C59⋊#95C2211yescharacteristic
22#121×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#107×C59—21no—
25#102×C59—21no—
26C22⋊C8×C59C2211yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59D411yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37C22×Dic59D411yescharacteristic
38#11745687—42no—
39#11745687—42no—
40C2×D236D411yescharacteristic
41C2×C4×D59—21no—
42C2×Dic118—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59D411yescharacteristic
47C22⋊C4×C59—21no—
48C22⋊Dic59—21no—
49(C2×D59)⋊C4—21no—
50(C2×D59)⋊C4—21no—
51C4⋊Dic59D411yescharacteristic
52Dic59⋊C4—21no—
53Dic59⋊C4—21no—
54Dic59⋊C4—21no—
55Dic59⋊C4—42no—
56C2×C59⋊C8—21no—
57C23×C59—21no—
58C23×C59C2×D411yescharacteristic
59C22×D59—21no—
60D4×C59—41no—
61D4×C59—41no—
62D4×C59—41no—
63C2×C4×C59—21no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C22⋊D59—42no—
71C22⋊D59—41no—
72C22⋊D59—41no—
73C22⋊D59—81no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—22no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—42no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59—41no—
83C2×Dic59D812yes—
84D236—41no—
85C4×D59—42no—
86Dic118—42no—
87C8×C59—41no—
88C59⋊C8—41no—
89C22×C59—21no—
90C22×C59—21no—
91C22×C59—41no—
92C22×C59—41no—
93C22×C59—41no—
94C22×C59#12011yescharacteristic
95C22×C59C2×D811yescharacteristic
96C22×C59AGL(1,ℤ/8)11yescharacteristic
97C2×D59—41no—
98C2×D59—41no—
99C2×D59—41no—
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—41no—
103C4×C59—81no—
104Dic59—22no—
105Dic59—42no—
106Dic59—41no—
107Dic59—41no—
108#1610—591nomaximal, Sylow
109C2×C59—21no—
110C2×C59—21no—
111C2×C59—81no—
112C2×C59#44711yescharacteristic
113C2×C59#45611yescharacteristic
114C2×C59#45811yescharacteristic
115D59—81no—
116#537—591no—
117#480—591no—
118#480D5911yescharacteristic, complemented
119#398—591no—
120#327—591no—
121#327—591no—
122#324—591no—
123C59#161011yescharacteristic, complemented, Sylow
124C2×#41—1181no—
125C22⋊Q8—1181no—
126C22⋊Q8—1181no—
127#121—591no—
128#121—1181no—
129#121—1181no—
130#121—1181no—
131#121C2×D5911yescharacteristic
132C2×C4⋊C4—591no—
133C2×C4⋊C4—1181no—
134C2×C4⋊C4C2×D5911yescharacteristic
135#107—21no—
136#107—1181no—
137#102—21no—
138#102—1181no—
139C22⋊C8—591no—
140C22⋊C8C2×D5911yescharacteristic
141#95—591no—
142#95—1181no—
143#41—2362no—
144#41—2362no—
145C2×Q8—1181no—
146C2×D4—21no—
147C2×D4—591no—
148C2×D4—1181no—
149C2×D4—1181no—
150C2×D4—1181no—
151C2×D4C22⋊D5911yescharacteristic
152C22×C4—21no—
153C22×C4—591no—
154C22×C4—591no—
155C22×C4—1181no—
156C22×C4—1181no—
157C22×C4—1181no—
158C22×C4C22×D5911yescharacteristic
159C2×C8—21no—
160C2×C8—1181no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—591no—
164C4⋊C4—1181no—
165C4⋊C4—1181no—
166C4⋊C4—1181no—
167C4⋊C4—2362no—
168C4⋊C4C22⋊D5911yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—1181no—
171C22⋊C4—1181no—
172C22⋊C4—1181no—
173C23—21no—
174C23—1181no—
175C23D4×D5911yescharacteristic
176Q8—2362no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—4721no—
181D4—2361no—
182D4—2362no—
183D4—2361no—
184D4—2361no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—592no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1182no—
194C2×C4—1181no—
195C2×C4—1181no—
196C2×C4—2362no—
197C2×C4—2362no—
198C2×C4—2361no—
199C2×C4—2361no—
200C2×C4—2361no—
201C2×C4D4×D5911yescharacteristic
202C2×C4C2×C22⋊D5911yescharacteristic
203C8—41no—
204C8—2361no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—2361no—
211C22—2361no—
212C22—2361no—
213C22#1427369511yescharacteristic
214C22D8×D5911yescharacteristic
215C22#1427375111yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—81no—
220C4—1182no—
221C4—2362no—
222C4—2361no—
223C4—2361no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—4721no—
228C2#1683753411yescharacteristic
229C2#1683758311yescharacteristic
230C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#480C2
socleC22×C59#120
hypercenter#480D59
hypocenterC59#1610
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #16837715C2semidirect
3. #16837333C2semidirect
4. #16837137C2semidirect
5. #16837136C2semidirect
6. #16837127C2semidirect
7. C59×#480C2semidirect
118. #480D59semidirect
123. C59#1610semidirect