Finite Group Databasebeta

← #21422641

Subgroups — #21422641

Order 7552.

252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 61 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#16837947C211yesmaximal, characteristic
2#16837456C211yesmaximal, characteristic, complemented
3#16837269C211yesmaximal, characteristic, complemented
4#16837137C211yesmaximal, characteristic, complemented
5#16837136C211yesmaximal, characteristic, complemented
6#16837135C211yesmaximal, characteristic, complemented
7C59×#327C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9#14273726C411yescharacteristic, complemented
10#14273723C411yescharacteristic, complemented
11#14273713—21no—
12#14273701C2211yescharacteristic
13#14273699—21no—
14D4×Dic59C411yescharacteristic, complemented
15#14273689C411yescharacteristic, complemented
16(C22⋊D59)⋊C4—21no—
17C2×C4×Dic59C2211yescharacteristic
18Dic59⋊C8—21no—
19C22⋊(C59⋊C8)C2211yescharacteristic
20#14273637—21no—
21C59⋊#95—21no—
22C59⋊#95—21no—
23C59⋊#95C2211yescharacteristic
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59C2×C411yescharacteristic
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×D236C2×C411yescharacteristic
41C2×C4×D59—21no—
42C2×Dic118—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59C2×C411yescharacteristic
45C22⋊C4×C59—21no—
46C22⋊Dic59—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49C4⋊Dic59C2×C411yescharacteristic
50Dic59⋊C4—21no—
51C4×Dic59C2×C411yescharacteristic
52C4×Dic59C2×C411yescharacteristic
53C4×Dic59D411yescharacteristic
54C4×Dic59D411yescharacteristic
55C2×C59⋊C8—21no—
56C23×C59—21no—
57C23×C59C2×D411yescharacteristic
58C22×D59—21no—
59D4×C59—41no—
60D4×C59—41no—
61D4×C59—41no—
62C2×C4×C59—21no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59C22×C411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C22⋊D59—42no—
70C22⋊D59—42no—
71C22⋊D59—41no—
72C22⋊D59—41no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—41no—
77C2×Dic59—42no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59C22⋊C411yescharacteristic
82C2×Dic59C22⋊C411yescharacteristic
83C2×Dic59C22⋊C411yescharacteristic
84C2×Dic59C22⋊C411yescharacteristic
85D236—41no—
86C4×D59—42no—
87Dic118—42no—
88C8×C59—41no—
89C59⋊C8—41no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59—41no—
93C22×C59—41no—
94C22×C59—41no—
95C22×C59C2×C22⋊C411yescharacteristic
96C22×C59AGL(1,ℤ/8)11yescharacteristic
97C22×C59AGL(1,ℤ/8)11yescharacteristic
98C2×D59—41no—
99C2×D59—41no—
100C2×D59—41no—
101C4×C59—21no—
102C4×C59—21no—
103C4×C59—41no—
104C4×C59—81no—
105Dic59—21no—
106Dic59—21no—
107Dic59—21no—
108Dic59—21no—
109Dic59—41no—
110Dic59—81no—
111#1514—591nomaximal, Sylow
112C2×C59—21no—
113C2×C59—21no—
114C2×C59—81no—
115C2×C59#41011yescharacteristic
116C2×C59#41811yescharacteristic
117C2×C59#42111yescharacteristic
118D59—81no—
119#532—591no—
120#432—591no—
121#383—591no—
122#327—591no—
123#327—591no—
124#327—591no—
125#327D5911yescharacteristic, complemented
126C59#151411yescharacteristic, complemented, Sylow
127C2×#41—1181no—
128C4⋊Q8—591no—
129#127—591no—
130#124—1181no—
131#121—591no—
132#121—1181no—
133#121C2×D5911yescharacteristic
134C4×D4—591no—
135C4×D4—591no—
136C4×D4—1181no—
137C2×C42—591no—
138C4⋊C8—1181no—
139C22⋊C8—591no—
140C22⋊C8C2×D5911yescharacteristic
141#97—1181no—
142#95—591no—
143#95—1181no—
144#95—1181no—
145#95C2×D5911yescharacteristic
146#41—2362no—
147#41—2362no—
148C2×Q8—1181no—
149C2×D4—21no—
150C2×D4—591no—
151C2×D4—1181no—
152C2×D4—1181no—
153C2×D4—1181no—
154C2×D4C4×D5911yescharacteristic
155C22×C4—21no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—1181no—
159C22×C4—1181no—
160C22×C4—1181no—
161C22×C4C22×D5911yescharacteristic
162C2×C8—21no—
163C2×C8—1181no—
164C4⋊C4—591no—
165C4⋊C4—1181no—
166C4⋊C4C4×D5911yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—1181no—
169C22⋊C4—1181no—
170C22⋊C4—1181no—
171C42—591no—
172C42—591no—
173C42—591no—
174C42—591no—
175C23—21no—
176C23—1181no—
177C23D4×D5911yescharacteristic
178Q8—2362no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—2361no—
183D4—2362no—
184D4—2362no—
185D4—2361no—
186D4—2361no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—591no—
193C2×C4—591no—
194C2×C4—591no—
195C2×C4—591no—
196C2×C4—1181no—
197C2×C4—1181no—
198C2×C4—1181no—
199C2×C4—2362no—
200C2×C4—2361no—
201C2×C4—2362no—
202C2×C4—2361no—
203C2×C4—2361no—
204C2×C4—2361no—
205C2×C4C2×C4×D5911yescharacteristic
206C2×C4D4×D5911yescharacteristic
207C8—41no—
208C8—2361no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—2361no—
215C22—2361no—
216C22—2361no—
217C22C22⋊C4×D5911yescharacteristic
218C22#1427375111yescharacteristic
219C22#1427375411yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—1181no—
225C4—1181no—
226C4—1181no—
227C4—1181no—
228C4—4721no—
229C4—2361no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—4721no—
234C2#1683737411yescharacteristic
235C2#1683740511yescharacteristic
236C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59C2×C22⋊C4
hypercenter#327D59
hypocenterC59#1514
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837456C2semidirect
3. #16837269C2semidirect
4. #16837137C2semidirect
5. #16837136C2semidirect
6. #16837135C2semidirect
7. C59×#327C2semidirect
9. #14273726C4semidirect
10. #14273723C4semidirect
14. D4×Dic59C4semidirect
15. #14273689C4semidirect
125. #327D59semidirect
126. C59#1514semidirect