Finite Group Databasebeta

← #21425306

Subgroups — #21425306

Order 7552.

326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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#16837969C211yesmaximal, characteristic
2#16837442C211yesmaximal, characteristic, complemented
3C2×#14273655C211yesmaximal, characteristic, complemented
4#16837401C211yesmaximal, characteristic, complemented
5C2×#14273644C211yesmaximal, characteristic, complemented
6#16837162C211yesmaximal, characteristic, complemented
7C59×#390C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C2×#11745664C2211yescharacteristic
11#14273723—21no—
12#14273714—21no—
13#14273698—21no—
14#14273698—21no—
15#14273696—22no—
16#14273686C2211yescharacteristic
17#14273660—21no—
18#14273658—21no—
19#14273655—22no—
20#14273650—21no—
21#14273647—21no—
22#14273644—22no—
23C22×D4×C59C2211yescharacteristic
24C2×C4⋊C4×C59C2211yescharacteristic
25C2×C22⋊C4×C59—22no—
26C2×C42×C59C2211yescharacteristic
27C24×C59D412yes—
28C2×D4×C59—21no—
29C2×D4×C59—21no—
30C2×D4×C59—21no—
31C2×D4×C59—21no—
32C2×D4×C59—21no—
33C2×D4×C59—21no—
34C22×C4×C59—21no—
35C22×C4×C59—21no—
36C22×C4×C59C2311yescharacteristic
37C2×C22⋊D59—21no—
38C2×C22⋊D59—22no—
39C2×C22⋊D59—22no—
40#11745685—21no—
41#11745685—21no—
42#11745685—21no—
43#11745685—21no—
44C2×D236D411yescharacteristic
45C2×C4×D59—21no—
46C2×Dic118D411yescharacteristic
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C22⋊C4×C59—44no—
50C42×C59—21no—
51C42×C59—21no—
52C22⋊Dic59—22no—
53C22⋊Dic59—22no—
54C22⋊Dic59—21no—
55C4⋊Dic59D411yescharacteristic
56C4⋊Dic59D411yescharacteristic
57C4×Dic59—21no—
58#11745664—21no—
59#11745664—21no—
60#11745664—21no—
61#11745664D412yescomplemented
62C2×C59⋊C8—21no—
63C2×C59⋊C8—21no—
64C23×C59—22no—
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—42no—
68C23×C59—42no—
69C23×C59C2×D411yescharacteristic
70C22×D59—21no—
71D4×C59—41no—
72D4×C59—41no—
73D4×C59—41no—
74D4×C59—41no—
75C2×C4×C59—22no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59—42no—
79C2×C4×C59—41no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D411yescharacteristic
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59#4111yescharacteristic
84C2×C4×C59#4111yescharacteristic
85C2×C4×C59#4111yescharacteristic
86C22⋊D59—41no—
87C22⋊D59—41no—
88C22⋊D59—82no—
89C22⋊D59—82no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93D236—21no—
94D236—21no—
95C4×D59—41no—
96C4×D59—41no—
97Dic118—21no—
98Dic118—21no—
99C59⋊C8—22no—
100C59⋊C8—41no—
101C22×C59—21no—
102C22×C59—21no—
103C22×C59—44no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—82no—
108C22×C59#12011yescharacteristic
109C22×C59#12111yescharacteristic
110C22×C59#12311yescharacteristic
111C2×D59—41no—
112C2×D59—41no—
113C2×D59—41no—
114C4×C59—42no—
115C4×C59—81no—
116C4×C59#12111yescharacteristic
117C4×C59#12111yescharacteristic
118C4×C59#12311yescharacteristic
119C4×C59#12411yescharacteristic
120Dic59—41no—
121Dic59—41no—
122Dic59—41no—
123#2037—591nomaximal, Sylow
124C2×C59—21no—
125C2×C59—21no—
126C2×C59—82no—
127C2×C59#39411yescharacteristic
128C2×C59#45311yescharacteristic
129C2×C59#45511yescharacteristic
130D59—81no—
131#535—591no—
132#428—591no—
133C2×#104—591no—
134#417—591no—
135C2×#100—591no—
136#390D5911yescharacteristic, complemented
137#339—591no—
138C59#203711yescharacteristic, complemented, Sylow
139C2×#41—591no—
140C22×D4C2×D5911yescharacteristic
141C2×M16—591no—
142C2×M16—591no—
143#127—1181no—
144#124—1181no—
145#121—1181no—
146#121—1181no—
147#120—1182no—
148#117—591no—
149C2×C4⋊C4C2×D5911yescharacteristic
150C2×C22⋊C4—22no—
151C2×C42C2×D5911yescharacteristic
152#107—1181no—
153#106—1181no—
154#104—1182no—
155#103—1181no—
156#102—1181no—
157#100—1182no—
158C24C22⋊D5912yes—
159#41—1181no—
160#41—1181no—
161#41—1181no—
162#41—1181no—
163C2×Q8—591no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—591no—
171C2×D4—1182no—
172C2×D4—1182no—
173C2×D4—1181no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—1181no—
177C22×C4C22×D5911yescharacteristic
178M16—592no—
179M16—1181no—
180M16—1181no—
181M16—1181no—
182C2×C8—1181no—
183C2×C8—1181no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—591no—
187C4⋊C4—591no—
188C22⋊C4—44no—
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C22⋊C4—1181no—
192C42—21no—
193C42—21no—
194C42—1181no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—1181no—
201C23C2×C22⋊D5911yescharacteristic
202Q8—1181no—
203Q8—1181no—
204D4—41no—
205D4—41no—
206D4—41no—
207D4—41no—
208D4—1181no—
209D4—1181no—
210D4—4722no—
211D4—4722no—
212D4—2361no—
213D4—2361no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—1181no—
222C2×C4—2361no—
223C2×C4—2361no—
224C2×C4#1174568511yescharacteristic
225C2×C4#1174568511yescharacteristic
226C2×C4D4×D5911yescharacteristic
227C2×C4D4×D5911yescharacteristic
228C2×C4D4×D5911yescharacteristic
229C2×C4#1174568711yescharacteristic
230C8—1182no—
231C8—2361no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—2361no—
240C22—2361no—
241C22—2361no—
242C22#1427369511yescharacteristic
243C22#1427369911yescharacteristic
244C22#1427371011yescharacteristic
245C4—42no—
246C4—81no—
247C4—2361no—
248C4—2361no—
249C4—2361no—
250C4#1427370011yescharacteristic
251C4#1427370011yescharacteristic
252C4#1427370911yescharacteristic
253C4#1427371311yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—4721no—
258C2#1683731711yescharacteristic
259C2#1683756911yescharacteristic
260C2#1683757911yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#390C2
socleC22×C59#120
hypercenter#390D59
hypocenterC59#2037
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #16837442C2semidirect
3. C2×#14273655C2semidirect
4. #16837401C2semidirect
5. C2×#14273644C2semidirect
6. #16837162C2semidirect
7. C59×#390C2semidirect
61. #11745664D4semidirect
136. #390D59semidirect
138. C59#2037semidirect