Finite Group Databasebeta

← #21425736

Subgroups — #21425736

Order 7552.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#16837910C211yesmaximal, characteristic
2#16837383C211yesmaximal, characteristic, complemented
3#16837374C211yesmaximal, characteristic, complemented
4#16837192C211yesmaximal, characteristic, complemented
5#16837190C211yesmaximal, characteristic, complemented
6#16837188C211yesmaximal, characteristic, complemented
7C59×#352C211yesmaximal, characteristic, complemented
8C2×#11745687C2211yescharacteristic
9C22×C4×D59C411yescharacteristic, complemented
10M16×D59—21no—
11#14273710C411yescharacteristic, complemented
12#14273705—21no—
13#14273700—21no—
14#14273697C411yescharacteristic, complemented
15#14273695C2211yescharacteristic
16#14273689—21no—
17(C22⋊D59)⋊C4—21no—
18#14273683—21no—
19#14273683C411yescharacteristic, complemented
20#14273645—21no—
21#14273644C2211yescharacteristic
22#14273642C2211yescharacteristic
23#14273641—21no—
24#123×C59C2211yescharacteristic
25#100×C59C2211yescharacteristic
26#99×C59C2211yescharacteristic
27C23×D59C2×C411yescharacteristic
28C2×D4×C59C2311yescharacteristic
29C22×C4×C59C2×C411yescharacteristic
30C2×C22⋊D59—21no—
31C2×C22⋊D59C2×C411yescharacteristic
32C2×C22⋊D59D411yescharacteristic
33C22×Dic59C2×C411yescharacteristic
34C22×Dic59D411yescharacteristic
35#11745687—41no—
36#11745687—41no—
37C2×D236—21no—
38C2×C4×D59—21no—
39C2×C4×D59—21no—
40C2×C4×D59—41no—
41C2×C4×D59—41no—
42C2×C4×D59D411yescharacteristic
43C2×Dic118D411yescharacteristic
44M16×C59—21no—
45C4⋊C4×C59—21no—
46C22⋊C4×C59—21no—
47C22⋊C4×C59—21no—
48C22⋊C4×C59C2×C411yescharacteristic
49C22⋊Dic59—21no—
50C22⋊Dic59C2×C411yescharacteristic
51(C2×D59)⋊C4—21no—
52(C2×D59)⋊C4—21no—
53(C2×D59)⋊C4—21no—
54Dic59⋊C4—21no—
55Dic59⋊C4—21no—
56Dic59⋊C4—41no—
57C4×Dic59—21no—
58C4×Dic59—41no—
59#11745664—21no—
60#11745659—41no—
61C8×D59—41no—
62C23×C59C22×C411yescharacteristic
63C23×C59C2×D411yescharacteristic
64C22×D59—21no—
65C22×D59—42no—
66C22×D59—41no—
67C22×D59C22⋊C411yescharacteristic
68D4×C59—41no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59C2×D411yescharacteristic
74C22⋊D59—41no—
75C22⋊D59—41no—
76C22⋊D59—42no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—21no—
81C2×Dic59—21no—
82C2×Dic59—41no—
83C2×Dic59C22⋊C411yescharacteristic
84C2×Dic59C22⋊C411yescharacteristic
85C2×Dic59C22⋊C411yescharacteristic
86D236—42no—
87C4×D59—21no—
88C4×D59—21no—
89C4×D59—42no—
90C4×D59—41no—
91C4×D59—41no—
92Dic118—41no—
93C8×C59—41no—
94C59⋊C8—41no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59—41no—
98C22×C59—41no—
99C22×C59C2×C22⋊C411yescharacteristic
100C2×D59—22no—
101C2×D59—21no—
102C2×D59—41no—
103C2×D59—42no—
104C2×D59—41no—
105C2×D59—41no—
106C2×D59—42no—
107C4×C59—21no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59—81no—
111Dic59—21no—
112Dic59—21no—
113Dic59—41no—
114Dic59—81no—
115Dic59#9911yescharacteristic
116Dic59#9911yescharacteristic
117#2120—591nomaximal, Sylow
118C2×C59—21no—
119C2×C59—41no—
120C2×C59—41no—
121C2×C59C2×#9911yescharacteristic
122D59—41no—
123D59—42no—
124#525—591no—
125#413—591no—
126#410—591no—
127#352—591no—
128#352D5911yescharacteristic, complemented
129AΣL(1,𝔽16)—591no—
130AΣL(1,𝔽16)—591no—
131C59#212011yescharacteristic, complemented, Sylow
132C2×#41—591no—
133C23×C4—591no—
134C2×M16—1181no—
135#123—591no—
136#123C2×D5911yescharacteristic
137C22⋊Q8—1181no—
138#121—1181no—
139#120—591no—
140#120—591no—
141C4×D4—1181no—
142C4×D4—1181no—
143#117—591no—
144#117—1181no—
145#101—1181no—
146#100—591no—
147#100C2×D5911yescharacteristic
148#99—591no—
149#99—1181no—
150#99C2×D5911yescharacteristic
151C24—591no—
152#41—2361no—
153#41—2361no—
154C2×Q8—591no—
155C2×D4—591no—
156C2×D4—591no—
157C2×D4—1181no—
158C2×D4—1181no—
159C2×D4C22×D5911yescharacteristic
160C22×C4—591no—
161C22×C4—591no—
162C22×C4—591no—
163C22×C4—1181no—
164C22×C4—1181no—
165C22×C4—2361no—
166C22×C4—2361no—
167C22×C4C4×D5911yescharacteristic
168M16—21no—
169M16—1181no—
170M16—2361no—
171C2×C8—2361no—
172C4⋊C4—21no—
173C4⋊C4—1181no—
174C4⋊C4—1181no—
175C4⋊C4—2361no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—591no—
179C22⋊C4—1181no—
180C22⋊C4—1181no—
181C22⋊C4—1181no—
182C22⋊C4—1181no—
183C22⋊C4C4×D5911yescharacteristic
184C42—1181no—
185C42—2361no—
186C23—591no—
187C23—1181no—
188C23—2361no—
189C23—2362no—
190C23C2×C4×D5911yescharacteristic
191C23D4×D5911yescharacteristic
192Q8—2361no—
193D4—41no—
194D4—2362no—
195D4—2361no—
196D4—2361no—
197D4—2362no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—591no—
203C2×C4—591no—
204C2×C4—591no—
205C2×C4—1181no—
206C2×C4—1181no—
207C2×C4—1181no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—1181no—
212C2×C4—2361no—
213C2×C4—2361no—
214C2×C4—2362no—
215C2×C4—2361no—
216C2×C4D4×D5911yescharacteristic
217C8—41no—
218C8—2361no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—1182no—
224C22—1181no—
225C22—2361no—
226C22—2361no—
227C22—2362no—
228C22—2362no—
229C22—2361no—
230C22C22⋊C4×D5911yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—591no—
236C4—591no—
237C4—1181no—
238C4—1181no—
239C4—4721no—
240C4—2361no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—2362no—
245C2—2361no—
246C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC23×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#352C2
socleC2×C59C2×#99
hypercenter#352D59
hypocenterC59#2120
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #16837383C2semidirect
3. #16837374C2semidirect
4. #16837192C2semidirect
5. #16837190C2semidirect
6. #16837188C2semidirect
7. C59×#352C2semidirect
9. C22×C4×D59C4semidirect
11. #14273710C4semidirect
14. #14273697C4semidirect
19. #14273683C4semidirect
128. #352D59semidirect
131. C59#2120semidirect