Finite Group Databasebeta

← #21425294

Subgroups — #21425294

Order 7552.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14273707C211yesmaximal, characteristic
2C2×#14273652C211yesmaximal, characteristic, complemented
3C2×#14273650C211yesmaximal, characteristic, complemented
4C2×(C2×D59)⋊C8C211yesmaximal, characteristic
5#16837259C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic, complemented
7C2×#106×C59C211yesmaximal, characteristic, complemented
8C22×Dic118C2211yescharacteristic
9C22×C4×D59C2211yescharacteristic
10C22×C59⋊C8C2211yescharacteristic
11#14273707—22no—
12#14273707—22no—
13C2×C4⋊Dic59—21no—
14C2×C4⋊Dic59C2211yescharacteristic
15C2×(C2×D59)⋊C4—21no—
16C2×(C2×D59)⋊C4—21no—
17#14273652—22no—
18#14273650—22no—
19(C2×D59)⋊C8—22no—
20C59⋊#95—21no—
21C22×C8×C59C2211yescharacteristic
22C2×C4⋊C4×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#106×C59—22no—
25C23×D59D411yescharacteristic
26C22×C4×C59—21no—
27C22×C4×C59—21no—
28C22×C4×C59C2311yescharacteristic
29C22×Dic59—21no—
30C22×Dic59—21no—
31C22×Dic59D411yescharacteristic
32C2×C4×D59—21no—
33C2×C4×D59—21no—
34C2×C4×D59—21no—
35C2×C4×D59—21no—
36C2×C4×D59—21no—
37C2×C4×D59—21no—
38C2×Dic118—21no—
39C2×Dic118—21no—
40C2×Dic118—21no—
41C2×Dic118—21no—
42C2×Dic118—21no—
43C2×Dic118D412yes—
44C2×C8×C59—21no—
45C2×C8×C59—21no—
46C2×C8×C59D412yes—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59D412yes—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—42no—
53C4⋊Dic59—24no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58C2×C59⋊C8—21no—
59C23×C59C2×D411yescharacteristic
60C22×D59—21no—
61C22×D59—21no—
62C22×D59—21no—
63C22×D59—21no—
64C22×D59—21no—
65C22×D59—21no—
66C22×D59SD1612yes—
67C2×C4×C59—22no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59#4111yescharacteristic
77C2×C4×C59#4111yescharacteristic
78C2×C4×C59#4111yescharacteristic
79C2×Dic59—21no—
80C2×Dic59—22no—
81C2×Dic59—21no—
82C2×Dic59—21no—
83C2×Dic59—41no—
84C2×Dic59—41no—
85C2×Dic59—41no—
86C2×Dic59—41no—
87C2×Dic59—41no—
88C4×D59—41no—
89C4×D59—41no—
90C4×D59—41no—
91C4×D59—41no—
92Dic118—22no—
93Dic118—22no—
94Dic118—41no—
95Dic118—41no—
96C8×C59—22no—
97C59⋊C8—41no—
98C22×C59#12011yescharacteristic
99C22×C59#12111yescharacteristic
100C22×C59#12311yescharacteristic
101C22×C59C2×SD1611yescharacteristic
102C22×C59#13511yescharacteristic
103C22×C59#13711yescharacteristic
104C22×C59#13711yescharacteristic
105C2×D59—22no—
106C2×D59—22no—
107C2×D59—22no—
108C2×D59—41no—
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—42no—
113C4×C59—81no—
114C4×C59#12111yescharacteristic
115C4×C59#12111yescharacteristic
116C4×C59#12311yescharacteristic
117C4×C59#12411yescharacteristic
118Dic59—42no—
119Dic59—41no—
120Dic59—81no—
121#2035—591nomaximal, Sylow
122C2×C59#39411yescharacteristic
123C2×C59#44811yescharacteristic
124C2×C59#45211yescharacteristic
125C2×C59#46511yescharacteristic
126C2×C59#47011yescharacteristic
127C2×C59#48311yescharacteristic
128C2×C59#48511yescharacteristic
129D59—42no—
130C2×C22⋊Q8—591no—
131C2×#106D5911yescharacteristic, complemented
132C2×#103—591no—
133C2×#103—591no—
134C2×C22⋊C8—591no—
135#380—591no—
136#340—591no—
137C59#203511yescharacteristic, complemented, Sylow
138C22×Q8—591no—
139C23×C4—591no—
140C22×C8—591no—
141C22×C8C2×D5911yescharacteristic
142C22⋊Q8—1182no—
143C22⋊Q8—1182no—
144C2×C4⋊C4—591no—
145C2×C4⋊C4—1181no—
146C2×C4⋊C4C2×D5911yescharacteristic
147C2×C4⋊C4C2×D5911yescharacteristic
148C2×C22⋊C4—1181no—
149C2×C22⋊C4—1181no—
150#106—22no—
151#103—1182no—
152#103—1182no—
153C22⋊C8—1182no—
154#95—1181no—
155C24—591no—
156C2×Q8—592no—
157C2×Q8—1181no—
158C2×Q8—1181no—
159C2×Q8—1181no—
160C2×Q8—1181no—
161C2×Q8—1181no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—591no—
165C22×C4—1181no—
166C22×C4—1181no—
167C22×C4—1181no—
168C22×C4—1181no—
169C22×C4—1181no—
170C22×C4—1181no—
171C22×C4—1181no—
172C22×C4—1181no—
173C22×C4C22×D5911yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—1181no—
177C2×C8—1181no—
178C2×C8—1181no—
179C2×C8D23612yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1184no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4C22⋊D5912yes—
187C22⋊C4—1184no—
188C22⋊C4—2362no—
189C23—592no—
190C23—1181no—
191C23—1181no—
192C23—1181no—
193C23—1181no—
194C23—1181no—
195C23—1181no—
196C23D4×D5911yescharacteristic
197Q8—1182no—
198Q8—1182no—
199Q8—2361no—
200Q8—2361no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1182no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—2361no—
212C2×C4—2361no—
213C2×C4—2361no—
214C2×C4—2361no—
215C2×C4—2361no—
216C2×C4—2361no—
217C2×C4—2361no—
218C2×C4—2361no—
219C2×C4—2361no—
220C2×C4C2×D23611yescharacteristic
221C2×C4#1174568511yescharacteristic
222C2×C4D4×D5911yescharacteristic
223C2×C4#1174568911yescharacteristic
224C2×C4#1174568911yescharacteristic
225C2×C4C2×C22⋊D5911yescharacteristic
226C8—22no—
227C8—2361no—
228C22—1182no—
229C22—1182no—
230C22—1182no—
231C22—2361no—
232C22—2361no—
233C22—2361no—
234C22—2361no—
235C22#1427369511yescharacteristic
236C22#1427370211yescharacteristic
237C22#1427371211yescharacteristic
238C22SD16×D5911yescharacteristic
239C22#1427374811yescharacteristic
240C22#1427375611yescharacteristic
241C22#1427375611yescharacteristic
242C4—42no—
243C4—81no—
244C4—4721no—
245C4—2361no—
246C4—2362no—
247C4#1427370111yescharacteristic
248C4#1427370211yescharacteristic
249C4#1427371211yescharacteristic
250C4#1427371611yescharacteristic
251C2—2362no—
252C2#1683731911yescharacteristic
253C2#1683753911yescharacteristic
254C2#1683756111yescharacteristic
255C2#1683763211yescharacteristic
256C2#1683766111yescharacteristic
257C2#1683773411yescharacteristic
258C2#1683774611yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#106×C59C2
socleC23×C59C2×D4
hypercenterC2×#106D59
hypocenterC59#2035
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#14273652C2semidirect
3. C2×#14273650C2semidirect
6. #16837164C2semidirect
7. C2×#106×C59C2semidirect
131. C2×#106D59semidirect
137. C59#2035semidirect