Finite Group Databasebeta

← #21424115

Subgroups — #21424115

Order 7552.

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

normal subgroups only

This group has 312 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
1#16837870C211yesmaximal, characteristic
2#16837425C211yesmaximal, characteristic, complemented
3C2×#14273655C211yesmaximal, characteristic
4C2×#14273653C211yesmaximal, characteristic
5C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
6#16837161C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273692C411yescharacteristic, complemented
11#14273692C411yescharacteristic, complemented
12#14273689C411yescharacteristic, complemented
13#14273689C411yescharacteristic, complemented
14(C22⋊D59)⋊C4—21no—
15(C22⋊D59)⋊C4—21no—
16#14273684—21no—
17C2×Dic59⋊C4—21no—
18C2×C4×Dic59C2211yescharacteristic
19C2×C4×Dic59C2211yescharacteristic
20C42×D59—21no—
21Dic59⋊C8—21no—
22Dic59⋊C8—21no—
23#14273655—22no—
24#14273653—22no—
25C59⋊#95—21no—
26C2×M16×C59C2211yescharacteristic
27#117×C59C2211yescharacteristic
28C2×C42×C59C2211yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C22×Dic59—21no—
33C22×Dic59D411yescharacteristic
34C22×Dic59D411yescharacteristic
35#11745685—21no—
36#11745685—21no—
37#11745685D412yes—
38#11745685Q812yes—
39C2×D236C2×C411yescharacteristic
40C2×C4×D59—21no—
41C2×C4×D59—21no—
42C2×C4×D59—21no—
43C2×Dic118C2×C411yescharacteristic
44M16×C59—21no—
45M16×C59—21no—
46C2×C8×C59—21no—
47C4⋊C4×C59C2×C411yescharacteristic
48C4⋊C4×C59C2×C411yescharacteristic
49C22⋊C4×C59—21no—
50C42×C59—21no—
51C42×C59—21no—
52C42×C59—21no—
53(C2×D59)⋊C4—21no—
54(C2×D59)⋊C4—21no—
55Dic59⋊C4—24no—
56Dic59⋊C4—21no—
57Dic59⋊C4—21no—
58C4×Dic59—21no—
59C4×Dic59—21no—
60C4×Dic59—21no—
61C4×Dic59—21no—
62C4×Dic59C2×C411yescharacteristic
63C4×Dic59C2×C411yescharacteristic
64C4×Dic59D411yescharacteristic
65C4×Dic59D411yescharacteristic
66#11745664—21no—
67#11745664—21no—
68C2×C59⋊C8—21no—
69C23×C59C2×D411yescharacteristic
70C22×D59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59—21no—
74C2×C4×C59—41no—
75C2×C4×C59—41no—
76C2×C4×C59C22×C411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×Q811yescharacteristic
80C2×C4×C59#4111yescharacteristic
81C2×C4×C59#4111yescharacteristic
82C22⋊D59—22no—
83C22⋊D59—22no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—41no—
88C2×Dic59—41no—
89C2×Dic59—41no—
90C2×Dic59C22⋊C411yescharacteristic
91C2×Dic59C22⋊C411yescharacteristic
92C2×Dic59C22⋊C411yescharacteristic
93C2×Dic59C22⋊C411yescharacteristic
94D236—21no—
95D236C4⋊C412yescomplemented
96C4×D59—22no—
97C4×D59—22no—
98C4×D59—42no—
99C4×D59—42no—
100Dic118—21no—
101Dic118C4⋊C412yescomplemented
102C8×C59—41no—
103C59⋊C8—41no—
104C22×C59—21no—
105C22×C59—21no—
106C22×C59C2×C22⋊C411yescharacteristic
107C22×C59#12111yescharacteristic
108C22×C59C22⋊Q811yescharacteristic
109C2×D59—22no—
110C2×D59—41no—
111C2×D59—41no—
112C4×C59—42no—
113C4×C59—41no—
114C4×C59—41no—
115C4×C59C2×C4⋊C411yescharacteristic
116C4×C59#11711yescharacteristic
117C4×C59#12111yescharacteristic
118C4×C59C22⋊Q811yescharacteristic
119Dic59—22no—
120Dic59—21no—
121Dic59—21no—
122Dic59—21no—
123Dic59—42no—
124Dic59#10412yescomplemented
125#1806—591nomaximal, Sylow
126C2×C59—21no—
127C2×C59—21no—
128C2×C59#38011yescharacteristic
129C2×C59C2×#10411yescharacteristic
130C2×C59#42111yescharacteristic
131D59—42no—
132C4×#41—591no—
133#423—591no—
134C2×#104—591no—
135C2×#104—591no—
136C4×C4⋊C4—591no—
137#339—591no—
138#339D5911yescharacteristic, complemented
139C59#180611yescharacteristic, complemented, Sylow
140C2×#41—591no—
141C2×M16—591no—
142C2×M16C2×D5911yescharacteristic
143C4×Q8—591no—
144C4×Q8—591no—
145C4×D4—591no—
146C4×D4—591no—
147C4×D4—1181no—
148C4×D4—1181no—
149#117—1181no—
150#117C2×D5911yescharacteristic
151C2×C4⋊C4—1181no—
152C2×C42—591no—
153C2×C42—591no—
154C2×C42—1181no—
155C2×C42C2×D5911yescharacteristic
156C4⋊C8—1181no—
157C4⋊C8—1181no—
158#104—1182no—
159#104—1182no—
160#95—1181no—
161#41—592no—
162#41—592no—
163#41—1181no—
164#41—1181no—
165C2×Q8—591no—
166C2×D4—591no—
167C2×D4—1181no—
168C22×C4—21no—
169C22×C4—591no—
170C22×C4—591no—
171C22×C4—1181no—
172C22×C4—1181no—
173C22×C4—1181no—
174C22×C4—1181no—
175C22×C4C22×D5911yescharacteristic
176M16—21no—
177M16—21no—
178M16—1181no—
179M16—1181no—
180C2×C8—21no—
181C2×C8—1181no—
182C4⋊C4—1181no—
183C4⋊C4—1181no—
184C4⋊C4—1184no—
185C4⋊C4C4×D5911yescharacteristic
186C4⋊C4C4×D5911yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1181no—
189C22⋊C4—1181no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—591no—
194C42—591no—
195C42—591no—
196C42—591no—
197C42—1181no—
198C42—1181no—
199C42—1181no—
200C42—1181no—
201C23—1181no—
202C23D4×D5911yescharacteristic
203Q8—592no—
204Q8—1181no—
205D4—592no—
206D4—1182no—
207D4—1182no—
208D4—1181no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—591no—
215C2×C4—591no—
216C2×C4—591no—
217C2×C4—591no—
218C2×C4—1182no—
219C2×C4—1181no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—2362no—
224C2×C4—2362no—
225C2×C4—2361no—
226C2×C4—2361no—
227C2×C4—2361no—
228C2×C4C2×C4×D5911yescharacteristic
229C2×C4#1174568511yescharacteristic
230C2×C4#1174568511yescharacteristic
231C2×C4D4×D5911yescharacteristic
232C2×C4D4×D5911yescharacteristic
233C2×C4Q8×D5911yescharacteristic
234C8—41no—
235C8—2361no—
236C22—21no—
237C22—21no—
238C22—1182no—
239C22—2361no—
240C22—2361no—
241C22C22⋊C4×D5911yescharacteristic
242C22#1427370011yescharacteristic
243C22#1427370511yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—592no—
248C4—1181no—
249C4—1181no—
250C4—1181no—
251C4—1182no—
252C4—2362no—
253C4C4⋊C4×D5911yescharacteristic
254C4#1427368411yescharacteristic
255C4#1427370011yescharacteristic
256C4#1427370511yescharacteristic
257C2—21no—
258C2—21no—
259C2—2362no—
260C2#1683726111yescharacteristic
261C2#104×D5911yescharacteristic
262C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59C2×C22⋊C4
hypercenter#339D59
hypocenterC59#1806
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16837425C2semidirect
5. C4×Dic59⋊C4C2semidirect
6. #16837161C2semidirect
7. C59×#339C2semidirect
10. #14273692C4semidirect
11. #14273692C4semidirect
12. #14273689C4semidirect
13. #14273689C4semidirect
95. D236C4⋊C4semidirect
101. Dic118C4⋊C4semidirect
124. Dic59#104semidirect
138. #339D59semidirect
139. C59#1806semidirect