Finite Group Databasebeta

← #21425105

Subgroups — #21425105

Order 7552.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#11745672C211yesmaximal, characteristic, complemented
2C2×#14273707C211yesmaximal, characteristic
3C2×#14273703C211yesmaximal, characteristic
4C2×#14273652C211yesmaximal, characteristic, complemented
5C2×(C2×D59)⋊C8C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic, complemented
7C2×#103×C59C211yesmaximal, characteristic, complemented
8C22×Dic118C2211yescharacteristic
9C22×C4×D59C2211yescharacteristic
10C2×#11745672—22no—
11C2×#11745672—22no—
12C2×#11745672—22no—
13C22×C59⋊C8C2211yescharacteristic
14#14273707—22no—
15#14273707—22no—
16#14273703—22no—
17#14273703—22no—
18C2×C4⋊Dic59—21no—
19C2×C4⋊Dic59C2211yescharacteristic
20C2×Dic59⋊C4—21no—
21C2×(C2×D59)⋊C4—21no—
22C2×(C2×D59)⋊C4—21no—
23#14273652—22no—
24(C2×D59)⋊C8—22no—
25C22×Q8×C59C2211yescharacteristic
26C22×C8×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2211yescharacteristic
28#103×C59—22no—
29C23×D59D411yescharacteristic
30C2×Q8×C59—21no—
31C2×Q8×C59—21no—
32C2×Q8×C59—21no—
33C2×Q8×C59—21no—
34C2×Q8×C59—21no—
35C2×Q8×C59D412yes—
36C22×C4×C59—21no—
37C22×C4×C59—21no—
38C22×C4×C59C2311yescharacteristic
39C22×Dic59—21no—
40C22×Dic59—21no—
41C22×Dic59D411yescharacteristic
42C2×C4×D59—21no—
43C2×C4×D59—21no—
44C2×C4×D59—21no—
45C2×C4×D59—21no—
46C2×C4×D59—21no—
47C2×C4×D59—21no—
48C2×Dic118—21no—
49C2×Dic118—21no—
50C2×Dic118—21no—
51C2×Dic118—21no—
52C2×Dic118—21no—
53C2×Dic118D412yes—
54C2×C8×C59—21no—
55C2×C8×C59—21no—
56C2×C8×C59—21no—
57C4⋊C4×C59—21no—
58C4⋊C4×C59D412yes—
59#11745672—28no—
60(C2×D59)⋊C4—24no—
61(C2×D59)⋊C4—24no—
62C4⋊Dic59—24no—
63C4⋊Dic59—21no—
64C4⋊Dic59D412yes—
65Dic59⋊C4—24no—
66C2×C59⋊C8—21no—
67C2×C59⋊C8—21no—
68C2×C59⋊C8D412yes—
69C23×C59C2×D411yescharacteristic
70C22×D59—21no—
71C22×D59—21no—
72C22×D59—21no—
73C22×D59—21no—
74C22×D59—21no—
75C22×D59—21no—
76C22×D59Q1612yescomplemented
77Q8×C59—22no—
78Q8×C59—22no—
79Q8×C59—41no—
80Q8×C59—41no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—41no—
84C2×C4×C59—41no—
85C2×C4×C59—41no—
86C2×C4×C59—41no—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2×D411yescharacteristic
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59#4111yescharacteristic
93C2×Dic59—21no—
94C2×Dic59—22no—
95C2×Dic59—21no—
96C2×Dic59—22no—
97C2×Dic59—21no—
98C2×Dic59—41no—
99C2×Dic59—41no—
100C2×Dic59—41no—
101C2×Dic59—41no—
102C4×D59—41no—
103C4×D59—41no—
104C4×D59—41no—
105C4×D59—41no—
106Dic118—22no—
107Dic118—22no—
108Dic118—41no—
109Dic118—41no—
110C8×C59—41no—
111C59⋊C8—22no—
112C22×C59#12011yescharacteristic
113C22×C59#12011yescharacteristic
114C22×C59#12111yescharacteristic
115C22×C59C2×Q1611yescharacteristic
116C22×C59#13511yescharacteristic
117C22×C59#13711yescharacteristic
118C22×C59#13711yescharacteristic
119C2×D59—22no—
120C2×D59—22no—
121C2×D59—22no—
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—41no—
125C2×D59—41no—
126C4×C59—42no—
127C4×C59—42no—
128C4×C59#12011yescharacteristic
129C4×C59#12111yescharacteristic
130C4×C59#12111yescharacteristic
131C4×C59#12711yescharacteristic
132Dic59—42no—
133Dic59—41no—
134Dic59—42no—
135#2001—591nomaximal, Sylow
136C2×C59#39211yescharacteristic
137C2×C59#45111yescharacteristic
138C2×C59#45111yescharacteristic
139C2×C59#45211yescharacteristic
140C2×C59#45211yescharacteristic
141C2×C59#46711yescharacteristic
142C2×C59#47011yescharacteristic
143D59—42no—
144C22×Q16—591no—
145C2×C22⋊Q8—591no—
146C2×C22⋊Q8—591no—
147C2×#103—591no—
148C2×#103D5911yescharacteristic, complemented
149C2×C22⋊C8—591no—
150#340—591no—
151C59#200111yescharacteristic, complemented, Sylow
152C22×Q8—591no—
153C22×Q8C2×D5911yescharacteristic
154C23×C4—591no—
155C2×Q16—1182no—
156C2×Q16—1182no—
157C2×Q16—1182no—
158C22×C8—591no—
159C22×C8C2×D5911yescharacteristic
160C22⋊Q8—1182no—
161C22⋊Q8—1182no—
162C22⋊Q8—1182no—
163C22⋊Q8—1182no—
164C2×C4⋊C4—591no—
165C2×C4⋊C4—1181no—
166C2×C4⋊C4—1181no—
167C2×C4⋊C4C2×D5911yescharacteristic
168C2×C22⋊C4—1181no—
169C2×C22⋊C4—1181no—
170#103—22no—
171#103—1182no—
172C22⋊C8—1182no—
173C24—591no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—592no—
180C2×Q8—1181no—
181C2×Q8—1181no—
182C2×Q8—1181no—
183C2×Q8—1181no—
184C2×Q8—1181no—
185C2×Q8D23612yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—591no—
189C22×C4—1181no—
190C22×C4—1181no—
191C22×C4—1181no—
192C22×C4—1181no—
193C22×C4—1181no—
194C22×C4—1181no—
195C22×C4—1181no—
196C22×C4—1181no—
197C22×C4C22×D5911yescharacteristic
198Q16—1188no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—592no—
203C2×C8—1181no—
204C2×C8—1181no—
205C4⋊C4—21no—
206C4⋊C4—592no—
207C4⋊C4—1184no—
208C4⋊C4—1184no—
209C4⋊C4—1181no—
210C4⋊C4C22⋊D5912yes—
211C22⋊C4—1184no—
212C22⋊C4—1184no—
213C23—592no—
214C23—1181no—
215C23—1181no—
216C23—1181no—
217C23—1181no—
218C23—1181no—
219C23—1181no—
220C23D4×D5911yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—41no—
224Q8—41no—
225Q8—1182no—
226Q8—1182no—
227Q8—2361no—
228Q8—2361no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1182no—
236C2×C4—1181no—
237C2×C4—1182no—
238C2×C4—1181no—
239C2×C4—1181no—
240C2×C4—2361no—
241C2×C4—2361no—
242C2×C4—2361no—
243C2×C4—2361no—
244C2×C4—2361no—
245C2×C4—2361no—
246C2×C4—2361no—
247C2×C4—2361no—
248C2×C4C2×D23611yescharacteristic
249C2×C4#1174568511yescharacteristic
250C2×C4D4×D5911yescharacteristic
251C2×C4D4×D5911yescharacteristic
252C2×C4D4×D5911yescharacteristic
253C2×C4C2×C22⋊D5911yescharacteristic
254C8—41no—
255C8—1182no—
256C22—1182no—
257C22—1182no—
258C22—1182no—
259C22—2361no—
260C22—2361no—
261C22—2361no—
262C22—2361no—
263C22#1427369511yescharacteristic
264C22#1427369711yescharacteristic
265C22#1427370011yescharacteristic
266C22Q16×D5911yescharacteristic
267C22#1427374811yescharacteristic
268C22#1427375611yescharacteristic
269C22#1427375911yescharacteristic
270C4—42no—
271C4—42no—
272C4—2361no—
273C4—2362no—
274C4—2362no—
275C4#1427369711yescharacteristic
276C4#1427370011yescharacteristic
277C4#1427370111yescharacteristic
278C4#1427372311yescharacteristic
279C2—2362no—
280C2#1683731111yescharacteristic
281C2#1683755611yescharacteristic
282C2#1683755911yescharacteristic
283C2#1683756111yescharacteristic
284C2#1683756711yescharacteristic
285C2#1683764211yescharacteristic
286C2#1683765911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#2001
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#11745672C2semidirect
4. C2×#14273652C2semidirect
6. #16837164C2semidirect
7. C2×#103×C59C2semidirect
76. C22×D59Q16semidirect
148. C2×#103D59semidirect
151. C59#2001semidirect