Finite Group Databasebeta

← #21435043

Subgroups — #21435043

Order 7552.

384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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#16837956C211yesmaximal, characteristic
2C4⋊Q8×D59C211yesmaximal, characteristic
3#16837780C212yesmaximal, complemented
4#16837751C212yesmaximal, complemented
5#16837613C211yesmaximal, characteristic, complemented
6#16837612C211yesmaximal, characteristic, complemented
7#16837609C211yesmaximal, characteristic, complemented
8#16837559C212yesmaximal
9#16837556C212yesmaximal
10#16837454C211yesmaximal, characteristic
11C59×#462C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2212yes—
13C2×Dic236C2212yes—
14C2×#11745672C2212yes—
15C2×#11745672C2212yes—
16#14273727C2211yescharacteristic
17#14273726—21no—
18#14273726—21no—
19#14273726C2211yescharacteristic
20#14273725C2212yes—
21#14273725C2211yescharacteristic
22#14273717—21no—
23#14273707C2211yescharacteristic
24#14273705—21no—
25#14273703C2211yescharacteristic
26C4×Dic118—21no—
27C4×Dic118C2211yescharacteristic
28#14273684—21no—
29C4⋊C4×D59—21no—
30C4⋊C4×D59—21no—
31C42×D59C2211yescharacteristic
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273651C2212yes—
35#14273650C2212yes—
36(C2×D59)⋊C8C2212yes—
37C8×Dic59C2212yes—
38C2×Q16×C59C2212yes—
39C4⋊Q8×C59C2211yescharacteristic
40C4×Q8×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59C2312yes—
44C2×Q8×C59C2311yescharacteristic
45Q8×D59—42no—
46Q8×D59—42no—
47C2×C4×D59—22no—
48C2×C4×D59D411yescharacteristic
49C2×C4×D59D411yescharacteristic
50C2×C4×D59C2311yescharacteristic
51C2×Dic118—21no—
52C2×Dic118—22no—
53C2×Dic118C2312yes—
54C2×Dic118C2311yescharacteristic
55Q16×C59—42no—
56C2×C8×C59C2312yes—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2311yescharacteristic
61C42×C59—21no—
62C42×C59C2311yescharacteristic
63#11745672—42no—
64#11745672—42no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59—21no—
69C4⋊Dic59—21no—
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73Dic59⋊C4—22no—
74Dic59⋊C4—21no—
75Dic59⋊C4—21no—
76Dic59⋊C4—21no—
77Dic59⋊C4—21no—
78C4×Dic59—21no—
79C4×Dic59D411yescharacteristic
80C4×Dic59D411yescharacteristic
81C4×Dic59C2311yescharacteristic
82C2×C59⋊C8C2312yes—
83Dic236—42no—
84C22×D59C2×D411yescharacteristic
85Q8×C59—21no—
86Q8×C59—22no—
87Q8×C59—21no—
88Q8×C59—22no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2411yescharacteristic
95C2×Dic59—21no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59C2×D411yescharacteristic
99C2×Dic59C2×D411yescharacteristic
100C2×Dic59C2×D411yescharacteristic
101C4×D59—21no—
102C4×D59—21no—
103C4×D59—22no—
104C4×D59—44no—
105C4×D59Q1614yescomplemented
106Dic118—21no—
107Dic118—22no—
108Dic118—21no—
109Dic118—22no—
110Dic118—44no—
111Dic118—42no—
112C8×C59—22no—
113C59⋊C8—22no—
114C22×C59C22×D411yescharacteristic
115C2×D59—21no—
116C2×D59—21no—
117C2×D59C2×Q1612yes—
118C4×C59—21no—
119C4×C59—42no—
120C4×C59—41no—
121C4×C59—41no—
122C4×C59C2×Q1612yes—
123C4×C59H(5,𝔽2)11yescharacteristic
124C4×C59H(5,𝔽2)11yescharacteristic
125Dic59—21no—
126Dic59—42no—
127Dic59—41no—
128Dic59—41no—
129Dic59C2×Q1612yes—
130Dic59#13712yes—
131#3209—591nomaximal, Sylow
132C2×C59#53511yescharacteristic
133C2×C59C22×Q1611yescharacteristic
134C2×C59C2×#13711yescharacteristic
135D59—22no—
136#533—591no—
137C2×C4⋊Q8—591no—
138#494—592no—
139#487—592no—
140#462—591no—
141#462—591no—
142#462—591no—
143#462D5911yescharacteristic, complemented
144#451—592no—
145#451—592no—
146#431—591no—
147C59#320911yescharacteristic, complemented, Sylow
148C22×Q8—592no—
149C2×Q16—592no—
150C2×Q16—592no—
151C2×Q16—592no—
152C2×Q16C2×D5912yes—
153C4⋊Q8—591no—
154C4⋊Q8—592no—
155C4⋊Q8—591no—
156C4⋊Q8—591no—
157C4⋊Q8—1181no—
158C4⋊Q8—1181no—
159C4⋊Q8C2×D5911yescharacteristic
160#125—1181no—
161C22⋊Q8—591no—
162C22⋊Q8—591no—
163C22⋊Q8—1181no—
164C4×Q8—591no—
165C4×Q8—1181no—
166C4×Q8C2×D5911yescharacteristic
167#117—1181no—
168C2×C4⋊C4—1181no—
169C2×C4⋊C4—1181no—
170C2×C42—591no—
171C4⋊C8—591no—
172C4⋊C8C2×D5911yescharacteristic
173#103—592no—
174#103—592no—
175#103—592no—
176#103C2×D5912yes—
177C22⋊C8—592no—
178C4×C8—592no—
179C2×Q8—592no—
180C2×Q8—591no—
181C2×Q8—1181no—
182C2×Q8—1182no—
183C2×Q8—2362no—
184C2×Q8—2362no—
185C2×Q8C22×D5912yes—
186C2×Q8C22×D5911yescharacteristic
187C22×C4—591no—
188C22×C4—591no—
189C22×C4—591no—
190C22×C4—1182no—
191Q16—42no—
192Q16—2362no—
193Q16—2362no—
194Q16—2362no—
195C2×C8—592no—
196C2×C8C22×D5912yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—591no—
201C4⋊C4—1182no—
202C4⋊C4—1182no—
203C4⋊C4—1181no—
204C4⋊C4—1181no—
205C4⋊C4—1181no—
206C4⋊C4—1181no—
207C4⋊C4—1181no—
208C4⋊C4—1181no—
209C4⋊C4—1181no—
210C4⋊C4—1181no—
211C4⋊C4C22×D5911yescharacteristic
212C22⋊C4—1181no—
213C22⋊C4—1181no—
214C42—21no—
215C42—591no—
216C42—591no—
217C42—591no—
218C42—1181no—
219C42C22×D5911yescharacteristic
220C23—591no—
221Q8—21no—
222Q8—22no—
223Q8—21no—
224Q8—22no—
225Q8—1181no—
226Q8—1182no—
227Q8—1181no—
228Q8—1182no—
229Q8—2362no—
230Q8—2364no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—591no—
235C2×C4—591no—
236C2×C4—594no—
237C2×C4—591no—
238C2×C4—1182no—
239C2×C4—1181no—
240C2×C4—1181no—
241C2×C4—1181no—
242C2×C4—1181no—
243C2×C4—1182no—
244C2×C4—2364no—
245C2×C4D4×D5911yescharacteristic
246C2×C4D4×D5911yescharacteristic
247C2×C4C23×D5911yescharacteristic
248C8—22no—
249C8—1182no—
250C22—592no—
251C22—1181no—
252C22—1181no—
253C22C2×D4×D5911yescharacteristic
254C4—21no—
255C4—41no—
256C4—42no—
257C4—41no—
258C4—592no—
259C4—592no—
260C4—1181no—
261C4—2361no—
262C4—2362no—
263C4—2361no—
264C4Q16×D5912yes—
265C4#1427377211yescharacteristic
266C4#1427377311yescharacteristic
267C2—1182no—
268C2#1683796811yescharacteristic
269C2C2×Q16×D5911yescharacteristic
270C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#462C2
socleC22×C59C22×D4
hypercenter#462D59
hypocenterC59#3209
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #16837780C2semidirect
4. #16837751C2semidirect
5. #16837613C2semidirect
6. #16837612C2semidirect
7. #16837609C2semidirect
11. C59×#462C2semidirect
105. C4×D59Q16semidirect
143. #462D59semidirect
147. C59#3209semidirect