Finite Group Databasebeta

← #21425110

Subgroups — #21425110

Order 7552.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14273752C211yesmaximal, characteristic, complemented
2#16837966C211yesmaximal, characteristic, complemented
3C2×#14273724C211yesmaximal, characteristic, complemented
4#16837408C211yesmaximal, characteristic, complemented
5C2×#14273643C211yesmaximal, characteristic, complemented
6#16837162C211yesmaximal, characteristic, complemented
7C2×#104×C59C211yesmaximal, characteristic, complemented
8C22×D236—22no—
9C22×D236C2211yescharacteristic
10C22×D236C2211yescharacteristic
11#14273752—22no—
12#14273752—22no—
13C2×#11745671—21no—
14C2×#11745669—21no—
15C2×#11745664C2211yescharacteristic
16#14273724—22no—
17#14273724—22no—
18#14273723—21no—
19#14273716—21no—
20#14273701—22no—
21#14273695—22no—
22#14273686C2211yescharacteristic
23#14273649—22no—
24#14273643—22no—
25C2×#41×C59C2211yescharacteristic
26C2×M16×C59C2211yescharacteristic
27C2×C42×C59C2211yescharacteristic
28#104×C59—22no—
29C23×D59—21no—
30C23×D59D412yes—
31#41×C59—21no—
32#41×C59—21no—
33#41×C59—21no—
34#41×C59—21no—
35C2×Q8×C59D411yescharacteristic, complemented
36C2×D4×C59—21no—
37C2×D4×C59D411yescharacteristic, complemented
38C22×C4×C59—21no—
39C22×C4×C59—21no—
40C22×C4×C59C2311yescharacteristic
41C2×C22⋊D59—24no—
42C2×D236—21no—
43C2×D236—21no—
44C2×D236—21no—
45C2×D236—21no—
46C2×D236—28no—
47C2×D236—21no—
48C2×D236—21no—
49C2×D236—21no—
50C2×D236—21no—
51C2×D236—21no—
52C2×D236—21no—
53C2×D236—21no—
54C2×D236—48no—
55C2×D236D412yescomplemented
56M16×C59—21no—
57M16×C59—21no—
58C2×C8×C59—21no—
59C42×C59—21no—
60C42×C59D412yescomplemented
61C22⋊Dic59—21no—
62#11745671—24no—
63#11745669—24no—
64(C2×D59)⋊C4—24no—
65C4⋊Dic59D412yescomplemented
66C4×Dic59—21no—
67#11745664—21no—
68#11745664D412yescomplemented
69C2×C59⋊C8—21no—
70C23×C59—21no—
71C23×C59C2×D411yescharacteristic
72C22×D59—22no—
73C22×D59—22no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—44no—
77C22×D59—44no—
78C22×D59—41no—
79C22×D59—41no—
80Q8×C59—21no—
81Q8×C59—21no—
82D4×C59—21no—
83D4×C59—21no—
84D4×C59—41no—
85D4×C59—41no—
86C2×C4×C59—24no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—41no—
90C2×C4×C59—41no—
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2×D411yescharacteristic
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59#4111yescharacteristic
97C22⋊D59—84no—
98C2×Dic59—22no—
99D236—22no—
100D236—22no—
101D236—416no—
102D236—41no—
103D236—41no—
104D236—41no—
105D236—41no—
106D236—41no—
107D236—41no—
108C8×C59—41no—
109C59⋊C8—22no—
110C22×C59—22no—
111C22×C59—41no—
112C22×C59—42no—
113C22×C59#12011yescharacteristic
114C22×C59#12011yescharacteristic
115C22×C59#12111yescharacteristic
116C2×D59—44no—
117C2×D59—44no—
118C2×D59—42no—
119C2×D59—42no—
120C2×D59—44no—
121C2×D59—82no—
122C2×D59—82no—
123C2×D59—82no—
124C4×C59—24no—
125C4×C59—41no—
126C4×C59#12011yescharacteristic
127C4×C59#12111yescharacteristic
128C4×C59#12111yescharacteristic
129C4×C59#12711yescharacteristic
130Dic59—42no—
131#2002—591nomaximal, Sylow
132C2×C59—21no—
133C2×C59—21no—
134C2×C59—81no—
135C2×C59#39211yescharacteristic
136C2×C59#45312yes—
137D59—82no—
138D59—82no—
139C2×AGL(1,ℤ/8)—591no—
140#535—591no—
141C2×#127—591no—
142C2×#104D5911yescharacteristic, complemented
143#418—591no—
144C2×#100—591no—
145#339—591no—
146C59#200211yescharacteristic, complemented, Sylow
147C2×#41C2×D5911yescharacteristic
148C22×D4—591no—
149C22×D4—591no—
150C22×D4—1182no—
151AGL(1,ℤ/8)—1182no—
152AGL(1,ℤ/8)—1182no—
153C2×SD16—1181no—
154C2×D8—1181no—
155C2×M16—591no—
156C2×M16C2×D5911yescharacteristic
157#127—1182no—
158#127—1181no—
159#127—1182no—
160#124—1181no—
161#121—1182no—
162#120—1182no—
163#117—591no—
164C2×C42C2×D5911yescharacteristic
165#104—22no—
166#102—1182no—
167#100—1182no—
168C24—592no—
169C24—1181no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D23611yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—592no—
177C2×D4—1188no—
178C2×D4—1184no—
179C2×D4—1181no—
180C2×D4—1181no—
181C2×D4—1181no—
182C2×D4—1181no—
183C2×D4—1181no—
184C2×D4—1181no—
185C2×D4—1181no—
186C2×D4—1181no—
187C2×D4—1181no—
188C2×D4—1181no—
189C2×D4—1181no—
190C2×D4—2368no—
191C2×D4D23611yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D5911yescharacteristic
195SD16—1184no—
196D8—1184no—
197M16—21no—
198M16—21no—
199M16—592no—
200M16—1181no—
201C2×C8—21no—
202C2×C8—1181no—
203C4⋊C4—592no—
204C22⋊C4—1184no—
205C22⋊C4—1181no—
206C42—21no—
207C42—1181no—
208C42C22⋊D5912yescomplemented
209C23—21no—
210C23—1182no—
211C23—1182no—
212C23—1182no—
213C23—1182no—
214C23—2364no—
215C23—2364no—
216C23—2361no—
217C23—2361no—
218C23D4×D5911yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—1182no—
226D4—1182no—
227D4—4724no—
228D4—23616no—
229D4—2361no—
230D4—2361no—
231D4—2361no—
232D4—2361no—
233D4—2361no—
234D4—2361no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—1182no—
241C2×C4C2×D23611yescharacteristic
242C2×C4#1174568511yescharacteristic
243C2×C4D4×D5911yescharacteristic
244C2×C4D4×D5911yescharacteristic
245C2×C4D4×D5911yescharacteristic
246C2×C4C2×C22⋊D5911yescharacteristic
247C8—41no—
248C8—1182no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—4722no—
253C22—4722no—
254C22—4722no—
255C22—2364no—
256C22—2364no—
257C22—2362no—
258C22—2362no—
259C22—2364no—
260C22#1427369511yescharacteristic
261C22#1427369711yescharacteristic
262C22#1427370011yescharacteristic
263C4—24no—
264C4—41no—
265C4—2362no—
266C4#1427369711yescharacteristic
267C4#1427370011yescharacteristic
268C4#1427370111yescharacteristic
269C4#1427372311yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—4722no—
274C2—4722no—
275C2#1683731111yescharacteristic
276C2#1683757112yes—
subgroupG/H
centerC22#14273697
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#104×C59C2
socleC22×C59#120
hypercenterC2×#104D59
hypocenterC59#2002
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. #16837966C2semidirect
3. C2×#14273724C2semidirect
4. #16837408C2semidirect
5. C2×#14273643C2semidirect
6. #16837162C2semidirect
7. C2×#104×C59C2semidirect
35. C2×Q8×C59D4semidirect
37. C2×D4×C59D4semidirect
55. C2×D236D4semidirect
60. C42×C59D4semidirect
65. C4⋊Dic59D4semidirect
68. #11745664D4semidirect
142. C2×#104D59semidirect
146. C59#2002semidirect
174. C2×Q8D236semidirect
191. C2×D4D236semidirect
208. C42C22⋊D59semidirect