Finite Group Databasebeta

← #21433836

Subgroups — #21433836

Order 7552.

446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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#16838200C211yesmaximal, characteristic
2C2×#14273760C211yesmaximal, characteristic, complemented
3C2×#14273757C211yesmaximal, characteristic, complemented
4#16838168C211yesmaximal, characteristic, complemented
5#16837676C214yesmaximal, complemented
6#16837664C214yesmaximal, complemented
7#16837450C211yesmaximal, characteristic, complemented
8C2×#14273645C211yesmaximal, characteristic, complemented
9C59×#413C211yesmaximal, characteristic, complemented
10C2×#11745685C2211yescharacteristic
11C22×Dic118C2211yescharacteristic
12#14273760—22no—
13#14273760C2214yes—
14#14273758C2212yes—
15#14273757—21no—
16#14273757—22no—
17#14273757—22no—
18#14273753C2212yes—
19#14273752—21no—
20#14273747—22no—
21C2×Dic236—21no—
22C2×#11745672C2212yescomplemented
23C2×#11745660—21no—
24C2×#11745670C2212yescomplemented
25#14273735C2214yes—
26#14273733—22no—
27C2×#11745664C2211yescharacteristic
28C2×#11745664C2211yescharacteristic
29M16×D59—22no—
30#14273662C2214yescomplemented
31#14273645C2214yescomplemented
32C2×#41×C59C2211yescharacteristic
33C2×M16×C59C2211yescharacteristic
34C2×M16×C59C2211yescharacteristic
35#101×C59C2212yescomplemented
36#100×C59C2212yescomplemented
37#41×C59—21no—
38#41×C59—21no—
39#41×C59—21no—
40#41×C59—21no—
41C2×Q8×C59C2311yescharacteristic
42C2×D4×C59—21no—
43C2×D4×C59C2311yescharacteristic
44C22×C4×C59—21no—
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—21no—
47C22×Dic59—21no—
48#11745685—21no—
49#11745685—21no—
50#11745685D412yes—
51#11745685C2312yes—
52C2×D236D411yescharacteristic
53C2×C4×D59—21no—
54C2×Dic118—21no—
55C2×Dic118—21no—
56C2×Dic118—21no—
57C2×Dic118—21no—
58C2×Dic118—21no—
59C2×Dic118D411yescharacteristic
60C2×Dic118C2312yes—
61M16×C59—21no—
62M16×C59—21no—
63M16×C59C2312yes—
64M16×C59C2312yes—
65C2×C8×C59—21no—
66C2×C8×C59—21no—
67#11745672—22no—
68#11745672—24no—
69#11745671—22no—
70#11745670—22no—
71#11745670—24no—
72#11745669—22no—
73#11745664—21no—
74#11745664D412yes—
75#11745664D412yes—
76#11745664C2312yes—
77C2×C59⋊C8—21no—
78C2×C59⋊C8C2312yes—
79Dic236—24no—
80#11745660—24no—
81#11745659—24no—
82C8×D59—24no—
83C23×C59—21no—
84C23×C59#4111yescharacteristic
85C22×D59—21no—
86Q8×C59—21no—
87Q8×C59—21no—
88D4×C59—21no—
89D4×C59—21no—
90D4×C59—41no—
91D4×C59—41no—
92C2×C4×C59—21no—
93C2×C4×C59—41no—
94C2×C4×C59—41no—
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59#4111yescharacteristic
100C2×C4×C59C2411yescharacteristic
101C22⋊D59—22no—
102C22⋊D59—22no—
103C2×Dic59—21no—
104C2×Dic59—22no—
105C2×Dic59—41no—
106C2×Dic59—41no—
107D236—21no—
108D236C2×D412yes—
109C4×D59—22no—
110C4×D59—22no—
111Dic118—21no—
112Dic118—22no—
113Dic118—22no—
114Dic118—41no—
115Dic118—41no—
116Dic118C2×D412yes—
117C8×C59—22no—
118C8×C59—22no—
119C59⋊C8—22no—
120C59⋊C8C2×D414yes—
121C22×C59—41no—
122C22×C59—41no—
123C22×C59—81no—
124C22×C59#12111yescharacteristic
125C22×C59#12111yescharacteristic
126C22×C59C2×#4111yescharacteristic
127C2×D59—22no—
128C2×D59—81no—
129C4×C59—41no—
130C4×C59#12111yescharacteristic
131C4×C59#12111yescharacteristic
132C4×C59C22×D411yescharacteristic
133C4×C59C22×D411yescharacteristic
134Dic59—22no—
135Dic59—42no—
136#3069—591nomaximal, Sylow
137C2×C59—21no—
138C2×C59—21no—
139C2×C59—21no—
140C2×C59—81no—
141C2×C59C2×#12111yescharacteristic
142D59—42no—
143#575—591no—
144C2×#137—591no—
145C2×#137—591no—
146#568—591no—
147#473—594no—
148#471—594no—
149#430—591no—
150#413D5911yescharacteristic, complemented
151C2×#101—591no—
152C59#306911yescharacteristic, complemented, Sylow
153C2×#41—591no—
154C2×#41C2×D5911yescharacteristic
155C22×Q8—591no—
156#137—592no—
157#137—594no—
158#137—1182no—
159#137—1182no—
160#137—1182no—
161#137—1181no—
162AGL(1,ℤ/8)—592no—
163AGL(1,ℤ/8)—1181no—
164#135—1182no—
165C2×Q16—592no—
166C2×Q16—1181no—
167C2×SD16—592no—
168C2×SD16—1181no—
169#131—594no—
170#131—1182no—
171C2×M16—591no—
172C2×M16—591no—
173C2×M16—1182no—
174C2×M16C2×D5911yescharacteristic
175C2×M16C2×D5911yescharacteristic
176#108—594no—
177#101—594no—
178#101C2×D5912yescomplemented
179#100C2×D5912yescomplemented
180#41—21no—
181#41—21no—
182#41—21no—
183#41—21no—
184#41—592no—
185#41—592no—
186#41—1181no—
187#41—1181no—
188C2×Q8—591no—
189C2×Q8—592no—
190C2×Q8—1181no—
191C2×Q8—1181no—
192C2×Q8—1181no—
193C2×Q8—1181no—
194C2×Q8—1181no—
195C2×Q8C22×D5911yescharacteristic
196C2×D4—21no—
197C2×D4—591no—
198C2×D4—1181no—
199C2×D4C22×D5911yescharacteristic
200C22×C4—21no—
201C22×C4—1181no—
202C22×C4—1181no—
203C22×C4C22×D5911yescharacteristic
204Q16—1184no—
205Q16—1184no—
206Q16—1182no—
207SD16—1184no—
208SD16—1184no—
209SD16—1182no—
210SD16—1182no—
211D8—1182no—
212M16—21no—
213M16—21no—
214M16—592no—
215M16—592no—
216M16—592no—
217M16—1184no—
218M16—1181no—
219M16C22×D5912yes—
220M16C22×D5912yes—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—592no—
224C2×C8—1184no—
225C2×C8—1181no—
226C23—21no—
227C23—1181no—
228C23#1174568511yescharacteristic
229Q8—21no—
230Q8—21no—
231Q8—592no—
232Q8—1181no—
233Q8—1182no—
234Q8—1182no—
235Q8—2361no—
236Q8—2361no—
237D4—21no—
238D4—21no—
239D4—41no—
240D4—41no—
241D4—592no—
242D4—1182no—
243D4—1182no—
244D4—1181no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—1181no—
249C2×C4—1182no—
250C2×C4—1182no—
251C2×C4—1182no—
252C2×C4—2361no—
253C2×C4—2361no—
254C2×C4#1174568511yescharacteristic
255C2×C4D4×D5911yescharacteristic
256C2×C4D4×D5911yescharacteristic
257C2×C4D4×D5911yescharacteristic
258C2×C4D4×D5911yescharacteristic
259C2×C4C23×D5911yescharacteristic
260C8—22no—
261C8—22no—
262C8—594no—
263C8—1182no—
264C22—41no—
265C22—41no—
266C22—81no—
267C22—1182no—
268C22—4721no—
269C22#1427370011yescharacteristic
270C22#1427370011yescharacteristic
271C22C2×#1174568511yescharacteristic
272C4—41no—
273C4—1182no—
274C4—2362no—
275C4#1427370011yescharacteristic
276C4#1427370011yescharacteristic
277C4C2×D4×D5911yescharacteristic
278C4C2×D4×D5911yescharacteristic
279C2—21no—
280C2—21no—
281C2—21no—
282C2—81no—
283C2—2362no—
284C2C2×#1427370011yescharacteristic
subgroupG/H
centerC2C2×#14273700
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#413C2
socleC2×C59C2×#121
hypercenter#413D59
hypocenterC59#3069
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C2×#14273760C2semidirect
3. C2×#14273757C2semidirect
4. #16838168C2semidirect
5. #16837676C2semidirect
6. #16837664C2semidirect
7. #16837450C2semidirect
8. C2×#14273645C2semidirect
9. C59×#413C2semidirect
22. C2×#11745672C22semidirect
24. C2×#11745670C22semidirect
30. #14273662C22semidirect
31. #14273645C22semidirect
35. #101×C59C22semidirect
36. #100×C59C22semidirect
150. #413D59semidirect
152. C59#3069semidirect
178. #101C2×D59semidirect
179. #100C2×D59semidirect