Finite Group Databasebeta

← #20252228

Subgroups — #20252228

Order 6016.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094053C211yesmaximal, characteristic
2#15689602C211yesmaximal, characteristic
3#15689599C211yesmaximal, characteristic, complemented
4#15689231C211yesmaximal, characteristic, complemented
5#15689227C211yesmaximal, characteristic, complemented
6#15689220C211yesmaximal, characteristic, complemented
7#15689217C211yesmaximal, characteristic, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9SD16×Dic47C211yesmaximal, characteristic, complemented
10C4×#10625335C211yesmaximal, characteristic, complemented
11#15689164C211yesmaximal, characteristic, complemented
12#15689116C211yesmaximal, characteristic
13#103×D47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094053C418yescomplemented
19C2×Dic188C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25C4×Dic94—21no—
26C4×Dic94C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28#13093989—21no—
29#13093989C2211yescharacteristic
30#13093989C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982—21no—
35#13093982C2211yescharacteristic
36#13093981—21no—
37#13093981C2211yescharacteristic
38#13093980—21no—
39C2×Dic47⋊C4—21no—
40C4⋊C4×D47C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093934C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C8×Dic47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59#97×C47C2211yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66Q8×D47—22no—
67Q8×D47C2×C414yescomplemented
68#10625352—22no—
69#10625352C2×C414yes—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47C2311yescharacteristic
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76SD16×C47C2×C414yescomplemented
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86#10625337C2×C414yescomplemented
87#10625335C2×C414yescomplemented
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110Dic188C2×C414yescomplemented
111#10625324C2×C414yescomplemented
112C8×D47—22no—
113C23×C47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47C22×C412yes—
117D4×C47—21no—
118D4×C47C22×C412yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—81no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—24no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—24no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—81no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C4×D47—24no—
137C4×D47—81no—
138C4×D47C22×C412yes—
139C4×D47#4112yes—
140Dic94—21no—
141Dic94—21no—
142Dic94—24no—
143Dic94C22×C412yes—
144Dic94C22×C412yes—
145C8×C47—21no—
146C8×C47C22×C412yes—
147C47⋊C8—21no—
148C47⋊C8C22×C412yes—
149C22×C47—22no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47C22×D411yescharacteristic
153C2×D47—21no—
154C2×D47—21no—
155C2×D47C4×D412yes—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C23×C411yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—22no—
164Dic47—22no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47C4×D412yes—
170#2947—471nomaximal, Sylow
171C2×C47—42no—
172C2×C47C2×C4×D411yescharacteristic
173C2×C47#57711yescharacteristic
174C2×C47#57811yescharacteristic
175D47—22no—
176C2×#137—471no—
177#520—471no—
178#519—471no—
179#441—471no—
180#441—471no—
181#440—471no—
182#440D4711yescharacteristic, complemented
183C4×Q16—471no—
184C4×Q16—471no—
185C4×SD16—471no—
186C4×SD16—471no—
187#428—471no—
188#416—471no—
189C2×#103—471no—
190#405—471no—
191C47#294711yescharacteristic, complemented, Sylow
192C2×#41—471no—
193C22×Q8—471no—
194#137—478no—
195C2×Q16—471no—
196C2×Q16—471no—
197C2×SD16—471no—
198C2×SD16C2×D4711yescharacteristic
199C2×M16—471no—
200C22×C8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—941no—
207C4×Q8—941no—
208C4×Q8C2×D4711yescharacteristic
209C4×D4—471no—
210C4×D4—941no—
211C4×D4—941no—
212C4×D4C2×D4711yescharacteristic
213#117—471no—
214#117—471no—
215#117—941no—
216#117—941no—
217#117—941no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—941no—
220#107—471no—
221#107C2×D4711yescharacteristic
222#106—471no—
223#106—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103C2×D4711yescharacteristic
230#102—471no—
231#102C2×D4711yescharacteristic
232#97—471no—
233#97C2×D4711yescharacteristic
234C4×C8—471no—
235C4×C8—471no—
236#41—474no—
237#41—942no—
238C2×Q8—474no—
239C2×Q8—471no—
240C2×Q8—471no—
241C2×Q8—941no—
242C2×Q8—942no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C22×C4—21no—
247C22×C4—471no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252Q16—474no—
253Q16—474no—
254SD16—474no—
255SD16C4×D4714yescomplemented
256M16—474no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—942no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—471no—
277C22⋊C4—471no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—21no—
281C42—471no—
282C42—941no—
283C42—941no—
284C42—941no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C23—21no—
290C23—471no—
291Q8—21no—
292Q8—472no—
293Q8—472no—
294Q8—944no—
295Q8—941no—
296Q8—941no—
297Q8C2×C4×D4712yes—
298D4—21no—
299D4—944no—
300D4C2×C4×D4712yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—471no—
306C2×C4—472no—
307C2×C4—472no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—944no—
311C2×C4—944no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—472no—
323C8—941no—
324C8C2×C4×D4712yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—472no—
329C22—941no—
330C22—941no—
331C22C2×D4×D4711yescharacteristic
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—472no—
338C4—942no—
339C4—942no—
340C4—941no—
341C4—941no—
342C4—1881no—
343C4—1881no—
344C4C22×C4×D4711yescharacteristic
345C4#41×D4711yescharacteristic
346C2—42no—
347C2—942no—
348C2C4×D4×D4711yescharacteristic
349C2#1568993311yescharacteristic
350C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#2947
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #15689599C2semidirect
4. #15689231C2semidirect
5. #15689227C2semidirect
6. #15689220C2semidirect
7. #15689217C2semidirect
8. C4×#10625337C2semidirect
9. SD16×Dic47C2semidirect
10. C4×#10625335C2semidirect
11. #15689164C2semidirect
13. #103×D47C2semidirect
14. #15689080C2semidirect
15. C47×#440C2semidirect
18. #13094053C4semidirect
67. Q8×D47C2×C4semidirect
76. SD16×C47C2×C4semidirect
86. #10625337C2×C4semidirect
87. #10625335C2×C4semidirect
110. Dic188C2×C4semidirect
111. #10625324C2×C4semidirect
182. #440D47semidirect
191. C47#2947semidirect
255. SD16C4×D47semidirect