Finite Group Databasebeta

← #20252210

Subgroups — #20252210

Order 6016.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094053C211yesmaximal, characteristic
2C4×#10625352C211yesmaximal, characteristic
3C4×Q8×D47C211yesmaximal, characteristic, complemented
4#15689231C211yesmaximal, characteristic, complemented
5#15689228C211yesmaximal, characteristic, complemented
6#15689223C211yesmaximal, characteristic, complemented
7#15689217C211yesmaximal, characteristic, complemented
8#15689215C211yesmaximal, characteristic, complemented
9#15689214C211yesmaximal, characteristic, complemented
10SD16×Dic47C211yesmaximal, characteristic, complemented
11#15689164C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic
14#15689075C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094053C418yescomplemented
19C2×Dic188C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×#10625324C2211yescharacteristic
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#13093982C2211yescharacteristic
35#13093980—21no—
36C4⋊C4×D47—21no—
37C4⋊C4×D47C2211yescharacteristic
38C2×C4×Dic47—21no—
39C42×D47—21no—
40C42×D47C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093935C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
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×D47D411yescharacteristic
73C2×C4×D47D411yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78SD16×C47C2×C414yescomplemented
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625337C2×C414yescomplemented
89#10625335C2×C414yescomplemented
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47D411yescharacteristic
106C4×Dic47D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110Dic188C2×C414yescomplemented
111#10625324—22no—
112#10625324C2×C414yescomplemented
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—42no—
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—42no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C4×D47—24no—
137C4×D47—22no—
138C4×D47—41no—
139C4×D47—42no—
140C4×D47C22×C412yes—
141C4×D47#4112yes—
142Dic94—21no—
143Dic94—21no—
144Dic94—24no—
145Dic94C22×C412yes—
146Dic94C22×C412yes—
147C8×C47—21no—
148C8×C47C22×C412yes—
149C47⋊C8—21no—
150C47⋊C8C22×C412yes—
151C22×C47—22no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47C4×D412yes—
158C4×C47—22no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C23×C411yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—22no—
166Dic47—22no—
167Dic47—21no—
168Dic47—41no—
169Dic47—41no—
170Dic47C4×D412yes—
171Dic47#13712yescomplemented
172C4×#137—471nomaximal, Sylow
173C2×C47—42no—
174C2×C47C2×C4×D411yescharacteristic
175C2×C47C2×#13711yescharacteristic
176C2×C47#57511yescharacteristic
177D47—22no—
178C2×#137—471no—
179C4×#41—471no—
180C2×C4×Q8—471no—
181#441—471no—
182#441—471no—
183#440—471no—
184#440D4711yescharacteristic, complemented
185C4×Q16—471no—
186C4×Q16—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189#428—471no—
190#419—471no—
191#417—471no—
192C4×M16—471no—
193C47C4×#13711yescharacteristic, complemented, Sylow
194C2×#41—471no—
195C22×Q8—471no—
196#137—478no—
197C2×Q16—471no—
198C2×Q16—471no—
199C2×SD16—471no—
200C2×SD16C2×D4711yescharacteristic
201C2×M16—471no—
202C2×M16—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×Q8—941no—
209C4×Q8—941no—
210C4×Q8C2×D4711yescharacteristic
211C4×D4—471no—
212C4×D4—941no—
213C4×D4—941no—
214C4×D4C2×D4711yescharacteristic
215#117—471no—
216#117—941no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—941no—
219C2×C42—471no—
220C2×C42—941no—
221C2×C42—941no—
222#107—471no—
223#107C2×D4711yescharacteristic
224#106—471no—
225#106—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103C2×D4711yescharacteristic
232#102—471no—
233#102C2×D4711yescharacteristic
234#97—471no—
235#97C2×D4711yescharacteristic
236C4×C8—471no—
237C4×C8—471no—
238#41—474no—
239#41—942no—
240C2×Q8—474no—
241C2×Q8—471no—
242C2×Q8—471no—
243C2×Q8—941no—
244C2×Q8—942no—
245C2×Q8C22×D4711yescharacteristic
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256Q16—474no—
257Q16—474no—
258SD16—474no—
259SD16C4×D4714yescomplemented
260M16—474no—
261M16—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—21no—
281C42—471no—
282C42—471no—
283C42—471no—
284C42—941no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42—941no—
289C42—941no—
290C42C22×D4711yescharacteristic
291C23—21no—
292C23—471no—
293Q8—21no—
294Q8—472no—
295Q8—472no—
296Q8—944no—
297Q8—941no—
298Q8—941no—
299Q8C2×C4×D4712yes—
300D4—21no—
301D4—944no—
302D4C2×C4×D4712yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—471no—
312C2×C4—942no—
313C2×C4—944no—
314C2×C4—944no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—1881no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4D4×D4711yescharacteristic
323C2×C4D4×D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—21no—
326C8—472no—
327C8—941no—
328C8C2×C4×D4712yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—472no—
333C22—941no—
334C22—941no—
335C22C2×D4×D4711yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—472no—
342C4—472no—
343C4—942no—
344C4—942no—
345C4—941no—
346C4—1881no—
347C4—1881no—
348C4C22×C4×D4711yescharacteristic
349C4#41×D4711yescharacteristic
350C2—42no—
351C2—942no—
352C2C4×D4×D4711yescharacteristic
353C2#137×D4711yescharacteristic
354C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47C4×#137
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. C4×Q8×D47C2semidirect
4. #15689231C2semidirect
5. #15689228C2semidirect
6. #15689223C2semidirect
7. #15689217C2semidirect
8. #15689215C2semidirect
9. #15689214C2semidirect
10. SD16×Dic47C2semidirect
11. #15689164C2semidirect
12. #15689130C2semidirect
14. #15689075C2semidirect
15. C47×#440C2semidirect
18. #13094053C4semidirect
67. Q8×D47C2×C4semidirect
78. SD16×C47C2×C4semidirect
88. #10625337C2×C4semidirect
89. #10625335C2×C4semidirect
110. Dic188C2×C4semidirect
112. #10625324C2×C4semidirect
171. Dic47#137semidirect
184. #440D47semidirect
193. C47C4×#137semidirect
259. SD16C4×D47semidirect