Finite Group Databasebeta

← #20253234

Subgroups — #20253234

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689750C211yesmaximal, characteristic, complemented
2#15689602C211yesmaximal, characteristic
3#15689431C211yesmaximal, characteristic, complemented
4#15689429C211yesmaximal, characteristic, complemented
5#15689425C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689417C211yesmaximal, characteristic, complemented
8#15689415C211yesmaximal, characteristic, complemented
9#15689401C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic, complemented
11#107×D47C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic
14#15689116C211yesmaximal, characteristic
15C47×#474C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094022—21no—
21#13094016C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094002—21no—
25#13094000—21no—
26C4×Dic94C2211yescharacteristic
27#13093989C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29C4×C22⋊D47—21no—
30(C22⋊D47)⋊C4—21no—
31#13093982C2211yescharacteristic
32#13093981C2211yescharacteristic
33#13093980—21no—
34C2×Dic47⋊C4—21no—
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093947C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093945C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65#10625352—22no—
66#10625352Q814yescomplemented
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C42×C47C2311yescharacteristic
80C22⋊Dic47—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4D411yescharacteristic
83(C2×D47)⋊C4D411yescharacteristic
84C4⋊Dic47—21no—
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C8×D47—22no—
106C23×C47—21no—
107C22×D47C2×D411yescharacteristic
108Q8×C47—81no—
109D4×C47—21no—
110D4×C47C2×Q812yes—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—81no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—24no—
119C2×Dic47—21no—
120C2×Dic47—24no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C4×D47—81no—
129C4×D47—81no—
130C4×D47C2×Q812yes—
131C4×D47#4112yes—
132Dic94—21no—
133Dic94—81no—
134Dic94C2×Q812yes—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47—22no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47C22⋊Q812yes—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47C22×Q811yescharacteristic
152C4×C47C2×#4111yescharacteristic
153Dic47—22no—
154Dic47—21no—
155Dic47—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47C22⋊Q812yes—
160#3083—471nomaximal, Sylow
161C2×C47—42no—
162C2×C47C2×C22⋊Q811yescharacteristic
163C2×C47#57611yescharacteristic
164C2×C47#57811yescharacteristic
165D47—22no—
166#544—471no—
167#520—471no—
168#479—471no—
169#479—471no—
170#478—471no—
171#478—471no—
172#477—471no—
173#477—471no—
174#474—471no—
175#474D4711yescharacteristic, complemented
176#428—471no—
177C2×#107—471no—
178#424—471no—
179#417—471no—
180#416—471no—
181C47#308311yescharacteristic, complemented, Sylow
182C2×#41—471no—
183C2×M16—471no—
184C22×C8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—941no—
187C4⋊Q8C2×D4711yescharacteristic
188#125—471no—
189#125—471no—
190#125—941no—
191C22⋊Q8—941no—
192C22⋊Q8—941no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×D4—471no—
196C4×D4—941no—
197C4×D4—941no—
198C4×D4C2×D4711yescharacteristic
199#117—471no—
200#117—471no—
201#117—941no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—941no—
205#107—471no—
206#107—471no—
207#107—471no—
208#107—471no—
209#107C2×D4711yescharacteristic
210#107C2×D4711yescharacteristic
211#106—471no—
212#106—471no—
213C4⋊C8—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8C2×D4711yescharacteristic
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102C2×D4711yescharacteristic
224#102C2×D4711yescharacteristic
225#41—474no—
226#41—942no—
227C2×Q8—21no—
228C2×Q8—471no—
229C2×Q8—941no—
230C2×D4—941no—
231C2×D4C22×D4711yescharacteristic
232C22×C4—21no—
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C42—471no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42C22×D4711yescharacteristic
272C23—21no—
273C23—471no—
274Q8—81no—
275Q8—472no—
276Q8—941no—
277Q8—3761no—
278D4—21no—
279D4—944no—
280D4Q8×D4712yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—471no—
286C2×C4—472no—
287C2×C4—472no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—944no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4D4×D4711yescharacteristic
299C2×C4D4×D4711yescharacteristic
300C2×C4C23×D4711yescharacteristic
301C8—21no—
302C8—21no—
303C8—941no—
304C8—941no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—472no—
309C22—941no—
310C22—941no—
311C22C2×D4×D4711yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—472no—
318C4—942no—
319C4—941no—
320C4—941no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4C2×Q8×D4711yescharacteristic
325C4#41×D4711yescharacteristic
326C2—42no—
327C2—942no—
328C2C22⋊Q8×D4711yescharacteristic
329C2#1568992411yescharacteristic
330C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3083
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689750C2semidirect
3. #15689431C2semidirect
4. #15689429C2semidirect
5. #15689425C2semidirect
6. #15689423C2semidirect
7. #15689417C2semidirect
8. #15689415C2semidirect
9. #15689401C2semidirect
10. #15689164C2semidirect
11. #107×D47C2semidirect
12. #15689148C2semidirect
15. C47×#474C2semidirect
66. #10625352Q8semidirect
175. #474D47semidirect
181. C47#3083semidirect