Finite Group Databasebeta

← #20253600

Subgroups — #20253600

Order 6016.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689731C211yesmaximal, characteristic, complemented
2#15689605C211yesmaximal, characteristic
3#15689457C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689432C211yesmaximal, characteristic, complemented
6#15689422C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689327C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic
10#15689284C211yesmaximal, characteristic
11#15689225C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625336C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic, complemented
15C47×#441C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20#13094022C2211yescharacteristic
21#13094019—21no—
22#13094018—21no—
23#13094016—21no—
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094004C2211yescharacteristic
27#13094000C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30C4×D188—21no—
31C4×D188C2211yescharacteristic
32#13093986—21no—
33#13093986C2211yescharacteristic
34#13093981—21no—
35#13093981C2211yescharacteristic
36C4⋊C4×D47—21no—
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61#10625354—22no—
62#10625354—22no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71Q16×C47—22no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C42×C47—21no—
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81#10625337—22no—
82#10625336—22no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—24no—
128D188—21no—
129D188#4112yes—
130C4×D47—24no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—81no—
134C4×D47—81no—
135C4×D47—81no—
136Dic94—21no—
137Dic94—21no—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—22no—
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—41no—
148C2×D47—41no—
149C4×C47—22no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C47C2×#4111yescharacteristic
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3120—471nomaximal, Sylow
164C2×C47#52511yescharacteristic
165C2×C47#57711yescharacteristic
166C2×C47#57811yescharacteristic
167D47—41no—
168D47—42no—
169#541—471no—
170#520—471no—
171#484—471no—
172#483—471no—
173#479—471no—
174#478—471no—
175#462—471no—
176#461—471no—
177#452—471no—
178#452—471no—
179#441D4711yescharacteristic, complemented
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312011yescharacteristic, complemented, Sylow
185C2×#41—471no—
186C2×Q16—471no—
187C2×Q16C2×D4711yescharacteristic
188C2×SD16—471no—
189C2×SD16—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#125—471no—
194#125—941no—
195#125—941no—
196C22⋊Q8—471no—
197C22⋊Q8—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8C2×D4711yescharacteristic
201C4×Q8C2×D4711yescharacteristic
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205C4×D4—941no—
206#117—471no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106C2×D4711yescharacteristic
214C4⋊C8—471no—
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97C2×D4711yescharacteristic
227C4×C8—471no—
228#41—942no—
229#41—942no—
230C2×Q8—471no—
231C2×Q8C22×D4711yescharacteristic
232C2×Q8C22×D4711yescharacteristic
233C2×D4—471no—
234C2×D4—941no—
235C22×C4—471no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240Q16—22no—
241Q16—942no—
242SD16—942no—
243SD16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—471no—
266C22⋊C4—471no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C42—21no—
272C42—21no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—471no—
278C23—941no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—941no—
283Q8—941no—
284Q8#1062535012yes—
285D4—472no—
286D4—944no—
287D4—941no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—944no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—3761no—
302C2×C4—3761no—
303C2×C4—3761no—
304C2×C4D4×D4711yescharacteristic
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—942no—
312C22—941no—
313C22—941no—
314C22—941no—
315C22—1881no—
316C22—1881no—
317C22C2×D4×D4711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—941no—
325C4—941no—
326C4—941no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4C2×#1062535011yescharacteristic
332C2—1881no—
333C2—1882no—
334C2#1568963211yescharacteristic
335C2#1568993211yescharacteristic
336C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #15689731C2semidirect
3. #15689457C2semidirect
4. #15689455C2semidirect
5. #15689432C2semidirect
6. #15689422C2semidirect
7. #15689331C2semidirect
8. #15689327C2semidirect
11. #15689225C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625336C2semidirect
14. #15689185C2semidirect
15. C47×#441C2semidirect
179. #441D47semidirect
184. C47#3120semidirect