Finite Group Databasebeta

← #20253619

Subgroups — #20253619

Order 6016.

370 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#15689744C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic
5#15689419C211yesmaximal, characteristic, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689281C211yesmaximal, characteristic, complemented
10#15689264C211yesmaximal, characteristic
11#15689231C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13C4×Dic188C211yesmaximal, characteristic, complemented
14C4×#10625325C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×Dic188C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094019—21no—
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094006—21no—
26#13094003C2211yescharacteristic
27#13094002—21no—
28#13093998C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×Dic94C2211yescharacteristic
34#13093989—21no—
35#13093989—21no—
36C4×D188C2211yescharacteristic
37#13093983C2211yescharacteristic
38#13093980—21no—
39#13093980—21no—
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C22×Dic47—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×Dic94—21no—
65C2×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C22⋊C4×C47D411yescharacteristic
78C22⋊C4×C47D411yescharacteristic
79C42×C47C2311yescharacteristic
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104Dic188—22no—
105Dic188—22no—
106#10625325—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—81no—
119C2×Dic47—24no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127D188—21no—
128D188—21no—
129C4×D47—81no—
130Dic94—24no—
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136Dic94#4112yes—
137Dic94#4112yes—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47—21no—
141C8×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47C22×D411yescharacteristic
146C2×D47—41no—
147C2×D47—41no—
148C2×D47—41no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47C2×#4111yescharacteristic
155C4×C47C2×#4111yescharacteristic
156Dic47—22no—
157Dic47—22no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3121—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47#52511yescharacteristic
166C2×C47#57711yescharacteristic
167C2×C47#57811yescharacteristic
168D47—81no—
169#542—471no—
170#519—471no—
171#485—471no—
172#482—471no—
173#477—471no—
174#475—471no—
175#464—471no—
176#464—471no—
177#451—471no—
178#448—471no—
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433D4711yescharacteristic, complemented
184C47#312111yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C2×Q16—471no—
187C2×Q16—471no—
188C2×SD16—471no—
189C2×SD16—471no—
190C4⋊Q8—471no—
191#126—941no—
192#124—471no—
193#124—941no—
194#123—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197#121—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×Q8—941no—
204C4×Q8—941no—
205C4×D4—471no—
206#117—471no—
207#117—941no—
208#117—941no—
209#117C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8C2×D4711yescharacteristic
215C4⋊C8C2×D4711yescharacteristic
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#102—471no—
223#102—471no—
224C22⋊C8C2×D4711yescharacteristic
225C22⋊C8C2×D4711yescharacteristic
226#97C2×D4711yescharacteristic
227C4×C8C2×D4711yescharacteristic
228C2×Q8—471no—
229C2×Q8—471no—
230C2×Q8—471no—
231C2×Q8—942no—
232C2×Q8—942no—
233C2×Q8—941no—
234C2×Q8—941no—
235C2×D4—471no—
236C2×D4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240Q16—942no—
241Q16—942no—
242SD16—942no—
243SD16—942no—
244C2×C8C22×D4711yescharacteristic
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4D18811yescharacteristic
260C4⋊C4D18811yescharacteristic
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4D18811yescharacteristic
268C22⋊C4D18811yescharacteristic
269C42—941no—
270C42—941no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42C22×D4711yescharacteristic
276C42C22×D4711yescharacteristic
277C23—941no—
278C23C2×D18811yescharacteristic
279Q8—472no—
280Q8—472no—
281Q8—944no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285Q8—941no—
286Q8—3761no—
287D4—941no—
288D4—941no—
289D4—3761no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—944no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—3761no—
301C2×C4C2×D18811yescharacteristic
302C2×C4C2×D18811yescharacteristic
303C2×C4C2×D18811yescharacteristic
304C2×C4C2×D18811yescharacteristic
305C2×C4C2×D18811yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—1881no—
315C22—1881no—
316C22—1881no—
317C22C22×D18811yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—942no—
324C4—942no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4#41×D4711yescharacteristic
332C2—41no—
333C2—3761no—
334C2#1568963511yescharacteristic
335C2#1568993511yescharacteristic
336C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
3. #15689465C2semidirect
5. #15689419C2semidirect
6. #15689409C2semidirect
7. #15689346C2semidirect
8. #15689346C2semidirect
9. #15689281C2semidirect
11. #15689231C2semidirect
12. #15689225C2semidirect
13. C4×Dic188C2semidirect
14. C4×#10625325C2semidirect
15. C47×#433C2semidirect
183. #433D47semidirect
184. C47#3121semidirect