Finite Group Databasebeta

← #20254812

Subgroups — #20254812

Order 6016.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689745C211yesmaximal, characteristic
2#15689734C211yesmaximal, characteristic, complemented
3#15689430C211yesmaximal, characteristic, complemented
4#15689424C211yesmaximal, characteristic, complemented
5#15689416C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689378C211yesmaximal, characteristic, complemented
8#15689372C211yesmaximal, characteristic
9#15689361C211yesmaximal, characteristic, complemented
10#15689355C211yesmaximal, characteristic
11#15689347C211yesmaximal, characteristic, complemented
12#15689347C211yesmaximal, characteristic, complemented
13#15689325C211yesmaximal, characteristic, complemented
14#15689148C211yesmaximal, characteristic, complemented
15C47×#462C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094019—21no—
22#13094019—21no—
23#13094018—21no—
24#13094016C2211yescharacteristic
25#13094014—21no—
26#13094014—21no—
27#13094013C2211yescharacteristic
28#13094012—21no—
29#13094009—21no—
30#13094002—21no—
31#13094000C2211yescharacteristic
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34#13093999C2211yescharacteristic
35Q8×Dic47C2211yescharacteristic
36Q8×Dic47C2211yescharacteristic
37C4×D188C2211yescharacteristic
38#13093981C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093948C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67Q16×C47—41no—
68Q16×C47—41no—
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C42×C47—21no—
76C42×C47C2311yescharacteristic
77#10625336—41no—
78#10625336—41no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
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×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—41no—
107C8×D47—41no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—21no—
130D188—21no—
131D188—81no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—81no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47C22×D411yescharacteristic
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47H(5,𝔽2)11yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3258—471nomaximal, Sylow
162C2×C47#53711yescharacteristic
163C2×C47#57711yescharacteristic
164C2×C47#57811yescharacteristic
165D47—41no—
166D47—81no—
167#542—471no—
168#541—471no—
169#479—471no—
170#478—471no—
171#477—471no—
172#475—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#464—471no—
178#464—471no—
179#462D4711yescharacteristic, complemented
180#461—471no—
181#424—471no—
182C47#325811yescharacteristic, complemented, Sylow
183C2×Q16C2×D4711yescharacteristic
184C2×Q16C2×D4711yescharacteristic
185C2×SD16—471no—
186C2×SD16—471no—
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8C2×D4711yescharacteristic
191#126—941no—
192#126—941no—
193#126—941no—
194#125—471no—
195#125—941no—
196#125—941no—
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—941no—
204#121—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8C2×D4711yescharacteristic
208C4×D4—471no—
209#117—471no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8—471no—
217C4⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226C2×Q8—941no—
227C2×Q8C22×D4711yescharacteristic
228C2×Q8C22×D4711yescharacteristic
229C2×Q8C22×D4711yescharacteristic
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—941no—
234Q16—41no—
235Q16—41no—
236SD16—1881no—
237SD16—1881no—
238M16—1881no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—1881no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—471no—
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⋊C4—941no—
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—471no—
262C22⋊C4—471no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—471no—
272C42—941no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—471no—
276C23—941no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—3761no—
284D4—941no—
285D4—941no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—21no—
304C8—21no—
305C8—941no—
306C8—941no—
307C22—941no—
308C22—941no—
309C22—941no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C2×D4×D4711yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—941no—
321C4—941no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#1309406911yescharacteristic
327C4#1309407111yescharacteristic
328C2—3761no—
329C2—1881no—
330C2#1568970211yescharacteristic
331C2#1568993211yescharacteristic
332C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#462C2
socleC22×C47C22×D4
hypercenter#462D47
hypocenterC47#3258
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #15689734C2semidirect
3. #15689430C2semidirect
4. #15689424C2semidirect
5. #15689416C2semidirect
6. #15689406C2semidirect
7. #15689378C2semidirect
9. #15689361C2semidirect
11. #15689347C2semidirect
12. #15689347C2semidirect
13. #15689325C2semidirect
14. #15689148C2semidirect
15. C47×#462C2semidirect
179. #462D47semidirect
182. C47#3258semidirect