Finite Group Databasebeta

← #20254831

Subgroups — #20254831

Order 6016.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689734C211yesmaximal, characteristic, complemented
2#15689724C211yesmaximal, characteristic
3#15689432C211yesmaximal, characteristic, complemented
4#15689428C211yesmaximal, characteristic, complemented
5#15689424C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689372C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689355C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689325C211yesmaximal, characteristic, complemented
12#15689321C211yesmaximal, characteristic, complemented
13#15689321C211yesmaximal, characteristic, complemented
14#15689148C211yesmaximal, characteristic, complemented
15C47×#461C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094020C2211yescharacteristic
21#13094019—21no—
22#13094019—21no—
23#13094016C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094014—21no—
27#13094007—21no—
28#13094006—21no—
29#13094000C2211yescharacteristic
30#13094000C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093997—21no—
34#13093995C2211yescharacteristic
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#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093945C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70SD16×C47—41no—
71SD16×C47—41no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80#10625336—41no—
81#10625336—41no—
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⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
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—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—81no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—81no—
125C22⋊D47—81no—
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188—21no—
135D188—81no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—81no—
139C8×C47—21no—
140C8×C47—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47H(5,𝔽2)11yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3260—471nomaximal, Sylow
167C2×C47—81no—
168C2×C47#53711yescharacteristic
169C2×C47#57711yescharacteristic
170C2×C47#57711yescharacteristic
171D47—41no—
172D47—81no—
173#541—471no—
174#540—471no—
175#479—471no—
176#479—471no—
177#478—471no—
178#478—471no—
179#468—471no—
180#468—471no—
181#465—471no—
182#465—471no—
183#461—471no—
184#461D4711yescharacteristic, complemented
185#460—471no—
186#460—471no—
187#424—471no—
188C47#326011yescharacteristic, complemented, Sylow
189C2×SD16—471no—
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192C2×SD16C2×D4711yescharacteristic
193C2×M16—471no—
194C22×C8—471no—
195C4⋊Q8C2×D4711yescharacteristic
196#127—471no—
197#126—941no—
198#126—941no—
199#125—471no—
200#125—471no—
201#125—941no—
202#125—941no—
203#123—941no—
204#123—941no—
205C22⋊Q8—471no—
206C22⋊Q8—471no—
207#121—471no—
208#121—471no—
209#121—941no—
210#121—941no—
211C4×Q8—471no—
212C4×Q8—471no—
213C4×D4—471no—
214C4×D4C2×D4711yescharacteristic
215#117—471no—
216#107—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8C2×D4711yescharacteristic
224#103—471no—
225#103—471no—
226#103C2×D4711yescharacteristic
227#103C2×D4711yescharacteristic
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232C2×Q8C22×D4711yescharacteristic
233C2×Q8C22×D4711yescharacteristic
234C2×D4—471no—
235C2×D4—941no—
236C2×D4—941no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—21no—
241C22×C4—471no—
242C22×C4—941no—
243SD16—41no—
244SD16—41no—
245SD16—1881no—
246SD16—1881no—
247M16—1881no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8—1881no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—471no—
271C22⋊C4—471no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—471no—
278C42—941no—
279C42—941no—
280C42C22×D4711yescharacteristic
281C23—21no—
282C23—471no—
283C23—941no—
284Q8—21no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288D4—21no—
289D4—21no—
290D4—941no—
291D4—941no—
292D4—3761no—
293D4—3761no—
294D4—3761no—
295D4—3761no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—3761no—
309C2×C4D4×D4711yescharacteristic
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—21no—
314C8—941no—
315C8—941no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—941no—
320C22—941no—
321C22—941no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—941no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4#1309406911yescharacteristic
338C4#1309407111yescharacteristic
339C2—81no—
340C2—3761no—
341C2—1881no—
342C2#1568970211yescharacteristic
343C2#1568992911yescharacteristic
344C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3260
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689734C2semidirect
3. #15689432C2semidirect
4. #15689428C2semidirect
5. #15689424C2semidirect
6. #15689423C2semidirect
7. #15689372C2semidirect
8. #15689366C2semidirect
9. #15689355C2semidirect
10. #15689349C2semidirect
11. #15689325C2semidirect
12. #15689321C2semidirect
13. #15689321C2semidirect
14. #15689148C2semidirect
15. C47×#461C2semidirect
184. #461D47semidirect
188. C47#3260semidirect