Finite Group Databasebeta

← #20254795

Subgroups — #20254795

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689738C211yesmaximal, characteristic, complemented
2#15689727C211yesmaximal, characteristic, complemented
3#15689431C211yesmaximal, characteristic, complemented
4#15689423C211yesmaximal, characteristic, complemented
5#15689411C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689368C211yesmaximal, characteristic, complemented
9#15689356C211yesmaximal, characteristic, complemented
10#15689351C211yesmaximal, characteristic, complemented
11#15689336C211yesmaximal, characteristic, complemented
12#15689336C211yesmaximal, characteristic, complemented
13#15689320C211yesmaximal, characteristic, complemented
14#15689148C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×#10625335C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094017—21no—
22#13094016C2211yescharacteristic
23#13094011C2211yescharacteristic
24#13094010—21no—
25#13094007—21no—
26#13094005—21no—
27#13094005—21no—
28#13094004C2211yescharacteristic
29#13094003—21no—
30#13093996—21no—
31#13093996—21no—
32#13093995C2211yescharacteristic
33#13093995C2211yescharacteristic
34#13093995C2211yescharacteristic
35C4×Dic94C2211yescharacteristic
36D4×Dic47C2211yescharacteristic
37D4×Dic47C2211yescharacteristic
38#13093981C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093945C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54#127×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73D8×C47—41no—
74D8×C47—41no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C42×C47C2311yescharacteristic
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625335—41no—
88#10625335—41no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4D411yescharacteristic
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—41no—
107C8×D47—41no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C22×D47C2×D411yescharacteristic
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119D4×C47—81no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—81no—
126C22⋊D47—81no—
127C22⋊D47—81no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C4×D47—21no—
138C4×D47—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—81no—
142C8×C47—21no—
143C8×C47—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47H(5,𝔽2)11yescharacteristic
163C4×C472−1+411yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3257—471nomaximal, Sylow
172C2×C47—81no—
173C2×C47—81no—
174C2×C47—81no—
175C2×C47#53711yescharacteristic
176C2×C47#57611yescharacteristic
177C2×C47#57711yescharacteristic
178D47—41no—
179#542—471no—
180#540—471no—
181#479—471no—
182#478—471no—
183#476—471no—
184#474—471no—
185#469—471no—
186#468—471no—
187#466—471no—
188#465—471no—
189#463—471no—
190#463—471no—
191#460—471no—
192#459D4711yescharacteristic, complemented
193#424—471no—
194C47#325711yescharacteristic, complemented, Sylow
195C2×SD16—471no—
196C2×SD16—471no—
197C2×D8C2×D4711yescharacteristic
198C2×D8C2×D4711yescharacteristic
199C2×M16—471no—
200C22×C8—471no—
201C4⋊Q8—471no—
202#127C2×D4711yescharacteristic
203#126—941no—
204#125—471no—
205#124—471no—
206#124—941no—
207#123—941no—
208#123—941no—
209#123—941no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—471no—
214#121—471no—
215#121—941no—
216#121—941no—
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4C2×D4711yescharacteristic
221#117—471no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229C4⋊C8C2×D4711yescharacteristic
230#103—471no—
231#103—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237#102C2×D4711yescharacteristic
238C2×Q8—471no—
239C2×Q8—941no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C2×D4C22×D4711yescharacteristic
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—471no—
250C22×C4—941no—
251C22×C4—941no—
252SD16—1881no—
253SD16—1881no—
254D8—41no—
255D8—41no—
256M16—1881no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—1881no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4C22×D4711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—471no—
275C22⋊C4—471no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—471no—
285C42—941no—
286C42C22×D4711yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—471no—
291Q8—941no—
292Q8—941no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—21no—
323C8—941no—
324C8—941no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—941no—
335C22—941no—
336C22—941no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—941no—
342C4—941no—
343C4—941no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4#1309406911yescharacteristic
349C4#1309407111yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—1881no—
354C2#1568970211yescharacteristic
355C2#1568992411yescharacteristic
356C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3257
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689738C2semidirect
2. #15689727C2semidirect
3. #15689431C2semidirect
4. #15689423C2semidirect
5. #15689411C2semidirect
6. #15689401C2semidirect
7. #15689373C2semidirect
8. #15689368C2semidirect
9. #15689356C2semidirect
10. #15689351C2semidirect
11. #15689336C2semidirect
12. #15689336C2semidirect
13. #15689320C2semidirect
14. #15689148C2semidirect
15. C47×#459C2semidirect
192. #459D47semidirect
194. C47#3257semidirect