Finite Group Databasebeta

← #20255822

Subgroups — #20255822

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689813C211yesmaximal, characteristic, complemented
2#15689529C211yesmaximal, characteristic, complemented
3#15689458C211yesmaximal, characteristic, complemented
4#15689453C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689434C211yesmaximal, characteristic, complemented
7#15689423C211yesmaximal, characteristic, complemented
8#15689415C211yesmaximal, characteristic, complemented
9#15689367C211yesmaximal, characteristic, complemented
10#15689350C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689163C211yesmaximal, characteristic, complemented
14C2×#13093957C211yesmaximal, characteristic, complemented
15C47×#547C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094014—21no—
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093983C2211yescharacteristic
27#13093980—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093957C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47—21no—
49C4⋊Q8×C47C2211yescharacteristic
50#123×C47—21no—
51#123×C47—21no—
52C22⋊Q8×C47—21no—
53#121×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—44no—
60C2×Q8×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47D411yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×Dic47—21no—
71C2×Dic94C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88#10625335—22no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100#10625329—22no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C23×C47C2×D411yescharacteristic
109Q8×C47—42no—
110D4×C47—22no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114D4×C47—42no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135Dic94—21no—
136Dic94—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C47⋊C8#4112yescomplemented
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47AGL(1,ℤ/8)12yes—
150C22×C47C22×D411yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3343—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—41no—
167C2×C47—81no—
168C2×C47#54711yescharacteristic
169C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C47#57811yescharacteristic
171#552—471no—
172#547D4711yescharacteristic
173#501—471no—
174#484—471no—
175#483—471no—
176#482—471no—
177#480—471no—
178#478—471no—
179#477—471no—
180#468—471no—
181#465—471no—
182#440—471no—
183#435—471no—
184#428—471no—
185C2×#107—471no—
186C47#334311yescharacteristic, complemented, Sylow
187C2×#41—21no—
188C2×SD16—471no—
189C2×M16—471no—
190C22×C8—471no—
191C4⋊Q8C2×D4711yescharacteristic
192#126—941no—
193#125—471no—
194#125—941no—
195#123—21no—
196#123—21no—
197#123—941no—
198C22⋊Q8—21no—
199C22⋊Q8—471no—
200C22⋊Q8—471no—
201#121C2×D4711yescharacteristic
202#121C2×D4711yescharacteristic
203C4×Q8—471no—
204C4×D4C2×D4711yescharacteristic
205C4×D4C2×D4711yescharacteristic
206#117—471no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C4⋊C4C2×D4711yescharacteristic
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227C22⋊C8—471no—
228C22⋊C8—471no—
229#97—471no—
230#41—44no—
231C2×Q8—21no—
232C2×Q8—471no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊D4711yescharacteristic
236C2×D4C22×D4711yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—941no—
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243SD16—942no—
244M16—942no—
245C2×C8—471no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—942no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22⋊D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4C22⋊D4711yescharacteristic
273C22⋊C4C22⋊D4711yescharacteristic
274C42—941no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—21no—
278C23C2×C22⋊D4711yescharacteristic
279C23C2×C22⋊D4711yescharacteristic
280Q8—42no—
281Q8—941no—
282Q8—941no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—1882no—
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C2×C22⋊D4711yescharacteristic
306C2×C4C2×C22⋊D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—472no—
309C8—941no—
310C8—941no—
311C8—941no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1309405012yes—
321C22C22×C22⋊D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407111yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2#1568977211yescharacteristic
339C2C2×#1309405011yescharacteristic
340C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#547C2
socleC22×C47C22×D4
hypercenter#547D47
hypocenterC47#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
2. #15689529C2semidirect
3. #15689458C2semidirect
4. #15689453C2semidirect
5. #15689444C2semidirect
6. #15689434C2semidirect
7. #15689423C2semidirect
8. #15689415C2semidirect
9. #15689367C2semidirect
10. #15689350C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689163C2semidirect
14. C2×#13093957C2semidirect
140. C47⋊C8#41semidirect
186. C47#3343semidirect