Finite Group Databasebeta

← #20255433

Subgroups — #20255433

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic94C211yesmaximal, characteristic
2#15689493C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689453C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689333C211yesmaximal, characteristic, complemented
9#15689278C211yesmaximal, characteristic, complemented
10#15689278C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic
13#15689131C211yesmaximal, characteristic, complemented
14C2×#13093947C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094024C2211yescharacteristic
24#13094023—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13094001—21no—
29C4×Dic94C2211yescharacteristic
30D4×Dic47—21no—
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47—21no—
50#125×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47D411yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×Dic47—21no—
65C22×Dic47—21no—
66C2×Dic94—22no—
67C2×Dic94—22no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94—41no—
71C2×Dic94—41no—
72C2×Dic94C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47D411yescharacteristic
89C22⋊C4×C47D411yescharacteristic
90C42×C47—21no—
91C42×C47—21no—
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95#10625337—22no—
96#10625337—41no—
97#10625337—41no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115D4×C47—22no—
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—21no—
123C2×C4×C47—21no—
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—
135C2×Dic47—42no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—42no—
142Dic94—42no—
143Dic94#4112yes—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47#13712yes—
154C22×C47C22×D411yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47H(5,𝔽2)11yescharacteristic
165Dic47—22no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3312—471nomaximal, Sylow
170C2×C47—22no—
171C2×C47—41no—
172C2×C47#54611yescharacteristic
173C2×C47C2×#13711yescharacteristic
174C2×C47#57811yescharacteristic
175#552D4711yescharacteristic
176D4×Q8—471no—
177#491—471no—
178#485—471no—
179#483—471no—
180#479—471no—
181#470—471no—
182#467—471no—
183#462—471no—
184#451—471no—
185#451—471no—
186#441—471no—
187#435—471no—
188#419—471no—
189C2×#103—471no—
190C47#331211yescharacteristic, complemented, Sylow
191C22×Q8—471no—
192C22×Q8—471no—
193C2×Q16—471no—
194C2×Q16—471no—
195C2×Q16—471no—
196C2×M16—471no—
197C22×C8—471no—
198C4⋊Q8—471no—
199C4⋊Q8—941no—
200#126—21no—
201#125—21no—
202#125C2×D4711yescharacteristic
203#123—21no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206C22⋊Q8—941no—
207C22⋊Q8—941no—
208C22⋊Q8C2×D4711yescharacteristic
209C22⋊Q8C2×D4711yescharacteristic
210C4×Q8—471no—
211C4×Q8C2×D4711yescharacteristic
212C4×D4—941no—
213C4×D4C2×D4711yescharacteristic
214#117—21no—
215#117C2×D4711yescharacteristic
216C2×C4⋊C4C2×D4711yescharacteristic
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231C22⋊C8—471no—
232C22⋊C8—471no—
233#97—471no—
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8—471no—
237C2×Q8—942no—
238C2×Q8—942no—
239C2×Q8—941no—
240C2×Q8—941no—
241C2×Q8—1881no—
242C2×Q8—1881no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4C22⋊D4711yescharacteristic
245C22×C4—21no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250Q16—942no—
251Q16—1881no—
252Q16—1881no—
253M16—1881no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8—471no—
258C2×C8—1881no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22⋊D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4C22⋊D4711yescharacteristic
281C22⋊C4C22⋊D4711yescharacteristic
282C42—21no—
283C42—21no—
284C42—941no—
285C42C22×D4711yescharacteristic
286C23C2×C22⋊D4711yescharacteristic
287C23C2×C22⋊D4711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—472no—
291Q8—941no—
292Q8—941no—
293Q8—941no—
294Q8—941no—
295Q8—941no—
296Q8—1882no—
297Q8—1882no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4C2×C22⋊D4711yescharacteristic
315C2×C4C2×C22⋊D4711yescharacteristic
316C2×C4C2×C22⋊D4711yescharacteristic
317C2×C4C2×C22⋊D4711yescharacteristic
318C2×C4C23×D4711yescharacteristic
319C8—941no—
320C8—941no—
321C8—941no—
322C8—941no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1309405412yes—
329C22C22×C22⋊D4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—942no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4#41×D4711yescharacteristic
343C4#1309407011yescharacteristic
344C2—22no—
345C2—41no—
346C2#1568976111yescharacteristic
347C2C2×#1309405411yescharacteristic
348C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689493C2semidirect
3. #15689464C2semidirect
4. #15689453C2semidirect
5. #15689427C2semidirect
6. #15689379C2semidirect
7. #15689362C2semidirect
8. #15689333C2semidirect
9. #15689278C2semidirect
10. #15689278C2semidirect
11. #15689228C2semidirect
13. #15689131C2semidirect
14. C2×#13093947C2semidirect
190. C47#3312semidirect