Finite Group Databasebeta

← #20255444

Subgroups — #20255444

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
1#15689814C211yesmaximal, characteristic
2Q8×D188C211yesmaximal, characteristic
3#15689492C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689455C211yesmaximal, characteristic, complemented
6#15689430C211yesmaximal, characteristic, complemented
7#15689380C211yesmaximal, characteristic, complemented
8#15689363C211yesmaximal, characteristic, complemented
9#15689333C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11#15689277C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic
13#15689130C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#441C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094024—21no—
23#13094024C2211yescharacteristic
24#13094018—21no—
25#13094016C2211yescharacteristic
26#13094014—21no—
27#13094009—21no—
28#13094004—21no—
29#13094004—21no—
30#13094004C2211yescharacteristic
31#13094004C2211yescharacteristic
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34C4×D188—21no—
35C4×D188C2211yescharacteristic
36#13093982C2211yescharacteristic
37#13093981—21no—
38C4⋊C4×D47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61Q8×D47—22no—
62Q8×D47—22no—
63Q8×D47—41no—
64Q8×D47—41no—
65C2×D188D411yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2311yescharacteristic
75Q16×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C42×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85#10625337—41no—
86#10625337—41no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4D411yescharacteristic
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625324—41no—
110C8×D47—41no—
111C22×D47C2×D411yescharacteristic
112C22×D47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47#4112yes—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—42no—
136C4×D47—42no—
137C4×D47—42no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—42no—
143Dic94—42no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47#13712yes—
155C4×C47—22no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47H(5,𝔽2)11yescharacteristic
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3312—471nomaximal, Sylow
170C2×C47#54611yescharacteristic
171C2×C47C2×#13711yescharacteristic
172C2×C47#57811yescharacteristic
173D47—22no—
174D47—41no—
175#552—471no—
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#441D4711yescharacteristic, complemented
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×Q16C2×D4711yescharacteristic
196C2×M16—471no—
197C22×C8—471no—
198C4⋊Q8—471no—
199C4⋊Q8—941no—
200#126—941no—
201#125—471no—
202#125—941no—
203#123—941no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206C22⋊Q8—471no—
207C22⋊Q8—471no—
208C22⋊Q8—941no—
209C22⋊Q8—941no—
210C4×Q8C2×D4711yescharacteristic
211C4×Q8C2×D4711yescharacteristic
212C4×D4—471no—
213C4×D4—941no—
214#117—471no—
215#117—941no—
216C2×C4⋊C4—471no—
217#107—471no—
218#106—471no—
219#106C2×D4711yescharacteristic
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#103C2×D4711yescharacteristic
230#103C2×D4711yescharacteristic
231C22⋊C8—471no—
232C22⋊C8—471no—
233#97C2×D4711yescharacteristic
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8—941no—
237C2×Q8—941no—
238C2×Q8—942no—
239C2×Q8—942no—
240C2×Q8—1881no—
241C2×Q8—1881no—
242C2×Q8C22×D4711yescharacteristic
243C2×Q8C22×D4711yescharacteristic
244C2×D4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250Q16—22no—
251Q16—1881no—
252Q16—1881no—
253M16—1881no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—1881no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C42—21no—
283C42—21no—
284C42—941no—
285C42C22×D4711yescharacteristic
286C23—471no—
287C23—471no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—941no—
292Q8—941no—
293Q8—941no—
294Q8—941no—
295Q8—1882no—
296Q8—1882no—
297Q8#1062535012yes—
298D4—942no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4D4×D4711yescharacteristic
317C2×C4D4×D4711yescharacteristic
318C2×C4C23×D4711yescharacteristic
319C8—21no—
320C8—21no—
321C8—941no—
322C8—941no—
323C22—472no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22C2×D4×D4711yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—941no—
337C4—941no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4C2×#1062535011yescharacteristic
343C4#1309407011yescharacteristic
344C2—942no—
345C2—1881no—
346C2#1568976911yescharacteristic
347C2#137×D4711yescharacteristic
348C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #15689492C2semidirect
4. #15689467C2semidirect
5. #15689455C2semidirect
6. #15689430C2semidirect
7. #15689380C2semidirect
8. #15689363C2semidirect
9. #15689333C2semidirect
10. #15689277C2semidirect
11. #15689277C2semidirect
13. #15689130C2semidirect
14. #103×D47C2semidirect
15. C47×#441C2semidirect
186. #441D47semidirect
190. C47#3312semidirect