Finite Group Databasebeta

← #20253425

Subgroups — #20253425

Order 6016.

384 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic
3#15689460C211yesmaximal, characteristic
4#15689457C211yesmaximal, characteristic
5#15689417C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689332C211yesmaximal, characteristic, complemented
8#15689331C211yesmaximal, characteristic, complemented
9#15689280C211yesmaximal, characteristic
10#15689277C211yesmaximal, characteristic
11C4×Dic188C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625337C211yesmaximal, characteristic, complemented
14#15689174C211yesmaximal, characteristic
15C4×Q16×C47C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094014—21no—
23#13094004C2211yescharacteristic
24#13094002—21no—
25#13094000C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94—21no—
29C4×Dic94C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31#13093989—21no—
32#13093989C2211yescharacteristic
33#13093981—21no—
34C4⋊C4×D47—21no—
35C4⋊C4×D47C2211yescharacteristic
36C42×D47—21no—
37C42×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61Q8×D47—22no—
62Q8×D47—22no—
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47D411yescharacteristic
66C2×C4×D47D411yescharacteristic
67C2×C4×D47C2311yescharacteristic
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71C2×Dic94C2311yescharacteristic
72Q16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C42×C47—21no—
80C42×C47—21no—
81C42×C47C2311yescharacteristic
82#10625337—22no—
83#10625337—22no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—22no—
108C22×D47C2×D411yescharacteristic
109Q8×C47—21no—
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47#4112yes—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C4×D47—24no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—41no—
131C4×D47—42no—
132C4×D47Q1614yescomplemented
133Dic94—24no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138Dic94#4112yes—
139C8×C47—21no—
140C8×C47—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47C22×D411yescharacteristic
144C2×D47—21no—
145C2×D47—21no—
146C2×D47C2×Q1612yes—
147C4×C47—22no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×Q1612yes—
153C4×C47C2×#4111yescharacteristic
154C4×C47C2×#4111yescharacteristic
155Dic47—21no—
156Dic47—22no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47C2×Q1612yes—
162#3104—471nomaximal, Sylow
163C2×C47#52511yescharacteristic
164C2×C47C22×Q1611yescharacteristic
165C2×C47#57511yescharacteristic
166D47—22no—
167#533—471no—
168C2×C4×Q8—471no—
169#484—471no—
170#484—471no—
171#477—471no—
172#477—471no—
173#462—471no—
174#462—471no—
175#451—471no—
176#451—471no—
177C4×Q16—471no—
178C4×Q16—471no—
179C4×Q16—471no—
180C4×Q16D4711yescharacteristic, complemented
181#431—471no—
182C47#310411yescharacteristic, complemented, Sylow
183C22×Q8—471no—
184C2×Q16—471no—
185C2×Q16—471no—
186C2×Q16—471no—
187C2×Q16C2×D4711yescharacteristic
188C4⋊Q8—471no—
189C4⋊Q8—471no—
190#125—941no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C22⋊Q8—941no—
194C4×Q8—471no—
195C4×Q8—471no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8—941no—
199C4×Q8—941no—
200C4×Q8—941no—
201C4×Q8C2×D4711yescharacteristic
202C4×Q8C2×D4711yescharacteristic
203#117—941no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—941no—
206C2×C42—471no—
207C2×C42—941no—
208#107—471no—
209#107—471no—
210#107—471no—
211#107C2×D4711yescharacteristic
212C4⋊C8—471no—
213C4⋊C8—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222C22⋊C8—471no—
223C22⋊C8—471no—
224C4×C8—471no—
225C4×C8C2×D4711yescharacteristic
226C2×Q8—471no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×Q8—941no—
230C2×Q8—942no—
231C2×Q8—942no—
232C2×Q8C22×D4711yescharacteristic
233C2×Q8C22×D4711yescharacteristic
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—941no—
238C22×C4—941no—
239Q16—22no—
240Q16—942no—
241Q16—942no—
242Q16—942no—
243C2×C8—471no—
244C2×C8—471no—
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—21no—
266C42—21no—
267C42—471no—
268C42—471no—
269C42—471no—
270C42—941no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—471no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—472no—
280Q8—944no—
281Q8—941no—
282Q8—941no—
283Q8—941no—
284Q8—1882no—
285Q8#1062535012yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—471no—
291C2×C4—474no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—944no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—1881no—
302C2×C4—1882no—
303C2×C4D4×D4711yescharacteristic
304C2×C4D4×D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C8—21no—
307C8—21no—
308C8—941no—
309C8—941no—
310C22—472no—
311C22—941no—
312C22—941no—
313C22C2×D4×D4711yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—472no—
320C4—941no—
321C4—942no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4Q16×D4712yes—
327C4#41×D4711yescharacteristic
328C4C2×#1062535011yescharacteristic
329C2—942no—
330C2#1568963211yescharacteristic
331C2C2×Q16×D4711yescharacteristic
332C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3104
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
5. #15689417C2semidirect
6. #15689416C2semidirect
7. #15689332C2semidirect
8. #15689331C2semidirect
11. C4×Dic188C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625337C2semidirect
15. C4×Q16×C47C2semidirect
132. C4×D47Q16semidirect
180. C4×Q16D47semidirect
182. C47#3104semidirect