Finite Group Databasebeta

← #20255441

Subgroups — #20255441

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#15689813C211yesmaximal, characteristic
2D4×Dic94C211yesmaximal, characteristic
3#15689492C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689454C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689364C211yesmaximal, characteristic, complemented
9#15689334C211yesmaximal, characteristic, complemented
10#15689281C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689231C211yesmaximal, characteristic, complemented
13#15689133C211yesmaximal, characteristic, complemented
14C2×#13093949C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×Dic188C2211yescharacteristic
19C2×Dic188C2211yescharacteristic
20C2×Dic188C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094023—21no—
23#13094017—21no—
24#13094016C2211yescharacteristic
25#13094014—21no—
26#13094005—21no—
27#13094003C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic
30#13094003C2211yescharacteristic
31#13094001—21no—
32#13094001—21no—
33C4×Dic94C2211yescharacteristic
34C4×Dic94C2211yescharacteristic
35D4×Dic47—21no—
36#13093983C2211yescharacteristic
37#13093980—21no—
38C2×C4⋊Dic47C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093949C2211yescharacteristic
51#13093949C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—41no—
70C2×Dic94—41no—
71C2×Dic94C2311yescharacteristic
72C2×Dic94C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2311yescharacteristic
75M16×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108Dic188—22no—
109Dic188—41no—
110Dic188—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113D4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133C2×Dic47—42no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—42no—
142Dic94—42no—
143Dic94#4112yes—
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47—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×C47C2×#4111yescharacteristic
160C4×C47H(5,𝔽2)11yescharacteristic
161Dic47—22no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
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#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#441—471no—
187#435D4711yescharacteristic
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×M16C2×D4711yescharacteristic
197C22×C8C2×D4711yescharacteristic
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×Q8—471no—
211C4×Q8—471no—
212C4×D4—941no—
213C4×D4C2×D4711yescharacteristic
214#117—471no—
215#117—941no—
216C2×C4⋊C4—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic
232C22⋊C8C2×D4711yescharacteristic
233#97C2×D4711yescharacteristic
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×Q8—942no—
239C2×Q8—942no—
240C2×Q8—941no—
241C2×Q8—941no—
242C2×Q8—1881no—
243C2×Q8—1881no—
244C2×D4D18811yescharacteristic
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250Q16—942no—
251Q16—1881no—
252Q16—1881no—
253M16—41no—
254C2×C8—41no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
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⋊C4—941no—
274C4⋊C4D18811yescharacteristic
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4D18811yescharacteristic
281C22⋊C4D18811yescharacteristic
282C42—941no—
283C42—941no—
284C42—941no—
285C42C22×D4711yescharacteristic
286C23C2×D18811yescharacteristic
287C23C2×D18811yescharacteristic
288Q8—472no—
289Q8—941no—
290Q8—941no—
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—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4C2×D18811yescharacteristic
315C2×C4C2×D18811yescharacteristic
316C2×C4C2×D18811yescharacteristic
317C2×C4C2×D18811yescharacteristic
318C2×C4C23×D4711yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1309405712yes—
329C22C22×D18811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—942no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4#41×D4711yescharacteristic
343C4#1309406911yescharacteristic
344C2—22no—
345C2—41no—
346C2#1568976811yescharacteristic
347C2C2×#1309405711yescharacteristic
348C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3312
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #15689492C2semidirect
4. #15689465C2semidirect
5. #15689454C2semidirect
6. #15689431C2semidirect
7. #15689381C2semidirect
8. #15689364C2semidirect
9. #15689334C2semidirect
10. #15689281C2semidirect
11. #15689281C2semidirect
12. #15689231C2semidirect
13. #15689133C2semidirect
14. C2×#13093949C2semidirect
190. C47#3312semidirect