Finite Group Databasebeta

← #20257464

Subgroups — #20257464

Order 6016.

1104 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689855C213yesmaximal, complemented
2Q8×Dic94C211yesmaximal, characteristic, complemented
3#15689831C213yesmaximal, complemented
4#15689792C211yesmaximal, characteristic, complemented
5#15689784C211yesmaximal, characteristic, complemented
6#15689777C213yesmaximal, complemented
7#15689773C213yesmaximal, complemented
8#15689746C213yesmaximal, complemented
9#15689742C213yesmaximal, complemented
10#15689668C213yesmaximal, complemented
11#15689653C213yesmaximal, complemented
12#15689606C211yesmaximal, characteristic, complemented
13#15689605C211yesmaximal, characteristic, complemented
14C2×Q8×Dic47C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2216yes—
18#13094024C2213yes—
19#13094023C2213yes—
20#13094023C2213yes—
21#13094020C2213yes—
22#13094019C2213yes—
23#13094017C2213yes—
24#13094014C2213yes—
25#13094013C2213yes—
26#13094010C2216yes—
27#13094010C2213yes—
28#13094008C2216yes—
29#13094008C2213yes—
30#13094006C2216yes—
31#13094005C2213yes—
32#13094004C2216yes—
33#13094001C2216yes—
34#13094001C2211yescharacteristic
35#13094000C2213yes—
36#13093998C2213yes—
37#13093998C2213yes—
38#13093996C2213yes—
39#13093995C2213yes—
40Q8×Dic47C2213yes—
41Q8×Dic47C2211yescharacteristic
42Q8×Dic47C2211yescharacteristic
43Q8×Dic47C2213yes—
44Q8×Dic47C2211yescharacteristic
45C4×Dic94C2213yes—
46C4×D188C2213yes—
47D4×Dic47C2213yes—
48D4×Dic47C2213yes—
49#13093986C2213yes—
50C4×C22⋊D47C2213yes—
51C4×C22⋊D47C2213yes—
52(C22⋊D47)⋊C4C2216yes—
53#13093983C2213yes—
54#13093981C2213yes—
55C2×C4⋊Dic47C2213yes—
56C2×C4⋊Dic47C2213yes—
57C4⋊C4×D47C2213yes—
58C2×C4×Dic47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C22×Q8×C47C2211yescharacteristic
61#124×C47C2213yes—
62C22⋊Q8×C47C2213yes—
63#121×C47C2213yes—
64C4×Q8×C47C2211yescharacteristic
65C4×D4×C47C2213yes—
66#41×C47—24no—
67C2×Q8×C47—24no—
68C2×Q8×C47C2313yes—
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47C2313yes—
71C2×D4×C47C2313yes—
72C22×C4×C47C2313yes—
73C22×C4×C47C2313yes—
74C2×C22⋊D47C2313yes—
75C2×C22⋊D47C2313yes—
76C2×C22⋊D47C2316yes—
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2313yes—
79C22×Dic47C2316yes—
80#10625354—24no—
81#10625352—412no—
82C2×D188C2313yes—
83C2×C4×D47C2313yes—
84C2×C4×D47C2316yes—
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2316yes—
87C4⋊C4×C47C2313yes—
88C4⋊C4×C47C2313yes—
89C22⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47C2313yes—
91C22⋊C4×C47C2316yes—
92C42×C47C2313yes—
93C22⋊Dic47C2313yes—
94C22⋊Dic47C2313yes—
95C22⋊Dic47C2311yescharacteristic
96C22⋊Dic47C2313yes—
97(C2×D47)⋊C4C2313yes—
98(C2×D47)⋊C4C2313yes—
99(C2×D47)⋊C4C2316yes—
100(C2×D47)⋊C4C2313yes—
101(C2×D47)⋊C4C2313yes—
102C4⋊Dic47C2313yes—
103C4⋊Dic47C2313yes—
104C4⋊Dic47C2313yes—
105C4⋊Dic47C2313yes—
106C4⋊Dic47C2316yes—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2313yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2311yescharacteristic
111Dic47⋊C4C2313yes—
112Dic47⋊C4C2311yescharacteristic
113Dic47⋊C4C2313yes—
114Dic47⋊C4C2313yes—
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2313yes—
119C4×Dic47C2313yes—
120C23×C47C2413yes—
121C23×C47C2411yescharacteristic
122C22×D47C2413yes—
123Q8×C47—26no—
124Q8×C47#4114yescomplemented
125D4×C47—26no—
126D4×C47—26no—
127C2×C4×C47—26no—
128C2×C4×C47—26no—
129C2×C4×C47C2413yes—
130C2×C4×C47C2413yes—
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C2×C4×C47C2413yes—
134C22⋊D47—26no—
135C22⋊D47—26no—
136C22⋊D47—46no—
137C2×Dic47—26no—
138C2×Dic47—22no—
139C2×Dic47—46no—
140C2×Dic47C2411yescharacteristic
141C2×Dic47C2411yescharacteristic
142C2×Dic47C2413yes—
143C2×Dic47C2413yes—
144C2×Dic47C2413yes—
145C2×Dic47C2411yescharacteristic
146C2×Dic47C2411yescharacteristic
147D188—26no—
148C4×D47—26no—
149C4×D47—46no—
150Dic94—22no—
151Dic94—46no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—23no—
155C22×C47—23no—
156C22×C47—23no—
157C22×C47H(5,𝔽2)12yes—
158C22×C47C2511yescharacteristic
159C2×D47—23no—
160C2×D47—23no—
161C2×D47—23no—
162C4×C47—21no—
163C4×C47—23no—
164C4×C47—23no—
165C4×C47—21no—
166C4×C47C2×#4116yes—
167Dic47—21no—
168Dic47—23no—
169Dic47—23no—
170Dic47—23no—
171Dic47—21no—
172Dic47—21no—
173Dic472−1+412yes—
174#3522—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—43no—
177C2×C47C22×#4111yescharacteristic
178C2×C47C2×H(5,𝔽2)11yescharacteristic
179C2×C47C2×2−1+411yescharacteristic
180D47—43no—
181#559—473no—
182Q82—471no—
183#554—473no—
184#550—471no—
185#548—471no—
186#548D4711yescharacteristic, complemented
187#547—473no—
188#547—473no—
189#542—473no—
190#542—473no—
191#532—473no—
192#529—473no—
193#520—471no—
194#520—471no—
195C2×C4×Q8—471no—
196C47#352211yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C2×#41—476no—
199C2×#41C2×D4711yescharacteristic
200C22×Q8C2×D4711yescharacteristic
201C4⋊Q8—473no—
202C4⋊Q8—473no—
203C4⋊Q8—473no—
204#127—473no—
205#126—473no—
206#126—473no—
207#125—473no—
208#124—473no—
209#124—473no—
210#124—476no—
211#124C2×D4713yes—
212#123—473no—
213#123—473no—
214#123—476no—
215#123—476no—
216C22⋊Q8—473no—
217C22⋊Q8—476no—
218C22⋊Q8—471no—
219C22⋊Q8—476no—
220C22⋊Q8C2×D4713yes—
221#121—473no—
222#121—473no—
223#121—473no—
224#121—473no—
225#121C2×D4713yes—
226C4×Q8—471no—
227C4×Q8—473no—
228C4×Q8—471no—
229C4×Q8—473no—
230C4×Q8—471no—
231C4×Q8—473no—
232C4×Q8C2×D4711yescharacteristic
233C4×D4—473no—
234C4×D4—473no—
235C4×D4—473no—
236C4×D4—473no—
237C4×D4—473no—
238C4×D4—476no—
239C4×D4—473no—
240C4×D4C2×D4713yes—
241#117—473no—
242#117—473no—
243C2×C4⋊C4—473no—
244C2×C4⋊C4—473no—
245C2×C4⋊C4—473no—
246C2×C42—473no—
247#41—24no—
248#41—944no—
249#41—18812no—
250C2×Q8—24no—
251C2×Q8—471no—
252C2×Q8—476no—
253C2×Q8C22×D4713yes—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—473no—
256C2×D4—473no—
257C2×D4—476no—
258C2×D4—473no—
259C2×D4C22×D4713yes—
260C2×D4C22×D4713yes—
261C22×C4—471no—
262C22×C4—473no—
263C22×C4—476no—
264C22×C4—473no—
265C22×C4—476no—
266C22×C4C22×D4713yes—
267C22×C4C22×D4713yes—
268C4⋊C4—473no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—473no—
272C4⋊C4—473no—
273C4⋊C4—473no—
274C4⋊C4—473no—
275C4⋊C4—473no—
276C4⋊C4—473no—
277C4⋊C4—473no—
278C4⋊C4—476no—
279C4⋊C4—471no—
280C4⋊C4—473no—
281C4⋊C4C22×D4713yes—
282C4⋊C4C22×D4713yes—
283C22⋊C4—473no—
284C22⋊C4—473no—
285C22⋊C4—471no—
286C22⋊C4—473no—
287C22⋊C4—473no—
288C22⋊C4—473no—
289C22⋊C4—473no—
290C22⋊C4—476no—
291C22⋊C4—473no—
292C22⋊C4C22×D4716yes—
293C22⋊C4C22×D4711yescharacteristic
294C22⋊C4C22×D4713yes—
295C42—473no—
296C42—473no—
297C42—473no—
298C42—473no—
299C42—473no—
300C42C22×D4713yes—
301C23—473no—
302C23C23×D4713yes—
303C23C23×D4711yescharacteristic
304Q8—26no—
305Q8—942no—
306Q8—1886no—
307Q8#1062535214yescomplemented
308D4—26no—
309D4—26no—
310D4—946no—
311D4—946no—
312D4—946no—
313D4—1886no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—471no—
319C2×C4—473no—
320C2×C4—473no—
321C2×C4—473no—
322C2×C4—471no—
323C2×C4—942no—
324C2×C4—946no—
325C2×C4—946no—
326C2×C4—1886no—
327C2×C4—1886no—
328C2×C4C23×D4713yes—
329C2×C4C23×D4711yescharacteristic
330C2×C4C23×D4713yes—
331C2×C4C23×D4711yescharacteristic
332C2×C4C23×D4713yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—943no—
339C22—943no—
340C22—943no—
341C22#1309407012yes—
342C22C24×D4711yescharacteristic
343C4—21no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—472no—
348C4—941no—
349C4—943no—
350C4—943no—
351C4—943no—
352C4—941no—
353C4—941no—
354C4C2×#1062535216yes—
355C2—22no—
356C2—43no—
357C2—1883no—
358C2C22×#1062535211yescharacteristic
359C2C2×#1309407011yescharacteristic
360C22−1+4×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3522
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689855C2semidirect
2. Q8×Dic94C2semidirect
3. #15689831C2semidirect
4. #15689792C2semidirect
5. #15689784C2semidirect
6. #15689777C2semidirect
7. #15689773C2semidirect
8. #15689746C2semidirect
9. #15689742C2semidirect
10. #15689668C2semidirect
11. #15689653C2semidirect
12. #15689606C2semidirect
13. #15689605C2semidirect
14. C2×Q8×Dic47C2semidirect
15. C47×#548C2semidirect
124. Q8×C47#41semidirect
186. #548D47semidirect
196. C47#3522semidirect
307. Q8#10625352semidirect