Finite Group Databasebeta

← #20247673

Subgroups — #20247673

Order 6016.

512 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093981C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689065C211yesmaximal, characteristic, complemented
4#15689064C211yesmaximal, characteristic, complemented
5#15689057C211yesmaximal, characteristic, complemented
6#15689056C211yesmaximal, characteristic, complemented
7#15689008C211yesmaximal, characteristic, complemented
8#15689007C211yesmaximal, characteristic, complemented
9#15689004C211yesmaximal, characteristic, complemented
10#15688997C211yesmaximal, characteristic
11#15688994C211yesmaximal, characteristic
12#15688985C211yesmaximal, characteristic
13#15688985C211yesmaximal, characteristic
14#15688985C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13093981—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C4⋊C4×D47—24no—
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×C4×Dic47C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×C4×D47D414yes—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—22no—
79C42×C47—22no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84C4⋊Dic47—22no—
85C4⋊Dic47—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92C4×Dic47—22no—
93C23×C47C2411yescharacteristic
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47C2×D412yes—
99C22×D47#4112yes—
100C22×D47#4112yes—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D412yes—
121C2×C4×C47#4112yes—
122C2×Dic47—21no—
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—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47C2×D412yes—
142C2×Dic47#4112yes—
143C4×D47—28no—
144C4×D47—28no—
145C4×D47—44no—
146C22×C47C22×D411yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C47C2×#4111yescharacteristic
150C22×C47C2×#4111yescharacteristic
151C22×C472−1+411yescharacteristic
152C22×C472−1+411yescharacteristic
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—22no—
156C2×D47—22no—
157C2×D47—22no—
158C2×D47—22no—
159C2×D47#12314yes—
160C4×C47—22no—
161C4×C47—22no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167Dic47—22no—
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#2484—471nomaximal, Sylow
175C2×C47C2×#12311yescharacteristic
176C2×C47#52511yescharacteristic
177C2×C47#53611yescharacteristic
178C2×C47#55211yescharacteristic
179C2×C47#55211yescharacteristic
180C2×C47#55211yescharacteristic
181C2×C47#55211yescharacteristic
182D47—24no—
183C2×#117—471no—
184C22×C4⋊C4—471no—
185#400—471no—
186#400—471no—
187#398—471no—
188#398—471no—
189#387—471no—
190#387—471no—
191#387—471no—
192#387D4711yescharacteristic, complemented
193#385—471no—
194#385—471no—
195#381—471no—
196#381—471no—
197#381—471no—
198C47#248411yescharacteristic, complemented, Sylow
199C23×C4—471no—
200C23×C4—471no—
201C23×C4—471no—
202#117—944no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—944no—
212C2×C4⋊C4C2×D4711yescharacteristic
213C2×C4⋊C4C2×D4711yescharacteristic
214C2×C22⋊C4—471no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—471no—
217C2×C22⋊C4—471no—
218C2×C42—471no—
219C2×C42C2×D4711yescharacteristic
220#95—471no—
221#95—471no—
222#95—471no—
223#95—471no—
224#95—471no—
225#95—471no—
226#95—471no—
227#95—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232#95C2×D4711yescharacteristic
233#95C2×D4711yescharacteristic
234#95C2×D4711yescharacteristic
235#95C2×D4711yescharacteristic
236C24—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—474no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—942no—
246C22×C4—942no—
247C22×C4—942no—
248C22×C4—942no—
249C22×C4—942no—
250C22×C4—942no—
251C22×C4—942no—
252C22×C4—942no—
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C22×C4C22×D4711yescharacteristic
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C4⋊C4—942no—
265C4⋊C4—942no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—942no—
269C4⋊C4—942no—
270C22⋊C4—942no—
271C22⋊C4—942no—
272C22⋊C4—942no—
273C22⋊C4—942no—
274C42—22no—
275C42—942no—
276C23—472no—
277C23—472no—
278C23—472no—
279C23—941no—
280C23—941no—
281C23—941no—
282C23—941no—
283C23C23×D4711yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—472no—
304C2×C4—472no—
305C2×C4—948no—
306C2×C4—948no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—1884no—
327C2×C4#1062535012yes—
328C2×C4D4×D4712yes—
329C22—474no—
330C22—942no—
331C22—942no—
332C22—942no—
333C22—942no—
334C22—942no—
335C22—942no—
336C22C2×D4×D4711yescharacteristic
337C22#41×D4711yescharacteristic
338C22#41×D4711yescharacteristic
339C22#41×D4711yescharacteristic
340C22C2×#1062535011yescharacteristic
341C22#1309407111yescharacteristic
342C22#1309407211yescharacteristic
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—942no—
351C4—942no—
352C4—1881no—
353C4—1881no—
354C4—1881no—
355C4—1881no—
356C4—1881no—
357C2—944no—
358C2#123×D4711yescharacteristic
359C2#1568963211yescharacteristic
360C2#1568969611yescharacteristic
361C2#1568980511yescharacteristic
362C2#1568980911yescharacteristic
363C2#1568981211yescharacteristic
364C2#1568981411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2484
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #15689065C2semidirect
4. #15689064C2semidirect
5. #15689057C2semidirect
6. #15689056C2semidirect
7. #15689008C2semidirect
8. #15689007C2semidirect
9. #15689004C2semidirect
15. C47×#387C2semidirect
192. #387D47semidirect
198. C47#2484semidirect