Finite Group Databasebeta

← #20248668

Subgroups — #20248668

Order 6016.

436 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689053C211yesmaximal, characteristic, complemented
2#15689046C211yesmaximal, characteristic
3#15689044C211yesmaximal, characteristic, complemented
4#15689035C211yesmaximal, characteristic
5#15689027C211yesmaximal, characteristic, complemented
6#15689011C211yesmaximal, characteristic
7#15689011C211yesmaximal, characteristic
8#15689009C211yesmaximal, characteristic, complemented
9#15689008C211yesmaximal, characteristic, complemented
10#15689004C211yesmaximal, characteristic, complemented
11#15688987C211yesmaximal, characteristic, complemented
12#15688983C211yesmaximal, characteristic
13C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic47C211yesmaximal, characteristic
15C47×#385C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C23×C4×C47C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C22×C4×C47—22no—
53C22×C4×C47—22no—
54C22×C4×C47—41no—
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
68C22×Dic47C2311yescharacteristic
69C2×Dic94—22no—
70C2×Dic94—41no—
71C2×Dic94—41no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—41no—
76C22⋊Dic47—22no—
77C22⋊Dic47—41no—
78C22⋊Dic47—41no—
79C22⋊Dic47Q814yescomplemented
80C4⋊Dic47—22no—
81C4⋊Dic47—22no—
82C4⋊Dic47—41no—
83Dic47⋊C4—22no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87C4×Dic47—22no—
88C4×Dic47—22no—
89C4×Dic47—41no—
90C4×Dic47—41no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47C2×Q812yes—
98C23×C47C2411yescharacteristic
99C2×C4×C47—21no—
100C2×C4×C47—21no—
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—44no—
115C2×C4×C47#4112yes—
116C2×C4×C47#4112yes—
117C2×C4×C47#4112yes—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
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×Dic47C2×Q812yes—
140C2×Dic47C2×Q812yes—
141C2×Dic47#4112yes—
142Dic94—44no—
143C22×C47—22no—
144C22×C47—22no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×Q811yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47C2×#4111yescharacteristic
154C22×C47C2×#4111yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C47H(5,𝔽2)11yescharacteristic
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163Dic47—22no—
164Dic47—22no—
165Dic47—22no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#2574—471nomaximal, Sylow
172C2×C47—42no—
173C2×C47#52911yescharacteristic
174C2×C47#53311yescharacteristic
175C2×C47#53811yescharacteristic
176C2×C47#55111yescharacteristic
177C2×C47#55411yescharacteristic
178C2×C47#55411yescharacteristic
179C2×C47#55511yescharacteristic
180#398—471no—
181#396—471no—
182#395—471no—
183#393—471no—
184#391—471no—
185#388—471no—
186#388—471no—
187#387—471no—
188#387—471no—
189#387—471no—
190#385D4711yescharacteristic
191#382—471no—
192#380—471no—
193C4×C4⋊C4—471no—
194C4×C22⋊C4—471no—
195C47#257411yescharacteristic, complemented, Sylow
196C22×Q8—471no—
197C23×C4C2×D4711yescharacteristic
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4C2×D4711yescharacteristic
206C2×C4⋊C4C2×D4711yescharacteristic
207C2×C22⋊C4—471no—
208C2×C22⋊C4—471no—
209C2×C22⋊C4—471no—
210C2×C22⋊C4—471no—
211C2×C22⋊C4C2×D4711yescharacteristic
212C2×C22⋊C4C2×D4711yescharacteristic
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217#95—471no—
218#95—471no—
219#95—471no—
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#95C2×D4711yescharacteristic
230#95C2×D4711yescharacteristic
231C24C22×D4711yescharacteristic
232C2×Q8—942no—
233C2×Q8—1881no—
234C2×Q8—1881no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—942no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—474no—
264C22⋊C4—942no—
265C22⋊C4—1881no—
266C22⋊C4—1881no—
267C42—942no—
268C42—942no—
269C42—1881no—
270C42—1881no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D4712yes—
278C23C23×D4711yescharacteristic
279Q8—1884no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
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—44no—
296C2×C4—472no—
297C2×C4—472no—
298C2×C4—472no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
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—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#1062535012yes—
321C2×C4#1062535212yes—
322C2×C4#1062535212yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×Q8×D4711yescharacteristic
331C22#41×D4711yescharacteristic
332C22C2×#1062535211yescharacteristic
333C22C2×#1062535211yescharacteristic
334C22C2×#1062535011yescharacteristic
335C22#1309406911yescharacteristic
336C22#1309407011yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—942no—
344C4—942no—
345C4—942no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C2—42no—
352C2#1568965311yescharacteristic
353C2#1568967511yescharacteristic
354C2#1568970911yescharacteristic
355C2#1568980411yescharacteristic
356C2#1568982811yescharacteristic
357C2#1568983111yescharacteristic
358C2#1568983811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2574
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #15689053C2semidirect
3. #15689044C2semidirect
5. #15689027C2semidirect
8. #15689009C2semidirect
9. #15689008C2semidirect
10. #15689004C2semidirect
11. #15688987C2semidirect
13. C4⋊C4×Dic47C2semidirect
79. C22⋊Dic47Q8semidirect
195. C47#2574semidirect