Finite Group Databasebeta

← #20250350

Subgroups — #20250350

Order 6016.

476 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094019C211yesmaximal, characteristic, complemented
2C2×#13094018C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689058C211yesmaximal, characteristic, complemented
5#15689047C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689041C211yesmaximal, characteristic
8#15689040C211yesmaximal, characteristic
9#15689024C211yesmaximal, characteristic
10#15689020C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15689018C211yesmaximal, characteristic, complemented
13#15689014C211yesmaximal, characteristic, complemented
14#15689012C211yesmaximal, characteristic, complemented
15C47×#389C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17#13094019—24no—
18#13094018—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×D188—22no—
69C2×D188—41no—
70C2×D188—41no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C42×C47—22no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—41no—
85(C2×D47)⋊C4—41no—
86(C2×D47)⋊C4—41no—
87(C2×D47)⋊C4—41no—
88C4⋊Dic47—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4D414yescomplemented
97C4×Dic47—22no—
98C4×Dic47—41no—
99C23×C47C2411yescharacteristic
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—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×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47C2×D412yes—
134C2×C4×C47#4112yes—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47C2×D412yes—
151C2×Dic47C2×D412yes—
152C2×Dic47#4112yes—
153D188—44no—
154C22×C47C22×D411yescharacteristic
155C22×C47C2×#4111yescharacteristic
156C22×C47C2×#4111yescharacteristic
157C22×C47H(5,𝔽2)11yescharacteristic
158C22×C47H(5,𝔽2)11yescharacteristic
159C22×C472−1+411yescharacteristic
160C22×C472−1+411yescharacteristic
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C4×C47—22no—
176C4×C47—22no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182Dic47—22no—
183Dic47—22no—
184Dic47—22no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188#2727—471nomaximal, Sylow
189C2×C47#53711yescharacteristic
190C2×C47#53811yescharacteristic
191C2×C47#53911yescharacteristic
192C2×C47#54711yescharacteristic
193C2×C47#55011yescharacteristic
194C2×C47#55611yescharacteristic
195C2×C47#56311yescharacteristic
196D47—81no—
197D47—81no—
198C2×#126—471no—
199C2×#126—471no—
200#399—471no—
201#399—471no—
202#396—471no—
203#396—471no—
204#394—471no—
205#394—471no—
206#390—471no—
207#389—471no—
208#389—471no—
209#389—471no—
210#389D4711yescharacteristic, complemented
211#388—471no—
212#388—471no—
213C47#272711yescharacteristic, complemented, Sylow
214C22×D4—471no—
215#126—944no—
216#126—944no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4C2×D4711yescharacteristic
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C4⋊C4C2×D4711yescharacteristic
229C2×C4⋊C4C2×D4711yescharacteristic
230C2×C22⋊C4—471no—
231C2×C22⋊C4—471no—
232C2×C22⋊C4—471no—
233C2×C22⋊C4—471no—
234C2×C22⋊C4—471no—
235C2×C22⋊C4—471no—
236C2×C22⋊C4—471no—
237C2×C22⋊C4—471no—
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C42—471no—
243C2×C42—471no—
244C2×C42C2×D4711yescharacteristic
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95C2×D4711yescharacteristic
250#95C2×D4711yescharacteristic
251C24—471no—
252C24—471no—
253C2×D4—942no—
254C2×D4—1881no—
255C2×D4—1881no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C22×C4C22×D4711yescharacteristic
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—474no—
274C4⋊C4—942no—
275C4⋊C4—942no—
276C4⋊C4—942no—
277C4⋊C4—942no—
278C4⋊C4—942no—
279C4⋊C4—1881no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C22⋊C4—942no—
283C22⋊C4—942no—
284C22⋊C4—942no—
285C22⋊C4—942no—
286C22⋊C4—942no—
287C22⋊C4—942no—
288C22⋊C4—942no—
289C22⋊C4—942no—
290C22⋊C4—1881no—
291C22⋊C4—1881no—
292C22⋊C4—1881no—
293C22⋊C4—1881no—
294C42—22no—
295C42—942no—
296C42—1881no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23—941no—
302C23—941no—
303C23—941no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23C23×D4711yescharacteristic
312D4—1884no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—472no—
333C2×C4—472no—
334C2×C4—472no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4#1062535012yes—
351C2×C4D4×D4712yes—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22C2×D4×D4711yescharacteristic
367C22#41×D4711yescharacteristic
368C22C2×#1062535011yescharacteristic
369C22#1309406911yescharacteristic
370C22#1309407011yescharacteristic
371C22#1309407211yescharacteristic
372C22#1309407211yescharacteristic
373C4—22no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—942no—
381C4—942no—
382C4—942no—
383C4—1881no—
384C4—1881no—
385C4—1881no—
386C2—3761no—
387C2—3761no—
388C2#1568970311yescharacteristic
389C2#1568970611yescharacteristic
390C2#1568972111yescharacteristic
391C2#1568977411yescharacteristic
392C2#1568979111yescharacteristic
393C2#1568984511yescharacteristic
394C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2727
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. C2×#13094018C2semidirect
3. #15689058C2semidirect
4. #15689058C2semidirect
5. #15689047C2semidirect
6. #15689045C2semidirect
10. #15689020C2semidirect
11. #15689018C2semidirect
12. #15689018C2semidirect
13. #15689014C2semidirect
14. #15689012C2semidirect
15. C47×#389C2semidirect
96. Dic47⋊C4D4semidirect
210. #389D47semidirect
213. C47#2727semidirect