Finite Group Databasebeta

← #20249252

Subgroups — #20249252

Order 6016.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3#15689059C211yesmaximal, characteristic, complemented
4#15689058C211yesmaximal, characteristic, complemented
5#15689044C211yesmaximal, characteristic, complemented
6#15689043C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic
8#15689038C211yesmaximal, characteristic
9#15689036C211yesmaximal, characteristic, complemented
10#15689035C211yesmaximal, characteristic, complemented
11#15689015C211yesmaximal, characteristic, complemented
12#15689014C211yesmaximal, characteristic, complemented
13#15689011C211yesmaximal, characteristic, complemented
14#15688990C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19#13094010—24no—
20C4×Dic94—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—22no—
62C2×C22⋊D47—41no—
63C2×C22⋊D47—41no—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×Dic94—22no—
72C2×Dic94—22no—
73C2×Dic94—22no—
74C2×Dic94—22no—
75C2×Dic94—41no—
76C2×Dic94—41no—
77C4⋊C4×C47—41no—
78C22⋊C4×C47—22no—
79C22⋊C4×C47—22no—
80C22⋊C4×C47—41no—
81C42×C47—22no—
82C22⋊Dic47—22no—
83C22⋊Dic47—22no—
84C22⋊Dic47—41no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—41no—
90(C2×D47)⋊C4—41no—
91C4⋊Dic47—22no—
92C4⋊Dic47—41no—
93Dic47⋊C4—22no—
94Dic47⋊C4—22no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97C4×Dic47—22no—
98C4×Dic47D414yes—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47C2411yescharacteristic
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×C47C2×D412yes—
131C2×C4×C47#4112yes—
132C22⋊D47—44no—
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×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×Dic47—21no—
151C2×Dic47C2×D412yes—
152C2×Dic47C2×D412yes—
153C2×Dic47#4112yes—
154Dic94—28no—
155Dic94—44no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47C22×D411yescharacteristic
164C22×C47C2×#4111yescharacteristic
165C22×C47C2×#4111yescharacteristic
166C22×C47H(5,𝔽2)11yescharacteristic
167C22×C47H(5,𝔽2)11yescharacteristic
168C22×C472−1+411yescharacteristic
169C22×C472−1+411yescharacteristic
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C4×C47—22no—
178C4×C47—22no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183Dic47—22no—
184Dic47—22no—
185Dic47—22no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190#2632—471nomaximal, Sylow
191C2×C47—81no—
192C2×C47#52511yescharacteristic
193C2×C47#53511yescharacteristic
194C2×C47#53611yescharacteristic
195C2×C47#54211yescharacteristic
196C2×C47#54211yescharacteristic
197C2×C47#54211yescharacteristic
198C2×C47#54211yescharacteristic
199D47—81no—
200C2×#124—471no—
201C2×C4×Q8—471no—
202#399—471no—
203#399—471no—
204#395—471no—
205#395—471no—
206#394—471no—
207#394—471no—
208#393—471no—
209#393—471no—
210#388—471no—
211#388—471no—
212#388—471no—
213#388D4711yescharacteristic, complemented
214#383—471no—
215C47#263211yescharacteristic, complemented, Sylow
216C22×Q8—471no—
217C22×Q8—471no—
218C22×D4—471no—
219#124—944no—
220C4×Q8—944no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C22⋊C4—471no—
229C2×C22⋊C4—471no—
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⋊C4C2×D4711yescharacteristic
238C2×C22⋊C4C2×D4711yescharacteristic
239C2×C22⋊C4C2×D4711yescharacteristic
240C2×C42—471no—
241C2×C42—471no—
242C2×C42C2×D4711yescharacteristic
243#95—471no—
244#95—471no—
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95—471no—
250#95—471no—
251#95C2×D4711yescharacteristic
252#95C2×D4711yescharacteristic
253C24—471no—
254C24C22×D4711yescharacteristic
255C2×Q8—942no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—942no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C2×D4—942no—
262C2×D4—1881no—
263C2×D4—1881no—
264C22×C4—471no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C22×C4C22×D4711yescharacteristic
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—942no—
279C4⋊C4—942no—
280C4⋊C4—942no—
281C4⋊C4—1881no—
282C4⋊C4—1881no—
283C4⋊C4—1881no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—942no—
288C22⋊C4—942no—
289C22⋊C4—942no—
290C22⋊C4—942no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—1881no—
294C22⋊C4—1881no—
295C22⋊C4—1881no—
296C42—22no—
297C42—474no—
298C42—942no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23—941no—
312C23—941no—
313C23C23×D4711yescharacteristic
314Q8—948no—
315Q8—1884no—
316D4—1884no—
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—21no—
333C2×C4—472no—
334C2×C4—472no—
335C2×C4—472no—
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—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4#1062535012yes—
355C2×C4D4×D4712yes—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22C2×D4×D4711yescharacteristic
371C22#41×D4711yescharacteristic
372C22C2×#1062535011yescharacteristic
373C22#1309406911yescharacteristic
374C22#1309407011yescharacteristic
375C22#1309407111yescharacteristic
376C22#1309407111yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—942no—
384C4—942no—
385C4—942no—
386C4—1881no—
387C4—1881no—
388C4—1881no—
389C4—1881no—
390C2—81no—
391C2—3761no—
392C2#1568963211yescharacteristic
393C2#1568968911yescharacteristic
394C2#1568969511yescharacteristic
395C2#1568973711yescharacteristic
396C2#1568973811yescharacteristic
397C2#1568973911yescharacteristic
398C2#1568974411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2632
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
3. #15689059C2semidirect
4. #15689058C2semidirect
5. #15689044C2semidirect
6. #15689043C2semidirect
9. #15689036C2semidirect
10. #15689035C2semidirect
11. #15689015C2semidirect
12. #15689014C2semidirect
13. #15689011C2semidirect
14. #15688990C2semidirect
15. C47×#388C2semidirect
213. #388D47semidirect
215. C47#2632semidirect