Finite Group Databasebeta

← #20250244

Subgroups — #20250244

Order 6016.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094017C211yesmaximal, characteristic, complemented
2C2×#13094005C211yesmaximal, characteristic
3#15689064C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689056C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689037C211yesmaximal, characteristic
8#15689020C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689011C211yesmaximal, characteristic, complemented
11#15689011C211yesmaximal, characteristic, complemented
12#15688998C211yesmaximal, characteristic, complemented
13#15688995C211yesmaximal, characteristic, complemented
14#15688992C211yesmaximal, characteristic, complemented
15C47×#394C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17#13094017—24no—
18#13094005—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C2×D4×C47—22no—
56C2×D4×C47—41no—
57C2×D4×C47—41no—
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47—22no—
64C22×Dic47—41no—
65C22×Dic47—41no—
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C4⋊C4×C47—41no—
75C22⋊C4×C47—22no—
76C22⋊C4×C47—22no—
77C22⋊C4×C47—22no—
78C22⋊C4×C47—41no—
79C22⋊Dic47—22no—
80C22⋊Dic47—22no—
81C22⋊Dic47—22no—
82C22⋊Dic47—22no—
83C22⋊Dic47—22no—
84C22⋊Dic47—41no—
85C22⋊Dic47D414yes—
86C4⋊Dic47—22no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—22no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97C4×Dic47—22no—
98C4×Dic47—22no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47C2×D412yes—
113C23×C47C2411yescharacteristic
114D4×C47—44no—
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#4112yes—
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×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×Dic47—44no—
152C2×Dic47C2×D412yes—
153C2×Dic47C2×D412yes—
154C2×Dic47#4112yes—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47—22no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47C22×D411yescharacteristic
170C22×C47C2×#4111yescharacteristic
171C22×C47C2×#4111yescharacteristic
172C22×C47H(5,𝔽2)11yescharacteristic
173C22×C47H(5,𝔽2)11yescharacteristic
174C22×C472−1+411yescharacteristic
175C22×C472−1+411yescharacteristic
176C4×C47—22no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181Dic47—22no—
182Dic47—22no—
183Dic47—22no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189#2718—471nomaximal, Sylow
190C2×C47—42no—
191C2×C47—81no—
192C2×C47#53511yescharacteristic
193C2×C47#53911yescharacteristic
194C2×C47#54211yescharacteristic
195C2×C47#54711yescharacteristic
196C2×C47#54711yescharacteristic
197C2×C47#55311yescharacteristic
198C2×C47#56311yescharacteristic
199C2×#126—471no—
200C2×#123—471no—
201#400—471no—
202#399—471no—
203#398—471no—
204#396—471no—
205#394—471no—
206#394D4711yescharacteristic
207#389—471no—
208#388—471no—
209#388—471no—
210#388—471no—
211#385—471no—
212#385—471no—
213#384—471no—
214C47#271811yescharacteristic, complemented, Sylow
215C22×D4C2×D4711yescharacteristic
216C23×C4—471no—
217#126—944no—
218#123—944no—
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⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4C2×D4711yescharacteristic
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⋊C4C2×D4711yescharacteristic
239C2×C22⋊C4C2×D4711yescharacteristic
240C2×C22⋊C4C2×D4711yescharacteristic
241C2×C22⋊C4C2×D4711yescharacteristic
242C2×C42—471no—
243C2×C42—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
252C24C22×D4711yescharacteristic
253C24C22×D4711yescharacteristic
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—471no—
265C22×C4—942no—
266C22×C4—1881no—
267C22×C4—1881no—
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—942no—
275C4⋊C4—942no—
276C4⋊C4—942no—
277C4⋊C4—942no—
278C4⋊C4—942no—
279C4⋊C4—942no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C4⋊C4—1881no—
283C4⋊C4—1881no—
284C4⋊C4—1881no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—474no—
290C22⋊C4—942no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—942no—
294C22⋊C4—942no—
295C22⋊C4—1881no—
296C42—942no—
297C42—942no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23D4×D4712yes—
312C23C23×D4711yescharacteristic
313D4—44no—
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—472no—
329C2×C4—472no—
330C2×C4—472no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
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—941no—
351C2×C4—941no—
352C2×C4—1884no—
353C2×C4#1062535212yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C2×D4×D4711yescharacteristic
369C22#41×D4711yescharacteristic
370C22C2×#1062535211yescharacteristic
371C22#1309406911yescharacteristic
372C22#1309406911yescharacteristic
373C22#1309407111yescharacteristic
374C22#1309407111yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—942no—
381C4—942no—
382C4—942no—
383C4—1881no—
384C4—1881no—
385C4—1881no—
386C4—1881no—
387C4—1881no—
388C2—42no—
389C2—81no—
390C2#1568968811yescharacteristic
391C2#1568971811yescharacteristic
392C2#1568973711yescharacteristic
393C2#1568977111yescharacteristic
394C2#1568977311yescharacteristic
395C2#1568982011yescharacteristic
396C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2718
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094017C2semidirect
3. #15689064C2semidirect
4. #15689059C2semidirect
5. #15689056C2semidirect
6. #15689046C2semidirect
8. #15689020C2semidirect
9. #15689016C2semidirect
10. #15689011C2semidirect
11. #15689011C2semidirect
12. #15688998C2semidirect
13. #15688995C2semidirect
14. #15688992C2semidirect
214. C47#2718semidirect