Finite Group Databasebeta

← #20249979

Subgroups — #20249979

Order 6016.

506 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic
2C2×#13094002C211yesmaximal, characteristic, complemented
3#15689050C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689044C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic
7#15689035C211yesmaximal, characteristic, complemented
8#15689028C211yesmaximal, characteristic, complemented
9#15689027C211yesmaximal, characteristic, complemented
10#15689017C211yesmaximal, characteristic, complemented
11#15689012C211yesmaximal, characteristic, complemented
12#15689006C211yesmaximal, characteristic, complemented
13#15688999C211yesmaximal, characteristic
14#15688985C211yesmaximal, characteristic, complemented
15C47×#397C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094010—24no—
21#13094002—24no—
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
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
50#95×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—22no—
63C2×C22⋊D47—41no—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×Dic94—22no—
75C2×Dic94—22no—
76C2×Dic94—22no—
77C2×Dic94—22no—
78C2×Dic94—41no—
79C2×Dic94—41no—
80C4⋊C4×C47—22no—
81C22⋊C4×C47—22no—
82C22⋊C4×C47—41no—
83C22⋊C4×C47—41no—
84C22⋊Dic47—22no—
85C22⋊Dic47—22no—
86C22⋊Dic47—41no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—41no—
90(C2×D47)⋊C4—41no—
91(C2×D47)⋊C4D414yes—
92C4⋊Dic47—22no—
93C4⋊Dic47—41no—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—41no—
97C4×Dic47—22no—
98C4×Dic47—41no—
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×D47C2×D412yes—
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×C47C2×D412yes—
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×Dic47#4112yes—
153C2×Dic47#4112yes—
154C4×D47—44no—
155Dic94—44no—
156Dic94—44no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C22×C47C2×#4111yescharacteristic
166C22×C47C2×#4111yescharacteristic
167C22×C47H(5,𝔽2)11yescharacteristic
168C22×C47H(5,𝔽2)11yescharacteristic
169C22×C472−1+411yescharacteristic
170C22×C472−1+411yescharacteristic
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—22no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184Dic47—22no—
185Dic47—22no—
186Dic47—22no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191#2700—471nomaximal, Sylow
192C2×C47—81no—
193C2×C47#53611yescharacteristic
194C2×C47#54211yescharacteristic
195C2×C47#54211yescharacteristic
196C2×C47#54611yescharacteristic
197C2×C47#54611yescharacteristic
198C2×C47#55611yescharacteristic
199C2×C47#56211yescharacteristic
200D47—42no—
201C2×#124—471no—
202C2×C22⋊Q8—471no—
203#397—471no—
204#397D4711yescharacteristic, complemented
205#396—471no—
206#395—471no—
207#394—471no—
208#393—471no—
209#391—471no—
210#391—471no—
211#388—471no—
212#388—471no—
213#387—471no—
214#386—471no—
215#381—471no—
216C47#270011yescharacteristic, complemented, Sylow
217C22×Q8—471no—
218C22×Q8—471no—
219C22×D4—471no—
220C23×C4—471no—
221#124—944no—
222C22⋊Q8—944no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4C2×D4711yescharacteristic
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—
242#95—471no—
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
253#95C2×D4711yescharacteristic
254C24—471no—
255C24C22×D4711yescharacteristic
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—942no—
259C2×Q8—942no—
260C2×Q8—1881no—
261C2×Q8—1881no—
262C2×D4—942no—
263C2×D4—942no—
264C2×D4—1881no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—942no—
273C22×C4—942no—
274C22×C4—1881no—
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277C22×C4C22×D4711yescharacteristic
278C22×C4C22×D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—942no—
283C4⋊C4—942no—
284C4⋊C4—942no—
285C4⋊C4—1881no—
286C4⋊C4—1881no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—474no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—942no—
294C22⋊C4—942no—
295C22⋊C4—1881no—
296C22⋊C4—1881no—
297C22⋊C4—1881no—
298C42—942no—
299C42—1881no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—472no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23—941no—
312C23—941no—
313C23—941no—
314C23C23×D4711yescharacteristic
315Q8—1884no—
316Q8—1884no—
317D4—1884no—
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—21no—
334C2×C4—21no—
335C2×C4—472no—
336C2×C4—472no—
337C2×C4—472no—
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—941no—
355C2×C4—941no—
356C2×C4—1884no—
357C2×C4D4×D4712yes—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—942no—
366C22—942no—
367C22—942no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22C2×D4×D4711yescharacteristic
373C22#41×D4711yescharacteristic
374C22#41×D4711yescharacteristic
375C22#1309406911yescharacteristic
376C22#1309407011yescharacteristic
377C22#1309407111yescharacteristic
378C22#1309407111yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—942no—
386C4—942no—
387C4—942no—
388C4—1881no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C2—81no—
393C2—1882no—
394C2#1568969311yescharacteristic
395C2#1568973911yescharacteristic
396C2#1568974111yescharacteristic
397C2#1568976511yescharacteristic
398C2#1568977011yescharacteristic
399C2#1568984011yescharacteristic
400C2#1568987011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2700
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#13094002C2semidirect
3. #15689050C2semidirect
4. #15689046C2semidirect
5. #15689044C2semidirect
7. #15689035C2semidirect
8. #15689028C2semidirect
9. #15689027C2semidirect
10. #15689017C2semidirect
11. #15689012C2semidirect
12. #15689006C2semidirect
14. #15688985C2semidirect
15. C47×#397C2semidirect
204. #397D47semidirect
216. C47#2700semidirect