Finite Group Databasebeta

← #20249805

Subgroups — #20249805

Order 6016.

512 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×#13094006C211yesmaximal, characteristic
2#15689061C211yesmaximal, characteristic, complemented
3#15689056C211yesmaximal, characteristic, complemented
4#15689053C211yesmaximal, characteristic, complemented
5#15689051C211yesmaximal, characteristic, complemented
6#15689038C211yesmaximal, characteristic
7#15689034C211yesmaximal, characteristic, complemented
8#15689030C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689013C211yesmaximal, characteristic, complemented
11#15689002C211yesmaximal, characteristic
12#15688994C211yesmaximal, characteristic, complemented
13#15688986C211yesmaximal, characteristic, complemented
14#15688980C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13094006—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C22×Q8×C47C2211yescharacteristic
46C23×C4×C47C2211yescharacteristic
47C22⋊Q8×C47—24no—
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C2×Q8×C47—22no—
56C2×Q8×C47—22no—
57C2×Q8×C47—41no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—41no—
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—22no—
68C2×C22⋊D47—22no—
69C2×C22⋊D47—41no—
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—41no—
80C4⋊C4×C47—22no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—22no—
83C22⋊C4×C47—22no—
84C22⋊C4×C47D414yes—
85C22⋊Dic47—22no—
86C22⋊Dic47—41no—
87C22⋊Dic47—41no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—41no—
92(C2×D47)⋊C4—41no—
93C4⋊Dic47—22no—
94C4⋊Dic47—41no—
95Dic47⋊C4—22no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—41no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47C2×D412yes—
106C23×C47C2411yescharacteristic
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47#4112yes—
114Q8×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—21no—
130C2×C4×C47—44no—
131C2×C4×C47C2×D412yes—
132C2×C4×C47C2×D412yes—
133C2×C4×C47#4112yes—
134C22⋊D47—44no—
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—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C4×D47—44no—
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—22no—
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—22no—
180C4×C47—22no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191#2687—471nomaximal, Sylow
192C2×C47—42no—
193C2×C47#53611yescharacteristic
194C2×C47#53911yescharacteristic
195C2×C47#54211yescharacteristic
196C2×C47#54611yescharacteristic
197C2×C47#54611yescharacteristic
198C2×C47#55211yescharacteristic
199C2×C47#56211yescharacteristic
200D47—42no—
201C2×#123—471no—
202C2×C22⋊Q8D4711yescharacteristic, complemented
203#400—471no—
204#398—471no—
205#398—471no—
206#397—471no—
207#394—471no—
208#393—471no—
209#391—471no—
210#388—471no—
211#388—471no—
212#386—471no—
213#385—471no—
214#381—471no—
215#380—471no—
216C47#268711yescharacteristic, complemented, Sylow
217C22×Q8C2×D4711yescharacteristic
218C22×D4—471no—
219C23×C4—471no—
220C23×C4C2×D4711yescharacteristic
221#123—944no—
222C22⋊Q8—24no—
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×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
239C2×C22⋊C4C2×D4711yescharacteristic
240C2×C22⋊C4C2×D4711yescharacteristic
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#95—471no—
252#95—471no—
253#95—471no—
254C24—471no—
255C24C22×D4711yescharacteristic
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×D4—942no—
260C2×D4—942no—
261C2×D4—1881no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
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—22no—
283C4⋊C4—22no—
284C4⋊C4—942no—
285C4⋊C4—942no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C4⋊C4—1881no—
289C22⋊C4—22no—
290C22⋊C4—942no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—942no—
294C22⋊C4—1881no—
295C22⋊C4—1881no—
296C22⋊C4—1881no—
297C22⋊C4—1881no—
298C22⋊C4C22⋊D4714yes—
299C42—1881no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—472no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23—941no—
312C23—941no—
313C23C2×C22⋊D4712yes—
314C23C23×D4711yescharacteristic
315Q8—44no—
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—44no—
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—941no—
353C2×C4—941no—
354C2×C4—1884no—
355C2×C4#1062535212yes—
356C2×C4C2×C22⋊D4712yes—
357C2×C4C2×C22⋊D4712yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—942no—
366C22—942no—
367C22—942no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22C22×C22⋊D4711yescharacteristic
373C22#41×D4711yescharacteristic
374C22C2×#1062535211yescharacteristic
375C22#1309406911yescharacteristic
376C22#1309407011yescharacteristic
377C22#1309407211yescharacteristic
378C22#1309407211yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—1881no—
386C4—1881no—
387C4—1881no—
388C4—1881no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C2—42no—
393C2—1882no—
394C2#1568969711yescharacteristic
395C2#1568971911yescharacteristic
396C2#1568974611yescharacteristic
397C2#1568976111yescharacteristic
398C2#1568976711yescharacteristic
399C2#1568980711yescharacteristic
400C2#1568986911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2687
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689056C2semidirect
4. #15689053C2semidirect
5. #15689051C2semidirect
7. #15689034C2semidirect
8. #15689030C2semidirect
9. #15689016C2semidirect
10. #15689013C2semidirect
12. #15688994C2semidirect
13. #15688986C2semidirect
14. #15688980C2semidirect
15. C2×C22⋊Q8×C47C2semidirect
202. C2×C22⋊Q8D47semidirect
216. C47#2687semidirect