Finite Group Databasebeta

← C47×#2692 #20240302

Subgroups — C47×#2692 #20240302

Order 6016.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
3C47×#399C211yesmaximal, characteristic, complemented
4C47×#398C211yesmaximal, characteristic, complemented
5C47×#396C211yesmaximal, characteristic, complemented
6C47×#395C211yesmaximal, characteristic, complemented
7C47×#393C211yesmaximal, characteristic, complemented
8C47×#393C211yesmaximal, characteristic, complemented
9C47×#391C211yesmaximal, characteristic, complemented
10C47×#390C211yesmaximal, characteristic
11C47×#387C211yesmaximal, characteristic, complemented
12C47×#386C211yesmaximal, characteristic
13C47×#386C211yesmaximal, characteristic
14C47×#385C211yesmaximal, characteristic, complemented
15C47×#380C211yesmaximal, characteristic, complemented
16C22×Q8×C47C2211yescharacteristic
17C22×Q8×C47C2211yescharacteristic
18C22×D4×C47C2211yescharacteristic
19C23×C4×C47C2211yescharacteristic
20C23×C4×C47C2211yescharacteristic
21C22⋊Q8×C47—24no—
22C22⋊Q8×C47—24no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C22⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2211yescharacteristic
37C2×C22⋊C4×C47C2211yescharacteristic
38C2×C22⋊C4×C47C2211yescharacteristic
39C2×C22⋊C4×C47C2211yescharacteristic
40C2×C22⋊C4×C47C2211yescharacteristic
41C2×C22⋊C4×C47C2211yescharacteristic
42C2×C42×C47C2211yescharacteristic
43#95×C47C2211yescharacteristic
44#95×C47C2211yescharacteristic
45#95×C47C2211yescharacteristic
46#95×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C2×Q8×C47—22no—
56C2×Q8×C47—22no—
57C2×Q8×C47—22no—
58C2×Q8×C47—41no—
59C2×Q8×C47—41no—
60C2×Q8×C47—41no—
61C2×D4×C47—41no—
62C2×D4×C47—41no—
63C2×D4×C47Q814yescomplemented
64C22×C4×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C22×C4×C47C2311yescharacteristic
82C22×C4×C47C2311yescharacteristic
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47—22no—
86C4⋊C4×C47—22no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47D414yescomplemented
92C22⋊C4×C47—22no—
93C22⋊C4×C47—22no—
94C22⋊C4×C47—22no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C42×C47—41no—
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×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47C2×Q812yes—
116C23×C47C2×Q812yes—
117C23×C47C2411yescharacteristic
118Q8×C47—44no—
119Q8×C47—44no—
120D4×C47—44no—
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×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—44no—
156C2×C4×C47—44no—
157C2×C4×C47C2×D412yes—
158C2×C4×C47C2×D412yes—
159C2×C4×C47C2×D412yes—
160C2×C4×C47C2×Q812yes—
161C2×C4×C47#4112yes—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22×D411yescharacteristic
177C22×C47C22×Q811yescharacteristic
178C22×C47C2×#4111yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C47H(5,𝔽2)11yescharacteristic
181C22×C47H(5,𝔽2)11yescharacteristic
182C22×C472−1+411yescharacteristic
183C4×C47—22no—
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—22no—
187C4×C47—22no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47—41no—
195C4×C47—41no—
196#2692C4711yesmaximal, characteristic, direct product factor, Sylow
197C2×C47—42no—
198C2×C47—42no—
199C2×C47#53511yescharacteristic
200C2×C47#54211yescharacteristic
201C2×C47#54311yescharacteristic
202C2×C47#54611yescharacteristic
203C2×C47D4×Q811yescharacteristic
204C2×C47#55411yescharacteristic
205C2×C47#56211yescharacteristic
206C2×C22⋊Q8C2×C4711yescharacteristic, complemented
207C2×C22⋊Q8C2×C4711yescharacteristic, complemented
208#399C2×C4711yescharacteristic, complemented
209#398C2×C4711yescharacteristic, complemented
210#396C2×C4711yescharacteristic, complemented
211#395C2×C4711yescharacteristic, complemented
212#393C2×C4711yescharacteristic, complemented
213#393C2×C4711yescharacteristic, complemented
214#391C2×C4711yescharacteristic, complemented
215#390C2×C4711yescharacteristic
216#387C2×C4711yescharacteristic, complemented
217#386C2×C4711yescharacteristic
218#386C2×C4711yescharacteristic
219#385C2×C4711yescharacteristic, complemented
220#380C2×C4711yescharacteristic, complemented
221C47#269211yescharacteristic, direct product factor, Sylow
222C22×Q8C22×C4711yescharacteristic
223C22×Q8C22×C4711yescharacteristic
224C22×D4C22×C4711yescharacteristic
225C23×C4C22×C4711yescharacteristic
226C23×C4C22×C4711yescharacteristic
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C2×C4⋊C4C22×C4711yescharacteristic
230C2×C4⋊C4C22×C4711yescharacteristic
231C2×C4⋊C4C22×C4711yescharacteristic
232C2×C4⋊C4C22×C4711yescharacteristic
233C2×C4⋊C4C22×C4711yescharacteristic
234C2×C4⋊C4C22×C4711yescharacteristic
235C2×C4⋊C4C22×C4711yescharacteristic
236C2×C4⋊C4C22×C4711yescharacteristic
237C2×C4⋊C4C22×C4711yescharacteristic
238C2×C22⋊C4C22×C4711yescharacteristic
239C2×C22⋊C4C22×C4711yescharacteristic
240C2×C22⋊C4C22×C4711yescharacteristic
241C2×C22⋊C4C22×C4711yescharacteristic
242C2×C22⋊C4C22×C4711yescharacteristic
243C2×C22⋊C4C22×C4711yescharacteristic
244C2×C22⋊C4C22×C4711yescharacteristic
245C2×C22⋊C4C22×C4711yescharacteristic
246C2×C22⋊C4C22×C4711yescharacteristic
247C2×C22⋊C4C22×C4711yescharacteristic
248C2×C42C22×C4711yescharacteristic
249#95C22×C4711yescharacteristic
250#95C22×C4711yescharacteristic
251#95C22×C4711yescharacteristic
252#95C22×C4711yescharacteristic
253#95C22×C4711yescharacteristic
254#95C22×C4711yescharacteristic
255#95C22×C4711yescharacteristic
256#95C22×C4711yescharacteristic
257#95C22×C4711yescharacteristic
258#95C22×C4711yescharacteristic
259C24C23×C4711yescharacteristic
260C24C23×C4711yescharacteristic
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4Q8×C4714yescomplemented
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4C23×C4711yescharacteristic
277C22×C4C23×C4711yescharacteristic
278C22×C4C23×C4711yescharacteristic
279C22×C4C23×C4711yescharacteristic
280C22×C4C23×C4711yescharacteristic
281C22×C4C23×C4711yescharacteristic
282C22×C4C23×C4711yescharacteristic
283C22×C4C23×C4711yescharacteristic
284C22×C4C23×C4711yescharacteristic
285C22×C4C23×C4711yescharacteristic
286C22×C4C23×C4711yescharacteristic
287C22×C4C23×C4711yescharacteristic
288C22×C4C23×C4711yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4D4×C4714yescomplemented
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×Q8×C4712yes—
322C23C2×Q8×C4712yes—
323C23C24×C4711yescharacteristic
324Q8—44no—
325Q8—44no—
326D4—44no—
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—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4C2×D4×C4712yes—
364C2×C4C2×D4×C4712yes—
365C2×C4C2×D4×C4712yes—
366C2×C4C2×Q8×C4712yes—
367C2×C4#41×C4712yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22C22×D4×C4711yescharacteristic
383C22C22×Q8×C4711yescharacteristic
384C22C2×#41×C4711yescharacteristic
385C22H(5,𝔽2)×C4711yescharacteristic
386C22H(5,𝔽2)×C4711yescharacteristic
387C22H(5,𝔽2)×C4711yescharacteristic
388C222−1+4×C4711yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C2—42no—
403C2—42no—
404C2C47×#53511yescharacteristic
405C2C47×#54211yescharacteristic
406C2C47×#54311yescharacteristic
407C2C47×#54611yescharacteristic
408C2D4×Q8×C4711yescharacteristic
409C2C47×#55411yescharacteristic
410C2C47×#56211yescharacteristic
subgroupG/H
center, socleC23×C47C24
commutator, Frattini, cosocleC23C24×C47
prime radicalC22×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×C47C2semidirect
2. C2×C22⋊Q8×C47C2semidirect
3. C47×#399C2semidirect
4. C47×#398C2semidirect
5. C47×#396C2semidirect
6. C47×#395C2semidirect
7. C47×#393C2semidirect
8. C47×#393C2semidirect
9. C47×#391C2semidirect
11. C47×#387C2semidirect
14. C47×#385C2semidirect
15. C47×#380C2semidirect
63. C2×D4×C47Q8semidirect
91. C4⋊C4×C47D4semidirect
196. #2692C47direct (N × H)
206. C2×C22⋊Q8C2×C47semidirect
207. C2×C22⋊Q8C2×C47semidirect
208. #399C2×C47semidirect
209. #398C2×C47semidirect
210. #396C2×C47semidirect
211. #395C2×C47semidirect
212. #393C2×C47semidirect
213. #393C2×C47semidirect
214. #391C2×C47semidirect
216. #387C2×C47semidirect
219. #385C2×C47semidirect
220. #380C2×C47semidirect
221. C47#2692direct (N × H)
269. C2×D4Q8×C47semidirect
297. C4⋊C4D4×C47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C22⋊Q8×C472
C47×#3992
C47×#3982
C47×#3962
C47×#3952
C47×#3932
C47×#3912
C47×#3902
C47×#3872
C47×#3862
C47×#3852
C47×#3802
#269247