Finite Group Databasebeta

← C47×#36577 #26076275

Subgroups — C47×#36577 #26076275

Order 12032.

2312 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#557C211yesmaximal, characteristic, complemented
2C22×C4×Q8×C47C211yesmaximal, characteristic
3C47×#2857C213yesmaximal
4C47×#2582C213yesmaximal, complemented
5C47×#2568C213yesmaximal, complemented
6C47×#2453C216yesmaximal, complemented
7C47×#2442C216yesmaximal
8C47×#2351C212yesmaximal, complemented
9Q8×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C47C212yesmaximal
11C4×C22⋊Q8×C47C213yesmaximal
12C23×Q8×C47C2211yescharacteristic
13C47×#557—28no—
14C2×C4⋊Q8×C47C2213yes—
15C2×#125×C47C2216yes—
16C2×C22⋊Q8×C47C2213yes—
17C2×C4×Q8×C47—28no—
18C2×C4×Q8×C47C2213yes—
19C2×C4×Q8×C47C2213yes—
20C2×C4×Q8×C47C2212yes—
21C2×C4×Q8×C47C2212yes—
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×Q8×C47C2213yes—
24C2×C4×Q8×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2213yes—
26C22×C42×C47C2213yes—
27C47×#400C22112yes—
28C47×#398C22112yes—
29C47×#391C2213yes—
30C47×#391C2216yes—
31C47×#391C2216yes—
32C47×#391C2216yes—
33C47×#389C2213yes—
34C47×#389C2216yes—
35C47×#389C2216yes—
36C47×#389C2216yes—
37C47×#389C2216yes—
38C47×#387C2216yes—
39C47×#385C2216yes—
40C47×#384C2213yes—
41C47×#382C2216yes—
42C47×#380C2211yescharacteristic
43C47×#380C2216yes—
44C47×#380C2216yes—
45C4×C4⋊C4×C47C2213yes—
46C4×C4⋊C4×C47C2216yes—
47C4×C22⋊C4×C47C2216yes—
48C22×Q8×C47—24no—
49C22×Q8×C47—24no—
50C22×Q8×C47Q818yescomplemented
51C22×Q8×C47C2313yes—
52C22×Q8×C47C2313yes—
53C22×Q8×C47C2311yescharacteristic
54C23×C4×C47C2313yes—
55C23×C4×C47C2313yes—
56C23×C4×C47C2311yescharacteristic
57C4⋊Q8×C47—212no—
58#125×C47—224no—
59C22⋊Q8×C47—212no—
60C4×Q8×C47—24no—
61C4×Q8×C47—28no—
62C4×Q8×C47—28no—
63C4×Q8×C47—212no—
64C4×Q8×C47—212no—
65C4×Q8×C47—212no—
66C4×Q8×C47D418yes—
67C2×C4⋊C4×C47—212no—
68C2×C4⋊C4×C47C2313yes—
69C2×C4⋊C4×C47C2316yes—
70C2×C4⋊C4×C47C2311yescharacteristic
71C2×C4⋊C4×C47C2316yes—
72C2×C4⋊C4×C47C2316yes—
73C2×C4⋊C4×C47C2316yes—
74C2×C4⋊C4×C47C2313yes—
75C2×C4⋊C4×C47C2316yes—
76C2×C4⋊C4×C47C2316yes—
77C2×C4⋊C4×C47C2311yescharacteristic
78C2×C4⋊C4×C47C2316yes—
79C2×C4⋊C4×C47C2316yes—
80C2×C4⋊C4×C47C2313yes—
81C2×C22⋊C4×C47C2316yes—
82C2×C22⋊C4×C47C2312yes—
83C2×C42×C47—212no—
84C2×C42×C47C2313yes—
85C2×C42×C47C2313yes—
86C2×C42×C47C2313yes—
87C2×C42×C47C2316yes—
88C2×C42×C47C2316yes—
89C2×C42×C47C2313yes—
90#95×C47C2316yes—
91#95×C47C2316yes—
92#95×C47C2312yes—
93#95×C47C2316yes—
94#95×C47C2316yes—
95#95×C47C23112yes—
96#95×C47C23112yes—
97C24×C47C2411yescharacteristic
98C2×Q8×C47—232no—
99C2×Q8×C47—26no—
100C2×Q8×C47—26no—
101C2×Q8×C47—26no—
102C2×Q8×C47—26no—
103C2×Q8×C47—26no—
104C2×Q8×C47C2×D414yes—
105C2×Q8×C47C2×Q8112yes—
106C2×Q8×C47C2×Q814yes—
107C2×Q8×C47#4114yes—
108C22×C4×C47—22no—
109C22×C4×C47—26no—
110C22×C4×C47—26no—
111C22×C4×C47—22no—
112C22×C4×C47—26no—
113C22×C4×C47—26no—
114C22×C4×C47—43no—
115C22×C4×C47C2×Q8112yes—
116C22×C4×C47#4114yes—
117C22×C4×C47C2412yes—
118C22×C4×C47C2412yes—
119C22×C4×C47C2413yes—
120C22×C4×C47C2416yes—
121C22×C4×C47C2416yes—
122C22×C4×C47C2413yes—
123C22×C4×C47C2413yes—
124C22×C4×C47C2411yescharacteristic
125C22×C4×C47C2413yes—
126C22×C4×C47C2411yescharacteristic
127C4⋊C4×C47—212no—
128C4⋊C4×C47—26no—
129C4⋊C4×C47—22no—
130C4⋊C4×C47—212no—
131C4⋊C4×C47—212no—
132C4⋊C4×C47—212no—
133C4⋊C4×C47—212no—
134C4⋊C4×C47—26no—
135C4⋊C4×C47—212no—
136C4⋊C4×C47—22no—
137C4⋊C4×C47—46no—
138C4⋊C4×C47—46no—
139C4⋊C4×C47C2×D4112yes—
140C22⋊C4×C47—212no—
141C22⋊C4×C47—24no—
142C42×C47—26no—
143C42×C47—26no—
144C42×C47—26no—
145C42×C47—212no—
146C42×C47—212no—
147C42×C47C2×D4112yes—
148C23×C47—21no—
149C23×C47—21no—
150C23×C47—21no—
151C23×C47—21no—
152C23×C47C22×Q812yes—
153C23×C47C2×#4112yes—
154C23×C472−1+412yes—
155C23×C47C2511yescharacteristic
156Q8×C47—224no—
157Q8×C47—412no—
158Q8×C47C22⋊Q8116yescomplemented
159C2×C4×C47—21no—
160C2×C4×C47—23no—
161C2×C4×C47—23no—
162C2×C4×C47—21no—
163C2×C4×C47—23no—
164C2×C4×C47—23no—
165C2×C4×C47—224no—
166C2×C4×C47—28no—
167C2×C4×C47—22no—
168C2×C4×C47—23no—
169C2×C4×C47—26no—
170C2×C4×C47—22no—
171C2×C4×C47—26no—
172C2×C4×C47—26no—
173C2×C4×C47—26no—
174C2×C4×C47—22no—
175C2×C4×C47—22no—
176C2×C4×C47—22no—
177C2×C4×C47—23no—
178C2×C4×C47—26no—
179C2×C4×C47—26no—
180C2×C4×C47—22no—
181C2×C4×C47—23no—
182C2×C4×C47—412no—
183C2×C4×C47C22×D416yes—
184C2×C4×C47C22×D416yes—
185C2×C4×C47C22×D412yes—
186C2×C4×C47C22×Q816yes—
187C2×C4×C47C22×Q816yes—
188C2×C4×C47C2×#4112yes—
189C2×C4×C47C2×#4116yes—
190C2×C4×C47C2×#4112yes—
191C2×C4×C472−1+412yes—
192#36577C4711yesmaximal, characteristic, direct product factor, Sylow
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47#55714yescomplemented
200C22×C47C23×D411yescharacteristic
201C22×C47C23×Q811yescharacteristic
202C22×C47C22×#4111yescharacteristic
203C22×C47C22×#4111yescharacteristic
204C22×C47C2×2−1+411yescharacteristic
205C22×C47C2×2−1+411yescharacteristic
206C22×C47#58511yescharacteristic
207C4×C47—26no—
208C4×C47—22no—
209C4×C47—26no—
210C4×C47—46no—
211C4×C47—46no—
212C4×C47—42no—
213C4×C47—43no—
214C4×C47—42no—
215C4×C47C2×C22⋊Q8112yes—
216C4×C47#54814yes—
217C2×#557C2×C4711yescharacteristic, complemented
218C22×C4×Q8C2×C4711yescharacteristic
219#2857C2×C4713yes—
220#2582C2×C4713yescomplemented
221#2568C2×C4713yescomplemented
222#2453C2×C4716yescomplemented
223#2442C2×C4716yes—
224#2351C2×C4712yescomplemented
225Q8×C4⋊C4C2×C4711yescharacteristic, complemented
226Q8×C22⋊C4C2×C4712yes—
227C4×C22⋊Q8C2×C4713yes—
228C2×C47—24no—
229C2×C47C22×C22⋊Q811yescharacteristic
230C2×C47C2×#54811yescharacteristic
231C2×C47C2×#55711yescharacteristic
232C2×C47#348011yescharacteristic
233C2×C47#348911yescharacteristic
234C2×C47#350211yescharacteristic
235C2×C47#352311yescharacteristic
236C23×Q8C22×C4711yescharacteristic
237#557—28no—
238C2×C4⋊Q8C22×C4713yes—
239C2×#125C22×C4716yes—
240C2×C22⋊Q8C22×C4713yes—
241C2×C4×Q8—28no—
242C2×C4×Q8C22×C4713yes—
243C2×C4×Q8C22×C4713yes—
244C2×C4×Q8C22×C4712yes—
245C2×C4×Q8C22×C4712yes—
246C2×C4×Q8C22×C4711yescharacteristic
247C2×C4×Q8C22×C4713yes—
248C2×C4×Q8C22×C4711yescharacteristic
249C22×C4⋊C4C22×C4713yes—
250C22×C42C22×C4713yes—
251#400C22×C47112yes—
252#398C22×C47112yes—
253#391C22×C4713yes—
254#391C22×C4716yes—
255#391C22×C4716yes—
256#391C22×C4716yes—
257#389C22×C4713yes—
258#389C22×C4716yes—
259#389C22×C4716yes—
260#389C22×C4716yes—
261#389C22×C4716yes—
262#387C22×C4716yes—
263#385C22×C4716yes—
264#384C22×C4713yes—
265#382C22×C4716yes—
266#380C22×C4716yes—
267#380C22×C4716yes—
268#380C22×C4711yescharacteristic
269C4×C4⋊C4C22×C4713yes—
270C4×C4⋊C4C22×C4716yes—
271C4×C22⋊C4C22×C4716yes—
272C47#3657711yescharacteristic, direct product factor, Sylow
273C22×Q8—24no—
274C22×Q8—24no—
275C22×Q8Q8×C4718yescomplemented
276C22×Q8C23×C4713yes—
277C22×Q8C23×C4713yes—
278C22×Q8C23×C4711yescharacteristic
279C23×C4C23×C4713yes—
280C23×C4C23×C4713yes—
281C23×C4C23×C4711yescharacteristic
282C4⋊Q8—212no—
283#125—224no—
284C22⋊Q8—212no—
285C4×Q8—24no—
286C4×Q8—28no—
287C4×Q8—28no—
288C4×Q8—212no—
289C4×Q8—212no—
290C4×Q8—212no—
291C4×Q8D4×C4718yes—
292C2×C4⋊C4—212no—
293C2×C4⋊C4C23×C4713yes—
294C2×C4⋊C4C23×C4716yes—
295C2×C4⋊C4C23×C4711yescharacteristic
296C2×C4⋊C4C23×C4716yes—
297C2×C4⋊C4C23×C4716yes—
298C2×C4⋊C4C23×C4716yes—
299C2×C4⋊C4C23×C4713yes—
300C2×C4⋊C4C23×C4716yes—
301C2×C4⋊C4C23×C4716yes—
302C2×C4⋊C4C23×C4711yescharacteristic
303C2×C4⋊C4C23×C4716yes—
304C2×C4⋊C4C23×C4716yes—
305C2×C4⋊C4C23×C4713yes—
306C2×C22⋊C4C23×C4716yes—
307C2×C22⋊C4C23×C4712yes—
308C2×C42—212no—
309C2×C42C23×C4716yes—
310C2×C42C23×C4713yes—
311C2×C42C23×C4713yes—
312C2×C42C23×C4713yes—
313C2×C42C23×C4716yes—
314C2×C42C23×C4713yes—
315#95C23×C4716yes—
316#95C23×C4716yes—
317#95C23×C4712yes—
318#95C23×C4716yes—
319#95C23×C4716yes—
320#95C23×C47112yes—
321#95C23×C47112yes—
322C24C24×C4711yescharacteristic
323C2×Q8—232no—
324C2×Q8—26no—
325C2×Q8—26no—
326C2×Q8—26no—
327C2×Q8—26no—
328C2×Q8—26no—
329C2×Q8C2×D4×C4714yes—
330C2×Q8C2×Q8×C47112yes—
331C2×Q8C2×Q8×C4714yes—
332C2×Q8#41×C4714yes—
333C22×C4—22no—
334C22×C4—26no—
335C22×C4—26no—
336C22×C4—22no—
337C22×C4—26no—
338C22×C4—26no—
339C22×C4—43no—
340C22×C4C2×Q8×C47112yes—
341C22×C4#41×C4714yes—
342C22×C4C24×C4712yes—
343C22×C4C24×C4713yes—
344C22×C4C24×C4716yes—
345C22×C4C24×C4716yes—
346C22×C4C24×C4712yes—
347C22×C4C24×C4713yes—
348C22×C4C24×C4713yes—
349C22×C4C24×C4711yescharacteristic
350C22×C4C24×C4713yes—
351C22×C4C24×C4711yescharacteristic
352C4⋊C4—212no—
353C4⋊C4—26no—
354C4⋊C4—22no—
355C4⋊C4—212no—
356C4⋊C4—212no—
357C4⋊C4—212no—
358C4⋊C4—212no—
359C4⋊C4—26no—
360C4⋊C4—212no—
361C4⋊C4—22no—
362C4⋊C4—46no—
363C4⋊C4—46no—
364C4⋊C4C2×D4×C47112yes—
365C22⋊C4—212no—
366C22⋊C4—24no—
367C42—26no—
368C42—26no—
369C42—26no—
370C42—212no—
371C42—212no—
372C42C2×D4×C47112yes—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23C22×Q8×C4712yes—
378C23C2×#41×C4712yes—
379C232−1+4×C4712yes—
380C23C25×C4711yescharacteristic
381Q8—224no—
382Q8—412no—
383Q8C22⋊Q8×C47116yescomplemented
384C2×C4—21no—
385C2×C4—23no—
386C2×C4—23no—
387C2×C4—21no—
388C2×C4—23no—
389C2×C4—23no—
390C2×C4—224no—
391C2×C4—28no—
392C2×C4—22no—
393C2×C4—23no—
394C2×C4—26no—
395C2×C4—22no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—23no—
403C2×C4—26no—
404C2×C4—26no—
405C2×C4—22no—
406C2×C4—23no—
407C2×C4—412no—
408C2×C4C22×D4×C4716yes—
409C2×C4C22×D4×C4716yes—
410C2×C4C22×D4×C4712yes—
411C2×C4C22×Q8×C4716yes—
412C2×C4C22×Q8×C4716yes—
413C2×C4C2×#41×C4712yes—
414C2×C4C2×#41×C4716yes—
415C2×C4C2×#41×C4712yes—
416C2×C42−1+4×C4712yes—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22C47×#55714yescomplemented
424C22C23×D4×C4711yescharacteristic
425C22C23×Q8×C4711yescharacteristic
426C22C22×#41×C4711yescharacteristic
427C22C22×#41×C4711yescharacteristic
428C22C2×2−1+4×C4711yescharacteristic
429C22C2×2−1+4×C4711yescharacteristic
430C22C47×#58511yescharacteristic
431C4—26no—
432C4—22no—
433C4—26no—
434C4—46no—
435C4—46no—
436C4—43no—
437C4—42no—
438C4—42no—
439C4C2×C22⋊Q8×C47112yes—
440C4C47×#54814yes—
441C2—24no—
442C2C22×C22⋊Q8×C4711yescharacteristic
443C2C2×C47×#54811yescharacteristic
444C2C2×C47×#55711yescharacteristic
445C2C47×#348011yescharacteristic
446C2C47×#348911yescharacteristic
447C2C47×#350211yescharacteristic
448C2C47×#352311yescharacteristic
subgroupG/H
center, socleC23×C47C25
commutator, Frattini, cosocleC23C25×C47
prime radicalC24×C47C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#557C2semidirect
4. C47×#2582C2semidirect
5. C47×#2568C2semidirect
6. C47×#2453C2semidirect
8. C47×#2351C2semidirect
9. Q8×C4⋊C4×C47C2semidirect
50. C22×Q8×C47Q8semidirect
158. Q8×C47C22⋊Q8semidirect
192. #36577C47direct (N × H)
199. C22×C47#557semidirect
217. C2×#557C2×C47semidirect
220. #2582C2×C47semidirect
221. #2568C2×C47semidirect
222. #2453C2×C47semidirect
224. #2351C2×C47semidirect
225. Q8×C4⋊C4C2×C47semidirect
272. C47#36577direct (N × H)
275. C22×Q8Q8×C47semidirect
383. Q8C22⋊Q8×C47semidirect
423. C22C47×#557semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5572
C22×C4×Q8×C472
C47×#28572
C47×#25822
C47×#25682
C47×#24532
C47×#24422
C47×#23512
Q8×C4⋊C4×C472
Q8×C22⋊C4×C472
C4×C22⋊Q8×C472
#3657747