Finite Group Databasebeta

← C47×#61322 #26101020

Subgroups — C47×#61322 #26101020

Order 12032.

1782 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C47C211yesmaximal, characteristic
2C2×C47×#557C211yesmaximal, characteristic, complemented
3C47×#3374C216yesmaximal, complemented
4C47×#3372C216yesmaximal, complemented
5C47×#3363C212yesmaximal, complemented
6C47×#3359C212yesmaximal, complemented
7C47×#3139C213yesmaximal, complemented
8C47×#3078C213yesmaximal, complemented
9C47×#3039C213yesmaximal
10Q8×M16×C47C211yesmaximal, characteristic, complemented
11C4×#137×C47C213yesmaximal
12C2×#137×C47C2213yes—
13Q82×C47C2211yescharacteristic
14C47×#557—21no—
15C47×#557—23no—
16C47×#557C2212yes—
17C47×#557C2216yes—
18C47×#557C2213yes—
19C47×#554—23no—
20C47×#554C2213yes—
21D4×Q8×C47—21no—
22D4×Q8×C47C2211yescharacteristic
23C47×#533—23no—
24C47×#533C2213yes—
25C2×C4⋊Q8×C47C2213yes—
26C2×#125×C47—23no—
27C4×#41×C47C2213yes—
28C2×C4×Q8×C47—21no—
29C2×C4×Q8×C47—21no—
30C2×C4×Q8×C47C2213yes—
31C2×C4×Q8×C47C2211yescharacteristic
32C47×#491C22112yes—
33C47×#487C2216yes—
34C47×#487C2216yes—
35C47×#479C22112yes—
36C47×#477C2216yes—
37C47×#475C2216yes—
38C47×#462C2216yes—
39C47×#462C2216yes—
40C47×#461C2216yes—
41C47×#461C2216yes—
42C47×#446C2216yes—
43C8×Q8×C47C2212yes—
44C47×#441C2216yes—
45C47×#440C2216yes—
46C4×Q16×C47C2216yes—
47C4×SD16×C47C2216yes—
48C47×#428C2213yes—
49C47×#423C2213yes—
50C47×#419C2216yes—
51C47×#419C2213yes—
52C47×#417C2211yescharacteristic
53C4×M16×C47C2213yes—
54C2×#41×C47C2311yescharacteristic
55C22×Q8×C47—21no—
56C22×Q8×C47D411yescharacteristic
57C22×Q8×C47C2313yes—
58#137×C47—212no—
59C2×Q16×C47C2316yes—
60C2×SD16×C47C2316yes—
61C2×M16×C47C2313yes—
62C2×M16×C47C2311yescharacteristic
63C4⋊Q8×C47—23no—
64C4⋊Q8×C47—23no—
65C4⋊Q8×C47—23no—
66C4⋊Q8×C47—23no—
67C4⋊Q8×C47C2316yes—
68C4⋊Q8×C47C2316yes—
69C4⋊Q8×C47C2313yes—
70C4⋊Q8×C47C2313yes—
71#125×C47—26no—
72#125×C47—212no—
73#125×C47—26no—
74#125×C47—26no—
75#125×C47C2316yes—
76C22⋊Q8×C47—23no—
77C22⋊Q8×C47—23no—
78C22⋊Q8×C47—23no—
79C22⋊Q8×C47—23no—
80C22⋊Q8×C47—26no—
81C4×Q8×C47—21no—
82C4×Q8×C47—26no—
83C4×Q8×C47—22no—
84C4×Q8×C47—23no—
85C4×Q8×C47—23no—
86C4×Q8×C47—23no—
87C4×Q8×C47—23no—
88C4×Q8×C47—23no—
89C4×Q8×C47D411yescharacteristic
90C4×Q8×C47D413yes—
91C4×Q8×C47C2313yes—
92C4×Q8×C47C2313yes—
93C4×Q8×C47C2316yes—
94C4×Q8×C47C2316yes—
95C4×Q8×C47C2311yescharacteristic
96C4×Q8×C47C2313yes—
97C4×D4×C47—23no—
98C4×D4×C47—23no—
99C4×D4×C47C2313yes—
100C4×D4×C47C2313yes—
101#117×C47—23no—
102#117×C47C2313yes—
103C2×C4⋊C4×C47—23no—
104C2×C4⋊C4×C47—23no—
105C2×C4⋊C4×C47—23no—
106C2×C4⋊C4×C47—23no—
107C2×C4⋊C4×C47D413yes—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C42×C47—23no—
110C2×C42×C47—23no—
111C2×C42×C47C2313yes—
112#107×C47C2316yes—
113#106×C47C2316yes—
114C4⋊C8×C47C2316yes—
115C4⋊C8×C47C2316yes—
116#103×C47C23112yes—
117#103×C47C23112yes—
118#103×C47C2316yes—
119#103×C47C2316yes—
120#103×C47C2312yes—
121#102×C47C2312yes—
122#97×C47C2316yes—
123C4×C8×C47C2316yes—
124#41×C47—22no—
125#41×C47#4114yes—
126C2×Q8×C47—24no—
127C2×Q8×C47—23no—
128C2×Q8×C47—23no—
129C2×Q8×C47—23no—
130C2×Q8×C47—26no—
131C2×Q8×C47—26no—
132C2×Q8×C47—44no—
133C2×Q8×C47C2×D413yes—
134C2×Q8×C47C2×D411yescharacteristic
135C2×Q8×C47C2416yes—
136C2×Q8×C47C2411yescharacteristic
137C2×D4×C47—21no—
138C2×D4×C47C2411yescharacteristic
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—23no—
142C22×C4×C47—23no—
143C22×C4×C47—23no—
144C22×C4×C47C2×D413yes—
145C22×C4×C47C2×D413yes—
146C22×C4×C47C2411yescharacteristic
147Q16×C47—212no—
148SD16×C47—212no—
149M16×C47—26no—
150M16×C47—22no—
151C2×C8×C47C2412yes—
152C2×C8×C47C2416yes—
153C4⋊C4×C47—26no—
154C4⋊C4×C47—23no—
155C4⋊C4×C47—26no—
156C4⋊C4×C47—26no—
157C4⋊C4×C47—26no—
158C4⋊C4×C47—26no—
159C4⋊C4×C47—26no—
160C4⋊C4×C47—26no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—23no—
163C4⋊C4×C47—23no—
164C4⋊C4×C47—23no—
165C4⋊C4×C47—26no—
166C4⋊C4×C47C2×D413yes—
167C4⋊C4×C47C2×D416yes—
168C4⋊C4×C47C2×D413yes—
169C4⋊C4×C47C2413yes—
170C4⋊C4×C47C2413yes—
171C4⋊C4×C47C2412yes—
172C22⋊C4×C47—23no—
173C22⋊C4×C47—23no—
174C22⋊C4×C47—23no—
175C42×C47—23no—
176C42×C47—23no—
177C42×C47—23no—
178C42×C47—26no—
179C42×C47—26no—
180C42×C47C2×D413yes—
181C42×C47C2×D413yes—
182C42×C47C2413yes—
183C42×C47C2413yes—
184C23×C47—21no—
185C23×C47C22×D411yescharacteristic
186Q8×C47—26no—
187Q8×C47—21no—
188Q8×C47—26no—
189Q8×C47—26no—
190Q8×C47—46no—
191Q8×C47—46no—
192Q8×C47—83no—
193Q8×C47#13714yescomplemented
194Q8×C47C2×#4112yes—
195D4×C47—24no—
196D4×C47—21no—
197D4×C47C2×#4112yes—
198C2×C4×C47—21no—
199C2×C4×C47—24no—
200C2×C4×C47—26no—
201C2×C4×C47—22no—
202C2×C4×C47—23no—
203C2×C4×C47—23no—
204C2×C4×C47—26no—
205C2×C4×C47—43no—
206C2×C4×C47—42no—
207C2×C4×C47—46no—
208C2×C4×C47—46no—
209C2×C4×C47—83no—
210C2×C4×C47C22×D413yes—
211C2×C4×C47C22×D413yes—
212C2×C4×C47C22×D413yes—
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C22×D413yes—
215C2×C4×C47C2×#4112yes—
216C2×C4×C472−1+412yes—
217C2×C4×C47C2511yescharacteristic
218C8×C47—26no—
219C8×C47—22no—
220#61322C4711yesmaximal, characteristic, direct product factor, Sylow
221C22×C47—21no—
222C22×C47—21no—
223C22×C47—22no—
224C22×C47—41no—
225C22×C47—41no—
226C22×C47#54812yes—
227C22×C47C23×D411yescharacteristic
228C4×C47—23no—
229C4×C47—23no—
230C4×C47—22no—
231C4×C47—23no—
232C4×C47—42no—
233C4×C47—43no—
234C4×C47—46no—
235C4×C47—43no—
236C4×C47#54812yes—
237C4×C47C2×#13716yes—
238C4×C47C22×#4111yescharacteristic
239C4×C47C2×2−1+411yescharacteristic
240Q8×#41C2×C4711yescharacteristic
241C2×#557C2×C4711yescharacteristic, complemented
242#3374C2×C4716yescomplemented
243#3372C2×C4716yescomplemented
244#3363C2×C4712yescomplemented
245#3359C2×C4712yescomplemented
246#3139C2×C4713yescomplemented
247#3078C2×C4713yescomplemented
248#3039C2×C4713yes—
249Q8×M16C2×C4711yescharacteristic, complemented
250C4×#137C2×C4713yes—
251C2×C47—22no—
252C2×C47—42no—
253C2×C47C2×#54811yescharacteristic
254C2×C47C22×#13711yescharacteristic
255C2×C47#358611yescharacteristic
256C2×#137C22×C4713yes—
257Q82C22×C4711yescharacteristic
258#557—21no—
259#557—23no—
260#557C22×C4712yes—
261#557C22×C4716yes—
262#557C22×C4713yes—
263#554—23no—
264#554C22×C4713yes—
265D4×Q8—21no—
266D4×Q8C22×C4711yescharacteristic
267#533—23no—
268#533C22×C4713yes—
269C2×C4⋊Q8C22×C4713yes—
270C2×#125—23no—
271C4×#41C22×C4713yes—
272C2×C4×Q8—21no—
273C2×C4×Q8—21no—
274C2×C4×Q8C22×C4713yes—
275C2×C4×Q8C22×C4711yescharacteristic
276#491C22×C47112yes—
277#487C22×C4716yes—
278#487C22×C4716yes—
279#479C22×C47112yes—
280#477C22×C4716yes—
281#475C22×C4716yes—
282#462C22×C4716yes—
283#462C22×C4716yes—
284#461C22×C4716yes—
285#461C22×C4716yes—
286#446C22×C4716yes—
287C8×Q8C22×C4712yes—
288#441C22×C4716yes—
289#440C22×C4716yes—
290C4×Q16C22×C4716yes—
291C4×SD16C22×C4716yes—
292#428C22×C4713yes—
293#423C22×C4713yes—
294#419C22×C4716yes—
295#419C22×C4713yes—
296#417C22×C4711yescharacteristic
297C4×M16C22×C4713yes—
298C47#6132211yescharacteristic, direct product factor, Sylow
299C2×#41C23×C4711yescharacteristic
300C22×Q8—21no—
301C22×Q8D4×C4711yescharacteristic
302C22×Q8C23×C4713yes—
303#137—212no—
304C2×Q16C23×C4716yes—
305C2×SD16C23×C4716yes—
306C2×M16C23×C4713yes—
307C2×M16C23×C4711yescharacteristic
308C4⋊Q8—23no—
309C4⋊Q8—23no—
310C4⋊Q8—23no—
311C4⋊Q8—23no—
312C4⋊Q8C23×C4716yes—
313C4⋊Q8C23×C4716yes—
314C4⋊Q8C23×C4713yes—
315C4⋊Q8C23×C4713yes—
316#125—26no—
317#125—212no—
318#125—26no—
319#125—26no—
320#125C23×C4716yes—
321C22⋊Q8—23no—
322C22⋊Q8—23no—
323C22⋊Q8—23no—
324C22⋊Q8—23no—
325C22⋊Q8—26no—
326C4×Q8—21no—
327C4×Q8—26no—
328C4×Q8—22no—
329C4×Q8—23no—
330C4×Q8—23no—
331C4×Q8—23no—
332C4×Q8—23no—
333C4×Q8—23no—
334C4×Q8D4×C4711yescharacteristic
335C4×Q8D4×C4713yes—
336C4×Q8C23×C4716yes—
337C4×Q8C23×C4716yes—
338C4×Q8C23×C4713yes—
339C4×Q8C23×C4713yes—
340C4×Q8C23×C4711yescharacteristic
341C4×Q8C23×C4713yes—
342C4×D4—23no—
343C4×D4—23no—
344C4×D4C23×C4713yes—
345C4×D4C23×C4713yes—
346#117—23no—
347#117C23×C4713yes—
348C2×C4⋊C4—23no—
349C2×C4⋊C4—23no—
350C2×C4⋊C4—23no—
351C2×C4⋊C4—23no—
352C2×C4⋊C4D4×C4713yes—
353C2×C4⋊C4C23×C4711yescharacteristic
354C2×C42—23no—
355C2×C42—23no—
356C2×C42C23×C4713yes—
357#107C23×C4716yes—
358#106C23×C4716yes—
359C4⋊C8C23×C4716yes—
360C4⋊C8C23×C4716yes—
361#103C23×C4712yes—
362#103C23×C4716yes—
363#103C23×C4716yes—
364#103C23×C47112yes—
365#103C23×C47112yes—
366#102C23×C4712yes—
367#97C23×C4716yes—
368C4×C8C23×C4716yes—
369#41—22no—
370#41#41×C4714yes—
371C2×Q8—24no—
372C2×Q8—23no—
373C2×Q8—23no—
374C2×Q8—23no—
375C2×Q8—26no—
376C2×Q8—26no—
377C2×Q8—44no—
378C2×Q8C2×D4×C4713yes—
379C2×Q8C2×D4×C4711yescharacteristic
380C2×Q8C24×C4716yes—
381C2×Q8C24×C4711yescharacteristic
382C2×D4—21no—
383C2×D4C24×C4711yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—23no—
387C22×C4—23no—
388C22×C4—23no—
389C22×C4C2×D4×C4713yes—
390C22×C4C2×D4×C4713yes—
391C22×C4C24×C4711yescharacteristic
392Q16—212no—
393SD16—212no—
394M16—26no—
395M16—22no—
396C2×C8C24×C4712yes—
397C2×C8C24×C4716yes—
398C4⋊C4—26no—
399C4⋊C4—23no—
400C4⋊C4—26no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4—26no—
404C4⋊C4—26no—
405C4⋊C4—26no—
406C4⋊C4—21no—
407C4⋊C4—23no—
408C4⋊C4—23no—
409C4⋊C4—23no—
410C4⋊C4—26no—
411C4⋊C4C2×D4×C4713yes—
412C4⋊C4C2×D4×C4716yes—
413C4⋊C4C2×D4×C4713yes—
414C4⋊C4C24×C4712yes—
415C4⋊C4C24×C4713yes—
416C4⋊C4C24×C4713yes—
417C22⋊C4—23no—
418C22⋊C4—23no—
419C22⋊C4—23no—
420C42—23no—
421C42—23no—
422C42—23no—
423C42—26no—
424C42—26no—
425C42C2×D4×C4713yes—
426C42C2×D4×C4713yes—
427C42C24×C4713yes—
428C42C24×C4713yes—
429C23—21no—
430C23C22×D4×C4711yescharacteristic
431Q8—26no—
432Q8—21no—
433Q8—26no—
434Q8—26no—
435Q8—46no—
436Q8—46no—
437Q8—83no—
438Q8#137×C4714yescomplemented
439Q8C2×#41×C4712yes—
440D4—24no—
441D4—21no—
442D4C2×#41×C4712yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—26no—
446C2×C4—22no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—26no—
450C2×C4—43no—
451C2×C4—42no—
452C2×C4—46no—
453C2×C4—46no—
454C2×C4—83no—
455C2×C4C22×D4×C4713yes—
456C2×C4C22×D4×C4713yes—
457C2×C4C22×D4×C4713yes—
458C2×C4C22×D4×C4711yescharacteristic
459C2×C4C22×D4×C4713yes—
460C2×C4C2×#41×C4712yes—
461C2×C42−1+4×C4712yes—
462C2×C4C25×C4711yescharacteristic
463C8—26no—
464C8—22no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22C47×#54812yes—
471C22C23×D4×C4711yescharacteristic
472C4—23no—
473C4—23no—
474C4—23no—
475C4—22no—
476C4—43no—
477C4—42no—
478C4—43no—
479C4—46no—
480C4C47×#54812yes—
481C4C2×#137×C4716yes—
482C4C22×#41×C4711yescharacteristic
483C4C2×2−1+4×C4711yescharacteristic
484C2—22no—
485C2—42no—
486C2C2×C47×#54811yescharacteristic
487C2C22×#137×C4711yescharacteristic
488C2C47×#358611yescharacteristic
subgroupG/H
center, socleC22×C47C23×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC2×#41×C47C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C4×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#557C2semidirect
3. C47×#3374C2semidirect
4. C47×#3372C2semidirect
5. C47×#3363C2semidirect
6. C47×#3359C2semidirect
7. C47×#3139C2semidirect
8. C47×#3078C2semidirect
10. Q8×M16×C47C2semidirect
193. Q8×C47#137semidirect
220. #61322C47direct (N × H)
241. C2×#557C2×C47semidirect
242. #3374C2×C47semidirect
243. #3372C2×C47semidirect
244. #3363C2×C47semidirect
245. #3359C2×C47semidirect
246. #3139C2×C47semidirect
247. #3078C2×C47semidirect
249. Q8×M16C2×C47semidirect
298. C47#61322direct (N × H)
438. Q8#137×C47semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C472
C2×C47×#5572
C47×#33742
C47×#33722
C47×#33632
C47×#33592
C47×#31392
C47×#30782
C47×#30392
Q8×M16×C472
C4×#137×C472
#6132247