Finite Group Databasebeta

← C47×#63032 #26102730

Subgroups — C47×#63032 #26102730

Order 12032.

6420 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3563C2112yesmaximal, complemented
2C47×#3556C213yesmaximal, complemented
3C47×#3555C216yesmaximal, complemented
4C47×#3552C216yesmaximal, complemented
5C47×#3523C212yesmaximal, complemented
6C47×#3523C216yesmaximal, complemented
7C47×#3516C214yesmaximal, complemented
8C47×#3515C216yesmaximal, complemented
9C47×#3509C213yesmaximal, complemented
10C47×#3503C213yesmaximal, complemented
11C47×#3503C211yesmaximal, characteristic, complemented
12C47×#3502C212yesmaximal, complemented
13C47×#3482C213yesmaximal, complemented
14C47×#3482C211yesmaximal, characteristic, complemented
15C47×#3482C211yesmaximal, characteristic, complemented
16Q8×#41×C47C212yesmaximal, complemented
17C2×C47×#557C212yesmaximal, complemented
18C47×#564C22112yes—
19C47×#563C22124yes—
20Q82×C47C2216yes—
21Q82×C47C2212yes—
22C47×#557C2216yes—
23C47×#557C2216yes—
24C47×#557C22112yes—
25C47×#557C2213yes—
26C47×#557C2216yes—
27C47×#557C2216yes—
28C47×#557C2216yes—
29C47×#557C22112yes—
30C47×#557C2211yescharacteristic
31C47×#557C2214yes—
32C47×#557C2212yes—
33C47×#557C2216yes—
34C47×#557C2211yescharacteristic
35C47×#556C2216yes—
36C47×#556C2216yes—
37C47×#556C2213yes—
38C47×#556C22112yes—
39C47×#556C2213yes—
40C47×#556C2213yes—
41C47×#554C22112yes—
42C47×#554C2216yes—
43C47×#554C22112yes—
44C47×#554C2216yes—
45C47×#553C22112yes—
46C47×#552C22112yes—
47C47×#552C22112yes—
48C47×#552C2216yes—
49C47×#552C2216yes—
50C47×#552C22112yes—
51C47×#552C22124yes—
52C47×#552C22112yes—
53C47×#552C2216yes—
54D4×Q8×C47C2216yes—
55D4×Q8×C47C22112yes—
56D4×Q8×C47C2211yescharacteristic
57D4×Q8×C47C2214yes—
58D4×Q8×C47C2213yes—
59D4×Q8×C47C2211yescharacteristic
60C47×#548C2216yes—
61C47×#548C2212yes—
62C47×#548C2212yes—
63C47×#547C2213yes—
64C47×#547C2211yescharacteristic
65C47×#547C2213yes—
66C47×#547C2216yes—
67C47×#544C22112yes—
68C47×#544C2216yes—
69C47×#544C22112yes—
70C47×#544C2216yes—
71C47×#542C22112yes—
72C47×#541C22112yes—
73C47×#541C22112yes—
74C47×#541C22112yes—
75C47×#541C22124yes—
76C47×#541C22112yes—
77C47×#541C22112yes—
78C47×#539C22124yes—
79C47×#536C2216yes—
80C47×#533C2216yes—
81C47×#533C2216yes—
82C47×#533C2213yes—
83C47×#533C2213yes—
84C47×#533C2213yes—
85C47×#533C22112yes—
86C47×#533C2216yes—
87C47×#533C2216yes—
88C2×C4⋊Q8×C47C2216yes—
89C2×C4⋊Q8×C47C2213yes—
90C47×#529C2216yes—
91C47×#529C2216yes—
92C47×#529C2216yes—
93C47×#529C22112yes—
94C47×#529C22112yes—
95C2×#125×C47C22112yes—
96C47×#520C2216yes—
97C47×#520C2212yes—
98C47×#519C2214yes—
99C47×#519C2216yes—
100C4×#41×C47C2216yes—
101C4×#41×C47C2213yes—
102C4×#41×C47C2211yescharacteristic
103C4×#41×C47C2213yes—
104C2×C4×Q8×C47C2214yes—
105C2×C4×Q8×C47C2216yes—
106C2×C4×Q8×C47C2212yes—
107C2×C4×Q8×C47C2212yes—
108C2×#41×C47C2312yes—
109C2×#41×C47C2313yes—
110C2×#41×C47C2311yescharacteristic
111C2×#41×C47C2313yes—
112C22×Q8×C47C2312yes—
113C22×Q8×C47C2312yes—
114C22×Q8×C47C2316yes—
115C22×Q8×C47C2316yes—
116C4⋊Q8×C47C2313yes—
117C4⋊Q8×C47C2316yes—
118C4⋊Q8×C47C2313yes—
119C4⋊Q8×C47C2316yes—
120C4⋊Q8×C47C23112yes—
121C4⋊Q8×C47C2316yes—
122C4⋊Q8×C47C23112yes—
123C4⋊Q8×C47C23112yes—
124C4⋊Q8×C47C2313yes—
125C4⋊Q8×C47C2311yescharacteristic
126C4⋊Q8×C47C2313yes—
127C4⋊Q8×C47C2313yes—
128C4⋊Q8×C47C2316yes—
129C4⋊Q8×C47C23112yes—
130C4⋊Q8×C47C23112yes—
131C4⋊Q8×C47C2316yes—
132C4⋊Q8×C47C23124yes—
133#126×C47C23124yes—
134#126×C47C23112yes—
135#126×C47C23112yes—
136#126×C47C23112yes—
137#126×C47C23112yes—
138#126×C47C23112yes—
139#126×C47C23124yes—
140#126×C47C23124yes—
141#125×C47C2316yes—
142#125×C47C23112yes—
143#125×C47C23124yes—
144#125×C47C23124yes—
145#125×C47C23112yes—
146#125×C47C23112yes—
147#125×C47C2316yes—
148#125×C47C23112yes—
149#125×C47C2316yes—
150#125×C47C23112yes—
151#125×C47C23112yes—
152#125×C47C2316yes—
153#125×C47C23124yes—
154#125×C47C23112yes—
155#125×C47C2316yes—
156#125×C47C2316yes—
157#125×C47C23124yes—
158#125×C47C23124yes—
159#125×C47C23124yes—
160#124×C47C2316yes—
161#124×C47C2316yes—
162#124×C47C2316yes—
163#124×C47C23112yes—
164#123×C47C23112yes—
165#123×C47C2314yes—
166#123×C47C23112yes—
167#123×C47C23112yes—
168#123×C47C23112yes—
169#123×C47C23124yes—
170C22⋊Q8×C47C2316yes—
171C22⋊Q8×C47C2316yes—
172C22⋊Q8×C47C23112yes—
173C22⋊Q8×C47C2316yes—
174C22⋊Q8×C47C23112yes—
175C22⋊Q8×C47C2316yes—
176C22⋊Q8×C47C2312yes—
177C22⋊Q8×C47C23112yes—
178C22⋊Q8×C47C23112yes—
179C22⋊Q8×C47C23124yes—
180C22⋊Q8×C47C2316yes—
181C22⋊Q8×C47C2316yes—
182C22⋊Q8×C47C2316yes—
183C22⋊Q8×C47C2316yes—
184C22⋊Q8×C47C2316yes—
185C22⋊Q8×C47C2316yes—
186C22⋊Q8×C47C23112yes—
187C22⋊Q8×C47C23112yes—
188C22⋊Q8×C47C23124yes—
189C22⋊Q8×C47C23124yes—
190#121×C47C2312yes—
191#121×C47C2316yes—
192#121×C47C23112yes—
193#121×C47C2316yes—
194C4×Q8×C47C2312yes—
195C4×Q8×C47C2311yescharacteristic
196C4×Q8×C47C2311yescharacteristic
197C4×Q8×C47C2313yes—
198C4×Q8×C47C2312yes—
199C4×Q8×C47C2316yes—
200C4×Q8×C47C2314yes—
201C4×Q8×C47C2316yes—
202C4×Q8×C47C2316yes—
203C4×Q8×C47C2316yes—
204C4×Q8×C47C23112yes—
205C4×Q8×C47C23112yes—
206C4×Q8×C47C2316yes—
207C4×Q8×C47C2316yes—
208C4×Q8×C47C23112yes—
209C4×Q8×C47C2316yes—
210C4×Q8×C47C23112yes—
211C4×Q8×C47C2313yes—
212C4×Q8×C47C2316yes—
213C4×Q8×C47C2313yes—
214C4×Q8×C47C2313yes—
215C4×Q8×C47C2316yes—
216C4×Q8×C47C23112yes—
217C4×Q8×C47C23112yes—
218C4×Q8×C47C23112yes—
219C4×Q8×C47C23112yes—
220C4×Q8×C47C23112yes—
221C4×Q8×C47C23112yes—
222C4×D4×C47C2311yescharacteristic
223C4×D4×C47C2313yes—
224C4×D4×C47C2311yescharacteristic
225C4×D4×C47C2316yes—
226C4×D4×C47C2313yes—
227C4×D4×C47C2313yes—
228C4×D4×C47C2316yes—
229C4×D4×C47C2313yes—
230C4×D4×C47C2316yes—
231C4×D4×C47C2316yes—
232C4×D4×C47C2316yes—
233C4×D4×C47C23112yes—
234C4×D4×C47C23112yes—
235C4×D4×C47C23124yes—
236C4×D4×C47C23112yes—
237#117×C47C2313yes—
238#117×C47C23112yes—
239#117×C47C2316yes—
240#117×C47C2316yes—
241#117×C47C2313yes—
242#117×C47C2316yes—
243#117×C47C2313yes—
244#117×C47C2316yes—
245#117×C47C23112yes—
246#117×C47C23124yes—
247#117×C47C23112yes—
248#117×C47C2316yes—
249#117×C47C2316yes—
250#117×C47C23112yes—
251C2×C4⋊C4×C47C2312yes—
252C2×C4⋊C4×C47C2316yes—
253C2×C4⋊C4×C47C23112yes—
254C2×C4⋊C4×C47C23112yes—
255C2×C4⋊C4×C47C2316yes—
256C2×C4⋊C4×C47C23112yes—
257C2×C4⋊C4×C47C2316yes—
258C2×C4⋊C4×C47C2316yes—
259C2×C42×C47C23112yes—
260C2×C42×C47C2316yes—
261C2×C42×C47C2316yes—
262C2×C42×C47C2313yes—
263#41×C47—24no—
264#41×C47—28no—
265#41×C47—212no—
266#41×C47—46no—
267C2×Q8×C47—28no—
268C2×Q8×C47—28no—
269C2×Q8×C47—412no—
270C2×Q8×C47—412no—
271C2×Q8×C47C2416yes—
272C2×Q8×C47C2416yes—
273C2×Q8×C47C2412yes—
274C2×Q8×C47C2413yes—
275C2×Q8×C47C2416yes—
276C2×Q8×C47C2413yes—
277C2×Q8×C47C24112yes—
278C2×Q8×C47C24112yes—
279C2×Q8×C47C2411yescharacteristic
280C2×D4×C47C2416yes—
281C2×D4×C47C2414yes—
282C2×D4×C47C2413yes—
283C2×D4×C47C2411yescharacteristic
284C2×D4×C47C2416yes—
285C2×D4×C47C2411yescharacteristic
286C22×C4×C47C2414yes—
287C22×C4×C47C2416yes—
288C22×C4×C47C2412yes—
289C22×C4×C47C2412yes—
290C22×C4×C47C2416yes—
291C22×C4×C47C2413yes—
292C22×C4×C47C2413yes—
293C22×C4×C47C2416yes—
294C22×C4×C47C2413yes—
295C22×C4×C47C24112yes—
296C22×C4×C47C2416yes—
297C22×C4×C47C24112yes—
298C4⋊C4×C47C2416yes—
299C4⋊C4×C47C2411yescharacteristic
300C4⋊C4×C47C2413yes—
301C4⋊C4×C47C24112yes—
302C4⋊C4×C47C2413yes—
303C4⋊C4×C47C2416yes—
304C4⋊C4×C47C2416yes—
305C4⋊C4×C47C24112yes—
306C4⋊C4×C47C2416yes—
307C4⋊C4×C47C2416yes—
308C4⋊C4×C47C2416yes—
309C4⋊C4×C47C24112yes—
310C4⋊C4×C47C24124yes—
311C4⋊C4×C47C2412yes—
312C4⋊C4×C47C2414yes—
313C4⋊C4×C47C24112yes—
314C4⋊C4×C47C24112yes—
315C4⋊C4×C47C24124yes—
316C4⋊C4×C47C24112yes—
317C4⋊C4×C47C24112yes—
318C4⋊C4×C47C2413yes—
319C4⋊C4×C47C2411yescharacteristic
320C4⋊C4×C47C2416yes—
321C4⋊C4×C47C2412yes—
322C4⋊C4×C47C2413yes—
323C4⋊C4×C47C2416yes—
324C4⋊C4×C47C24112yes—
325C4⋊C4×C47C2416yes—
326C4⋊C4×C47C2416yes—
327C4⋊C4×C47C24112yes—
328C4⋊C4×C47C2416yes—
329C4⋊C4×C47C24124yes—
330C4⋊C4×C47C24112yes—
331C4⋊C4×C47C2416yes—
332C4⋊C4×C47C24112yes—
333C22⋊C4×C47C2416yes—
334C22⋊C4×C47C2416yes—
335C22⋊C4×C47C24112yes—
336C22⋊C4×C47C2412yes—
337C22⋊C4×C47C2412yes—
338C22⋊C4×C47C24112yes—
339C22⋊C4×C47C2414yes—
340C22⋊C4×C47C24112yes—
341C22⋊C4×C47C24112yes—
342C22⋊C4×C47C24112yes—
343C22⋊C4×C47C2416yes—
344C22⋊C4×C47C24112yes—
345C22⋊C4×C47C2416yes—
346C22⋊C4×C47C2416yes—
347C42×C47C2413yes—
348C42×C47C2411yescharacteristic
349C42×C47C2413yes—
350C42×C47C2416yes—
351C42×C47C2413yes—
352C42×C47C24112yes—
353C42×C47C2416yes—
354C42×C47C2416yes—
355C42×C47C24112yes—
356C42×C47C2416yes—
357C42×C47C2416yes—
358C42×C47C2416yes—
359C42×C47C24112yes—
360C42×C47C24124yes—
361C23×C47C2512yes—
362C23×C47C2513yes—
363C23×C47C2512yes—
364Q8×C47—212no—
365Q8×C47—212no—
366Q8×C47—24no—
367Q8×C47—26no—
368Q8×C47—212no—
369Q8×C47—26no—
370Q8×C47—412no—
371Q8×C47—412no—
372Q8×C472−1+414yes—
373D4×C47—212no—
374D4×C47—28no—
375D4×C47—26no—
376D4×C47—22no—
377D4×C47—46no—
378D4×C472−1+414yes—
379C2×C4×C47—28no—
380C2×C4×C47—212no—
381C2×C4×C47—212no—
382C2×C4×C47—212no—
383C2×C4×C47—26no—
384C2×C4×C47—24no—
385C2×C4×C47—26no—
386C2×C4×C47—24no—
387C2×C4×C47—26no—
388C2×C4×C47—412no—
389C2×C4×C47—412no—
390C2×C4×C47—46no—
391C2×C4×C47C2512yes—
392C2×C4×C47C2516yes—
393C2×C4×C47C2516yes—
394C2×C4×C47C2512yes—
395C2×C4×C47C2514yes—
396C2×C4×C47C2516yes—
397C2×C4×C47C2511yescharacteristic
398C2×C4×C47C2513yes—
399C2×C4×C47C2513yes—
400C2×C4×C47C25112yes—
401C2×C4×C47C2516yes—
402C2×C4×C47C2513yes—
403C2×C4×C47C2511yescharacteristic
404C2×C4×C47C2511yescharacteristic
405#63032C4711yesmaximal, characteristic, direct product factor, Sylow
406C22×C47—22no—
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—22no—
410C22×C47—23no—
411C22×C47—23no—
412C22×C47—23no—
413C22×C47—22no—
414C22×C47C2×2−1+414yes—
415C22×C47C2611yescharacteristic
416C4×C47—22no—
417C4×C47—23no—
418C4×C47—21no—
419C4×C47—24no—
420C4×C47—26no—
421C4×C47—26no—
422C4×C47—26no—
423C4×C47—23no—
424C4×C47—22no—
425C4×C47—26no—
426C4×C47—212no—
427C4×C47C2×2−1+416yes—
428C4×C47C2×2−1+412yes—
429C4×C47#58512yes—
430#3563C2×C47112yescomplemented
431#3556C2×C4713yescomplemented
432#3555C2×C4716yescomplemented
433#3552C2×C4716yescomplemented
434#3523C2×C4712yescomplemented
435#3523C2×C4716yescomplemented
436#3516C2×C4714yescomplemented
437#3515C2×C4716yescomplemented
438#3509C2×C4713yescomplemented
439#3503C2×C4713yescomplemented
440#3503C2×C4711yescharacteristic, complemented
441#3502C2×C4712yescomplemented
442#3482C2×C4713yescomplemented
443#3482C2×C4711yescharacteristic, complemented
444#3482C2×C4711yescharacteristic, complemented
445Q8×#41C2×C4712yescomplemented
446C2×#557C2×C4712yescomplemented
447C2×C47—24no—
448C2×C47—42no—
449C2×C47—43no—
450C2×C47C22×2−1+411yescharacteristic
451C2×C47C22×2−1+411yescharacteristic
452C2×C47C2×#58511yescharacteristic
453#564C22×C47112yes—
454#563C22×C47124yes—
455Q82C22×C4712yes—
456Q82C22×C4716yes—
457#557C22×C4711yescharacteristic
458#557C22×C4714yes—
459#557C22×C4712yes—
460#557C22×C4716yes—
461#557C22×C4716yes—
462#557C22×C47112yes—
463#557C22×C4716yes—
464#557C22×C4711yescharacteristic
465#557C22×C4713yes—
466#557C22×C4716yes—
467#557C22×C47112yes—
468#557C22×C4716yes—
469#557C22×C4716yes—
470#556C22×C4713yes—
471#556C22×C4713yes—
472#556C22×C4716yes—
473#556C22×C4713yes—
474#556C22×C4716yes—
475#556C22×C47112yes—
476#554C22×C4716yes—
477#554C22×C47112yes—
478#554C22×C4716yes—
479#554C22×C47112yes—
480#553C22×C47112yes—
481#552C22×C4716yes—
482#552C22×C47112yes—
483#552C22×C4716yes—
484#552C22×C4716yes—
485#552C22×C47112yes—
486#552C22×C47112yes—
487#552C22×C47124yes—
488#552C22×C47112yes—
489D4×Q8C22×C4711yescharacteristic
490D4×Q8C22×C4714yes—
491D4×Q8C22×C4713yes—
492D4×Q8C22×C4711yescharacteristic
493D4×Q8C22×C4716yes—
494D4×Q8C22×C47112yes—
495#548C22×C4712yes—
496#548C22×C4712yes—
497#548C22×C4716yes—
498#547C22×C4711yescharacteristic
499#547C22×C4713yes—
500#547C22×C4716yes—
501#547C22×C4713yes—
502#544C22×C47112yes—
503#544C22×C4716yes—
504#544C22×C47112yes—
505#544C22×C4716yes—
506#542C22×C47112yes—
507#541C22×C47112yes—
508#541C22×C47112yes—
509#541C22×C47112yes—
510#541C22×C47112yes—
511#541C22×C47112yes—
512#541C22×C47124yes—
513#539C22×C47124yes—
514#536C22×C4716yes—
515#533C22×C4716yes—
516#533C22×C47112yes—
517#533C22×C4716yes—
518#533C22×C4713yes—
519#533C22×C4713yes—
520#533C22×C4713yes—
521#533C22×C4716yes—
522#533C22×C4716yes—
523C2×C4⋊Q8C22×C4716yes—
524C2×C4⋊Q8C22×C4713yes—
525#529C22×C4716yes—
526#529C22×C47112yes—
527#529C22×C4716yes—
528#529C22×C4716yes—
529#529C22×C47112yes—
530C2×#125C22×C47112yes—
531#520C22×C4716yes—
532#520C22×C4712yes—
533#519C22×C4714yes—
534#519C22×C4716yes—
535C4×#41C22×C4716yes—
536C4×#41C22×C4713yes—
537C4×#41C22×C4711yescharacteristic
538C4×#41C22×C4713yes—
539C2×C4×Q8C22×C4714yes—
540C2×C4×Q8C22×C4716yes—
541C2×C4×Q8C22×C4712yes—
542C2×C4×Q8C22×C4712yes—
543C47#6303211yescharacteristic, direct product factor, Sylow
544C2×#41C23×C4712yes—
545C2×#41C23×C4713yes—
546C2×#41C23×C4711yescharacteristic
547C2×#41C23×C4713yes—
548C22×Q8C23×C4712yes—
549C22×Q8C23×C4712yes—
550C22×Q8C23×C4716yes—
551C22×Q8C23×C4716yes—
552C4⋊Q8C23×C4713yes—
553C4⋊Q8C23×C4716yes—
554C4⋊Q8C23×C4713yes—
555C4⋊Q8C23×C4716yes—
556C4⋊Q8C23×C47112yes—
557C4⋊Q8C23×C4716yes—
558C4⋊Q8C23×C47112yes—
559C4⋊Q8C23×C47112yes—
560C4⋊Q8C23×C4713yes—
561C4⋊Q8C23×C4711yescharacteristic
562C4⋊Q8C23×C4713yes—
563C4⋊Q8C23×C4713yes—
564C4⋊Q8C23×C4716yes—
565C4⋊Q8C23×C47112yes—
566C4⋊Q8C23×C47112yes—
567C4⋊Q8C23×C4716yes—
568C4⋊Q8C23×C47124yes—
569#126C23×C47124yes—
570#126C23×C47112yes—
571#126C23×C47112yes—
572#126C23×C47112yes—
573#126C23×C47112yes—
574#126C23×C47112yes—
575#126C23×C47124yes—
576#126C23×C47124yes—
577#125C23×C4716yes—
578#125C23×C47112yes—
579#125C23×C47124yes—
580#125C23×C47124yes—
581#125C23×C47112yes—
582#125C23×C47112yes—
583#125C23×C4716yes—
584#125C23×C47112yes—
585#125C23×C4716yes—
586#125C23×C47112yes—
587#125C23×C47112yes—
588#125C23×C4716yes—
589#125C23×C47124yes—
590#125C23×C47112yes—
591#125C23×C4716yes—
592#125C23×C4716yes—
593#125C23×C47124yes—
594#125C23×C47124yes—
595#125C23×C47124yes—
596#124C23×C4716yes—
597#124C23×C4716yes—
598#124C23×C4716yes—
599#124C23×C47112yes—
600#123C23×C47112yes—
601#123C23×C4714yes—
602#123C23×C47112yes—
603#123C23×C47112yes—
604#123C23×C47112yes—
605#123C23×C47124yes—
606C22⋊Q8C23×C4716yes—
607C22⋊Q8C23×C4716yes—
608C22⋊Q8C23×C47112yes—
609C22⋊Q8C23×C4716yes—
610C22⋊Q8C23×C47112yes—
611C22⋊Q8C23×C4716yes—
612C22⋊Q8C23×C4712yes—
613C22⋊Q8C23×C47112yes—
614C22⋊Q8C23×C47112yes—
615C22⋊Q8C23×C47124yes—
616C22⋊Q8C23×C4716yes—
617C22⋊Q8C23×C4716yes—
618C22⋊Q8C23×C4716yes—
619C22⋊Q8C23×C4716yes—
620C22⋊Q8C23×C4716yes—
621C22⋊Q8C23×C4716yes—
622C22⋊Q8C23×C47112yes—
623C22⋊Q8C23×C47112yes—
624C22⋊Q8C23×C47124yes—
625C22⋊Q8C23×C47124yes—
626#121C23×C4712yes—
627#121C23×C4716yes—
628#121C23×C47112yes—
629#121C23×C4716yes—
630C4×Q8C23×C4712yes—
631C4×Q8C23×C4711yescharacteristic
632C4×Q8C23×C4711yescharacteristic
633C4×Q8C23×C4713yes—
634C4×Q8C23×C4712yes—
635C4×Q8C23×C4716yes—
636C4×Q8C23×C4714yes—
637C4×Q8C23×C4716yes—
638C4×Q8C23×C4716yes—
639C4×Q8C23×C4716yes—
640C4×Q8C23×C47112yes—
641C4×Q8C23×C47112yes—
642C4×Q8C23×C4716yes—
643C4×Q8C23×C4716yes—
644C4×Q8C23×C47112yes—
645C4×Q8C23×C4716yes—
646C4×Q8C23×C47112yes—
647C4×Q8C23×C4713yes—
648C4×Q8C23×C4716yes—
649C4×Q8C23×C4713yes—
650C4×Q8C23×C4713yes—
651C4×Q8C23×C4716yes—
652C4×Q8C23×C47112yes—
653C4×Q8C23×C47112yes—
654C4×Q8C23×C47112yes—
655C4×Q8C23×C47112yes—
656C4×Q8C23×C47112yes—
657C4×Q8C23×C47112yes—
658C4×D4C23×C4711yescharacteristic
659C4×D4C23×C4713yes—
660C4×D4C23×C4711yescharacteristic
661C4×D4C23×C4716yes—
662C4×D4C23×C4713yes—
663C4×D4C23×C4713yes—
664C4×D4C23×C4716yes—
665C4×D4C23×C4713yes—
666C4×D4C23×C4716yes—
667C4×D4C23×C4716yes—
668C4×D4C23×C4716yes—
669C4×D4C23×C47112yes—
670C4×D4C23×C47112yes—
671C4×D4C23×C47124yes—
672C4×D4C23×C47112yes—
673#117C23×C4713yes—
674#117C23×C47112yes—
675#117C23×C4716yes—
676#117C23×C4716yes—
677#117C23×C4713yes—
678#117C23×C4716yes—
679#117C23×C4713yes—
680#117C23×C4716yes—
681#117C23×C47112yes—
682#117C23×C47124yes—
683#117C23×C47112yes—
684#117C23×C4716yes—
685#117C23×C4716yes—
686#117C23×C47112yes—
687C2×C4⋊C4C23×C4712yes—
688C2×C4⋊C4C23×C4716yes—
689C2×C4⋊C4C23×C47112yes—
690C2×C4⋊C4C23×C47112yes—
691C2×C4⋊C4C23×C4716yes—
692C2×C4⋊C4C23×C47112yes—
693C2×C4⋊C4C23×C4716yes—
694C2×C4⋊C4C23×C4716yes—
695C2×C42C23×C47112yes—
696C2×C42C23×C4716yes—
697C2×C42C23×C4716yes—
698C2×C42C23×C4713yes—
699#41—24no—
700#41—28no—
701#41—212no—
702#41—46no—
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—412no—
706C2×Q8—412no—
707C2×Q8C24×C4716yes—
708C2×Q8C24×C4716yes—
709C2×Q8C24×C4712yes—
710C2×Q8C24×C4713yes—
711C2×Q8C24×C4716yes—
712C2×Q8C24×C4713yes—
713C2×Q8C24×C47112yes—
714C2×Q8C24×C47112yes—
715C2×Q8C24×C4711yescharacteristic
716C2×D4C24×C4716yes—
717C2×D4C24×C4714yes—
718C2×D4C24×C4713yes—
719C2×D4C24×C4711yescharacteristic
720C2×D4C24×C4716yes—
721C2×D4C24×C4711yescharacteristic
722C22×C4C24×C4714yes—
723C22×C4C24×C4716yes—
724C22×C4C24×C4712yes—
725C22×C4C24×C4712yes—
726C22×C4C24×C4716yes—
727C22×C4C24×C4713yes—
728C22×C4C24×C4713yes—
729C22×C4C24×C4716yes—
730C22×C4C24×C4713yes—
731C22×C4C24×C47112yes—
732C22×C4C24×C4716yes—
733C22×C4C24×C47112yes—
734C4⋊C4C24×C4716yes—
735C4⋊C4C24×C4711yescharacteristic
736C4⋊C4C24×C4713yes—
737C4⋊C4C24×C47112yes—
738C4⋊C4C24×C4713yes—
739C4⋊C4C24×C4716yes—
740C4⋊C4C24×C4716yes—
741C4⋊C4C24×C47112yes—
742C4⋊C4C24×C4716yes—
743C4⋊C4C24×C4716yes—
744C4⋊C4C24×C4716yes—
745C4⋊C4C24×C47112yes—
746C4⋊C4C24×C47124yes—
747C4⋊C4C24×C4712yes—
748C4⋊C4C24×C4714yes—
749C4⋊C4C24×C47112yes—
750C4⋊C4C24×C47112yes—
751C4⋊C4C24×C47124yes—
752C4⋊C4C24×C47112yes—
753C4⋊C4C24×C47112yes—
754C4⋊C4C24×C4713yes—
755C4⋊C4C24×C4711yescharacteristic
756C4⋊C4C24×C4716yes—
757C4⋊C4C24×C4712yes—
758C4⋊C4C24×C4713yes—
759C4⋊C4C24×C4716yes—
760C4⋊C4C24×C47112yes—
761C4⋊C4C24×C4716yes—
762C4⋊C4C24×C4716yes—
763C4⋊C4C24×C47112yes—
764C4⋊C4C24×C4716yes—
765C4⋊C4C24×C47124yes—
766C4⋊C4C24×C47112yes—
767C4⋊C4C24×C4716yes—
768C4⋊C4C24×C47112yes—
769C22⋊C4C24×C4716yes—
770C22⋊C4C24×C4716yes—
771C22⋊C4C24×C47112yes—
772C22⋊C4C24×C4712yes—
773C22⋊C4C24×C4712yes—
774C22⋊C4C24×C47112yes—
775C22⋊C4C24×C4714yes—
776C22⋊C4C24×C47112yes—
777C22⋊C4C24×C47112yes—
778C22⋊C4C24×C47112yes—
779C22⋊C4C24×C4716yes—
780C22⋊C4C24×C47112yes—
781C22⋊C4C24×C4716yes—
782C22⋊C4C24×C4716yes—
783C42C24×C4713yes—
784C42C24×C4711yescharacteristic
785C42C24×C4713yes—
786C42C24×C4716yes—
787C42C24×C4713yes—
788C42C24×C47112yes—
789C42C24×C4716yes—
790C42C24×C4716yes—
791C42C24×C47112yes—
792C42C24×C4716yes—
793C42C24×C4716yes—
794C42C24×C4716yes—
795C42C24×C47112yes—
796C42C24×C47124yes—
797C23C25×C4712yes—
798C23C25×C4713yes—
799C23C25×C4712yes—
800Q8—212no—
801Q8—212no—
802Q8—24no—
803Q8—26no—
804Q8—212no—
805Q8—26no—
806Q8—412no—
807Q8—412no—
808Q82−1+4×C4714yes—
809D4—212no—
810D4—28no—
811D4—26no—
812D4—22no—
813D4—46no—
814D42−1+4×C4714yes—
815C2×C4—28no—
816C2×C4—212no—
817C2×C4—212no—
818C2×C4—212no—
819C2×C4—26no—
820C2×C4—24no—
821C2×C4—26no—
822C2×C4—24no—
823C2×C4—26no—
824C2×C4—412no—
825C2×C4—412no—
826C2×C4—46no—
827C2×C4C25×C4712yes—
828C2×C4C25×C4716yes—
829C2×C4C25×C4716yes—
830C2×C4C25×C4712yes—
831C2×C4C25×C4714yes—
832C2×C4C25×C4716yes—
833C2×C4C25×C4711yescharacteristic
834C2×C4C25×C4713yes—
835C2×C4C25×C4713yes—
836C2×C4C25×C47112yes—
837C2×C4C25×C4716yes—
838C2×C4C25×C4713yes—
839C2×C4C25×C4711yescharacteristic
840C2×C4C25×C4711yescharacteristic
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—23no—
846C22—23no—
847C22—23no—
848C22—22no—
849C22C2×2−1+4×C4714yes—
850C22C26×C4711yescharacteristic
851C4—22no—
852C4—23no—
853C4—21no—
854C4—24no—
855C4—26no—
856C4—26no—
857C4—26no—
858C4—23no—
859C4—22no—
860C4—26no—
861C4—212no—
862C4C2×2−1+4×C4716yes—
863C4C2×2−1+4×C4712yes—
864C4C47×#58512yes—
865C2—24no—
866C2—42no—
867C2—43no—
868C2C22×2−1+4×C4711yescharacteristic
869C2C22×2−1+4×C4711yescharacteristic
870C2C2×C47×#58511yescharacteristic
subgroupG/H
center, socleC22×C47C26
commutator, Frattini, cosocleC22C26×C47
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3563C2semidirect
2. C47×#3556C2semidirect
3. C47×#3555C2semidirect
4. C47×#3552C2semidirect
5. C47×#3523C2semidirect
6. C47×#3523C2semidirect
7. C47×#3516C2semidirect
8. C47×#3515C2semidirect
9. C47×#3509C2semidirect
10. C47×#3503C2semidirect
11. C47×#3503C2semidirect
12. C47×#3502C2semidirect
13. C47×#3482C2semidirect
14. C47×#3482C2semidirect
15. C47×#3482C2semidirect
16. Q8×#41×C47C2semidirect
17. C2×C47×#557C2semidirect
405. #63032C47direct (N × H)
430. #3563C2×C47semidirect
431. #3556C2×C47semidirect
432. #3555C2×C47semidirect
433. #3552C2×C47semidirect
434. #3523C2×C47semidirect
435. #3523C2×C47semidirect
436. #3516C2×C47semidirect
437. #3515C2×C47semidirect
438. #3509C2×C47semidirect
439. #3503C2×C47semidirect
440. #3503C2×C47semidirect
441. #3502C2×C47semidirect
442. #3482C2×C47semidirect
443. #3482C2×C47semidirect
444. #3482C2×C47semidirect
445. Q8×#41C2×C47semidirect
446. C2×#557C2×C47semidirect
543. C47#63032direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35632
C47×#35562
C47×#35552
C47×#35522
C47×#35232
C47×#35162
C47×#35152
C47×#35092
C47×#35032
C47×#35022
C47×#34822
Q8×#41×C472
C2×C47×#5572
#6303247