Finite Group Databasebeta

← C47×#63047 #26102745

Subgroups — C47×#63047 #26102745

Order 12032.

6492 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3567C216yesmaximal, complemented
2C47×#3563C213yesmaximal, complemented
3C47×#3559C213yesmaximal, complemented
4C47×#3559C216yesmaximal, complemented
5C47×#3553C216yesmaximal, complemented
6C47×#3548C213yesmaximal, complemented
7C47×#3539C216yesmaximal, complemented
8C47×#3539C2112yesmaximal, complemented
9C47×#3529C212yesmaximal, complemented
10C47×#3529C211yesmaximal, characteristic, complemented
11C47×#3517C213yesmaximal, complemented
12C47×#3515C213yesmaximal, complemented
13C47×#3512C213yesmaximal, complemented
14C47×#3492C216yesmaximal, complemented
15C47×#564C2216yescomplemented
16C47×#563C2213yes—
17C47×#563C2216yes—
18C47×#563C2216yescomplemented
19C47×#562C2216yes—
20C47×#562C2213yes—
21C47×#562C2216yes—
22C47×#562C2213yes—
23C47×#562C2216yescomplemented
24C47×H(3,𝔽4)C2211yescharacteristic
25C47×#560C22112yes—
26C47×#560C2216yes—
27C47×#560C22112yescomplemented
28C47×#557C2213yescomplemented
29C47×#557C2211yescharacteristic, complemented
30C47×#554C2213yes—
31C47×#554C2216yescomplemented
32C47×#554C2216yescomplemented
33C47×#554C22112yescomplemented
34C47×#554C2213yescomplemented
35C47×#553C22112yes—
36C47×#553C2216yes—
37C47×#553C22112yes—
38C47×#553C2216yes—
39C47×#553C22112yescomplemented
40C47×#553C22112yescomplemented
41C47×#553C2216yescomplemented
42C47×#553C22112yescomplemented
43C47×#553C22112yescomplemented
44C47×#553C2216yescomplemented
45C47×#552C2216yes—
46C47×#552C22112yescomplemented
47C47×#552C22112yescomplemented
48C47×#552C22112yescomplemented
49C47×#552C2216yescomplemented
50C47×#552C2216yescomplemented
51C47×#552C2216yescomplemented
52C47×#550C2216yes—
53C47×#550C2216yes—
54C47×#550C2213yes—
55C47×#550C2216yescomplemented
56C47×#550C2211yescharacteristic, complemented
57C47×#547C22112yes—
58C47×#547C2213yes—
59C47×#547C2213yes—
60C47×#547C2216yescomplemented
61C47×#547C2216yescomplemented
62C47×#547C2216yescomplemented
63C47×#547C22112yescomplemented
64C47×#544C2216yescomplemented
65C47×#544C2216yescomplemented
66C47×#541C2216yescomplemented
67C47×#541C22112yescomplemented
68C47×#541C2216yescomplemented
69C47×#540C22112yes—
70C47×#540C22112yes—
71C47×#540C2216yes—
72C47×#540C22112yescomplemented
73C47×#540C2216yescomplemented
74C47×#540C22112yescomplemented
75C47×#539C22112yes—
76C47×#539C2216yes—
77C47×#539C22112yescomplemented
78C47×#539C22112yescomplemented
79C47×#539C22112yescomplemented
80C47×#539C2216yescomplemented
81C47×#539C22112yescomplemented
82C47×#539C22112yescomplemented
83C47×#537C2216yes—
84C47×#537C2216yes—
85C47×#537C2213yes—
86C47×#537C2213yescomplemented
87C47×#537C22112yescomplemented
88C47×#533C2213yescomplemented
89C47×#532C2213yes—
90C47×#532C2216yes—
91C47×#532C2213yescomplemented
92C47×#529C2216yes—
93C47×#529C2213yes—
94C47×#529C2213yes—
95C47×#529C2216yes—
96C47×#529C2216yescomplemented
97C47×#529C2216yescomplemented
98C2×#125×C47C2216yescomplemented
99C2×#125×C47C2213yescomplemented
100C47×#525C2216yes—
101C47×#525C22112yes—
102C47×#525C2216yescomplemented
103C47×#525C22112yescomplemented
104C47×#520C2213yes—
105C47×#520C2216yescomplemented
106C47×#520C2211yescharacteristic, complemented
107C4×#41×C47C2213yescomplemented
108C22×C4⋊C4×C47C2212yescomplemented
109C2×#41×C47C2313yes—
110C2×#41×C47C2313yes—
111C2×#41×C47C2316yes—
112C2×#41×C47C2311yescharacteristic
113C2×#41×C47C2316yes—
114C2×#41×C47C23112yes—
115C2×#41×C47C2312yes—
116C2×#41×C47C2316yes—
117C23×C4×C47C2312yes—
118C23×C4×C47C2314yes—
119C4⋊Q8×C47C2313yes—
120C4⋊Q8×C47C2316yes—
121C4⋊Q8×C47C2313yes—
122C4⋊Q8×C47C2313yes—
123C4⋊Q8×C47C2313yes—
124C4⋊Q8×C47C23112yes—
125#127×C47C2316yes—
126#127×C47C2313yes—
127#127×C47C2313yes—
128#127×C47C23112yes—
129#126×C47C2316yes—
130#126×C47C23112yes—
131#126×C47C23112yes—
132#126×C47C2316yes—
133#126×C47C23112yes—
134#126×C47C23112yes—
135#126×C47C23112yes—
136#126×C47C23112yes—
137#126×C47C23112yes—
138#126×C47C23112yes—
139#125×C47C2313yes—
140#125×C47C2316yes—
141#125×C47C2316yes—
142#125×C47C23112yes—
143#125×C47C2316yes—
144#125×C47C23112yes—
145#125×C47C2316yes—
146#125×C47C2316yes—
147#125×C47C2316yes—
148#125×C47C2316yes—
149#125×C47C2313yes—
150#125×C47C23112yes—
151#125×C47C23112yes—
152#125×C47C23112yes—
153#125×C47C23112yes—
154#125×C47C23112yes—
155#125×C47C23112yes—
156#124×C47C2313yes—
157#124×C47C2313yes—
158#124×C47C2313yes—
159#124×C47C2313yes—
160#124×C47C2316yes—
161#123×C47C2316yes—
162#123×C47C23112yes—
163#123×C47C2316yes—
164#123×C47C23112yes—
165#123×C47C23112yes—
166#123×C47C23112yes—
167#123×C47C23112yes—
168#123×C47C2316yes—
169#123×C47C23112yes—
170#123×C47C23112yes—
171#123×C47C2316yes—
172#123×C47C23112yes—
173#123×C47C23112yes—
174#123×C47C23112yes—
175#123×C47C23112yes—
176#123×C47C23112yes—
177#123×C47C23112yes—
178#123×C47C23112yes—
179#123×C47C23112yes—
180C22⋊Q8×C47C23112yes—
181C22⋊Q8×C47C2316yes—
182C22⋊Q8×C47C2316yes—
183C22⋊Q8×C47C23112yes—
184C22⋊Q8×C47C23112yes—
185C22⋊Q8×C47C2316yes—
186C22⋊Q8×C47C2316yes—
187C22⋊Q8×C47C23112yes—
188C22⋊Q8×C47C2316yes—
189C22⋊Q8×C47C2313yes—
190C22⋊Q8×C47C2316yes—
191C22⋊Q8×C47C2313yes—
192C22⋊Q8×C47C2316yes—
193C22⋊Q8×C47C2316yes—
194C22⋊Q8×C47C2316yes—
195C22⋊Q8×C47C2316yes—
196C22⋊Q8×C47C23112yes—
197C22⋊Q8×C47C23112yes—
198C22⋊Q8×C47C23112yes—
199C22⋊Q8×C47C23112yes—
200#121×C47C23112yes—
201#121×C47C23112yes—
202#121×C47C2316yes—
203#121×C47C2316yes—
204#121×C47C23112yes—
205#121×C47C2316yes—
206#121×C47C2316yes—
207#121×C47C23112yes—
208#121×C47C2313yes—
209#121×C47C2316yes—
210#121×C47C2313yes—
211#121×C47C2316yes—
212#121×C47C2316yes—
213#121×C47C2316yes—
214#121×C47C2316yes—
215#121×C47C23112yes—
216#121×C47C23112yes—
217#121×C47C2316yes—
218#121×C47C2316yes—
219#121×C47C2316yes—
220#121×C47C23112yes—
221#121×C47C23112yes—
222#121×C47C23112yes—
223#121×C47C23112yes—
224#121×C47C23112yes—
225#121×C47C23112yes—
226#121×C47C23112yes—
227#121×C47C23112yes—
228#120×C47C2316yes—
229#120×C47C2316yes—
230#120×C47C23112yes—
231C4×Q8×C47C2313yes—
232C4×Q8×C47C2313yes—
233C4×Q8×C47C2316yes—
234C4×Q8×C47C2312yes—
235C4×Q8×C47C2316yes—
236C4×Q8×C47C2311yescharacteristic
237C4×Q8×C47C2312yes—
238C4×Q8×C47C2311yescharacteristic
239C4×Q8×C47C2316yes—
240C4×Q8×C47C2316yes—
241C4×D4×C47C2313yes—
242C4×D4×C47C2316yes—
243C4×D4×C47C2313yes—
244C4×D4×C47C2316yes—
245C4×D4×C47C2316yes—
246C4×D4×C47C23112yes—
247C4×D4×C47C23112yes—
248C4×D4×C47C23112yes—
249C4×D4×C47C2316yes—
250C4×D4×C47C2316yes—
251C4×D4×C47C2313yes—
252C4×D4×C47C2313yes—
253C4×D4×C47C2316yes—
254C4×D4×C47C2316yes—
255C4×D4×C47C2316yes—
256C4×D4×C47C23112yes—
257C4×D4×C47C23112yes—
258C4×D4×C47C23112yes—
259C4×D4×C47C23112yes—
260C4×D4×C47C23112yes—
261C4×D4×C47C2316yes—
262C4×D4×C47C23112yes—
263C4×D4×C47C23112yes—
264C4×D4×C47C2316yes—
265#117×C47C2313yes—
266#117×C47C2316yes—
267#117×C47C2316yes—
268#117×C47C2316yes—
269#117×C47C23112yes—
270#117×C47C23112yes—
271#117×C47C23112yes—
272#117×C47C23112yes—
273#117×C47C2316yes—
274C2×C4⋊C4×C47C2316yes—
275C2×C4⋊C4×C47C2316yes—
276C2×C4⋊C4×C47C23112yes—
277C2×C4⋊C4×C47C2313yes—
278C2×C4⋊C4×C47C2313yes—
279C2×C4⋊C4×C47C23112yes—
280C2×C4⋊C4×C47C2316yes—
281C2×C4⋊C4×C47C23112yes—
282C2×C4⋊C4×C47C2316yes—
283C2×C4⋊C4×C47C2316yes—
284C2×C4⋊C4×C47C2316yes—
285C2×C42×C47C2316yes—
286C2×C42×C47C2313yes—
287C24×C47C2412yes—
288#41×C47—46no—
289#41×C47—42no—
290#41×C47—412no—
291#41×C47—46no—
292#41×C47—86no—
293#41×C47—812no—
294#41×C47—82no—
295#41×C47—86no—
296C2×Q8×C47C2413yes—
297C2×Q8×C47C2411yescharacteristic
298C2×Q8×C47C2413yes—
299C2×Q8×C47C2411yescharacteristic
300C2×Q8×C47C2416yes—
301C2×Q8×C47C2416yes—
302C2×Q8×C47C2411yescharacteristic
303C2×D4×C47C2413yes—
304C2×D4×C47C2413yes—
305C2×D4×C47C24112yes—
306C2×D4×C47C2416yes—
307C2×D4×C47C2416yes—
308C2×D4×C47C2413yes—
309C2×D4×C47C2416yes—
310C2×D4×C47C24112yes—
311C2×D4×C47C2413yes—
312C2×D4×C47C2416yes—
313C2×D4×C47C2413yes—
314C2×D4×C47C2416yes—
315C2×D4×C47C24112yes—
316C2×D4×C47C24112yes—
317C2×D4×C47C2416yes—
318C22×C4×C47—44no—
319C22×C4×C47—84no—
320C22×C4×C47C2413yes—
321C22×C4×C47C2416yes—
322C22×C4×C47C2413yes—
323C22×C4×C47C2416yes—
324C22×C4×C47C2416yes—
325C22×C4×C47C2416yes—
326C22×C4×C47C2413yes—
327C22×C4×C47C2416yes—
328C22×C4×C47C24112yes—
329C22×C4×C47C2416yes—
330C22×C4×C47C24112yes—
331C22×C4×C47C24112yes—
332C22×C4×C47C24112yes—
333C22×C4×C47C2416yes—
334C4⋊C4×C47C2411yescharacteristic
335C4⋊C4×C47C2416yes—
336C4⋊C4×C47C24112yes—
337C4⋊C4×C47C24112yes—
338C4⋊C4×C47C2413yes—
339C4⋊C4×C47C2416yes—
340C4⋊C4×C47C2416yes—
341C4⋊C4×C47C2416yes—
342C4⋊C4×C47C24112yes—
343C4⋊C4×C47C2413yes—
344C4⋊C4×C47C2416yes—
345C4⋊C4×C47C2413yes—
346C4⋊C4×C47C24112yes—
347C4⋊C4×C47C24112yes—
348C4⋊C4×C47C24112yes—
349C4⋊C4×C47C24112yes—
350C4⋊C4×C47C2416yes—
351C4⋊C4×C47C24112yes—
352C4⋊C4×C47C24112yes—
353C4⋊C4×C47C2416yes—
354C4⋊C4×C47C24112yes—
355C4⋊C4×C47C2416yes—
356C4⋊C4×C47C2416yes—
357C4⋊C4×C47C2416yes—
358C4⋊C4×C47C2416yes—
359C4⋊C4×C47C2416yes—
360C4⋊C4×C47C2416yes—
361C4⋊C4×C47C2413yes—
362C4⋊C4×C47C2413yes—
363C22⋊C4×C47C2416yes—
364C22⋊C4×C47C2416yes—
365C22⋊C4×C47C24112yes—
366C22⋊C4×C47C2416yes—
367C22⋊C4×C47C24112yes—
368C22⋊C4×C47C2416yes—
369C22⋊C4×C47C2416yes—
370C22⋊C4×C47C2416yes—
371C22⋊C4×C47C24112yes—
372C22⋊C4×C47C2416yes—
373C22⋊C4×C47C2416yes—
374C22⋊C4×C47C24112yes—
375C22⋊C4×C47C24112yes—
376C22⋊C4×C47C2416yes—
377C22⋊C4×C47C2416yes—
378C22⋊C4×C47C24112yes—
379C22⋊C4×C47C24112yes—
380C22⋊C4×C47C24112yes—
381C22⋊C4×C47C2416yes—
382C42×C47C2413yes—
383C42×C47C2416yes—
384C42×C47C2416yes—
385C42×C47C2413yes—
386C42×C47C2413yes—
387C42×C47C2413yes—
388C42×C47C2416yes—
389C42×C47C24112yes—
390C42×C47C24112yes—
391C23×C47—42no—
392C23×C47—42no—
393C23×C47—42no—
394C23×C47C2516yes—
395C23×C47C2513yes—
396C23×C47C2516yes—
397Q8×C47—26no—
398Q8×C47—41no—
399Q8×C47—43no—
400Q8×C47—41no—
401Q8×C47—46no—
402Q8×C47—46no—
403Q8×C47—41no—
404D4×C47—26no—
405D4×C47—412no—
406D4×C47—43no—
407D4×C47—46no—
408D4×C47—46no—
409D4×C47—46no—
410D4×C47—43no—
411D4×C47—43no—
412D4×C47—412no—
413D4×C47—46no—
414D4×C47—412no—
415D4×C47—46no—
416D4×C47—412no—
417D4×C47—43no—
418D4×C47—46no—
419C2×C4×C47—212no—
420C2×C4×C47—26no—
421C2×C4×C47—46no—
422C2×C4×C47—412no—
423C2×C4×C47—412no—
424C2×C4×C47—46no—
425C2×C4×C47—46no—
426C2×C4×C47—43no—
427C2×C4×C47—412no—
428C2×C4×C47—46no—
429C2×C4×C47—46no—
430C2×C4×C47—46no—
431C2×C4×C47—412no—
432C2×C4×C47—43no—
433C2×C4×C47C2513yes—
434C2×C4×C47C2512yes—
435C2×C4×C47C2513yes—
436C2×C4×C47C2516yes—
437C2×C4×C47C2513yes—
438C2×C4×C47C2516yes—
439C2×C4×C47C2513yes—
440C2×C4×C47C2516yes—
441C2×C4×C47C2513yes—
442C2×C4×C47C25112yes—
443C2×C4×C47C2511yescharacteristic
444#63047C4711yesmaximal, characteristic, direct product factor, Sylow
445C22×C47—26no—
446C22×C47—23no—
447C22×C47—26no—
448C22×C47—26no—
449C22×C47—23no—
450C22×C47—26no—
451C22×C47—23no—
452C22×C47—26no—
453C22×C47—26no—
454C22×C47—48no—
455C22×C47C2611yescharacteristic
456C4×C47—26no—
457C4×C47—23no—
458C4×C47—26no—
459C4×C47—22no—
460C4×C47—212no—
461C4×C47—23no—
462C4×C47—23no—
463C4×C47—26no—
464C4×C47—23no—
465C4×C47—23no—
466C4×C47#58512yes—
467#3567C2×C4716yescomplemented
468#3563C2×C4713yescomplemented
469#3559C2×C4713yescomplemented
470#3559C2×C4716yescomplemented
471#3553C2×C4716yescomplemented
472#3548C2×C4713yescomplemented
473#3539C2×C4716yescomplemented
474#3539C2×C47112yescomplemented
475#3529C2×C4712yescomplemented
476#3529C2×C4711yescharacteristic, complemented
477#3517C2×C4713yescomplemented
478#3515C2×C4713yescomplemented
479#3512C2×C4713yescomplemented
480#3492C2×C4716yescomplemented
481C2×C47—43no—
482C2×C47—46no—
483C2×C47—46no—
484C2×C47C2×#58511yescharacteristic
485C2×C47H(7,𝔽2)11yescharacteristic
486C2×C472−1+611yescharacteristic
487#564C22×C4716yescomplemented
488#563C22×C4713yes—
489#563C22×C4716yes—
490#563C22×C4716yescomplemented
491#562C22×C4716yes—
492#562C22×C4713yes—
493#562C22×C4716yes—
494#562C22×C4713yes—
495#562C22×C4716yescomplemented
496H(3,𝔽4)C22×C4711yescharacteristic
497#560C22×C47112yes—
498#560C22×C4716yes—
499#560C22×C47112yescomplemented
500#557C22×C4711yescharacteristic, complemented
501#557C22×C4713yescomplemented
502#554C22×C4713yes—
503#554C22×C4716yescomplemented
504#554C22×C47112yescomplemented
505#554C22×C4713yescomplemented
506#554C22×C4716yescomplemented
507#553C22×C4716yes—
508#553C22×C47112yes—
509#553C22×C4716yes—
510#553C22×C47112yes—
511#553C22×C4716yescomplemented
512#553C22×C4716yescomplemented
513#553C22×C47112yescomplemented
514#553C22×C47112yescomplemented
515#553C22×C47112yescomplemented
516#553C22×C47112yescomplemented
517#552C22×C4716yes—
518#552C22×C4716yescomplemented
519#552C22×C47112yescomplemented
520#552C22×C4716yescomplemented
521#552C22×C47112yescomplemented
522#552C22×C4716yescomplemented
523#552C22×C47112yescomplemented
524#550C22×C4716yes—
525#550C22×C4713yes—
526#550C22×C4716yes—
527#550C22×C4711yescharacteristic, complemented
528#550C22×C4716yescomplemented
529#547C22×C4713yes—
530#547C22×C47112yes—
531#547C22×C4713yes—
532#547C22×C4716yescomplemented
533#547C22×C4716yescomplemented
534#547C22×C4716yescomplemented
535#547C22×C47112yescomplemented
536#544C22×C4716yescomplemented
537#544C22×C4716yescomplemented
538#541C22×C4716yescomplemented
539#541C22×C4716yescomplemented
540#541C22×C47112yescomplemented
541#540C22×C4716yes—
542#540C22×C47112yes—
543#540C22×C47112yes—
544#540C22×C4716yescomplemented
545#540C22×C47112yescomplemented
546#540C22×C47112yescomplemented
547#539C22×C47112yes—
548#539C22×C4716yes—
549#539C22×C47112yescomplemented
550#539C22×C47112yescomplemented
551#539C22×C47112yescomplemented
552#539C22×C47112yescomplemented
553#539C22×C47112yescomplemented
554#539C22×C4716yescomplemented
555#537C22×C4716yes—
556#537C22×C4713yes—
557#537C22×C4716yes—
558#537C22×C4713yescomplemented
559#537C22×C47112yescomplemented
560#533C22×C4713yescomplemented
561#532C22×C4713yes—
562#532C22×C4716yes—
563#532C22×C4713yescomplemented
564#529C22×C4716yes—
565#529C22×C4713yes—
566#529C22×C4716yes—
567#529C22×C4713yes—
568#529C22×C4716yescomplemented
569#529C22×C4716yescomplemented
570C2×#125C22×C4713yescomplemented
571C2×#125C22×C4716yescomplemented
572#525C22×C4716yes—
573#525C22×C47112yes—
574#525C22×C4716yescomplemented
575#525C22×C47112yescomplemented
576#520C22×C4713yes—
577#520C22×C4716yescomplemented
578#520C22×C4711yescharacteristic, complemented
579C4×#41C22×C4713yescomplemented
580C22×C4⋊C4C22×C4712yescomplemented
581C47#6304711yescharacteristic, direct product factor, Sylow
582C2×#41C23×C4713yes—
583C2×#41C23×C4713yes—
584C2×#41C23×C4716yes—
585C2×#41C23×C4711yescharacteristic
586C2×#41C23×C4716yes—
587C2×#41C23×C47112yes—
588C2×#41C23×C4712yes—
589C2×#41C23×C4716yes—
590C23×C4C23×C4712yes—
591C23×C4C23×C4714yes—
592C4⋊Q8C23×C4713yes—
593C4⋊Q8C23×C4716yes—
594C4⋊Q8C23×C4713yes—
595C4⋊Q8C23×C4713yes—
596C4⋊Q8C23×C4713yes—
597C4⋊Q8C23×C47112yes—
598#127C23×C4716yes—
599#127C23×C4713yes—
600#127C23×C4713yes—
601#127C23×C47112yes—
602#126C23×C4716yes—
603#126C23×C47112yes—
604#126C23×C47112yes—
605#126C23×C4716yes—
606#126C23×C47112yes—
607#126C23×C47112yes—
608#126C23×C47112yes—
609#126C23×C47112yes—
610#126C23×C47112yes—
611#126C23×C47112yes—
612#125C23×C4713yes—
613#125C23×C4716yes—
614#125C23×C4716yes—
615#125C23×C47112yes—
616#125C23×C4716yes—
617#125C23×C47112yes—
618#125C23×C4716yes—
619#125C23×C4716yes—
620#125C23×C4716yes—
621#125C23×C4716yes—
622#125C23×C4713yes—
623#125C23×C47112yes—
624#125C23×C47112yes—
625#125C23×C47112yes—
626#125C23×C47112yes—
627#125C23×C47112yes—
628#125C23×C47112yes—
629#124C23×C4713yes—
630#124C23×C4713yes—
631#124C23×C4713yes—
632#124C23×C4713yes—
633#124C23×C4716yes—
634#123C23×C4716yes—
635#123C23×C47112yes—
636#123C23×C4716yes—
637#123C23×C47112yes—
638#123C23×C47112yes—
639#123C23×C47112yes—
640#123C23×C47112yes—
641#123C23×C4716yes—
642#123C23×C47112yes—
643#123C23×C47112yes—
644#123C23×C4716yes—
645#123C23×C47112yes—
646#123C23×C47112yes—
647#123C23×C47112yes—
648#123C23×C47112yes—
649#123C23×C47112yes—
650#123C23×C47112yes—
651#123C23×C47112yes—
652#123C23×C47112yes—
653C22⋊Q8C23×C47112yes—
654C22⋊Q8C23×C4716yes—
655C22⋊Q8C23×C4716yes—
656C22⋊Q8C23×C47112yes—
657C22⋊Q8C23×C47112yes—
658C22⋊Q8C23×C4716yes—
659C22⋊Q8C23×C4716yes—
660C22⋊Q8C23×C47112yes—
661C22⋊Q8C23×C4716yes—
662C22⋊Q8C23×C4713yes—
663C22⋊Q8C23×C4716yes—
664C22⋊Q8C23×C4713yes—
665C22⋊Q8C23×C4716yes—
666C22⋊Q8C23×C4716yes—
667C22⋊Q8C23×C4716yes—
668C22⋊Q8C23×C4716yes—
669C22⋊Q8C23×C47112yes—
670C22⋊Q8C23×C47112yes—
671C22⋊Q8C23×C47112yes—
672C22⋊Q8C23×C47112yes—
673#121C23×C47112yes—
674#121C23×C47112yes—
675#121C23×C4716yes—
676#121C23×C4716yes—
677#121C23×C47112yes—
678#121C23×C4716yes—
679#121C23×C4716yes—
680#121C23×C47112yes—
681#121C23×C4713yes—
682#121C23×C4716yes—
683#121C23×C4713yes—
684#121C23×C4716yes—
685#121C23×C4716yes—
686#121C23×C4716yes—
687#121C23×C4716yes—
688#121C23×C47112yes—
689#121C23×C47112yes—
690#121C23×C4716yes—
691#121C23×C4716yes—
692#121C23×C4716yes—
693#121C23×C47112yes—
694#121C23×C47112yes—
695#121C23×C47112yes—
696#121C23×C47112yes—
697#121C23×C47112yes—
698#121C23×C47112yes—
699#121C23×C47112yes—
700#121C23×C47112yes—
701#120C23×C4716yes—
702#120C23×C4716yes—
703#120C23×C47112yes—
704C4×Q8C23×C4713yes—
705C4×Q8C23×C4713yes—
706C4×Q8C23×C4716yes—
707C4×Q8C23×C4712yes—
708C4×Q8C23×C4716yes—
709C4×Q8C23×C4711yescharacteristic
710C4×Q8C23×C4712yes—
711C4×Q8C23×C4711yescharacteristic
712C4×Q8C23×C4716yes—
713C4×Q8C23×C4716yes—
714C4×D4C23×C4713yes—
715C4×D4C23×C4716yes—
716C4×D4C23×C4713yes—
717C4×D4C23×C4716yes—
718C4×D4C23×C4716yes—
719C4×D4C23×C47112yes—
720C4×D4C23×C47112yes—
721C4×D4C23×C47112yes—
722C4×D4C23×C4716yes—
723C4×D4C23×C4716yes—
724C4×D4C23×C4713yes—
725C4×D4C23×C4713yes—
726C4×D4C23×C4716yes—
727C4×D4C23×C4716yes—
728C4×D4C23×C4716yes—
729C4×D4C23×C47112yes—
730C4×D4C23×C47112yes—
731C4×D4C23×C47112yes—
732C4×D4C23×C47112yes—
733C4×D4C23×C47112yes—
734C4×D4C23×C4716yes—
735C4×D4C23×C47112yes—
736C4×D4C23×C47112yes—
737C4×D4C23×C4716yes—
738#117C23×C4713yes—
739#117C23×C4716yes—
740#117C23×C4716yes—
741#117C23×C4716yes—
742#117C23×C47112yes—
743#117C23×C47112yes—
744#117C23×C47112yes—
745#117C23×C47112yes—
746#117C23×C4716yes—
747C2×C4⋊C4C23×C4716yes—
748C2×C4⋊C4C23×C4716yes—
749C2×C4⋊C4C23×C47112yes—
750C2×C4⋊C4C23×C4713yes—
751C2×C4⋊C4C23×C4713yes—
752C2×C4⋊C4C23×C47112yes—
753C2×C4⋊C4C23×C4716yes—
754C2×C4⋊C4C23×C47112yes—
755C2×C4⋊C4C23×C4716yes—
756C2×C4⋊C4C23×C4716yes—
757C2×C4⋊C4C23×C4716yes—
758C2×C42C23×C4716yes—
759C2×C42C23×C4713yes—
760C24C24×C4712yes—
761#41—46no—
762#41—42no—
763#41—412no—
764#41—46no—
765#41—86no—
766#41—812no—
767#41—82no—
768#41—86no—
769C2×Q8C24×C4713yes—
770C2×Q8C24×C4711yescharacteristic
771C2×Q8C24×C4713yes—
772C2×Q8C24×C4711yescharacteristic
773C2×Q8C24×C4716yes—
774C2×Q8C24×C4716yes—
775C2×Q8C24×C4711yescharacteristic
776C2×D4C24×C4713yes—
777C2×D4C24×C4713yes—
778C2×D4C24×C47112yes—
779C2×D4C24×C4716yes—
780C2×D4C24×C4716yes—
781C2×D4C24×C4713yes—
782C2×D4C24×C4716yes—
783C2×D4C24×C47112yes—
784C2×D4C24×C4713yes—
785C2×D4C24×C4716yes—
786C2×D4C24×C4713yes—
787C2×D4C24×C4716yes—
788C2×D4C24×C47112yes—
789C2×D4C24×C47112yes—
790C2×D4C24×C4716yes—
791C22×C4—44no—
792C22×C4—84no—
793C22×C4C24×C4713yes—
794C22×C4C24×C4716yes—
795C22×C4C24×C4713yes—
796C22×C4C24×C4716yes—
797C22×C4C24×C4716yes—
798C22×C4C24×C4716yes—
799C22×C4C24×C4713yes—
800C22×C4C24×C4716yes—
801C22×C4C24×C47112yes—
802C22×C4C24×C4716yes—
803C22×C4C24×C47112yes—
804C22×C4C24×C47112yes—
805C22×C4C24×C47112yes—
806C22×C4C24×C4716yes—
807C4⋊C4C24×C4711yescharacteristic
808C4⋊C4C24×C4716yes—
809C4⋊C4C24×C47112yes—
810C4⋊C4C24×C47112yes—
811C4⋊C4C24×C4713yes—
812C4⋊C4C24×C4716yes—
813C4⋊C4C24×C4716yes—
814C4⋊C4C24×C4716yes—
815C4⋊C4C24×C47112yes—
816C4⋊C4C24×C4713yes—
817C4⋊C4C24×C4716yes—
818C4⋊C4C24×C4713yes—
819C4⋊C4C24×C47112yes—
820C4⋊C4C24×C47112yes—
821C4⋊C4C24×C47112yes—
822C4⋊C4C24×C47112yes—
823C4⋊C4C24×C4716yes—
824C4⋊C4C24×C47112yes—
825C4⋊C4C24×C47112yes—
826C4⋊C4C24×C4716yes—
827C4⋊C4C24×C47112yes—
828C4⋊C4C24×C4716yes—
829C4⋊C4C24×C4716yes—
830C4⋊C4C24×C4716yes—
831C4⋊C4C24×C4716yes—
832C4⋊C4C24×C4716yes—
833C4⋊C4C24×C4716yes—
834C4⋊C4C24×C4713yes—
835C4⋊C4C24×C4713yes—
836C22⋊C4C24×C4716yes—
837C22⋊C4C24×C4716yes—
838C22⋊C4C24×C47112yes—
839C22⋊C4C24×C4716yes—
840C22⋊C4C24×C47112yes—
841C22⋊C4C24×C4716yes—
842C22⋊C4C24×C4716yes—
843C22⋊C4C24×C4716yes—
844C22⋊C4C24×C47112yes—
845C22⋊C4C24×C4716yes—
846C22⋊C4C24×C4716yes—
847C22⋊C4C24×C47112yes—
848C22⋊C4C24×C47112yes—
849C22⋊C4C24×C4716yes—
850C22⋊C4C24×C4716yes—
851C22⋊C4C24×C47112yes—
852C22⋊C4C24×C47112yes—
853C22⋊C4C24×C47112yes—
854C22⋊C4C24×C4716yes—
855C42C24×C4713yes—
856C42C24×C4716yes—
857C42C24×C4716yes—
858C42C24×C4713yes—
859C42C24×C4713yes—
860C42C24×C4713yes—
861C42C24×C4716yes—
862C42C24×C47112yes—
863C42C24×C47112yes—
864C23—42no—
865C23—42no—
866C23—42no—
867C23C25×C4716yes—
868C23C25×C4713yes—
869C23C25×C4716yes—
870Q8—26no—
871Q8—41no—
872Q8—43no—
873Q8—41no—
874Q8—46no—
875Q8—46no—
876Q8—41no—
877D4—26no—
878D4—412no—
879D4—43no—
880D4—46no—
881D4—46no—
882D4—46no—
883D4—43no—
884D4—43no—
885D4—412no—
886D4—46no—
887D4—412no—
888D4—46no—
889D4—412no—
890D4—43no—
891D4—46no—
892C2×C4—212no—
893C2×C4—26no—
894C2×C4—46no—
895C2×C4—412no—
896C2×C4—412no—
897C2×C4—46no—
898C2×C4—46no—
899C2×C4—43no—
900C2×C4—412no—
901C2×C4—46no—
902C2×C4—46no—
903C2×C4—46no—
904C2×C4—412no—
905C2×C4—43no—
906C2×C4C25×C4713yes—
907C2×C4C25×C4712yes—
908C2×C4C25×C4713yes—
909C2×C4C25×C4716yes—
910C2×C4C25×C4713yes—
911C2×C4C25×C4716yes—
912C2×C4C25×C4713yes—
913C2×C4C25×C4716yes—
914C2×C4C25×C4713yes—
915C2×C4C25×C47112yes—
916C2×C4C25×C4711yescharacteristic
917C22—26no—
918C22—23no—
919C22—26no—
920C22—26no—
921C22—23no—
922C22—26no—
923C22—23no—
924C22—26no—
925C22—26no—
926C22—48no—
927C22C26×C4711yescharacteristic
928C4—26no—
929C4—23no—
930C4—26no—
931C4—22no—
932C4—212no—
933C4—23no—
934C4—23no—
935C4—26no—
936C4—23no—
937C4—23no—
938C4C47×#58512yes—
939C2—46no—
940C2—43no—
941C2—46no—
942C2C2×C47×#58511yescharacteristic
943C2C47×H(7,𝔽2)11yescharacteristic
944C2C47×2−1+611yescharacteristic
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×#3567C2semidirect
2. C47×#3563C2semidirect
3. C47×#3559C2semidirect
4. C47×#3559C2semidirect
5. C47×#3553C2semidirect
6. C47×#3548C2semidirect
7. C47×#3539C2semidirect
8. C47×#3539C2semidirect
9. C47×#3529C2semidirect
10. C47×#3529C2semidirect
11. C47×#3517C2semidirect
12. C47×#3515C2semidirect
13. C47×#3512C2semidirect
14. C47×#3492C2semidirect
15. C47×#564C22semidirect
18. C47×#563C22semidirect
23. C47×#562C22semidirect
27. C47×#560C22semidirect
28. C47×#557C22semidirect
29. C47×#557C22semidirect
31. C47×#554C22semidirect
32. C47×#554C22semidirect
33. C47×#554C22semidirect
34. C47×#554C22semidirect
39. C47×#553C22semidirect
40. C47×#553C22semidirect
41. C47×#553C22semidirect
42. C47×#553C22semidirect
43. C47×#553C22semidirect
44. C47×#553C22semidirect
46. C47×#552C22semidirect
47. C47×#552C22semidirect
48. C47×#552C22semidirect
49. C47×#552C22semidirect
50. C47×#552C22semidirect
51. C47×#552C22semidirect
55. C47×#550C22semidirect
56. C47×#550C22semidirect
60. C47×#547C22semidirect
61. C47×#547C22semidirect
62. C47×#547C22semidirect
63. C47×#547C22semidirect
64. C47×#544C22semidirect
65. C47×#544C22semidirect
66. C47×#541C22semidirect
67. C47×#541C22semidirect
68. C47×#541C22semidirect
72. C47×#540C22semidirect
73. C47×#540C22semidirect
74. C47×#540C22semidirect
77. C47×#539C22semidirect
78. C47×#539C22semidirect
79. C47×#539C22semidirect
80. C47×#539C22semidirect
81. C47×#539C22semidirect
82. C47×#539C22semidirect
86. C47×#537C22semidirect
87. C47×#537C22semidirect
88. C47×#533C22semidirect
91. C47×#532C22semidirect
96. C47×#529C22semidirect
97. C47×#529C22semidirect
98. C2×#125×C47C22semidirect
99. C2×#125×C47C22semidirect
102. C47×#525C22semidirect
103. C47×#525C22semidirect
105. C47×#520C22semidirect
106. C47×#520C22semidirect
107. C4×#41×C47C22semidirect
108. C22×C4⋊C4×C47C22semidirect
444. #63047C47direct (N × H)
467. #3567C2×C47semidirect
468. #3563C2×C47semidirect
469. #3559C2×C47semidirect
470. #3559C2×C47semidirect
471. #3553C2×C47semidirect
472. #3548C2×C47semidirect
473. #3539C2×C47semidirect
474. #3539C2×C47semidirect
475. #3529C2×C47semidirect
476. #3529C2×C47semidirect
477. #3517C2×C47semidirect
478. #3515C2×C47semidirect
479. #3512C2×C47semidirect
480. #3492C2×C47semidirect
487. #564C22×C47semidirect
490. #563C22×C47semidirect
495. #562C22×C47semidirect
499. #560C22×C47semidirect
500. #557C22×C47semidirect
501. #557C22×C47semidirect
503. #554C22×C47semidirect
504. #554C22×C47semidirect
505. #554C22×C47semidirect
506. #554C22×C47semidirect
511. #553C22×C47semidirect
512. #553C22×C47semidirect
513. #553C22×C47semidirect
514. #553C22×C47semidirect
515. #553C22×C47semidirect
516. #553C22×C47semidirect
518. #552C22×C47semidirect
519. #552C22×C47semidirect
520. #552C22×C47semidirect
521. #552C22×C47semidirect
522. #552C22×C47semidirect
523. #552C22×C47semidirect
527. #550C22×C47semidirect
528. #550C22×C47semidirect
532. #547C22×C47semidirect
533. #547C22×C47semidirect
534. #547C22×C47semidirect
535. #547C22×C47semidirect
536. #544C22×C47semidirect
537. #544C22×C47semidirect
538. #541C22×C47semidirect
539. #541C22×C47semidirect
540. #541C22×C47semidirect
544. #540C22×C47semidirect
545. #540C22×C47semidirect
546. #540C22×C47semidirect
549. #539C22×C47semidirect
550. #539C22×C47semidirect
551. #539C22×C47semidirect
552. #539C22×C47semidirect
553. #539C22×C47semidirect
554. #539C22×C47semidirect
558. #537C22×C47semidirect
559. #537C22×C47semidirect
560. #533C22×C47semidirect
563. #532C22×C47semidirect
568. #529C22×C47semidirect
569. #529C22×C47semidirect
570. C2×#125C22×C47semidirect
571. C2×#125C22×C47semidirect
574. #525C22×C47semidirect
575. #525C22×C47semidirect
577. #520C22×C47semidirect
578. #520C22×C47semidirect
579. C4×#41C22×C47semidirect
580. C22×C4⋊C4C22×C47semidirect
581. C47#63047direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35672
C47×#35632
C47×#35592
C47×#35532
C47×#35482
C47×#35392
C47×#35292
C47×#35172
C47×#35152
C47×#35122
C47×#34922
#6304747