Finite Group Databasebeta

← #26222738

Subgroups — #26222738

Order 12032.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252837C211yesmaximal, characteristic
2C2×#15689243C211yesmaximal, characteristic, complemented
3C2×#15689238C211yesmaximal, characteristic, complemented
4#20251813C211yesmaximal, characteristic, complemented
5#20244308C211yesmaximal, characteristic, complemented
6#20244161C211yesmaximal, characteristic, complemented
7#20244033C211yesmaximal, characteristic, complemented
8#20244033C211yesmaximal, characteristic, complemented
9#20243718C211yesmaximal, characteristic, complemented
10#20243718C211yesmaximal, characteristic, complemented
11#20243405C211yesmaximal, characteristic, complemented
12#20243260C211yesmaximal, characteristic, complemented
13#20243230C211yesmaximal, characteristic, complemented
14#20243223C211yesmaximal, characteristic, complemented
15C47×#2932C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094044C2211yescharacteristic
18C2×#13094030C2211yescharacteristic
19C2×#13094030C2211yescharacteristic
20C4×#10625350C2211yescharacteristic
21#15689342C411yescharacteristic, complemented
22#15689342C411yescharacteristic, complemented
23#15689335C411yescharacteristic, complemented
24#15689335C411yescharacteristic, complemented
25#15689330C411yescharacteristic, complemented
26#15689325C411yescharacteristic, complemented
27#15689320C411yescharacteristic, complemented
28#15689315C411yescharacteristic, complemented
29#15689243—24no—
30#15689238—24no—
31C2×#13093959C2211yescharacteristic
32C2×#13093959C2211yescharacteristic
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34C2×#13093951C2211yescharacteristic
35C2×#13093951C2211yescharacteristic
36C2×#13093951C2211yescharacteristic
37C2×#13093951C2211yescharacteristic
38C2×#13093950C2211yescharacteristic
39C2×#13093950C2211yescharacteristic
40#15689119C2211yescharacteristic
41#15689119C2211yescharacteristic
42#15689080—21no—
43#15689080—21no—
44#15689078C2211yescharacteristic
45#15689078C2211yescharacteristic
46C4×#10625329C2211yescharacteristic
47#15689075—21no—
48C2×#13093934C2211yescharacteristic
49#97×D47—21no—
50C2×C8×Dic47C2211yescharacteristic
51C4×C4⋊Dic47C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688884C2211yescharacteristic
56#15688877C2211yescharacteristic
57#15688877C2211yescharacteristic
58C2×#131×C47C2211yescharacteristic
59C2×#131×C47C2211yescharacteristic
60C47×#532C2211yescharacteristic
61C47×#435—21no—
62C47×#435—21no—
63C47×#435—21no—
64C47×#435—21no—
65C47×#423C2211yescharacteristic
66C47×#408C2211yescharacteristic
67C47×#408C2211yescharacteristic
68C2×#97×C47C2211yescharacteristic
69C2×#10625350C2311yescharacteristic
70#13094044—22no—
71#13094044—22no—
72#13094044—22no—
73#13094044—22no—
74C2×#10625337C2×C411yescharacteristic
75C2×#10625337C2×C411yescharacteristic
76C2×#10625335C2×C411yescharacteristic
77C2×#10625335C2×C411yescharacteristic
78C2×#10625336C2×C411yescharacteristic
79C2×#10625336C2×C411yescharacteristic
80C2×#10625334C2×C411yescharacteristic
81C2×#10625334C2×C411yescharacteristic
82#13094030—22no—
83#13094030—22no—
84#13094030—22no—
85#13094030D414yescomplemented
86C2×#10625329C2311yescharacteristic
87C2×#10625329C2311yescharacteristic
88C2×#10625324—21no—
89C2×#10625324—21no—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—21no—
93C2×C8×D47—21no—
94C4×Dic94C2×C411yescharacteristic
95C4×Dic94C2×C411yescharacteristic
96C4×D188C2×C411yescharacteristic
97C4×D188C2×C411yescharacteristic
98C4×C22⋊D47—21no—
99C4×C22⋊D47—21no—
100#13093983C2311yescharacteristic
101#13093981—21no—
102C2×C4⋊Dic47—21no—
103C2×C4×Dic47C2311yescharacteristic
104C2×C4×Dic47C2311yescharacteristic
105C42×D47—21no—
106#13093959—22no—
107#13093959—22no—
108C4⋊(C47⋊C8)C2×C411yescharacteristic
109C4⋊(C47⋊C8)C2×C411yescharacteristic
110C4⋊(C47⋊C8)C2×C411yescharacteristic
111C4⋊(C47⋊C8)C2×C411yescharacteristic
112#13093951—22no—
113#13093951—22no—
114#13093951—22no—
115#13093951—22no—
116#13093950—22no—
117#13093950—22no—
118#13093948C2×C411yescharacteristic
119#13093948C2×C411yescharacteristic
120#13093948C2×C411yescharacteristic
121#13093948C2×C411yescharacteristic
122#13093945C2×C411yescharacteristic
123#13093945C2×C411yescharacteristic
124#13093945C2×C411yescharacteristic
125#13093945C2×C411yescharacteristic
126#13093935—21no—
127#13093934—22no—
128#13093934—21no—
129#13093934—21no—
130C4×C47⋊C8—21no—
131C8×Dic47—22no—
132C8×Dic47—21no—
133C8×Dic47—21no—
134C47⋊#95—21no—
135C2×#41×C47C2311yescharacteristic
136C2×#41×C47C2311yescharacteristic
137#131×C47—22no—
138#131×C47—22no—
139#131×C47—22no—
140#131×C47—22no—
141C2×M16×C47—21no—
142C2×M16×C47—21no—
143C2×M16×C47C2311yescharacteristic
144C2×M16×C47C2311yescharacteristic
145C22×C8×C47—21no—
146C22×C8×C47—21no—
147C22×C8×C47C2311yescharacteristic
148C22×C8×C47C2311yescharacteristic
149C4⋊Q8×C47C2×C411yescharacteristic
150#127×C47C2×C411yescharacteristic
151#124×C47C2×C411yescharacteristic
152#124×C47C2×C411yescharacteristic
153#121×C47—21no—
154#121×C47—21no—
155C4×D4×C47—21no—
156C4×D4×C47—21no—
157C2×C42×C47C2311yescharacteristic
158C4⋊C8×C47—21no—
159C4⋊C8×C47—21no—
160C22⋊C8×C47—21no—
161C22⋊C8×C47—21no—
162C22⋊C8×C47—21no—
163C22⋊C8×C47—21no—
164#97×C47D411yescharacteristic
165#97×C47D411yescharacteristic
166#97×C47D411yescharacteristic
167#97×C47D411yescharacteristic
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176C2×Q8×C47C22×C411yescharacteristic
177C2×Q8×C47C22×C411yescharacteristic
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47C22×C411yescharacteristic
183C2×D4×C47C22×C411yescharacteristic
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47#4111yescharacteristic
187C22×C4×C47#4111yescharacteristic
188C22×C4×C47C2411yescharacteristic
189C2×C22⋊D47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192#10625350—21no—
193#10625350—21no—
194#10625350C2×D412yes—
195#10625350#4112yes—
196C2×D188C22×C411yescharacteristic
197C2×C4×D47—21no—
198C2×C4×D47—21no—
199C2×C4×D47—21no—
200C2×Dic94C22×C411yescharacteristic
201M16×C47—21no—
202M16×C47—21no—
203M16×C47—21no—
204M16×C47—21no—
205M16×C47—42no—
206M16×C47—42no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—42no—
212C2×C8×C47—42no—
213C2×C8×C47C2×D411yescharacteristic
214C2×C8×C47C2×D411yescharacteristic
215C2×C8×C47C2×D412yes—
216C2×C8×C47C2×D411yescharacteristic
217C2×C8×C47C2×D411yescharacteristic
218C2×C8×C47#4112yes—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C22⋊C4×C47—21no—
222C22⋊C4×C47—21no—
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C42×C47C22×C411yescharacteristic
226C42×C47C22×C411yescharacteristic
227C42×C47C2×D411yescharacteristic
228C42×C47C2×D411yescharacteristic
229C22⋊Dic47—21no—
230#10625337—22no—
231#10625337—22no—
232#10625336—22no—
233#10625336—22no—
234#10625335—22no—
235#10625335—22no—
236#10625334—22no—
237#10625334—22no—
238(C2×D47)⋊C4—21no—
239(C2×D47)⋊C4—21no—
240C4⋊Dic47—42no—
241C4⋊Dic47C22×C411yescharacteristic
242C4⋊Dic47C22×C411yescharacteristic
243Dic47⋊C4—21no—
244Dic47⋊C4—21no—
245C4×Dic47—21no—
246C4×Dic47—21no—
247C4×Dic47—21no—
248C4×Dic47—21no—
249C4×Dic47—21no—
250C4×Dic47—21no—
251C4×Dic47—21no—
252#10625329—21no—
253#10625329—21no—
254#10625329C2×D412yes—
255#10625329#4112yes—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8C22×C411yescharacteristic
263C2×C47⋊C8C22×C411yescharacteristic
264C2×C47⋊C8C22×C411yescharacteristic
265C2×C47⋊C8C22×C411yescharacteristic
266#10625324—24no—
267#10625324—24no—
268C8×D47—24no—
269C8×D47—24no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47C2×#4111yescharacteristic
273C22×D47—21no—
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—21no—
278D4×C47—21no—
279D4×C47—21no—
280D4×C47—21no—
281D4×C47—21no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—81no—
287D4×C47—81no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47C4×D411yescharacteristic
300C2×C4×C47C23×C411yescharacteristic
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C22⋊D47—22no—
307C22⋊D47—22no—
308C2×Dic47—21no—
309C2×Dic47—22no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317D188—21no—
318D188C4×D412yes—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—81no—
322C4×D47—81no—
323Dic94—21no—
324Dic94C4×D412yes—
325C8×C47—21no—
326C8×C47—21no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47#12112yes—
330C8×C47#12112yes—
331C47⋊C8—21no—
332C47⋊C8—21no—
333C47⋊C8—21no—
334C47⋊C8—21no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337#21519—471nomaximal, Sylow
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47C2×C4×D411yescharacteristic
347C22×C47#52911yescharacteristic
348C22×C47#53211yescharacteristic
349C2×D47—22no—
350C2×D47—41no—
351C2×D47—41no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47C2×C4×D411yescharacteristic
359C4×C47C4×#4111yescharacteristic
360C4×C47C2×#12111yescharacteristic
361C4×C47#52511yescharacteristic
362Dic47—22no—
363Dic47—42no—
364Dic47—41no—
365Dic47—41no—
366Dic47—81no—
367#3035—471no—
368C2×#444—471no—
369C2×#443—471no—
370#2932D4711yescharacteristic, complemented
371#2875—471no—
372#1980—471no—
373#1950—471no—
374#1929—471no—
375#1929—471no—
376#1876—471no—
377#1876—471no—
378#1806—471no—
379#1771—471no—
380#1765—471no—
381#1764—471no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—81no—
385C2×C47—81no—
386C2×C47C4×#12111yescharacteristic
387C2×C47#295611yescharacteristic
388C2×C47#295711yescharacteristic
389D47—42no—
390C2×#135—471no—
391C2×#135—471no—
392C2×#131—471no—
393C2×#131—471no—
394C2×#131C2×D4711yescharacteristic
395C2×#131C2×D4711yescharacteristic
396#532C2×D4711yescharacteristic
397C4×#41—471no—
398#464—471no—
399#464—471no—
400#463—471no—
401#463—471no—
402#462—471no—
403#461—471no—
404#460—471no—
405#459—471no—
406#444—944no—
407#443—944no—
408#435—21no—
409#435—21no—
410#435—21no—
411#435—21no—
412C2×#108—471no—
413C2×#108—471no—
414#423C2×D4711yescharacteristic
415C2×C4⋊C8—471no—
416C2×#104—471no—
417C2×#104—471no—
418C2×#104—471no—
419C2×#104—471no—
420C2×#104—471no—
421C2×#104—471no—
422#416—471no—
423#416—471no—
424#408C2×D4711yescharacteristic
425#408C2×D4711yescharacteristic
426#405—471no—
427#405—471no—
428#405—941no—
429#405—941no—
430C4×M16—471no—
431C4×M16—941no—
432C2×#97—471no—
433C2×#97—941no—
434C2×#97C2×D4711yescharacteristic
435C2×C4×C8—471no—
436C4×C4⋊C4—471no—
437#341—471no—
438#341—471no—
439#339—471no—
440#339—471no—
441#336—471no—
442#336—471no—
443C47#2151911yescharacteristic, complemented, Sylow
444C2×#41—471no—
445C2×#41C22×D4711yescharacteristic
446C2×#41C22×D4711yescharacteristic
447#135—942no—
448#135—942no—
449#135—942no—
450#135—942no—
451C2×Q16—471no—
452C2×Q16—471no—
453C2×SD16—471no—
454C2×SD16—471no—
455C2×SD16—471no—
456C2×SD16—471no—
457C2×D8—471no—
458C2×D8—471no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—22no—
463#131—474no—
464#131—942no—
465#131—942no—
466#131—942no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—471no—
470C2×M16—471no—
471C2×M16—941no—
472C2×M16—941no—
473C2×M16C22×D4711yescharacteristic
474C2×M16C22×D4711yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—941no—
480C22×C8—941no—
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483C4⋊Q8C4×D4711yescharacteristic
484#127C4×D4711yescharacteristic
485#124C4×D4711yescharacteristic
486#124C4×D4711yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8—471no—
490C4×Q8—471no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—471no—
494C4×D4—471no—
495C4×D4—941no—
496C4×D4—941no—
497#117—471no—
498#117—941no—
499C2×C4⋊C4—941no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—941no—
503C2×C42C22×D4711yescharacteristic
504#108—942no—
505#108—942no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—471no—
509C4⋊C8—471no—
510C4⋊C8—471no—
511C4⋊C8—471no—
512#104—942no—
513#104—942no—
514#104—942no—
515#104—942no—
516#104—942no—
517#104—942no—
518#103—471no—
519#103—471no—
520#103—471no—
521#103—471no—
522#102—471no—
523#102—471no—
524#102—471no—
525#102—471no—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530#97—942no—
531#97—941no—
532#97—941no—
533#97—941no—
534#97C22⋊D4711yescharacteristic
535#97C22⋊D4711yescharacteristic
536#97C22⋊D4711yescharacteristic
537#97C22⋊D4711yescharacteristic
538C4×C8—942no—
539C4×C8—941no—
540C4×C8—941no—
541C4×C8—941no—
542#95—941no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—472no—
552#41—472no—
553#41—941no—
554#41—941no—
555C2×Q8—471no—
556C2×Q8C2×C4×D4711yescharacteristic
557C2×Q8C2×C4×D4711yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—471no—
563C2×D4—941no—
564C2×D4C2×C4×D4711yescharacteristic
565C2×D4C2×C4×D4711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4#1062535011yescharacteristic
574C22×C4#1062535011yescharacteristic
575C22×C4C23×D4711yescharacteristic
576Q16—942no—
577Q16—942no—
578SD16—942no—
579SD16—942no—
580SD16—942no—
581SD16—942no—
582D8—942no—
583D8—942no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—42no—
590M16—472no—
591M16—472no—
592M16—944no—
593M16—941no—
594M16—941no—
595M16—944no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—471no—
603C2×C8—471no—
604C2×C8—471no—
605C2×C8—471no—
606C2×C8—944no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—944no—
614C2×C8D4×D4712yes—
615C2×C8#1062535212yes—
616C2×C8C2×C22⋊D4711yescharacteristic
617C2×C8C2×C22⋊D4711yescharacteristic
618C2×C8C2×C22⋊D4711yescharacteristic
619C2×C8C2×C22⋊D4711yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—471no—
623C4⋊C4—471no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—1882no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—941no—
632C22⋊C4—941no—
633C22⋊C4—941no—
634C42—941no—
635C42—941no—
636C42—941no—
637C42—941no—
638C42—941no—
639C42—941no—
640C42—941no—
641C42C2×C4×D4711yescharacteristic
642C42C2×C4×D4711yescharacteristic
643C42C2×C22⋊D4711yescharacteristic
644C42C2×C22⋊D4711yescharacteristic
645C23—21no—
646C23—21no—
647C23—941no—
648C23C2×#1062535011yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—472no—
654Q8—941no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—81no—
664D4—81no—
665D4—472no—
666D4—942no—
667D4—942no—
668D4—941no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—941no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—3761no—
684C2×C4—3761no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4—1881no—
689C2×C4—1881no—
690C2×C4C4×C22⋊D4711yescharacteristic
691C2×C4C4×C22⋊D4711yescharacteristic
692C2×C4C4×C22⋊D4711yescharacteristic
693C2×C4C4×C22⋊D4711yescharacteristic
694C2×C4C22×C4×D4711yescharacteristic
695C2×C4C2×D4×D4711yescharacteristic
696C2×C4C22×C22⋊D4711yescharacteristic
697C2×C4#41×D4711yescharacteristic
698C2×C4#41×D4711yescharacteristic
699C2×C4C2×#1062535211yescharacteristic
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—941no—
705C8—941no—
706C8—941no—
707C8—941no—
708C8—942no—
709C8—942no—
710C8#1309399512yes—
711C8#1309399512yes—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—942no—
721C22—1881no—
722C22—1881no—
723C22C2×C4×C22⋊D4711yescharacteristic
724C22#1568965511yescharacteristic
725C22#1568967011yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—942no—
733C4—3761no—
734C4—1882no—
735C4—1881no—
736C4—1881no—
737C4C4×D4×D4711yescharacteristic
738C4C4×#1062535211yescharacteristic
739C4C2×#1309399511yescharacteristic
740C4#1568963011yescharacteristic
741C2—21no—
742C2—21no—
743C2—81no—
744C2—81no—
745C2—1882no—
746C2C4×#1309399511yescharacteristic
747C2#2025229511yescharacteristic
748C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2932C2
socleC22×C47C2×C4×D4
prime radical#20252837C2
cosocleC22×C4×C47C24
hypercenter#2932D47
hypocenterC47#21519
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. C2×#15689243C2semidirect
3. C2×#15689238C2semidirect
4. #20251813C2semidirect
5. #20244308C2semidirect
6. #20244161C2semidirect
7. #20244033C2semidirect
8. #20244033C2semidirect
9. #20243718C2semidirect
10. #20243718C2semidirect
11. #20243405C2semidirect
12. #20243260C2semidirect
13. #20243230C2semidirect
14. #20243223C2semidirect
15. C47×#2932C2semidirect
21. #15689342C4semidirect
22. #15689342C4semidirect
23. #15689335C4semidirect
24. #15689335C4semidirect
25. #15689330C4semidirect
26. #15689325C4semidirect
27. #15689320C4semidirect
28. #15689315C4semidirect
85. #13094030D4semidirect
370. #2932D47semidirect
443. C47#21519semidirect

Maximal subgroups

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

subgroupindex
#202528372
C2×#156892432
C2×#156892382
#202518132
#202443082
#202441612
#202440332
#202437182
#202434052
#202432602
#202432302
#202432232
C47×#29322
#2151947