Finite Group Databasebeta

← #26222744

Subgroups — #26222744

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#20252843C211yesmaximal, characteristic
2C2×#15689243C211yesmaximal, characteristic, complemented
3C2×#15689238C211yesmaximal, characteristic, complemented
4#20252107C211yesmaximal, characteristic, complemented
5#20244307C211yesmaximal, characteristic, complemented
6#20244163C211yesmaximal, characteristic, complemented
7#20244036C211yesmaximal, characteristic, complemented
8#20244036C211yesmaximal, characteristic, complemented
9#20243715C211yesmaximal, characteristic, complemented
10#20243715C211yesmaximal, characteristic, complemented
11#20243408C211yesmaximal, characteristic, complemented
12#20243260C211yesmaximal, characteristic, complemented
13#20243234C211yesmaximal, characteristic, complemented
14#20243227C211yesmaximal, characteristic, complemented
15C47×#2875C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094044C2211yescharacteristic
18C2×#13094030C2211yescharacteristic
19C2×#13094030C2211yescharacteristic
20#15689673C2211yescharacteristic
21#15689345C411yescharacteristic, complemented
22#15689345C411yescharacteristic, complemented
23#15689338C411yescharacteristic, complemented
24#15689338C411yescharacteristic, complemented
25#15689333C411yescharacteristic, complemented
26#15689328C411yescharacteristic, complemented
27#15689323C411yescharacteristic, complemented
28#15689318C411yescharacteristic, complemented
29#15689243—24no—
30#15689238—24no—
31#15689196—21no—
32#15689196—21no—
33#15689196—21no—
34#15689196—21no—
35C2×#13093959C2211yescharacteristic
36C2×#13093959C2211yescharacteristic
37#15689147C2211yescharacteristic
38C2×C4⋊(C47⋊C8)C2211yescharacteristic
39C2×#13093951C2211yescharacteristic
40C2×#13093951C2211yescharacteristic
41C2×#13093950C2211yescharacteristic
42C2×#13093950C2211yescharacteristic
43C2×#13093950C2211yescharacteristic
44C2×#13093950C2211yescharacteristic
45#15689117C2211yescharacteristic
46#15689117C2211yescharacteristic
47#15689089C2211yescharacteristic
48#15689089C2211yescharacteristic
49C2×#13093934C2211yescharacteristic
50C2×C8×Dic47C2211yescharacteristic
51C4×C4⋊Dic47C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688882C2211yescharacteristic
55#15688882C2211yescharacteristic
56#15688877C2211yescharacteristic
57#15688877C2211yescharacteristic
58C2×#131×C47C2211yescharacteristic
59C2×#131×C47C2211yescharacteristic
60C4×#41×C47C2211yescharacteristic
61C47×#405—21no—
62C47×#405—21no—
63C47×#405C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C4×M16×C47—21no—
66C4×M16×C47C2211yescharacteristic
67C2×#97×C47—21no—
68C2×#97×C47C2211yescharacteristic
69C2×#10625350C2311yescharacteristic
70C2×#10625350C2311yescharacteristic
71#13094044—22no—
72#13094044—22no—
73#13094044—22no—
74#13094044—22no—
75C2×#10625337C2×C411yescharacteristic
76C2×#10625337C2×C411yescharacteristic
77C2×#10625335C2×C411yescharacteristic
78C2×#10625335C2×C411yescharacteristic
79C2×#10625336C2×C411yescharacteristic
80C2×#10625336C2×C411yescharacteristic
81C2×#10625334C2×C411yescharacteristic
82C2×#10625334C2×C411yescharacteristic
83#13094030—22no—
84#13094030—22no—
85#13094030—22no—
86#13094030—22no—
87C2×#10625329C2311yescharacteristic
88C2×#10625329C2311yescharacteristic
89C2×#10625324—21no—
90C2×#10625324—21no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C2×C8×D47—21no—
94C2×C8×D47—21no—
95#13094024C2×C411yescharacteristic
96#13094021C2×C411yescharacteristic
97#13094012C2×C411yescharacteristic
98#13094012C2×C411yescharacteristic
99#13093998—21no—
100#13093998—21no—
101C4×D188—21no—
102C4×D188—21no—
103C2×C4⋊Dic47—21no—
104C2×C4×Dic47C2311yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106#13093959—22no—
107#13093959—22no—
108C4⋊(C47⋊C8)—21no—
109C4⋊(C47⋊C8)—21no—
110C4⋊(C47⋊C8)C2×C411yescharacteristic
111C4⋊(C47⋊C8)C2×C411yescharacteristic
112C4⋊(C47⋊C8)C2×C411yescharacteristic
113C4⋊(C47⋊C8)C2×C411yescharacteristic
114#13093951—22no—
115#13093951—22no—
116#13093950—22no—
117#13093950—22no—
118#13093950—22no—
119#13093950—22no—
120#13093947C2×C411yescharacteristic
121#13093947C2×C411yescharacteristic
122#13093947C2×C411yescharacteristic
123#13093947C2×C411yescharacteristic
124#13093944C2×C411yescharacteristic
125#13093944C2×C411yescharacteristic
126#13093944C2×C411yescharacteristic
127#13093944C2×C411yescharacteristic
128(C2×D47)⋊C8—21no—
129(C2×D47)⋊C8—21no—
130(C2×D47)⋊C8—21no—
131(C2×D47)⋊C8—21no—
132#13093934—22no—
133C8×Dic47—22no—
134C47⋊#95—21no—
135C2×#41×C47C2311yescharacteristic
136#131×C47—22no—
137#131×C47—22no—
138#131×C47—22no—
139#131×C47D414yescomplemented
140C2×M16×C47—21no—
141C2×M16×C47—21no—
142C2×M16×C47C2311yescharacteristic
143C2×M16×C47C2311yescharacteristic
144C22×C8×C47—21no—
145C22×C8×C47—21no—
146C22×C8×C47C2311yescharacteristic
147C22×C8×C47C2311yescharacteristic
148C4×Q8×C47C2×C411yescharacteristic
149C4×Q8×C47C2×C411yescharacteristic
150C4×D4×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47C2×C411yescharacteristic
153C4×D4×C47C2×C411yescharacteristic
154#117×C47—21no—
155#117×C47C2311yescharacteristic
156C2×C42×C47—21no—
157C2×C42×C47C2311yescharacteristic
158#97×C47—21no—
159#97×C47—21no—
160#97×C47—21no—
161#97×C47D411yescharacteristic
162#97×C47D411yescharacteristic
163#97×C47D411yescharacteristic
164#97×C47D411yescharacteristic
165C4×C8×C47—21no—
166C4×C8×C47—21no—
167C4×C8×C47—21no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47C2×D412yes—
171#41×C47#4112yes—
172C2×Q8×C47C22×C411yescharacteristic
173C2×D4×C47—21no—
174C2×D4×C47C22×C411yescharacteristic
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47#4111yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47C2411yescharacteristic
181C2×C22⋊D47—21no—
182C2×C22⋊D47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185#10625350—21no—
186#10625350—21no—
187#10625350—21no—
188#10625350—21no—
189#10625350—21no—
190#10625350—21no—
191#10625350—21no—
192#10625350—21no—
193C2×D188—21no—
194C2×D188—21no—
195C2×D188C22×C411yescharacteristic
196C2×D188C22×C411yescharacteristic
197C2×C4×D47—21no—
198C2×C4×D47—21no—
199C2×Dic94C22×C411yescharacteristic
200C2×Dic94C22×C411yescharacteristic
201M16×C47—24no—
202M16×C47—21no—
203M16×C47—21no—
204M16×C47—24no—
205M16×C47C2×D412yes—
206M16×C47#4112yes—
207C2×C8×C47—24no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—24no—
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—
221C4⋊C4×C47C22×C411yescharacteristic
222C4⋊C4×C47C22×C411yescharacteristic
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47C22×C411yescharacteristic
230C42×C47C22×C411yescharacteristic
231C42×C47C2×D411yescharacteristic
232C42×C47C2×D411yescharacteristic
233#10625337—22no—
234#10625337—22no—
235#10625336—22no—
236#10625336—22no—
237#10625335—22no—
238#10625335—22no—
239#10625334—22no—
240#10625334—22no—
241(C2×D47)⋊C4—21no—
242(C2×D47)⋊C4—21no—
243(C2×D47)⋊C4—21no—
244(C2×D47)⋊C4—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—42no—
248C4×Dic47—21no—
249C4×Dic47—21no—
250C4×Dic47—21no—
251C4×Dic47—21no—
252#10625329—21no—
253#10625329—21no—
254#10625329—21no—
255#10625329—21no—
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—42no—
267#10625324—42no—
268C8×D47—42no—
269C8×D47—42no—
270C23×C47—21no—
271C23×C47C2×#4111yescharacteristic
272C22×D47—21no—
273C22×D47—21no—
274Q8×C47—21no—
275Q8×C47C4×D412yes—
276D4×C47—22no—
277D4×C47—22no—
278D4×C47—21no—
279D4×C47C4×D412yes—
280C2×C4×C47—21no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—81no—
288C2×C4×C47—81no—
289C2×C4×C47C4×D411yescharacteristic
290C2×C4×C47C4×D411yescharacteristic
291C2×C4×C47C4×D411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C23×C411yescharacteristic
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C22⋊D47—41no—
300C22⋊D47—41no—
301C22⋊D47—41no—
302C22⋊D47—41no—
303C2×Dic47—22no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311D188—21no—
312D188—21no—
313D188—21no—
314D188—21no—
315D188—81no—
316D188—81no—
317C4×D47—41no—
318C4×D47—41no—
319C4×D47—41no—
320C4×D47—41no—
321Dic94—21no—
322Dic94—21no—
323Dic94—21no—
324Dic94—21no—
325C8×C47—22no—
326C8×C47—21no—
327C8×C47—22no—
328C8×C47—21no—
329C8×C47#12112yes—
330C8×C47#12112yes—
331C47⋊C8—21no—
332C47⋊C8—21no—
333C47⋊C8—21no—
334C47⋊C8—21no—
335C47⋊C8—41no—
336C47⋊C8—41no—
337#21519—471nomaximal, Sylow
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—22no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47C2×C4×D411yescharacteristic
344C22×C47#52911yescharacteristic
345C22×C47#53211yescharacteristic
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47C2×C4×D411yescharacteristic
360C4×C47C4×#4111yescharacteristic
361C4×C47C2×#12111yescharacteristic
362C4×C47#52511yescharacteristic
363Dic47—42no—
364Dic47—41no—
365Dic47—41no—
366Dic47—81no—
367#3035—471no—
368C2×#444—471no—
369C2×#443—471no—
370#2932—471no—
371#2875D4711yescharacteristic, complemented
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—42no—
385C2×C47C4×#12111yescharacteristic
386C2×C47#295611yescharacteristic
387C2×C47#295711yescharacteristic
388D47—81no—
389D47—81no—
390C2×#135—471no—
391C2×#135—471no—
392C2×#131—471no—
393C2×#131—471no—
394C2×#131C2×D4711yescharacteristic
395C2×#131C2×D4711yescharacteristic
396#532—471no—
397C4×#41C2×D4711yescharacteristic
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—941no—
409#435—941no—
410#435—941no—
411#435—941no—
412C2×#108—471no—
413C2×#108—471no—
414#423—471no—
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#408—471no—
425#408—471no—
426#405—21no—
427#405—21no—
428#405C2×D4711yescharacteristic
429#405C2×D4711yescharacteristic
430C4×M16—21no—
431C4×M16C2×D4711yescharacteristic
432C2×#97—21no—
433C2×#97—471no—
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×#41—471no—
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—942no—
463#131—942no—
464#131—942no—
465#131—942no—
466#131D18814yescomplemented
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⋊Q8—471no—
484#127—471no—
485#124—471no—
486#124—471no—
487#121—941no—
488#121—941no—
489C4×Q8C4×D4711yescharacteristic
490C4×Q8C4×D4711yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—941no—
494C4×D4—941no—
495C4×D4C4×D4711yescharacteristic
496C4×D4C4×D4711yescharacteristic
497#117—21no—
498#117C22×D4711yescharacteristic
499C2×C4⋊C4—941no—
500C2×C42—21no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42C22×D4711yescharacteristic
504#108—942no—
505#108—942no—
506C4⋊C8—471no—
507C4⋊C8—471no—
508C4⋊C8—471no—
509C4⋊C8—471no—
510C4⋊C8—941no—
511C4⋊C8—941no—
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—941no—
527C22⋊C8—941no—
528C22⋊C8—941no—
529C22⋊C8—941no—
530#97—21no—
531#97—21no—
532#97—21no—
533#97—942no—
534#97C22⋊D4711yescharacteristic
535#97C22⋊D4711yescharacteristic
536#97C22⋊D4711yescharacteristic
537#97C22⋊D4711yescharacteristic
538C4×C8—21no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—942no—
542#95—941no—
543#41—21no—
544#41—21no—
545#41—941no—
546#41—941no—
547#41—941no—
548#41—941no—
549#41—941no—
550#41—941no—
551#41—941no—
552#41—941no—
553#41C2×D18812yes—
554#41#1062535012yes—
555C2×Q8—471no—
556C2×Q8—471no—
557C2×Q8C2×C4×D4711yescharacteristic
558C2×D4—21no—
559C2×D4—471no—
560C2×D4—471no—
561C2×D4—941no—
562C2×D4—941no—
563C2×D4—941no—
564C2×D4—941no—
565C2×D4C2×C4×D4711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
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—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—941no—
589M16—941no—
590M16—941no—
591M16—941no—
592M16—1882no—
593M16—1882no—
594M16C2×D18812yes—
595M16#1062535012yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—24no—
602C2×C8—471no—
603C2×C8—471no—
604C2×C8—471no—
605C2×C8—471no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—1882no—
613C2×C8—1882no—
614C2×C8C2×D18812yes—
615C2×C8#1062535012yes—
616C2×C8C2×C22⋊D4711yescharacteristic
617C2×C8C2×C22⋊D4711yescharacteristic
618C2×C8C2×C22⋊D4711yescharacteristic
619C2×C8C2×C22⋊D4711yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—1882no—
625C4⋊C4C2×C4×D4711yescharacteristic
626C4⋊C4C2×C4×D4711yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—941no—
631C22⋊C4—941no—
632C22⋊C4—941no—
633C22⋊C4—941no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—941no—
638C42—941no—
639C42—941no—
640C42—941no—
641C42C2×C4×D4711yescharacteristic
642C42C2×C4×D4711yescharacteristic
643C42C2×C22⋊D4711yescharacteristic
644C42C2×C22⋊D4711yescharacteristic
645C23—21no—
646C23—941no—
647C23—941no—
648C23C2×#1062535011yescharacteristic
649Q8—21no—
650Q8—941no—
651Q8—941no—
652Q8—941no—
653Q8—941no—
654Q8C4×D18812yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—941no—
659D4—941no—
660D4—941no—
661D4—941no—
662D4—3761no—
663D4—3761no—
664D4—1881no—
665D4—1881no—
666D4—1881no—
667D4—1881no—
668D4C4×D18812yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—942no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
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×C4C22×C22⋊D4711yescharacteristic
696C2×C4C22×D18811yescharacteristic
697C2×C4C2×#1062535011yescharacteristic
698C2×C4C2×#1062535011yescharacteristic
699C2×C4C2×#1062535011yescharacteristic
700C8—22no—
701C8—21no—
702C8—22no—
703C8—21no—
704C8—941no—
705C8—941no—
706C8—941no—
707C8—941no—
708C8—1881no—
709C8—1881no—
710C8#1309399812yes—
711C8#1309399812yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—1881no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22C2×C4×C22⋊D4711yescharacteristic
724C22#1568965711yescharacteristic
725C22#1568967311yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—3761no—
734C4—1882no—
735C4—1881no—
736C4—1881no—
737C4C2×C4×D18811yescharacteristic
738C4C4×#1062535011yescharacteristic
739C4C2×#1309399811yescharacteristic
740C4#1568963411yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—3761no—
745C2—3761no—
746C2C4×#1309399811yescharacteristic
747C2#2025229511yescharacteristic
748C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2875C2
socleC22×C47C2×C4×D4
prime radical#20252843C2
cosocleC22×C4×C47C24
hypercenter#2875D47
hypocenterC47#21519
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C2×#15689243C2semidirect
3. C2×#15689238C2semidirect
4. #20252107C2semidirect
5. #20244307C2semidirect
6. #20244163C2semidirect
7. #20244036C2semidirect
8. #20244036C2semidirect
9. #20243715C2semidirect
10. #20243715C2semidirect
11. #20243408C2semidirect
12. #20243260C2semidirect
13. #20243234C2semidirect
14. #20243227C2semidirect
15. C47×#2875C2semidirect
21. #15689345C4semidirect
22. #15689345C4semidirect
23. #15689338C4semidirect
24. #15689338C4semidirect
25. #15689333C4semidirect
26. #15689328C4semidirect
27. #15689323C4semidirect
28. #15689318C4semidirect
139. #131×C47D4semidirect
371. #2875D47semidirect
443. C47#21519semidirect
466. #131D188semidirect

Maximal subgroups

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

subgroupindex
#202528432
C2×#156892432
C2×#156892382
#202521072
#202443072
#202441632
#202440362
#202437152
#202434082
#202432602
#202432342
#202432272
C47×#28752
#2151947