Finite Group Databasebeta

← #25117325

Subgroups — #25117325

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583036C211yesmaximal, characteristic
2C2×SD16×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582906C211yesmaximal, characteristic, complemented
4#19137638C211yesmaximal, characteristic
5Q8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#19135475C211yesmaximal, characteristic, complemented
7#19135269C211yesmaximal, characteristic, complemented
8#19135230C211yesmaximal, characteristic, complemented
9#19135030C211yesmaximal, characteristic
10#19134927C211yesmaximal, characteristic, complemented
11#19134847C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063283C2211yescharacteristic
23#14583036C418yescomplemented
24SD16×Dic43—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27#14582906—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805—21no—
38#14582805C2211yescharacteristic
39#14582804—21no—
40#14582804C2211yescharacteristic
41#14582799—21no—
42#14582795C2211yescharacteristic
43#14582793—21no—
44#14582776—21no—
45#14582756—21no—
46#14582756C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48C22⋊C4×Dic43—21no—
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—41no—
68C2×Q8×D43—41no—
69C2×Q8×D43C2×C414yescomplemented
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621883—41no—
75C2×#10621883—41no—
76C2×#10621883C2×C414yes—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063296—22no—
83#13063296C2×C414yes—
84Q8×Dic43—22no—
85Q8×Dic43—41no—
86D4×Dic43—22no—
87D4×Dic43—41no—
88#13063283—22no—
89#13063283—41no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4D411yescharacteristic
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063258—41no—
106#13063257—22no—
107#13063250—22no—
108#13063250C2×C414yescomplemented
109#13063249C2×C414yescomplemented
110#13063249D414yescomplemented
111#13063248—22no—
112#13063246—22no—
113(C2×D43)⋊C8C2×C414yescomplemented
114#13063236—41no—
115C8×Dic43—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95D411yescharacteristic
124C43⋊#95D411yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C2×SD16×C43—22no—
128C2×SD16×C43—22no—
129C2×SD16×C43C2×C414yes—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×Q8×C43—22no—
133C4×Q8×C43—41no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#103×C43—22no—
142#102×C43—41no—
143C24×C43—21no—
144C23×D43C2×D411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C2×Q8×C43C2×D412yes—
150C2×Q8×C43#4112yes—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C412yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—24no—
164C2×C22⋊D43—81no—
165C2×C22⋊D43—81no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—42no—
171C22×Dic43—42no—
172C22×Dic43—81no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176Q8×D43—28no—
177Q8×D43—44no—
178Q8×D43—44no—
179Q8×D43—44no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—24no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43C22×C412yes—
188C2×C4×D43#4112yes—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—24no—
195C2×Dic86—42no—
196C2×Dic86—42no—
197C2×Dic86C22×C412yes—
198SD16×C43—28no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43C22×C412yes—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—42no—
215C22⋊Dic43—24no—
216C22⋊Dic43—42no—
217#10621883—44no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—42no—
227C4⋊Dic43C22×C412yes—
228C4⋊Dic43C2×D412yes—
229Dic43⋊C4—81no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—42no—
233C4×Dic43—42no—
234C4×Dic43—81no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8C22×C412yes—
240C2×C43⋊C8C2×D412yes—
241#10621872—44no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43C4×D412yes—
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—22no—
260Q8×C43C4×D414yes—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—41no—
264D4×C43—41no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C22⋊D43—84no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—84no—
307C2×Dic43C4×D412yes—
308C2×Dic43#13712yes—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—48no—
314Dic86—22no—
315Dic86—22no—
316Dic86—48no—
317Dic86—41no—
318Dic86—41no—
319C8×C43—22no—
320C8×C43—41no—
321C43⋊C8—22no—
322C43⋊C8—22no—
323#22885—431nomaximal, Sylow
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43C2×C4×D411yescharacteristic
332C22×C43D4211yescharacteristic
333C22×C43#54611yescharacteristic
334C22×C43C2×#13711yescharacteristic
335C22×C43#57511yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57711yescharacteristic
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C4×C43—24no—
346C4×C43—41no—
347C4×C43—41no—
348C4×C43—81no—
349C4×C43—81no—
350C4×C43C2×C4×D411yescharacteristic
351C4×C43#51811yescharacteristic
352C4×C43#54611yescharacteristic
353C4×C43#55111yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359Dic43—41no—
360Dic43—81no—
361C2×#448—431no—
362C2×C4×SD16—431no—
363C2×#419—431no—
364#2363—431no—
365Q8×C22⋊C4—431no—
366#1973—431no—
367#1933—431no—
368#1927—431no—
369#1895—431no—
370#1880D4311yescharacteristic, complemented
371#1877—431no—
372#1863—431no—
373#1854—431no—
374#1763—431no—
375#1753—431no—
376C2×C43—82no—
377C2×C43#235811yescharacteristic
378C2×C43C4×#13711yescharacteristic
379C2×C43#294911yescharacteristic
380C2×C43#326611yescharacteristic
381C2×C43#327111yescharacteristic
382C2×C43#332611yescharacteristic
383C2×C43#332911yescharacteristic
384D43—42no—
385C23×Q8—431no—
386C22×SD16—431no—
387C22×SD16C2×D4311yescharacteristic
388C22×M16—431no—
389C2×#121—431no—
390C2×C4×Q8—431no—
391C2×C4×Q8C2×D4311yescharacteristic
392C2×C4×D4—431no—
393C2×#117—431no—
394#448—438no—
395C4×SD16—864no—
396C2×#107—431no—
397C2×#106—431no—
398#419—864no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103C2×D4311yescharacteristic
405C2×#102—431no—
406C2×#102C2×D4311yescharacteristic
407C2×C22⋊C8—431no—
408C2×#97—431no—
409C2×C4×C8—431no—
410#391—431no—
411#391—431no—
412#391—861no—
413#391—861no—
414#390—861no—
415#390C2×D4311yescharacteristic
416#389—431no—
417#388—861no—
418#386—861no—
419#380—431no—
420#380—861no—
421C4×C4⋊C4—431no—
422C4×C22⋊C4—431no—
423C4×C22⋊C4—861no—
424C4×C22⋊C4—861no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340C2×D4311yescharacteristic
429#336—431no—
430#336C2×D4311yescharacteristic
431C43#2288511yescharacteristic, complemented, Sylow
432C22×Q8—434no—
433C22×Q8—431no—
434C22×Q8—861no—
435C22×Q8—862no—
436C22×Q8—862no—
437C22×Q8—862no—
438C22×Q8—1721no—
439C22×Q8—1721no—
440C22×Q8C22×D4311yescharacteristic
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—434no—
449C2×SD16—1721no—
450C2×SD16—1721no—
451C2×SD16C4×D4314yes—
452C2×M16—862no—
453C2×M16—862no—
454C2×M16—1721no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#121—434no—
460#121—862no—
461C4×Q8—22no—
462C4×Q8—41no—
463C4×Q8—862no—
464C4×Q8—1721no—
465C4×D4—862no—
466C4×D4—1721no—
467#117—862no—
468#117—1721no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C42—21no—
486C2×C42—431no—
487C2×C42—861no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42C22×D4311yescharacteristic
491#107—1721no—
492#106—862no—
493#103—22no—
494#103—434no—
495#103—434no—
496#103—434no—
497#103—862no—
498#103—862no—
499#102—41no—
500#102—862no—
501C22⋊C8—434no—
502#97—1721no—
503C4×C8—862no—
504#95—431no—
505#95—431no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513C24—21no—
514C24—431no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—432no—
519C2×Q8—864no—
520C2×Q8—861no—
521C2×Q8—868no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—1722no—
527C2×Q8—1722no—
528C2×Q8—1724no—
529C2×Q8—1724no—
530C2×Q8—1724no—
531C2×Q8C2×C4×D4312yes—
532C2×Q8D4×D4312yes—
533C2×Q8#1062190012yes—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—864no—
540C2×D4—3441no—
541C2×D4—3441no—
542C2×D4C2×C4×D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—431no—
551C22×C4—864no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—3441no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4C23×D4311yescharacteristic
568SD16—28no—
569SD16—1724no—
570M16—1724no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—432no—
577C2×C8—432no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8C2×C4×D4312yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—3441no—
595C4⋊C4—1722no—
596C22⋊C4—42no—
597C22⋊C4—81no—
598C22⋊C4—862no—
599C22⋊C4—864no—
600C22⋊C4—1721no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C22⋊C4—1722no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42—861no—
608C42—861no—
609C42—3441no—
610C42—1722no—
611C42—1722no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—432no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23C2×D4×D4311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—862no—
631Q8—862no—
632Q8—1728no—
633Q8—1721no—
634Q8—1721no—
635Q8(C22⋊D43)⋊C414yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—3444no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—432no—
657C2×C4—432no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—862no—
672C2×C4—3444no—
673C2×C4—1728no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4C22×C4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4C2×#1062190011yescharacteristic
687C2×C4#1306337011yescharacteristic
688C2×C4#1306337111yescharacteristic
689C8—22no—
690C8—41no—
691C8—862no—
692C8—862no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—862no—
701C22—862no—
702C22—862no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22C4×D4×D4311yescharacteristic
708C22#1458353311yescharacteristic
709C22#1458353611yescharacteristic
710C22#137×D4311yescharacteristic
711C22#1458369511yescharacteristic
712C22#1458370511yescharacteristic
713C22#1458370611yescharacteristic
714C4—24no—
715C4—41no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—862no—
720C4—862no—
721C4—3441no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4—1721no—
726C4C2×(C22⋊D43)⋊C411yescharacteristic
727C4#1458337111yescharacteristic
728C4#1458353811yescharacteristic
729C4#1458357211yescharacteristic
730C2—82no—
731C2—1722no—
732C2#1913757511yescharacteristic
733C2#1914341711yescharacteristic
734C2#1914344911yescharacteristic
735C2#1914610011yescharacteristic
736C2#1914617511yescharacteristic
737C2#1914684111yescharacteristic
738C2#1914688211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#22885
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic43C2semidirect
3. C2×#14582906C2semidirect
5. Q8×(C2×D43)⋊C4C2semidirect
6. #19135475C2semidirect
7. #19135269C2semidirect
8. #19135230C2semidirect
10. #19134927C2semidirect
11. #19134847C2semidirect
12. #19134795C2semidirect
13. #19134425C2semidirect
14. #19134377C2semidirect
15. C43×#1880C2semidirect
23. #14583036C4semidirect
69. C2×Q8×D43C2×C4semidirect
108. #13063250C2×C4semidirect
109. #13063249C2×C4semidirect
110. #13063249D4semidirect
113. (C2×D43)⋊C8C2×C4semidirect
370. #1880D43semidirect
431. C43#22885semidirect

Maximal subgroups

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

subgroupindex
C2×#145830362
C2×SD16×Dic432
C2×#145829062
#191376382
Q8×(C2×D43)⋊C42
#191354752
#191352692
#191352302
#191350302
#191349272
#191348472
#191347952
#191344252
#191343772
C43×#18802
#2288543