Finite Group Databasebeta

← #25124975

Subgroups — #25124975

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×#14583507C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19137282C211yesmaximal, characteristic
4#19135931C211yesmaximal, characteristic, complemented
5#19135839C211yesmaximal, characteristic, complemented
6#19135800C211yesmaximal, characteristic, complemented
7#19135789C211yesmaximal, characteristic, complemented
8#19135739C211yesmaximal, characteristic, complemented
9#19135676C211yesmaximal, characteristic, complemented
10#19135599C211yesmaximal, characteristic
11#19135595C211yesmaximal, characteristic
12#19134426C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17#14583507—24no—
18#14583507—24no—
19C2×#13063323C2211yescharacteristic
20C2×#13063320—21no—
21C2×#13063319—21no—
22C2×#13063317—21no—
23C2×#13063316C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063305C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×#13063296C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30C4×#10621883—24no—
31C2×#13063256C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582799—21no—
43#14582795C2211yescharacteristic
44#14582793—21no—
45#14582778—21no—
46#14582772—21no—
47#14582756C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#440—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C4×D43C2311yescharacteristic
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063323—22no—
72#13063323—22no—
73#13063320—28no—
74#13063319—28no—
75#13063317—28no—
76#13063316—22no—
77#13063316—22no—
78#13063315—28no—
79#13063305—22no—
80#13063305—22no—
81#13063301—22no—
82#13063301—22no—
83#13063296—22no—
84#13063296—22no—
85C4×Dic86—22no—
86C4×Dic86D414yescomplemented
87#13063282—22no—
88#13063282—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×Dic43⋊C4D411yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063256—22no—
114#13063250—22no—
115#13063250—22no—
116#13063249—22no—
117#13063249—22no—
118#13063248—22no—
119#13063246—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122C4×C43⋊C8—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43—21no—
129C2×SD16×C43—22no—
130C2×SD16×C43—22no—
131C2×SD16×C43—22no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C4×Q8×C43—22no—
135C4×Q8×C43D414yescomplemented
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#107×C43—22no—
145#103×C43—22no—
146#102×C43—22no—
147#97×C43—22no—
148C24×C43—21no—
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C2×D412yes—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—42no—
166C22×C4×C43—81no—
167C22×C4×C43—81no—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—81no—
173C2×C22⋊D43—81no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C2×D412yes—
193SD16×C43—28no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43#4112yes—
200C4⋊C4×C43—24no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—42no—
206C42×C43—24no—
207C42×C43C2×D412yes—
208C42×C43C2×D412yes—
209C22⋊Dic43—24no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212#10621883—28no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—24no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43C2×D412yes—
225C4⋊Dic43#4112yes—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—81no—
234C4×Dic43—24no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—81no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8#4112yes—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C22×D411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263D4×C43—22no—
264D4×C43—22no—
265D4×C43—41no—
266D4×C43—41no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—41no—
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×C43—84no—
281C2×C4×C43#12012yes—
282C2×C4×C43#12012yes—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C22⋊D43—84no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—41no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319C8×C43—22no—
320C8×C43—41no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323#23584—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×#12011yescharacteristic
332C22×C43#52511yescharacteristic
333C22×C43#53211yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57711yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57811yescharacteristic
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43—81no—
350C4×C43#52511yescharacteristic
351C4×C43#52511yescharacteristic
352C4×C43#53211yescharacteristic
353C4×C43#53211yescharacteristic
354Dic43—42no—
355Dic43—42no—
356Dic43—41no—
357Dic43—41no—
358Dic43—41no—
359Dic43—42no—
360Dic43—81no—
361C2×#541—431no—
362C2×#440D4311yescharacteristic, complemented
363C2×C4×SD16—431no—
364#2324—431no—
365#2059—431no—
366#2043—431no—
367#2036—431no—
368#2035—431no—
369#2025—431no—
370#2013—431no—
371#2000—431no—
372#2000—431no—
373#1763—431no—
374C4×#103—431no—
375#1750—431no—
376C2×C43—82no—
377C2×C43#238811yescharacteristic
378C2×C43#301011yescharacteristic
379C2×C43#301311yescharacteristic
380C2×C43#312011yescharacteristic
381C2×C43#312311yescharacteristic
382C2×C43#317411yescharacteristic
383C2×C43#317811yescharacteristic
384D43—81no—
385C22×SD16—431no—
386C22×SD16C2×D4311yescharacteristic
387#541—864no—
388#541—864no—
389C2×C4⋊Q8—431no—
390C2×#126—861no—
391C2×#126—861no—
392C2×#125—431no—
393C2×#125—861no—
394C2×#125—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×#121—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×D4C2×D4311yescharacteristic
401C2×#117—431no—
402#440—24no—
403C4×SD16—864no—
404C2×#107C2×D4311yescharacteristic
405C2×#106—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103C2×D4311yescharacteristic
412C2×#102—431no—
413C2×#102C2×D4311yescharacteristic
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×#97C2×D4311yescharacteristic
417C2×C4×C8—431no—
418#390—431no—
419#390—861no—
420#389—431no—
421#388—861no—
422#386—861no—
423#385—861no—
424#380—431no—
425C4×C4⋊C4—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#336—431no—
431#336—431no—
432C43#2358411yescharacteristic, complemented, Sylow
433C22×Q8—431no—
434C22×Q8C22×D4311yescharacteristic
435C22×D4—861no—
436C22×D4C22×D4311yescharacteristic
437C23×C4—21no—
438C23×C4—431no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—862no—
443C2×SD16—862no—
444C2×SD16—862no—
445C22×C8—431no—
446C22×C8—431no—
447C22×C8C22×D4311yescharacteristic
448C22×C8C22×D4311yescharacteristic
449C4⋊Q8—862no—
450C4⋊Q8—862no—
451#126—868no—
452#126—868no—
453#125—868no—
454#125—862no—
455#125—868no—
456#125—862no—
457C22⋊Q8—862no—
458C22⋊Q8—862no—
459C22⋊Q8—862no—
460C22⋊Q8—862no—
461#121—862no—
462#121—862no—
463C4×Q8—22no—
464C4×Q8—434no—
465C4×Q8—862no—
466C4×Q8C22⋊D4314yescomplemented
467C4×D4—22no—
468C4×D4—22no—
469#117—862no—
470#117—862no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—21no—
497C2×C42—431no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501#107—22no—
502#106—862no—
503#103—22no—
504#103—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—862no—
509#102—22no—
510#102—862no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513#97—22no—
514C4×C8—862no—
515#95—861no—
516#95—861no—
517#95—861no—
518C24—21no—
519C24—431no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8C2×C22⋊D4312yes—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—864no—
538C2×D4—3441no—
539C2×D4—3441no—
540C2×D4#1062189812yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—861no—
551C22×C4—861no—
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×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563SD16—28no—
564SD16—868no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8#1062189812yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—432no—
583C4⋊C4—864no—
584C4⋊C4—864no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—864no—
588C4⋊C4—864no—
589C4⋊C4—862no—
590C4⋊C4—862no—
591C4⋊C4—864no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—3441no—
597C4⋊C4C2×C22⋊D4312yes—
598C22⋊C4—42no—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—862no—
603C22⋊C4—862no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C42—24no—
608C42—864no—
609C42—861no—
610C42—861no—
611C42—3441no—
612C42D4×D4312yes—
613C42C2×C22⋊D4312yes—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23C2×D4×D4311yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—862no—
634Q8—862no—
635Q8—1721no—
636Q8—1721no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—3444no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—862no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4#1306329312yes—
682C2×C4#1306329312yes—
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C22×C22⋊D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C8—22no—
690C8—41no—
691C8—862no—
692C8—1721no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—1721no—
701C22—1721no—
702C22—1721no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22C2×#1306329311yescharacteristic
708C22#1458340811yescharacteristic
709C22#1458344611yescharacteristic
710C22#1458370811yescharacteristic
711C22#1458370911yescharacteristic
712C22#1458370911yescharacteristic
713C22#1458371511yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—81no—
719C4—3441no—
720C4—1721no—
721C4—1722no—
722C4—1722no—
723C4—1721no—
724C4—1721no—
725C4—1722no—
726C4#1458340811yescharacteristic
727C4#1458341011yescharacteristic
728C4#1458344511yescharacteristic
729C4#1458344611yescharacteristic
730C2—82no—
731C2—3441no—
732C2#1913781011yescharacteristic
733C2#1914388011yescharacteristic
734C2#1914390911yescharacteristic
735C2#1914481311yescharacteristic
736C2#1914484611yescharacteristic
737C2#1914522111yescharacteristic
738C2#1914526111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#440D43
hypocenterC43#23584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583507C2semidirect
2. C2×C4×#10621883C2semidirect
4. #19135931C2semidirect
5. #19135839C2semidirect
6. #19135800C2semidirect
7. #19135789C2semidirect
8. #19135739C2semidirect
9. #19135676C2semidirect
12. #19134426C2semidirect
13. C4×#13063249C2semidirect
14. #19134364C2semidirect
15. C2×C43×#440C2semidirect
86. C4×Dic86D4semidirect
135. C4×Q8×C43D4semidirect
362. C2×#440D43semidirect
432. C43#23584semidirect
466. C4×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×C4×#106218832
#191372822
#191359312
#191358392
#191358002
#191357892
#191357392
#191356762
#191355992
#191355952
#191344262
C4×#130632492
#191343642
C2×C43×#4402
#2358443