Finite Group Databasebeta

← #25269689

Subgroups — #25269689

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142945C211yesmaximal, characteristic
2#19142943C211yesmaximal, characteristic
3#19142931C212yesmaximal
4#19140567C212yesmaximal
5#19140411C211yesmaximal, characteristic
6#19140410C211yesmaximal, characteristic
7#19140067C212yesmaximal, complemented
8#19140065C212yesmaximal, complemented
9#19140037C212yesmaximal, complemented
10#19140035C212yesmaximal, complemented
11#19139167C212yesmaximal, complemented
12#19139119C212yesmaximal, complemented
13#19138431C212yesmaximal, complemented
14#19138368C212yesmaximal, complemented
15#19137328C211yesmaximal, characteristic
16#19137195C212yesmaximal
17C4×#13063302C212yesmaximal
18C2×#14582750C211yesmaximal, characteristic
19C43×#2329C211yesmaximal, characteristic
20C2×#13063324C2211yescharacteristic
21C2×#13063323C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063302C2212yes—
24C2×C4×Dic86C2212yes—
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582840C2212yes—
31#14582840C2212yes—
32#14582839C2212yes—
33#14582839C2212yes—
34#14582837C2212yes—
35#14582837C2212yes—
36#14582833C2212yes—
37#14582832C2212yes—
38#14582832C2212yes—
39#14582832C2212yes—
40#14582830C2212yes—
41#14582829C2212yes—
42#14582829C2212yes—
43#14582829C2212yes—
44#14582820C2212yes—
45#14582818C2212yes—
46#14582806C2211yescharacteristic
47#14582804C2211yescharacteristic
48#14582803C2212yes—
49#14582803C2212yes—
50#14582803C2212yes—
51#14582803C2212yes—
52#14582803C2212yes—
53#14582798C2211yescharacteristic
54#14582796C2212yes—
55#14582796C2212yes—
56#14582796C2212yes—
57#14582795C2211yescharacteristic
58#14582794C2212yes—
59#14582794C2212yes—
60#14582794C2212yes—
61#14582794C2212yes—
62#14582786C2212yes—
63#14582786C2212yes—
64#14582785C2212yes—
65#14582785C2212yes—
66#14582783C2212yes—
67#14582783C2212yes—
68#14582783C2212yes—
69#14582783C2212yes—
70#14582782C2212yes—
71#14582782C2212yes—
72#14582781C2212yes—
73#14582781C2212yes—
74#14582781C2212yes—
75#14582781C2212yes—
76#14582781C2212yes—
77#14582781C2212yes—
78#14582774C2212yes—
79#14582772C2212yes—
80#14582771C2212yes—
81#14582768C2211yescharacteristic
82#14582768C2211yescharacteristic
83#14582760C2212yes—
84#14582760C2212yes—
85#14582759C2211yescharacteristic
86#14582757C2212yes—
87#14582757C2212yes—
88#14582757C2212yes—
89C4×Dic43⋊C4C2212yes—
90C4×Dic43⋊C4C2212yes—
91C4×C4⋊Dic43C2212yes—
92#14582750C2212yes—
93#14582750C2212yes—
94#14582750C2212yes—
95#14582750C2212yes—
96C4×C22⋊Dic43C2212yes—
97C2×C43⋊#95C2211yescharacteristic
98C2×C22⋊Q8×C43C2211yescharacteristic
99C43×#391C2212yes—
100C43×#389C2212yes—
101C43×#387C2212yes—
102C43×#387C2212yes—
103C43×#385C2212yes—
104C43×#380C2211yescharacteristic
105C4×C22⋊C4×C43C2212yes—
106C2×#95×C43C2211yescharacteristic
107C22×Dic86C2312yes—
108C22×Dic86C2311yescharacteristic
109C23×Dic43C2311yescharacteristic
110C23×Dic43C2311yescharacteristic
111C23×Dic43C2311yescharacteristic
112C23×Dic43C2311yescharacteristic
113#13063324—42no—
114#13063323—42no—
115#13063304—24no—
116#13063302—28no—
117C4×Dic86—44no—
118C2×C4⋊Dic43C2312yes—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2312yes—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2312yes—
124C2×Dic43⋊C4—24no—
125C2×Dic43⋊C4Q818yescomplemented
126C2×Dic43⋊C4C2312yes—
127C2×Dic43⋊C4C2312yes—
128C2×Dic43⋊C4C2312yes—
129C2×Dic43⋊C4C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2312yes—
136C2×Dic43⋊C4C2312yes—
137C2×Dic43⋊C4C2312yes—
138C2×Dic43⋊C4C2312yes—
139C2×Dic43⋊C4C2312yes—
140C2×Dic43⋊C4C2312yes—
141C2×Dic43⋊C4C2312yes—
142C2×Dic43⋊C4C2312yes—
143C2×C22⋊Dic43C2312yes—
144C2×C22⋊Dic43C2312yes—
145C2×C4×Dic43—24no—
146C2×C4×Dic43—42no—
147C2×C4×Dic43—42no—
148C2×C4×Dic43C2312yes—
149C2×C4×Dic43C2312yes—
150C2×C4×Dic43C2311yescharacteristic
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2311yescharacteristic
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2312yes—
158C43⋊#95C2312yes—
159C43⋊#95C2312yes—
160C43⋊#95C2312yes—
161C43⋊#95C2312yes—
162C43⋊#95C2312yes—
163C43⋊#95C2312yes—
164C43⋊#95C2312yes—
165C43⋊#95C2312yes—
166C43⋊#95C2312yes—
167C43⋊#95C2312yes—
168C43⋊#95C2312yes—
169C43⋊#95C2312yes—
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C22×Q8×C43C2311yescharacteristic
184C23×C4×C43C2311yescharacteristic
185C23×C4×C43C2311yescharacteristic
186C23×C4×C43C2311yescharacteristic
187C22⋊Q8×C43—24no—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2312yes—
191C2×C4⋊C4×C43C2312yes—
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2312yes—
196C2×C42×C43C2312yes—
197C2×C42×C43C2312yes—
198#95×C43C2312yes—
199#95×C43C2312yes—
200#95×C43C2312yes—
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205C24×C43C2411yescharacteristic
206C2×Q8×C43—22no—
207C2×Q8×C43—41no—
208C2×Q8×C43—41no—
209C22×C4×C43—22no—
210C22×C4×C43—41no—
211C22×C4×C43—41no—
212C22×C4×C43—41no—
213C22×C4×C43—41no—
214C22×C4×C43—41no—
215C22×C4×C43—41no—
216C22×C4×C43C2×Q814yes—
217C22×C4×C43#4114yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—41no—
232C22×Dic43—41no—
233C22×Dic43—41no—
234C22×Dic43—41no—
235C22×Dic43C2×Q814yes—
236C22×Dic43C2×Q814yes—
237C22×Dic43#4114yes—
238C22×Dic43C2412yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C22×Dic43C2412yes—
242C22×Dic43C2412yes—
243C22×Dic43C2412yes—
244C22×Dic43C2411yescharacteristic
245C22×Dic43C2411yescharacteristic
246C22×Dic43C2411yescharacteristic
247C22×Dic43C2411yescharacteristic
248C2×Dic86—24no—
249C2×Dic86—24no—
250C2×Dic86—24no—
251C2×Dic86—22no—
252C2×Dic86—41no—
253C2×Dic86—41no—
254C4⋊C4×C43—22no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—41no—
257C4⋊C4×C43—42no—
258C4⋊C4×C43—42no—
259C4⋊C4×C43—41no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C42×C43—42no—
263C42×C43—42no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C4⋊Dic43—22no—
267C4⋊Dic43—24no—
268C4⋊Dic43—41no—
269C4⋊Dic43—42no—
270C4⋊Dic43—42no—
271C4⋊Dic43—41no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—42no—
280Dic43⋊C4—42no—
281Dic43⋊C4—42no—
282Dic43⋊C4—42no—
283Dic43⋊C4—42no—
284Dic43⋊C4—42no—
285Dic43⋊C4—42no—
286Dic43⋊C4—42no—
287Dic43⋊C4C2×Q818yes—
288Dic43⋊C4C2×Q818yes—
289C4×Dic43—24no—
290C4×Dic43—24no—
291C4×Dic43—24no—
292C4×Dic43—22no—
293C4×Dic43—22no—
294C4×Dic43—41no—
295C4×Dic43—41no—
296C4×Dic43—42no—
297C4×Dic43—42no—
298C4×Dic43—42no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43C22×Q812yes—
304C23×C43C2×#4112yes—
305C23×C43C2×#4112yes—
306C23×C43C2511yescharacteristic
307Q8×C43—82no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—44no—
330C2×C4×C43—44no—
331C2×C4×C43—44no—
332C2×C4×C43C22×Q814yes—
333C2×C4×C43C2×#4112yes—
334C2×C4×C43C2×#4112yes—
335C2×Dic43—28no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—28no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—44no—
361C2×Dic43—44no—
362C2×Dic43C22×Q814yes—
363C2×Dic43C22×Q812yes—
364C2×Dic43C22×Q812yes—
365C2×Dic43C2×#4112yes—
366C2×Dic43C2×#4112yes—
367C2×Dic43H(5,𝔽2)12yes—
368C2×Dic432−1+412yes—
369Dic86—48no—
370Dic86—82no—
371#35015—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43#53314yes—
379C22×C43C23×Q811yescharacteristic
380C22×C43C22×#4111yescharacteristic
381C22×C43C22×#4111yescharacteristic
382C22×C43C2×H(5,𝔽2)11yescharacteristic
383C22×C43C2×2−1+411yescharacteristic
384C22×C43#58511yescharacteristic
385C22×C43#58511yescharacteristic
386C4×C43—24no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394Dic43—24no—
395Dic43—22no—
396Dic43—22no—
397Dic43—22no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43#53914yes—
404#2857—431no—
405#2857—431no—
406#2855—432no—
407#2646—432no—
408#2627—431no—
409#2627—431no—
410#2590—432no—
411#2590—432no—
412#2588—432no—
413#2588—432no—
414#2511—432no—
415#2507—432no—
416#2451—432no—
417#2446—432no—
418#2329—431no—
419#2329D4311yescharacteristic
420#2313—432no—
421C4×C22⋊Q8—432no—
422C2×C4×C4⋊C4—431no—
423C2×C43—24no—
424C2×C43C2×#53311yescharacteristic
425C2×C43C2×#53911yescharacteristic
426C2×C43#345511yescharacteristic
427C2×C43#350111yescharacteristic
428C2×C43#350211yescharacteristic
429C2×C43#350511yescharacteristic
430C2×C43#350711yescharacteristic
431C2×C4⋊Q8—431no—
432C2×C4⋊Q8—431no—
433C2×C22⋊Q8—431no—
434C2×C22⋊Q8—432no—
435C2×C22⋊Q8C2×D4311yescharacteristic
436C2×C4×Q8—432no—
437C22×C4⋊C4—431no—
438C22×C4⋊C4—431no—
439C22×C42—431no—
440C22×C42—431no—
441C22×C42—431no—
442#400—432no—
443#400—432no—
444#400—432no—
445#400—432no—
446#400—432no—
447#400—432no—
448#398—432no—
449#398—432no—
450#398—432no—
451#398—432no—
452#398—432no—
453#398—432no—
454#398—432no—
455#398—432no—
456#395—432no—
457#395—432no—
458#391—431no—
459#391—431no—
460#391—432no—
461#391—432no—
462#391—432no—
463#391—432no—
464#391—432no—
465#391C2×D4312yes—
466#389—432no—
467#389—432no—
468#389—432no—
469#389—432no—
470#389—431no—
471#389—431no—
472#389—432no—
473#389—432no—
474#389—432no—
475#389C2×D4312yes—
476#387—432no—
477#387—432no—
478#387—432no—
479#387—432no—
480#387—432no—
481#387—432no—
482#387—432no—
483#387—432no—
484#387—432no—
485#387—432no—
486#387—432no—
487#387—432no—
488#387—432no—
489#387—432no—
490#387—432no—
491#387—432no—
492#387C2×D4312yes—
493#387C2×D4312yes—
494#385—432no—
495#385—432no—
496#385—432no—
497#385C2×D4312yes—
498#384—431no—
499#384—431no—
500#381—432no—
501#381—432no—
502#380—431no—
503#380—432no—
504#380—432no—
505#380—432no—
506#380C2×D4311yescharacteristic
507C4×C4⋊C4—432no—
508C4×C4⋊C4—432no—
509C4×C4⋊C4—432no—
510C4×C4⋊C4—432no—
511C4×C4⋊C4—432no—
512C4×C4⋊C4—432no—
513C4×C4⋊C4—432no—
514C4×C22⋊C4—432no—
515C4×C22⋊C4C2×D4312yes—
516C2×#95—431no—
517C2×#95C2×D4311yescharacteristic
518C43#3501511yescharacteristic, complemented, Sylow
519C22×Q8—432no—
520C22×Q8—431no—
521C22×Q8C22×D4311yescharacteristic
522C23×C4—431no—
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—431no—
526C23×C4C22×D4311yescharacteristic
527C23×C4C22×D4311yescharacteristic
528C23×C4C22×D4311yescharacteristic
529C4⋊Q8—1722no—
530C4⋊Q8—1722no—
531C22⋊Q8—24no—
532C22⋊Q8—868no—
533C22⋊Q8—864no—
534C4×Q8—1724no—
535C2×C4⋊C4—438no—
536C2×C4⋊C4—432no—
537C2×C4⋊C4—432no—
538C2×C4⋊C4—432no—
539C2×C4⋊C4—432no—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—432no—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—432no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—432no—
547C2×C4⋊C4—432no—
548C2×C4⋊C4—432no—
549C2×C4⋊C4—432no—
550C2×C4⋊C4—432no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—432no—
553C2×C4⋊C4—432no—
554C2×C4⋊C4—432no—
555C2×C4⋊C4—432no—
556C2×C4⋊C4—432no—
557C2×C4⋊C4—432no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—864no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4312yes—
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C4⋊C4C22×D4312yes—
565C2×C4⋊C4C22×D4312yes—
566C2×C22⋊C4—432no—
567C2×C22⋊C4—432no—
568C2×C22⋊C4C22×D4312yes—
569C2×C22⋊C4C22×D4312yes—
570C2×C42—432no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—432no—
574C2×C42—432no—
575C2×C42—432no—
576C2×C42—432no—
577C2×C42—432no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—864no—
581C2×C42—1722no—
582C2×C42—1722no—
583C2×C42C22×D4312yes—
584C2×C42C22×D4312yes—
585#95—432no—
586#95—432no—
587#95—432no—
588#95—432no—
589#95—432no—
590#95—432no—
591#95—432no—
592#95—432no—
593#95—432no—
594#95—432no—
595#95—432no—
596#95—432no—
597#95—432no—
598#95—432no—
599#95—432no—
600#95—432no—
601#95—432no—
602#95—432no—
603#95—432no—
604#95—432no—
605#95—432no—
606#95—432no—
607#95—432no—
608#95—432no—
609#95—432no—
610#95C22×D4312yes—
611#95C22×D4312yes—
612#95C22×D4312yes—
613#95C22×D4312yes—
614#95C22×D4312yes—
615#95C22×D4312yes—
616#95C22×D4312yes—
617C24C23×D4311yescharacteristic
618C2×Q8—22no—
619C2×Q8—41no—
620C2×Q8—41no—
621C2×Q8—864no—
622C2×Q8—864no—
623C2×Q8—864no—
624C2×Q8—862no—
625C2×Q8—1721no—
626C2×Q8—1721no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—431no—
635C22×C4—434no—
636C22×C4—434no—
637C22×C4—432no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—434no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—1721no—
653C22×C4—1721no—
654C22×C4—1721no—
655C22×C4—1721no—
656C22×C4#1062189814yes—
657C22×C4Q8×D4314yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C22×C4C23×D4312yes—
662C22×C4C23×D4312yes—
663C22×C4C23×D4312yes—
664C22×C4C23×D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—438no—
673C4⋊C4—438no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—862no—
683C4⋊C4—1722no—
684C4⋊C4—1722no—
685C4⋊C4—1722no—
686C4⋊C4—1722no—
687C4⋊C4—1721no—
688C4⋊C4—1722no—
689C4⋊C4—1722no—
690C4⋊C4—1722no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C4⋊C4—1721no—
694C4⋊C4—1722no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—42no—
700C42—42no—
701C42—864no—
702C42—864no—
703C42—864no—
704C42—862no—
705C42—862no—
706C42—1722no—
707C42—1721no—
708C42—1721no—
709C42—1722no—
710C42—1722no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23C2×Q8×D4312yes—
716C23#41×D4312yes—
717C23C2×#1062189812yes—
718C23C24×D4311yescharacteristic
719Q8—82no—
720Q8—3442no—
721Q8—1728no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—434no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—868no—
754C2×C4—868no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—1724no—
779C2×C4—1724no—
780C2×C4C2×Q8×D4314yes—
781C2×C4C2×#1062189812yes—
782C2×C4C2×#1062189812yes—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22#1458345314yes—
790C22C22×Q8×D4311yescharacteristic
791C22C2×#41×D4311yescharacteristic
792C22C22×#1062189811yescharacteristic
793C22H(5,𝔽2)×D4311yescharacteristic
794C222−1+4×D4311yescharacteristic
795C22#1458373411yescharacteristic
796C22#1458373411yescharacteristic
797C4—24no—
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—434no—
806C4—864no—
807C4—862no—
808C4—862no—
809C4—862no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C4—1722no—
814C4—1722no—
815C2—24no—
816C2C2×#1458345311yescharacteristic
817C2#539×D4311yescharacteristic
818C2#1914797711yescharacteristic
819C2#1914839511yescharacteristic
820C2#1914840311yescharacteristic
821C2#1914842511yescharacteristic
822C2#1914845311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2329C2
prime radicalC24×C43C24
hypercenter#2329D43
hypocenterC43#35015
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2329

Complements

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

NH ≅ G/Ntype
7. #19140067C2semidirect
8. #19140065C2semidirect
9. #19140037C2semidirect
10. #19140035C2semidirect
11. #19139167C2semidirect
12. #19139119C2semidirect
13. #19138431C2semidirect
14. #19138368C2semidirect
125. C2×Dic43⋊C4Q8semidirect
518. C43#35015semidirect

Maximal subgroups

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

subgroupindex
#191429452
#191429432
#191429312
#191405672
#191404112
#191404102
#191400672
#191400652
#191400372
#191400352
#191391672
#191391192
#191384312
#191383682
#191373282
#191371952
C4×#130633022
C2×#145827502
C43×#23292
#3501543