Finite Group Databasebeta

← #25267537

Subgroups — #25267537

Order 11008.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140297C211yesmaximal, characteristic, complemented
2#19140275C212yesmaximal, complemented
3#19140266C211yesmaximal, characteristic, complemented
4#19140091C211yesmaximal, characteristic, complemented
5#19139869C212yesmaximal, complemented
6#19139446C212yesmaximal, complemented
7#19139416C212yesmaximal, complemented
8#19138777C212yesmaximal, complemented
9#19138747C212yesmaximal, complemented
10#19137885C211yesmaximal, characteristic, complemented
11#19137883C211yesmaximal, characteristic, complemented
12#19137830C212yesmaximal, complemented
13#19137142C211yesmaximal, characteristic, complemented
14#124×Dic43C212yesmaximal, complemented
15#121×Dic43C212yesmaximal, complemented
16#19137089C212yesmaximal, complemented
17#19137035C212yesmaximal, complemented
18C4×#13063281C212yesmaximal, complemented
19C43×#2555C211yesmaximal, characteristic
20C2×#13063312C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2212yes—
24C2×D4×Dic43C2211yescharacteristic
25C2×D4×Dic43C2212yes—
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063281C2212yes—
28C2×#13063281C2212yes—
29C2×#13063281C2212yes—
30C22×C4×Dic43C2212yes—
31#14582839C2211yescharacteristic
32#14582838C2211yescharacteristic
33#14582832C2212yes—
34#14582831C2212yes—
35#14582831C2211yescharacteristic
36#14582829C2211yescharacteristic
37#14582827C2212yes—
38#14582824C2212yes—
39#14582822C2212yes—
40#14582822C2212yes—
41#14582820C2212yes—
42#14582818C2211yescharacteristic
43#14582813C2212yes—
44#14582813C2212yes—
45#14582813C2212yes—
46#14582813C2211yescharacteristic
47#14582811C2212yes—
48#14582806C2212yes—
49#14582805C2211yescharacteristic
50#14582802C2212yes—
51#14582802C2212yes—
52#14582798C2212yes—
53#14582793C2212yes—
54#14582793C2212yes—
55#14582792C2212yes—
56#14582792C2212yes—
57#14582792C2212yes—
58#14582792C2212yes—
59#14582792C2212yes—
60#14582792C2212yes—
61#14582792C2212yes—
62#14582787C2212yes—
63#14582787C2212yes—
64#14582787C2212yes—
65#14582787C2212yes—
66#14582786C2212yes—
67#14582784C2212yes—
68#14582783C2212yes—
69#14582782C2212yes—
70#14582781C2212yes—
71#14582780C2212yes—
72#14582779C2212yes—
73#14582779C2212yes—
74#14582779C2212yes—
75#14582772C2212yes—
76#14582771C2212yes—
77#14582765C2212yes—
78#14582764C2211yescharacteristic
79#14582759C2212yes—
80C4⋊C4×Dic43C2212yes—
81C4×Dic43⋊C4C2212yes—
82C4×Dic43⋊C4C2212yes—
83#14582750C2212yes—
84#14582750C2212yes—
85C22⋊C4×Dic43C2212yes—
86C22⋊C4×Dic43C2212yes—
87C22⋊C4×Dic43C2212yes—
88C22⋊C4×Dic43C2212yes—
89C22⋊C4×Dic43C2212yes—
90C22⋊C4×Dic43C2212yes—
91C4×C22⋊Dic43C2212yes—
92#14582744C2211yescharacteristic
93#14582744C2211yescharacteristic
94#14582744C2212yes—
95#14582744C2212yes—
96C42×Dic43C2212yes—
97C42×Dic43C2211yescharacteristic
98C2×#124×C43C2212yes—
99C2×#121×C43C2212yes—
100C43×#395C2211yescharacteristic
101C43×#394C2211yescharacteristic
102C43×#392C2212yes—
103C43×#390C2211yescharacteristic
104C43×#388C2212yes—
105C43×#386C2212yes—
106C4×C22⋊C4×C43C2212yes—
107C22×Dic86C2311yescharacteristic
108C23×Dic43C2312yes—
109C23×Dic43C2312yes—
110C23×Dic43C2312yes—
111#13063312—24no—
112Q8×Dic43—42no—
113#13063290—42no—
114D4×Dic43—28no—
115D4×Dic43—42no—
116D4×Dic43—42no—
117D4×Dic43—44no—
118#13063281—28no—
119#13063281—28no—
120#13063281—28no—
121C2×C4⋊Dic43C2312yes—
122C2×C4⋊Dic43C2312yes—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2312yes—
126C2×C4⋊Dic43C2312yes—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4C2312yes—
129C2×Dic43⋊C4C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2311yescharacteristic
135C2×Dic43⋊C4C2311yescharacteristic
136C2×C22⋊Dic43C2312yes—
137C2×C22⋊Dic43C2312yes—
138C2×C22⋊Dic43C2312yes—
139C2×C22⋊Dic43C2312yes—
140C2×C22⋊Dic43C2312yes—
141C2×C22⋊Dic43C2312yes—
142C2×C22⋊Dic43C2312yes—
143C2×C22⋊Dic43C2312yes—
144C2×C22⋊Dic43C2312yes—
145C2×C22⋊Dic43C2312yes—
146C2×C22⋊Dic43C2312yes—
147C2×C22⋊Dic43C2312yes—
148C2×C22⋊Dic43C2312yes—
149C2×C4×Dic43—28no—
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2312yes—
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2312yes—
157C2×C4×Dic43C2311yescharacteristic
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2312yes—
160C2×C4×Dic43C2311yescharacteristic
161C2×C4×Dic43C2312yes—
162C2×C4×Dic43C2312yes—
163C2×C4×Dic43C2311yescharacteristic
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⋊#95C2311yescharacteristic
180C43⋊#95C2311yescharacteristic
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C22×Q8×C43C2311yescharacteristic
185C22×D4×C43C2312yes—
186C22×D4×C43C2312yes—
187C22×D4×C43C2311yescharacteristic
188C22×D4×C43C2311yescharacteristic
189C23×C4×C43C2312yes—
190#124×C43—28no—
191#121×C43—28no—
192C2×C4⋊C4×C43C2312yes—
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2312yes—
196C2×C22⋊C4×C43C2312yes—
197C2×C22⋊C4×C43C2312yes—
198C2×C22⋊C4×C43C2312yes—
199C2×C22⋊C4×C43C2312yes—
200C2×C22⋊C4×C43C2312yes—
201C2×C42×C43C2312yes—
202C2×C42×C43C2311yescharacteristic
203#95×C43C2311yescharacteristic
204#95×C43C2312yes—
205#95×C43C2312yes—
206#95×C43C2311yescharacteristic
207C24×C43C2412yes—
208C24×C43C2412yes—
209C2×Q8×C43—24no—
210C2×Q8×C43—41no—
211C2×D4×C43—24no—
212C2×D4×C43—24no—
213C2×D4×C43—22no—
214C2×D4×C43—24no—
215C2×D4×C43—24no—
216C2×D4×C43—24no—
217C2×D4×C43—42no—
218C2×D4×C43—41no—
219C2×D4×C43—41no—
220C2×D4×C43—42no—
221C2×D4×C43—41no—
222C22×C4×C43—24no—
223C22×C4×C43—24no—
224C22×C4×C43—42no—
225C22×C4×C43C2412yes—
226C22×C4×C43C2411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C22×C4×C43C2412yes—
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2412yes—
231C22×C4×C43C2412yes—
232C22×Dic43—24no—
233C22×Dic43—24no—
234C22×Dic43—24no—
235C22×Dic43—24no—
236C22×Dic43—24no—
237C22×Dic43—24no—
238C22×Dic43—24no—
239C22×Dic43—24no—
240C22×Dic43—24no—
241C22×Dic43C2412yes—
242C22×Dic43C2412yes—
243C22×Dic43C2411yescharacteristic
244C22×Dic43C2411yescharacteristic
245C22×Dic43C2412yes—
246C22×Dic43C2411yescharacteristic
247C22×Dic43C2412yes—
248C22×Dic43C2412yes—
249C22×Dic43C2412yes—
250C22×Dic43C2411yescharacteristic
251C2×Dic86—22no—
252C2×Dic86—41no—
253C2×Dic86—41no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—41no—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43#4118yes—
263C42×C43—24no—
264C42×C43—41no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271C22⋊Dic43—24no—
272C22⋊Dic43—42no—
273C22⋊Dic43—42no—
274C22⋊Dic43—42no—
275C22⋊Dic43—42no—
276C22⋊Dic43—42no—
277C22⋊Dic43—42no—
278C4⋊Dic43—24no—
279C4⋊Dic43—42no—
280C4⋊Dic43—42no—
281C4⋊Dic43—41no—
282C4⋊Dic43—41no—
283C4⋊Dic43—42no—
284C4⋊Dic43—41no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290Dic43⋊C4—24no—
291Dic43⋊C4—41no—
292Dic43⋊C4—41no—
293C4×Dic43—24no—
294C4×Dic43—24no—
295C4×Dic43—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298C4×Dic43—24no—
299C4×Dic43—24no—
300C4×Dic43—22no—
301C4×Dic43—22no—
302C4×Dic43—24no—
303C4×Dic43—22no—
304C4×Dic43—42no—
305C4×Dic43#4118yes—
306C4×Dic43#4114yes—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43C2×#4114yes—
321C23×C43C2511yescharacteristic
322Q8×C43—44no—
323D4×C43—48no—
324D4×C43—48no—
325D4×C43—44no—
326D4×C43—44no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—48no—
343C2×C4×C43C2×#4114yes—
344C2×C4×C43C2×#4112yes—
345C2×C4×C43C2×#4114yes—
346C2×C4×C43C2×#4114yes—
347C2×Dic43—216no—
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—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—48no—
373C2×Dic43—48no—
374C2×Dic43C2×#4114yes—
375C2×Dic43C2×#4114yes—
376C2×Dic43C2×#4114yes—
377C2×Dic43H(5,𝔽2)12yes—
378Dic86—44no—
379#34874—431nomaximal, Sylow
380C22×C43—24no—
381C22×C43—24no—
382C22×C43—24no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43C22×#4111yescharacteristic
395C22×C43C22×#4112yes—
396C22×C43C22×#4112yes—
397C22×C43C2×H(5,𝔽2)11yescharacteristic
398C22×C43#58511yescharacteristic
399C4×C43—22no—
400C4×C43—24no—
401C4×C43—24no—
402C4×C43—24no—
403C4×C43—42no—
404C4×C43—41no—
405C4×C43—41no—
406Dic43—24no—
407Dic43—24no—
408Dic43—41no—
409Dic43—41no—
410Dic43—42no—
411Dic43—42no—
412Dic43—42no—
413Dic43—42no—
414Dic43—41no—
415Dic43#55514yes—
416#2612—431no—
417#2610—432no—
418#2609—431no—
419#2593—431no—
420#2574—432no—
421#2555D4311yescharacteristic
422#2531—432no—
423#2529—432no—
424#2476—432no—
425#2474—432no—
426#2399—431no—
427#2398—431no—
428#2392—432no—
429C4×#124—431no—
430C4×#124—432no—
431C4×#121—432no—
432#2298—432no—
433#2290—432no—
434C4×#117—432no—
435C2×C43—44no—
436C2×C43—82no—
437C2×C43#344412yes—
438C2×C43#346011yescharacteristic
439C2×C43C2×#55511yescharacteristic
440C2×C43#347512yes—
441C2×C43#348111yescharacteristic
442C2×#124—431no—
443C2×#124C2×D4312yes—
444C2×#121C2×D4312yes—
445C2×C4×Q8—431no—
446C2×C4×Q8—431no—
447C2×C4×D4—432no—
448C2×C4×D4—431no—
449C2×C4×D4—432no—
450C2×C4×D4—431no—
451C2×#117—432no—
452C2×#117—432no—
453C2×#117—432no—
454C22×C42—432no—
455#400—431no—
456#400—431no—
457#398—431no—
458#398—432no—
459#398—432no—
460#398—431no—
461#397—432no—
462#397—432no—
463#396—432no—
464#396—432no—
465#395—431no—
466#395—432no—
467#395C2×D4311yescharacteristic
468#394—432no—
469#394—432no—
470#394—432no—
471#394—431no—
472#394C2×D4311yescharacteristic
473#393—432no—
474#392C2×D4312yes—
475#391—432no—
476#391—431no—
477#390—432no—
478#390—432no—
479#390C2×D4311yescharacteristic
480#389—432no—
481#388—432no—
482#388—432no—
483#388—432no—
484#388—432no—
485#388—432no—
486#388—432no—
487#388—432no—
488#388—432no—
489#388—432no—
490#388—432no—
491#388—432no—
492#388—432no—
493#388—432no—
494#388C2×D4312yes—
495#387—432no—
496#387—432no—
497#387—432no—
498#387—432no—
499#387—432no—
500#387—432no—
501#386—432no—
502#386—432no—
503#386—432no—
504#386C2×D4312yes—
505#385—432no—
506#385—432no—
507#382—431no—
508#382—432no—
509#380—432no—
510C4×C4⋊C4—432no—
511C4×C4⋊C4—432no—
512C4×C4⋊C4—432no—
513C4×C4⋊C4—432no—
514C4×C4⋊C4—432no—
515C4×C22⋊C4—432no—
516C4×C22⋊C4—432no—
517C4×C22⋊C4—432no—
518C4×C22⋊C4—432no—
519C4×C22⋊C4—432no—
520C4×C22⋊C4—432no—
521C4×C22⋊C4—432no—
522C4×C22⋊C4C2×D4312yes—
523#376—432no—
524#376—431no—
525#376—431no—
526#376—432no—
527C43—431no—
528C43—432no—
529C43#3487411yescharacteristic, complemented, Sylow
530C22×Q8—431no—
531C22×Q8C22×D4311yescharacteristic
532C22×D4C22×D4311yescharacteristic
533C22×D4C22×D4312yes—
534C22×D4C22×D4312yes—
535C22×D4C22×D4311yescharacteristic
536C23×C4—432no—
537C23×C4—432no—
538C23×C4—432no—
539C23×C4C22×D4312yes—
540#124—28no—
541#124—864no—
542#121—28no—
543C4×Q8—1722no—
544C4×Q8—1722no—
545C4×D4—868no—
546C4×D4—1722no—
547C4×D4—1724no—
548C4×D4—1722no—
549#117—868no—
550#117—868no—
551#117—868no—
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—432no—
559C2×C4⋊C4—432no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—432no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—432no—
567C2×C4⋊C4C22×D4312yes—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—432no—
570C2×C22⋊C4—432no—
571C2×C22⋊C4—432no—
572C2×C22⋊C4—432no—
573C2×C22⋊C4—432no—
574C2×C22⋊C4—432no—
575C2×C22⋊C4—432no—
576C2×C22⋊C4—432no—
577C2×C22⋊C4—432no—
578C2×C22⋊C4—432no—
579C2×C22⋊C4—432no—
580C2×C22⋊C4—432no—
581C2×C22⋊C4—432no—
582C2×C22⋊C4C22×D4312yes—
583C2×C22⋊C4C22×D4312yes—
584C2×C22⋊C4C22×D4312yes—
585C2×C22⋊C4C22×D4312yes—
586C2×C22⋊C4C22×D4312yes—
587C2×C22⋊C4C22×D4312yes—
588C2×C22⋊C4C22×D4312yes—
589C2×C42—431no—
590C2×C42—432no—
591C2×C42—432no—
592C2×C42—432no—
593C2×C42—432no—
594C2×C42—432no—
595C2×C42—431no—
596C2×C42—432no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—432no—
600C2×C42—432no—
601C2×C42—432no—
602C2×C42—432no—
603C2×C42—868no—
604C2×C42C22×D4312yes—
605C2×C42C22×D4311yescharacteristic
606#95—432no—
607#95—432no—
608#95—432no—
609#95—432no—
610#95—432no—
611#95—432no—
612#95—431no—
613#95—432no—
614#95—432no—
615#95—431no—
616#95—432no—
617#95—432no—
618#95—432no—
619#95—432no—
620#95—432no—
621#95—432no—
622#95—432no—
623#95—432no—
624#95—432no—
625#95—432no—
626#95C22×D4312yes—
627#95C22×D4312yes—
628#95C22×D4311yescharacteristic
629#95C22×D4311yescharacteristic
630C24C23×D4312yes—
631C24C23×D4312yes—
632C2×Q8—24no—
633C2×Q8—41no—
634C2×Q8—862no—
635C2×Q8—1721no—
636C2×Q8—1721no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—24no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—41no—
646C2×D4—41no—
647C2×D4—42no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—42no—
651C22×C4—431no—
652C22×C4—432no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—431no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—864no—
668C22×C4—864no—
669C22×C4—864no—
670C22×C4C23×D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4312yes—
674C22×C4C23×D4311yescharacteristic
675C22×C4C23×D4312yes—
676C22×C4C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—41no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—1721no—
687C4⋊C4—1722no—
688C4⋊C4—1721no—
689C4⋊C4—1721no—
690C4⋊C4—1721no—
691C4⋊C4—1722no—
692C4⋊C4—1721no—
693C4⋊C4—1722no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4#1062190018yes—
714C42—24no—
715C42—41no—
716C42—438no—
717C42—434no—
718C42—864no—
719C42—864no—
720C42—864no—
721C42—864no—
722C42—862no—
723C42—864no—
724C42—862no—
725C42—862no—
726C42—864no—
727C42—864no—
728C42—864no—
729C42—1722no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23C2×#1062190014yes—
744C23C24×D4311yescharacteristic
745Q8—44no—
746Q8—1724no—
747D4—48no—
748D4—48no—
749D4—44no—
750D4—44no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—48no—
767C2×C4—434no—
768C2×C4—432no—
769C2×C4—434no—
770C2×C4—434no—
771C2×C4—8616no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—861no—
787C2×C4—862no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—1728no—
797C2×C4—1728no—
798C2×C4#41×D4314yes—
799C2×C4#41×D4312yes—
800C2×C4C2×#1062190014yes—
801C2×C4C2×#1062190014yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22C2×#41×D4312yes—
817C22C2×#41×D4311yescharacteristic
818C22C22×#1062190012yes—
819C22H(5,𝔽2)×D4311yescharacteristic
820C22#1458373411yescharacteristic
821C4—24no—
822C4—24no—
823C4—24no—
824C4—22no—
825C4—42no—
826C4—41no—
827C4—41no—
828C4—434no—
829C4—864no—
830C4—864no—
831C4—1722no—
832C4—1722no—
833C4—1722no—
834C4—1721no—
835C4—1721no—
836C4—1721no—
837C4—1722no—
838C2—44no—
839C2—82no—
840C2#1914789012yes—
841C2#1914801411yescharacteristic
842C2#555×D4311yescharacteristic
843C2#1914814612yes—
844C2#1914819611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
Fitting, prime radicalC43×#2555C2
hypercenter#2555D43
hypocenterC43#34874
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2555

Complements

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

NH ≅ G/Ntype
1. #19140297C2semidirect
2. #19140275C2semidirect
3. #19140266C2semidirect
4. #19140091C2semidirect
5. #19139869C2semidirect
6. #19139446C2semidirect
7. #19139416C2semidirect
8. #19138777C2semidirect
9. #19138747C2semidirect
10. #19137885C2semidirect
11. #19137883C2semidirect
12. #19137830C2semidirect
13. #19137142C2semidirect
14. #124×Dic43C2semidirect
15. #121×Dic43C2semidirect
16. #19137089C2semidirect
17. #19137035C2semidirect
18. C4×#13063281C2semidirect
529. C43#34874semidirect

Maximal subgroups

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

subgroupindex
#191402972
#191402752
#191402662
#191400912
#191398692
#191394462
#191394162
#191387772
#191387472
#191378852
#191378832
#191378302
#191371422
#124×Dic432
#121×Dic432
#191370892
#191370352
C4×#130632812
C43×#25552
#3487443