Finite Group Databasebeta

← #25023349

Subgroups — #25023349

Order 11008.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic43C211yesmaximal, characteristic, complemented
2C2×#14582792C211yesmaximal, characteristic, complemented
3C2×#14582779C212yesmaximal, complemented
4#19132852C211yesmaximal, characteristic, complemented
5#19132840C211yesmaximal, characteristic, complemented
6#19132840C212yesmaximal, complemented
7#19132836C212yesmaximal, complemented
8#19132836C211yesmaximal, characteristic, complemented
9#19132820C211yesmaximal, characteristic, complemented
10#19132817C212yesmaximal, complemented
11C2×C43×#392C211yesmaximal, characteristic
12C24×Dic43C2212yes—
13C2×D4×Dic43—28no—
14C2×D4×Dic43—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×C22⋊Dic43C2212yes—
22C22×C22⋊Dic43C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24#14582792—24no—
25#14582779—28no—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C23×D4×C43C2211yescharacteristic
35C23×D4×C43C2212yes—
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C43×#392C418yescomplemented
39C2×#95×C43C2211yescharacteristic
40C23×Dic43—24no—
41C23×Dic43—24no—
42C23×Dic43—42no—
43C23×Dic43—42no—
44C23×Dic43—42no—
45C23×Dic43—42no—
46C23×Dic43D418yescomplemented
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53D4×Dic43—232no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—24no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—42no—
58C2×C22⋊Dic43—24no—
59C2×C22⋊Dic43—24no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—42no—
68C2×C22⋊Dic43—42no—
69C2×C22⋊Dic43—42no—
70C2×C22⋊Dic43—42no—
71C2×C22⋊Dic43—42no—
72C2×C22⋊Dic43—42no—
73C2×C22⋊Dic43—42no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43D414yescomplemented
76C43⋊#95—22no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—42no—
82C43⋊#95—42no—
83C43⋊#95—42no—
84C25×C43C2311yescharacteristic
85C25×C43C2312yes—
86C22×D4×C43—24no—
87C22×D4×C43—24no—
88C22×D4×C43—24no—
89C22×D4×C43—24no—
90C22×D4×C43—22no—
91C22×D4×C43—22no—
92C22×D4×C43—42no—
93C22×D4×C43—42no—
94C22×D4×C43—42no—
95C22×D4×C43—42no—
96C22×D4×C43C2×C414yes—
97C22×D4×C43C2×C418yescomplemented
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—42no—
104C2×C22⋊C4×C43—42no—
105C2×C22⋊C4×C43C2×C414yescomplemented
106C2×C22⋊C4×C43C2×C418yescomplemented
107#95×C43C2×C414yescomplemented
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43—21no—
121C24×C43—22no—
122C24×C43—21no—
123C24×C43—22no—
124C24×C43—21no—
125C24×C43—21no—
126C24×C43—22no—
127C24×C43—22no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43C22×C412yes—
131C24×C43C22×C414yes—
132C24×C43C2×D414yes—
133C24×C43#4114yes—
134C24×C43C2411yescharacteristic
135C2×D4×C43—216no—
136C2×D4×C43—28no—
137C2×D4×C43—28no—
138C2×D4×C43—28no—
139C2×D4×C43—216no—
140C2×D4×C43—216no—
141C2×D4×C43—48no—
142C2×D4×C43—48no—
143C2×D4×C43—48no—
144C2×D4×C43—48no—
145C2×D4×C43—48no—
146C2×D4×C43—48no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43C22×C414yes—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C22×C412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43#4112yes—
164C22×Dic43—216no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—21no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—21no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—21no—
192C22×Dic43—22no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—48no—
196C22×Dic43—48no—
197C22×Dic43—48no—
198C22×Dic43—48no—
199C22×Dic43—48no—
200C22×Dic43—48no—
201C22×Dic43C2×D414yes—
202C22×Dic43C2×D412yes—
203C22×Dic43C2×D414yes—
204C22×Dic43C2×D412yes—
205C22⋊C4×C43—28no—
206C22⋊C4×C43—48no—
207C22⋊Dic43—216no—
208C22⋊Dic43—48no—
209C22⋊Dic43—48no—
210C22⋊Dic43—48no—
211C22⋊Dic43—44no—
212C22⋊Dic43—44no—
213C4⋊Dic43—28no—
214C4⋊Dic43—44no—
215C4×Dic43—28no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—24no—
220C23×C43—24no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43—24no—
227C23×C43—24no—
228C23×C43—24no—
229C23×C43—24no—
230C23×C43—24no—
231C23×C43—24no—
232C23×C43—24no—
233C23×C43—24no—
234C23×C43—22no—
235C23×C43—24no—
236C23×C43—22no—
237C23×C43—24no—
238C23×C43—22no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43—42no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43—42no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43—42no—
252C23×C43—42no—
253C23×C43—42no—
254C23×C43—42no—
255C23×C43—41no—
256C23×C43—42no—
257C23×C43—41no—
258C23×C43—42no—
259C23×C43—42no—
260C23×C43—41no—
261C23×C43—42no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—42no—
265C23×C43—41no—
266C23×C43—42no—
267C23×C43—42no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—41no—
271C23×C43—42no—
272C23×C43—41no—
273C23×C43C4×D418yes—
274C23×C43C23×C411yescharacteristic
275C23×C43C22×D412yes—
276C23×C43C22×D411yescharacteristic
277C23×C43C2×#4112yes—
278C23×C43C2×#4111yescharacteristic
279C23×C43H(5,𝔽2)11yescharacteristic
280C23×C43H(5,𝔽2)12yes—
281C23×C43H(5,𝔽2)12yes—
282C23×C43H(5,𝔽2)11yescharacteristic
283C23×C43H(5,𝔽2)11yescharacteristic
284C23×C432−1+411yescharacteristic
285D4×C43—232no—
286D4×C43—432no—
287C2×C4×C43—24no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—24no—
296C2×C4×C43—42no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43C4×D414yes—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—24no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—432no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—41no—
330C2×Dic43—42no—
331C2×Dic43—41no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43#12014yes—
339#14299—431nomaximal, Sylow
340C22×C43—28no—
341C22×C43—28no—
342C22×C43—28no—
343C22×C43—44no—
344C22×C43—44no—
345C22×C43—44no—
346C22×C43—44no—
347C22×C43—44no—
348C22×C43—44no—
349C22×C43—44no—
350C22×C43—44no—
351C22×C43—44no—
352C22×C43—44no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43—42no—
357C22×C43—44no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—82no—
363C22×C43—81no—
364C22×C43—82no—
365C22×C43—81no—
366C22×C43C2×C4×D412yes—
367C22×C43C2×C4×D411yescharacteristic
368C22×C43#51811yescharacteristic
369C22×C43#51812yes—
370C22×C43#52011yescharacteristic
371C22×C43C2×#12011yescharacteristic
372C22×C43#52512yes—
373C22×C43#52511yescharacteristic
374C22×C43#53412yes—
375C22×C43#53412yes—
376C22×C43#53511yescharacteristic
377C22×C43#53511yescharacteristic
378C22×C43#53512yes—
379C22×C43#53511yescharacteristic
380C22×C43#53712yes—
381C22×C43#53711yescharacteristic
382C22×C43#53812yes—
383C22×C43#53812yes—
384C22×C43#53812yes—
385C22×C43#53912yes—
386C22×C43#54011yescharacteristic
387C22×C43#54012yes—
388C22×C43#54211yescharacteristic
389C4×C43—24no—
390C4×C43—44no—
391C4×C43—42no—
392Dic43—24no—
393Dic43—44no—
394Dic43—42no—
395Dic43—81no—
396Dic43—81no—
397Dic43—82no—
398C22×C4×D4—431no—
399C2×#392D4311yescharacteristic
400C2×#388—431no—
401C2×#386—432no—
402#1442—431no—
403#1439—432no—
404#1439—431no—
405#1438—432no—
406#1438—431no—
407#1434—431no—
408C22⋊#95—432no—
409C2×C43—48no—
410C2×C43—82no—
411C2×C43C4×#12011yescharacteristic
412C2×C43#232112yes—
413C2×C43#232411yescharacteristic
414C2×C43#232512yes—
415C2×C43#232811yescharacteristic
416C2×C43#261311yescharacteristic
417C2×C43#261511yescharacteristic
418C2×C43#263012yes—
419C2×C43#263111yescharacteristic
420C2×C43#263512yes—
421C2×C43#263611yescharacteristic
422C23×D4C2×D4311yescharacteristic
423C23×D4C2×D4312yes—
424C24×C4—432no—
425C2×C4×D4—864no—
426C2×C4×D4—868no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C22⋊C4—432no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—432no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—432no—
434C22×C22⋊C4—432no—
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C22⋊C4C2×D4312yes—
437C22×C42—431no—
438#392Dic4318yescomplemented
439#388—864no—
440#386—868no—
441C2×#95—431no—
442C2×#95—432no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—432no—
446C2×#95—432no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95C2×D4311yescharacteristic
450C43#1429911yescharacteristic, complemented, Sylow
451C25C22×D4311yescharacteristic
452C25C22×D4312yes—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4—42no—
463C22×D4C2×Dic4314yes—
464C22×D4C2×Dic4318yescomplemented
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—432no—
468C23×C4—438no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—432no—
472C23×C4—864no—
473C23×C4—864no—
474C23×C4—1722no—
475C23×C4—1722no—
476C23×C4—1722no—
477C23×C4—1722no—
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4312yes—
480C23×C4C22×D4311yescharacteristic
481C4×D4—8632no—
482C2×C4⋊C4—864no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—1722no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—864no—
495C2×C22⋊C4—862no—
496C2×C22⋊C4—862no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—1722no—
500C2×C22⋊C4—1722no—
501C2×C22⋊C4—1722no—
502C2×C22⋊C4—1722no—
503C2×C22⋊C4—1722no—
504C2×C22⋊C4—1722no—
505C2×C22⋊C4—1722no—
506C2×C22⋊C4C2×Dic4314yescomplemented
507C2×C22⋊C4C2×Dic4318yescomplemented
508C2×C42—434no—
509C2×C42—864no—
510#95—864no—
511#95—864no—
512#95—862no—
513#95—862no—
514#95—862no—
515#95—1722no—
516#95—1722no—
517#95—1722no—
518#95C2×Dic4314yescomplemented
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—22no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24D4×D4314yes—
542C24#1062190014yes—
543C24C22×Dic4312yes—
544C24C22×Dic4314yes—
545C24C23×D4311yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—216no—
551C2×D4—28no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—432no—
571C22×C4—434no—
572C22×C4—434no—
573C22×C4—432no—
574C22×C4—8616no—
575C22×C4—862no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—861no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—861no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—861no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—1728no—
606C22×C4—1728no—
607C22×C4—1728no—
608C22×C4—1728no—
609C22×C4—1728no—
610C22×C4—1728no—
611C22×C4D4×D4312yes—
612C22×C4#1062190012yes—
613C22×C4C22×Dic4314yes—
614C22×C4C22×Dic4312yes—
615C22×C4C22×Dic4312yes—
616C4⋊C4—868no—
617C4⋊C4—1724no—
618C22⋊C4—28no—
619C22⋊C4—48no—
620C22⋊C4—8616no—
621C22⋊C4—1724no—
622C22⋊C4—1728no—
623C22⋊C4—1724no—
624C22⋊C4—1728no—
625C22⋊C4—1728no—
626C42—868no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23D4×Dic4318yes—
685C23C23×Dic4311yescharacteristic
686C23C2×D4×D4312yes—
687C23C2×D4×D4311yescharacteristic
688C23C2×#1062190012yes—
689C23C2×#1062190011yescharacteristic
690C23#1306337012yes—
691C23#1306337011yescharacteristic
692C23#1306337012yes—
693C23#1306337011yescharacteristic
694C23#1306337111yescharacteristic
695C23#1306337211yescharacteristic
696D4—232no—
697D4—432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—434no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—17232no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1721no—
735C2×C4—1722no—
736C2×C4—1721no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4D4×Dic4314yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—44no—
770C22—82no—
771C22—81no—
772C22—82no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22C2×D4×Dic4311yescharacteristic
777C22C2×D4×Dic4312yes—
778C22#1458337411yescharacteristic
779C22#1458337412yes—
780C22#1458338211yescharacteristic
781C22#120×D4311yescharacteristic
782C22#1458340512yes—
783C22#1458340511yescharacteristic
784C22#1458345712yes—
785C22#1458345912yes—
786C22#1458346211yescharacteristic
787C22#1458346211yescharacteristic
788C22#1458346412yes—
789C22#1458346511yescharacteristic
790C22#1458347612yes—
791C22#1458347811yescharacteristic
792C22#1458348412yes—
793C22#1458348412yes—
794C22#1458348612yes—
795C22#1458349412yes—
796C22#1458350211yescharacteristic
797C22#1458350312yes—
798C22#1458351611yescharacteristic
799C4—24no—
800C4—42no—
801C4—44no—
802C4—864no—
803C4—3441no—
804C4—3442no—
805C4—3441no—
806C4—1724no—
807C4—1722no—
808C2—48no—
809C2—82no—
810C2#120×Dic4311yescharacteristic
811C2#1913725612yes—
812C2#1913729011yescharacteristic
813C2#1913730012yes—
814C2#1913732111yescharacteristic
815C2#1914030611yescharacteristic
816C2#1914031811yescharacteristic
817C2#1914043112yes—
818C2#1914044611yescharacteristic
819C2#1914047812yes—
820C2#1914048911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
Fitting, prime radicalC2×C43×#392C2
socle, cosocleC24×C43C24
hypercenterC2×#392D43
hypocenterC43#14299
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic43C2semidirect
2. C2×#14582792C2semidirect
3. C2×#14582779C2semidirect
4. #19132852C2semidirect
5. #19132840C2semidirect
6. #19132840C2semidirect
7. #19132836C2semidirect
8. #19132836C2semidirect
9. #19132820C2semidirect
10. #19132817C2semidirect
38. C43×#392C4semidirect
46. C23×Dic43D4semidirect
75. C2×C4×Dic43D4semidirect
97. C22×D4×C43C2×C4semidirect
105. C2×C22⋊C4×C43C2×C4semidirect
106. C2×C22⋊C4×C43C2×C4semidirect
107. #95×C43C2×C4semidirect
438. #392Dic43semidirect
450. C43#14299semidirect
464. C22×D4C2×Dic43semidirect
506. C2×C22⋊C4C2×Dic43semidirect
507. C2×C22⋊C4C2×Dic43semidirect
518. #95C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic432
C2×#145827922
C2×#145827792
#191328522
#191328402
#191328362
#191328202
#191328172
C2×C43×#3922
#1429943