Finite Group Databasebeta

← #25022983

Subgroups — #25022983

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582779C211yesmaximal, characteristic
2C2×#14582779C211yesmaximal, characteristic
3C2×#14582774C211yesmaximal, characteristic, complemented
4C22×C43⋊#95C211yesmaximal, characteristic, complemented
5#19132857C212yesmaximal, complemented
6#19132852C212yesmaximal, complemented
7#19132844C212yesmaximal, complemented
8#19132840C212yesmaximal, complemented
9#19132818C211yesmaximal, characteristic, complemented
10#19132817C211yesmaximal, characteristic, complemented
11C2×C43×#386C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20#14582779—24no—
21#14582779—24no—
22#14582774—24no—
23C2×C43⋊#95—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C23×D4×C43C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C43×#386C418yescomplemented
39C2×#95×C43C2212yes—
40C23×Dic43—22no—
41C23×Dic43—22no—
42C23×Dic43—22no—
43C23×Dic43—22no—
44C23×Dic43—42no—
45C23×Dic43—42no—
46C23×Dic43—42no—
47C23×Dic43—42no—
48C23×Dic43D414yes—
49C23×Dic43D414yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2312yes—
53C23×Dic43C2312yes—
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C2×C4⋊Dic43—24no—
57C2×C4⋊Dic43—42no—
58C2×C4⋊Dic43—42no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43—22no—
67C2×C22⋊Dic43—24no—
68C2×C22⋊Dic43—42no—
69C2×C22⋊Dic43—42no—
70C2×C22⋊Dic43—42no—
71C2×C22⋊Dic43—42no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—22no—
76C43⋊#95—22no—
77C43⋊#95—24no—
78C43⋊#95—42no—
79C43⋊#95—42no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C25×C43C2311yescharacteristic
83C25×C43C2311yescharacteristic
84C22×D4×C43—22no—
85C22×D4×C43—22no—
86C22×D4×C43—22no—
87C22×D4×C43—22no—
88C22×D4×C43—22no—
89C22×D4×C43—22no—
90C22×D4×C43C2×C414yes—
91C23×C4×C43—22no—
92C23×C4×C43—22no—
93C23×C4×C43—42no—
94C23×C4×C43—42no—
95C23×C4×C43C2×C414yes—
96C23×C4×C43C2312yes—
97C23×C4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—42no—
102C2×C22⋊C4×C43—42no—
103C2×C22⋊C4×C43C2×C414yes—
104C2×C22⋊C4×C43C2×C418yescomplemented
105#95×C43C2×C418yescomplemented
106C24×C43—22no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43—21no—
115C24×C43—21no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43C22×C412yes—
121C24×C43C22×C412yes—
122C24×C43C2×D412yes—
123C24×C43C2×D412yes—
124C24×C43#4112yes—
125C24×C43#4112yes—
126C24×C43#4112yes—
127C24×C43#4112yes—
128C24×C43C2411yescharacteristic
129C2×D4×C43—28no—
130C2×D4×C43—28no—
131C2×D4×C43—28no—
132C2×D4×C43—44no—
133C2×D4×C43—44no—
134C2×D4×C43—44no—
135C2×D4×C43—44no—
136C22×C4×C43—28no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—48no—
156C22×C4×C43—44no—
157C22×C4×C43—44no—
158C22×C4×C43—48no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C414yes—
161C22×C4×C43C22×C414yes—
162C22×Dic43—28no—
163C22×Dic43—28no—
164C22×Dic43—22no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—22no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—44no—
196C22×Dic43—44no—
197C22×Dic43—48no—
198C22×Dic43—44no—
199C22×Dic43—44no—
200C22×Dic43—48no—
201C22×Dic43—48no—
202C22×Dic43—48no—
203C22×Dic43C2×D412yes—
204C22×Dic43C2×D412yes—
205C22×Dic43C2×D414yes—
206C22⋊C4×C43—28no—
207C22⋊C4×C43—48no—
208C22⋊Dic43—48no—
209C22⋊Dic43—44no—
210C22⋊Dic43—44no—
211C22⋊Dic43—44no—
212C22⋊Dic43—44no—
213C4⋊Dic43—48no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—24no—
219C23×C43—22no—
220C23×C43—22no—
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—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—24no—
234C23×C43—24no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—42no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
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#11714yes—
254C23×C43C4×D414yes—
255C23×C43C4×D414yes—
256C23×C43#12114yes—
257C23×C43#12314yes—
258C23×C43#12414yes—
259C23×C43#12614yes—
260C23×C43C23×C411yescharacteristic
261C23×C43C22×D411yescharacteristic
262C23×C43C22×D411yescharacteristic
263C23×C43C2×#4111yescharacteristic
264C23×C43C2×#4111yescharacteristic
265C23×C43C2×#4111yescharacteristic
266C23×C43C2×#4111yescharacteristic
267C23×C43H(5,𝔽2)12yes—
268C23×C43H(5,𝔽2)12yes—
269C23×C43H(5,𝔽2)12yes—
270C23×C432−1+412yes—
271D4×C43—416no—
272C2×C4×C43—22no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—24no—
280C2×C4×C43—24no—
281C2×C4×C43—416no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×Dic43—24no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—24no—
298C2×Dic43—24no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—416no—
304C2×Dic43—416no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330#14259—431nomaximal, Sylow
331C22×C43—28no—
332C22×C43—24no—
333C22×C43—24no—
334C22×C43—28no—
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—24no—
339C22×C43—28no—
340C22×C43—28no—
341C22×C43—44no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—44no—
345C22×C43—42no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—82no—
351C22×C43—82no—
352C22×C43#38818yes—
353C22×C43C2×#11711yescharacteristic
354C22×C43C2×C4×D411yescharacteristic
355C22×C43C2×C4×D411yescharacteristic
356C22×C43#51812yes—
357C22×C43#52012yes—
358C22×C43C2×#12111yescharacteristic
359C22×C43C2×#12311yescharacteristic
360C22×C43C2×#12411yescharacteristic
361C22×C43C2×#12611yescharacteristic
362C22×C43#53412yes—
363C22×C43#53411yescharacteristic
364C22×C43#53411yescharacteristic
365C22×C43#53511yescharacteristic
366C22×C43#53611yescharacteristic
367C22×C43#53712yes—
368C22×C43#53812yes—
369C22×C43#53812yes—
370C22×C43#53812yes—
371C22×C43#53812yes—
372C22×C43#53912yes—
373C22×C43#53912yes—
374C22×C43#53912yes—
375C22×C43#53912yes—
376C4×C43—44no—
377C4×C43—44no—
378C4×C43—42no—
379Dic43—44no—
380Dic43—42no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384Dic43—82no—
385C2×#386—431no—
386C2×#386—431no—
387C2×#386D4311yescharacteristic
388C2×#385—431no—
389C22×#95—431no—
390#1443—432no—
391#1442—432no—
392#1440—432no—
393#1439—432no—
394C22⋊#95—431no—
395C22⋊#95—431no—
396C2×C43—28no—
397C2×C43—82no—
398C2×C43C2×#38811yescharacteristic
399C2×C43#231812yes—
400C2×C43#232111yescharacteristic
401C2×C43#232211yescharacteristic
402C2×C43#232512yes—
403C2×C43#261711yescharacteristic
404C2×C43#261811yescharacteristic
405C2×C43#262211yescharacteristic
406C2×C43#262311yescharacteristic
407C2×C43#263912yes—
408C2×C43#264312yes—
409C23×D4C2×D4311yescharacteristic
410C24×C4—431no—
411C24×C4—431no—
412C24×C4C2×D4311yescharacteristic
413C22×C4⋊C4—432no—
414C22×C22⋊C4—431no—
415C22×C22⋊C4—431no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—432no—
418C22×C22⋊C4—431no—
419C22×C22⋊C4C2×D4311yescharacteristic
420C22×C22⋊C4C2×D4312yes—
421#386—864no—
422#386—864no—
423#386Dic4318yescomplemented
424#385—864no—
425C2×#95—432no—
426C2×#95—432no—
427C2×#95—432no—
428C2×#95—431no—
429C2×#95—432no—
430C2×#95—431no—
431C2×#95—432no—
432C2×#95—432no—
433C2×#95—432no—
434C2×#95—432no—
435C2×#95—864no—
436C2×#95C2×D4312yes—
437C43#1425911yescharacteristic, complemented, Sylow
438C25C22×D4311yescharacteristic
439C25C22×D4311yescharacteristic
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4C2×Dic4314yes—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—432no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—434no—
455C23×C4—434no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—432no—
459C23×C4—862no—
460C23×C4—862no—
461C23×C4—862no—
462C23×C4—862no—
463C23×C4—1722no—
464C23×C4—1722no—
465C23×C4—1722no—
466C23×C4—1722no—
467C23×C4C2×Dic4314yes—
468C23×C4C22×D4312yes—
469C23×C4C22×D4312yes—
470C23×C4C22×D4311yescharacteristic
471C2×C4⋊C4—864no—
472C2×C4⋊C4—1722no—
473C2×C4⋊C4—1722no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—862no—
479C2×C22⋊C4—862no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—862no—
482C2×C22⋊C4—862no—
483C2×C22⋊C4—862no—
484C2×C22⋊C4—862no—
485C2×C22⋊C4—862no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—1722no—
488C2×C22⋊C4—1722no—
489C2×C22⋊C4—1722no—
490C2×C22⋊C4—1722no—
491C2×C22⋊C4C2×Dic4314yes—
492C2×C22⋊C4C2×Dic4318yescomplemented
493#95—864no—
494#95—864no—
495#95—864no—
496#95—862no—
497#95—862no—
498#95—864no—
499#95—1722no—
500#95—1722no—
501#95—1722no—
502#95—1722no—
503#95C2×Dic4318yescomplemented
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24#1062189812yes—
519C24#1062189812yes—
520C24D4×D4312yes—
521C24D4×D4312yes—
522C24#1062190012yes—
523C24#1062190012yes—
524C24C22×Dic4312yes—
525C24C22×Dic4312yes—
526C24C23×D4311yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—434no—
560C22×C4—868no—
561C22×C4—868no—
562C22×C4—862no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—862no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—862no—
580C22×C4—861no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—1728no—
594C22×C4—1724no—
595C22×C4—1724no—
596C22×C4—1724no—
597C22×C4—1724no—
598C22×C4—1728no—
599C22×C4—1728no—
600C22×C4—1728no—
601C22×C4C22×Dic4312yes—
602C22×C4C22×Dic4314yes—
603C22×C4C22×Dic4314yes—
604C4⋊C4—1728no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—1728no—
608C22⋊C4—1724no—
609C22⋊C4—1724no—
610C22⋊C4—1724no—
611C22⋊C4—1724no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#1306328414yes—
652C23D4×Dic4314yes—
653C23D4×Dic4314yes—
654C23#1306329814yes—
655C23#1306330714yes—
656C23#1306331114yes—
657C23#1306331814yes—
658C23C23×Dic4311yescharacteristic
659C23C2×D4×D4311yescharacteristic
660C23C2×D4×D4311yescharacteristic
661C23C2×#1062190011yescharacteristic
662C23C2×#1062190011yescharacteristic
663C23C2×#1062189811yescharacteristic
664C23C2×#1062189811yescharacteristic
665C23#1306337012yes—
666C23#1306337012yes—
667C23#1306337112yes—
668C23#1306337212yes—
669D4—416no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—864no—
696C2×C4—864no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—17216no—
719C2×C4—17216no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—82no—
746C22—82no—
747C22—81no—
748C22—81no—
749C22#1458279218yes—
750C22C2×#1306328411yescharacteristic
751C22C2×D4×Dic4311yescharacteristic
752C22C2×D4×Dic4311yescharacteristic
753C22#1458337412yes—
754C22#1458338212yes—
755C22C2×#1306329811yescharacteristic
756C22C2×#1306330711yescharacteristic
757C22C2×#1306331111yescharacteristic
758C22C2×#1306331811yescharacteristic
759C22#1458345712yes—
760C22#1458345911yescharacteristic
761C22#1458346011yescharacteristic
762C22#1458346411yescharacteristic
763C22#1458347111yescharacteristic
764C22#1458347612yes—
765C22#1458348212yes—
766C22#1458348212yes—
767C22#1458348412yes—
768C22#1458348612yes—
769C22#1458349112yes—
770C22#1458349112yes—
771C22#1458349312yes—
772C22#1458349412yes—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—3442no—
777C4—3441no—
778C4—3441no—
779C4—1722no—
780C4—1722no—
781C4—1724no—
782C2—28no—
783C2—82no—
784C2C2×#1458279211yescharacteristic
785C2#1913722812yes—
786C2#1913725611yescharacteristic
787C2#1913726711yescharacteristic
788C2#1913730012yes—
789C2#1914033511yescharacteristic
790C2#1914034311yescharacteristic
791C2#1914037211yescharacteristic
792C2#1914037911yescharacteristic
793C2#1914052512yes—
794C2#1914055012yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#386D43
hypocenterC43#14259
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#14582774C2semidirect
4. C22×C43⋊#95C2semidirect
5. #19132857C2semidirect
6. #19132852C2semidirect
7. #19132844C2semidirect
8. #19132840C2semidirect
9. #19132818C2semidirect
10. #19132817C2semidirect
38. C43×#386C4semidirect
104. C2×C22⋊C4×C43C2×C4semidirect
105. #95×C43C2×C4semidirect
423. #386Dic43semidirect
437. C43#14259semidirect
492. C2×C22⋊C4C2×Dic43semidirect
503. #95C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827792
C2×#145827742
C22×C43⋊#952
#191328572
#191328522
#191328442
#191328402
#191328182
#191328172
C2×C43×#3862
#1425943