Finite Group Databasebeta

← #25023604

Subgroups — #25023604

Order 11008.

2174 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582807C211yesmaximal, characteristic
2C2×#14582799C212yesmaximal, complemented
3C2×#14582793C212yesmaximal, complemented
4C2×#14582790C211yesmaximal, characteristic, complemented
5#19132858C211yesmaximal, characteristic, complemented
6#19132838C212yesmaximal, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132836C211yesmaximal, characteristic, complemented
9#19132834C212yesmaximal, complemented
10C4×C43⋊#95C211yesmaximal, characteristic, complemented
11C2×C43×#390C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2212yes—
13C22×Dic43⋊C4C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×C22⋊Dic43C2212yes—
16C22×C22⋊Dic43C2212yes—
17C22×C22⋊Dic43C2212yes—
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×C4×Dic43C2212yes—
23#14582807C418yescomplemented
24#14582799—28no—
25#14582793—28no—
26#14582790—24no—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C23×D4×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C22×C22⋊C4×C43C2212yes—
38C22×C42×C43C2211yescharacteristic
39C43×#390—24no—
40C24×D43C2311yescharacteristic
41C22×C22⋊D43—24no—
42C22×C22⋊D43—24no—
43C22×C22⋊D43—42no—
44C22×C22⋊D43—42no—
45C22×C22⋊D43—42no—
46C22×C22⋊D43—42no—
47C22×C22⋊D43C2×C418yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2312yes—
52C23×Dic43C2312yes—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4—42no—
58C2×C22⋊Dic43—24no—
59C2×C22⋊Dic43—24no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—42no—
63C2×C22⋊Dic43—42no—
64C2×C22⋊Dic43—42no—
65C2×C22⋊Dic43—42no—
66C2×C22⋊Dic43C2×C418yes—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—42no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4C2×C414yes—
77C2×C4×Dic43—42no—
78C2×C4×Dic43—42no—
79C2×C4×Dic43D418yescomplemented
80C43⋊#95—22no—
81C43⋊#95—22no—
82C43⋊#95—22no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95C2×C414yes—
87C25×C43C2312yes—
88C22×D4×C43—22no—
89C22×D4×C43—22no—
90C22×D4×C43—42no—
91C22×D4×C43—42no—
92C22×D4×C43C2×C414yes—
93C23×C4×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—42no—
99C2×C22⋊C4×C43—24no—
100C2×C22⋊C4×C43—24no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—42no—
104C2×C22⋊C4×C43—42no—
105C2×C42×C43—42no—
106C2×C42×C43D414yescomplemented
107C24×C43—22no—
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—22no—
121C24×C43C22×C414yes—
122C24×C43C2411yescharacteristic
123C23×D43—21no—
124C23×D43—22no—
125C23×D43—21no—
126C23×D43—22no—
127C23×D43—21no—
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43C22×C412yes—
134C2×D4×C43—28no—
135C2×D4×C43—48no—
136C2×D4×C43—44no—
137C2×D4×C43—44no—
138C2×D4×C43—48no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D414yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43#4112yes—
161C2×C22⋊D43—216no—
162C2×C22⋊D43—48no—
163C2×C22⋊D43—48no—
164C2×C22⋊D43—48no—
165C2×C22⋊D43—48no—
166C2×C22⋊D43—48no—
167C2×C22⋊D43—48no—
168C22×Dic43—21no—
169C22×Dic43—22no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—21no—
177C22×Dic43—22no—
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—21no—
188C22×Dic43—21no—
189C22×Dic43—22no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43C22×C412yes—
193C22×Dic43C22×C414yes—
194C22×Dic43C2×D414yes—
195C22×Dic43C2×D414yes—
196C22×Dic43#4114yes—
197C4⋊C4×C43—44no—
198C22⋊C4×C43—48no—
199C22⋊C4×C43—48no—
200C42×C43—44no—
201C22⋊Dic43—216no—
202C22⋊Dic43—48no—
203C22⋊Dic43—48no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—48no—
206(C2×D43)⋊C4—44no—
207(C2×D43)⋊C4—44no—
208Dic43⋊C4—48no—
209Dic43⋊C4—44no—
210C4×Dic43—48no—
211C23×C43—24no—
212C23×C43—24no—
213C23×C43—24no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43—42no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43C23×C411yescharacteristic
247C23×C43C22×D412yes—
248C23×C43C22×D411yescharacteristic
249C23×C43C2×#4112yes—
250C23×C43C2×#4111yescharacteristic
251C23×C43H(5,𝔽2)12yes—
252C23×C43H(5,𝔽2)11yescharacteristic
253C23×C43H(5,𝔽2)12yes—
254C23×C43H(5,𝔽2)11yescharacteristic
255C23×C43H(5,𝔽2)11yescharacteristic
256C23×C432−1+411yescharacteristic
257C22×D43—22no—
258C22×D43—24no—
259C22×D43—22no—
260C22×D43—24no—
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—42no—
265C22×D43—41no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—42no—
272C22×D43—41no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—41no—
278C22×D43—42no—
279C22×D43—41no—
280D4×C43—416no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—24no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43C4×D414yes—
302C2×C4×C43#12714yes—
303C22⋊D43—432no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—42no—
331C2×Dic43—41no—
332C2×Dic43C4×D418yes—
333#14321—431nomaximal, Sylow
334C22×C43—44no—
335C22×C43—44no—
336C22×C43—44no—
337C22×C43—44no—
338C22×C43—44no—
339C22×C43—44no—
340C22×C43—44no—
341C22×C43—82no—
342C22×C43—82no—
343C22×C43—82no—
344C22×C43—82no—
345C22×C43—82no—
346C22×C43—82no—
347C22×C43—82no—
348C22×C43—82no—
349C22×C43C2×C4×D412yes—
350C22×C43C2×C4×D411yescharacteristic
351C22×C43#51811yescharacteristic
352C22×C43#51812yes—
353C22×C43#52011yescharacteristic
354C22×C43C2×#12711yescharacteristic
355C22×C43#53211yescharacteristic
356C22×C43#53212yes—
357C22×C43#53412yes—
358C22×C43#53411yescharacteristic
359C22×C43#53512yes—
360C22×C43#53512yes—
361C22×C43#53511yescharacteristic
362C22×C43#53511yescharacteristic
363C22×C43#53712yes—
364C22×C43#53711yescharacteristic
365C22×C43#53812yes—
366C22×C43#53812yes—
367C22×C43#53812yes—
368C22×C43#54012yes—
369C22×C43#54011yescharacteristic
370C22×C43#54212yes—
371C22×C43#54211yescharacteristic
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—44no—
375C2×D43—44no—
376C2×D43—42no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—82no—
381C2×D43—81no—
382C2×D43—82no—
383C4×C43—24no—
384C4×C43—24no—
385C4×C43—42no—
386C4×C43—82no—
387Dic43—28no—
388Dic43—42no—
389Dic43—44no—
390Dic43—81no—
391Dic43—81no—
392C2×#392—431no—
393C2×#390—432no—
394C2×#390D4311yescharacteristic, complemented
395C2×#388—431no—
396C2×#388—432no—
397#1444—431no—
398#1439—431no—
399#1439—432no—
400#1438—431no—
401#1438—432no—
402C4×#95—431no—
403C2×C43—84no—
404C2×C43C4×#12711yescharacteristic
405C2×C43#232111yescharacteristic
406C2×C43#232112yes—
407C2×C43#232412yes—
408C2×C43#232411yescharacteristic
409C2×C43#265611yescharacteristic
410C2×C43#265711yescharacteristic
411C2×C43#266111yescharacteristic
412C2×C43#266112yes—
413C2×C43#266211yescharacteristic
414C2×C43#266212yes—
415D43—82no—
416C23×D4—432no—
417C23×D4C2×D4311yescharacteristic
418C22×C4⋊C4—431no—
419C22×C4⋊C4—432no—
420C22×C4⋊C4C2×D4311yescharacteristic
421C22×C22⋊C4—432no—
422C22×C22⋊C4—431no—
423C22×C22⋊C4—431no—
424C22×C22⋊C4—432no—
425C22×C22⋊C4—432no—
426C22×C22⋊C4—431no—
427C22×C22⋊C4—432no—
428C22×C22⋊C4C2×D4312yes—
429C22×C22⋊C4C2×D4312yes—
430C22×C42—432no—
431C22×C42C2×D4311yescharacteristic
432#392—438no—
433#390—24no—
434#390—868no—
435#388—868no—
436#388—864no—
437C2×#95—431no—
438C2×#95—432no—
439C2×#95—431no—
440C2×#95—432no—
441C2×#95—431no—
442C2×#95—432no—
443C2×#95—431no—
444C43#1432111yescharacteristic, complemented, Sylow
445C25—431no—
446C25C22×D4312yes—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—42no—
450C22×D4—42no—
451C22×D4—438no—
452C22×D4—864no—
453C22×D4—864no—
454C22×D4—1722no—
455C22×D4—1722no—
456C22×D4—1722no—
457C22×D4—1722no—
458C22×D4C4×D4314yes—
459C23×C4—432no—
460C23×C4—431no—
461C23×C4—432no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4C22×D4312yes—
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C23×C4C22×D4311yescharacteristic
468C2×C4⋊C4—22no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—864no—
471C2×C4⋊C4—864no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—1722no—
474C2×C4⋊C4—1722no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—438no—
482C2×C22⋊C4—434no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—862no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—864no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—862no—
492C2×C22⋊C4—862no—
493C2×C22⋊C4—1722no—
494C2×C22⋊C4—1722no—
495C2×C22⋊C4—1722no—
496C2×C22⋊C4—1722no—
497C2×C22⋊C4—1722no—
498C2×C22⋊C4—1722no—
499C2×C22⋊C4—1722no—
500C2×C42—42no—
501C2×C42—438no—
502C2×C42—1722no—
503C2×C42—1722no—
504C2×C42C22⋊D4314yescomplemented
505#95—434no—
506#95—864no—
507#95—864no—
508#95—864no—
509#95—862no—
510#95—862no—
511#95—862no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—432no—
527C24—862no—
528C24—861no—
529C24—862no—
530C24—861no—
531C24—861no—
532C24—862no—
533C24—862no—
534C24—861no—
535C24—861no—
536C24—861no—
537C24C2×C4×D4314yes—
538C24C23×D4311yescharacteristic
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—48no—
544C2×D4—8616no—
545C2×D4—1728no—
546C2×D4—1728no—
547C2×D4—1728no—
548C2×D4—1728no—
549C2×D4—1728no—
550C2×D4—1728no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—434no—
568C22×C4—434no—
569C22×C4—434no—
570C22×C4—432no—
571C22×C4—434no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
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—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—862no—
591C22×C4—861no—
592C22×C4—862no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4C2×C4×D4312yes—
597C22×C4#1062189812yes—
598C22×C4D4×D4314yes—
599C22×C4C2×C22⋊D4312yes—
600C22×C4C2×C22⋊D4312yes—
601C22×C4C2×C22⋊D4312yes—
602C4⋊C4—44no—
603C4⋊C4—1728no—
604C4⋊C4—1724no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—8616no—
608C22⋊C4—868no—
609C22⋊C4—1724no—
610C22⋊C4—1728no—
611C22⋊C4—1728no—
612C22⋊C4—1728no—
613C22⋊C4—1724no—
614C42—44no—
615C42—1728no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—864no—
652C23—862no—
653C23—862no—
654C23—864no—
655C23—862no—
656C23—1721no—
657C23—1721no—
658C23—1722no—
659C23—1722no—
660C23—1721no—
661C23—1722no—
662C23—1722no—
663C23—1721no—
664C23—1721no—
665C23—1722no—
666C23—1721no—
667C23—1722no—
668C23—1722no—
669C23—1722no—
670C23—1722no—
671C23—1721no—
672C23—1722no—
673C23—1721no—
674C23C22×C4×D4311yescharacteristic
675C23C2×D4×D4312yes—
676C23C22×C22⋊D4311yescharacteristic
677C23#41×D4312yes—
678C23C2×#1062189811yescharacteristic
679C23#1306337011yescharacteristic
680C23#1306337012yes—
681C23#1306337012yes—
682C23#1306337011yescharacteristic
683C23#1306337111yescharacteristic
684C23#1306337211yescharacteristic
685D4—416no—
686D4—17232no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—438no—
708C2×C4—864no—
709C2×C4—864no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—864no—
713C2×C4—864no—
714C2×C4—864no—
715C2×C4—862no—
716C2×C4—864no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1722no—
722C2×C4—1721no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1722no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4C4×C22⋊D4314yes—
737C2×C4#1306332114yes—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—3441no—
754C22—3441no—
755C22—3441no—
756C22—3442no—
757C22—3441no—
758C22—3442no—
759C22—1724no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22—1724no—
764C22C4×D4×D4312yes—
765C22C2×C4×C22⋊D4311yescharacteristic
766C22#1458337111yescharacteristic
767C22#1458337212yes—
768C22#1458337811yescharacteristic
769C22C2×#1306332111yescharacteristic
770C22#1458344511yescharacteristic
771C22#1458344612yes—
772C22#1458345712yes—
773C22#1458345811yescharacteristic
774C22#1458346212yes—
775C22#1458346212yes—
776C22#1458346611yescharacteristic
777C22#1458346611yescharacteristic
778C22#1458347612yes—
779C22#1458347711yescharacteristic
780C22#1458348112yes—
781C22#1458348312yes—
782C22#1458348712yes—
783C22#1458349912yes—
784C22#1458350011yescharacteristic
785C22#1458351312yes—
786C22#1458351411yescharacteristic
787C4—24no—
788C4—24no—
789C4—42no—
790C4—82no—
791C4—868no—
792C4—3441no—
793C4—3441no—
794C4—1724no—
795C4—1722no—
796C2—84no—
797C2—3442no—
798C2C4×#1306332111yescharacteristic
799C2#1913725311yescharacteristic
800C2#1913725412yes—
801C2#1913728112yes—
802C2#1913728211yescharacteristic
803C2#1914069911yescharacteristic
804C2#1914070211yescharacteristic
805C2#1914072411yescharacteristic
806C2#1914072512yes—
807C2#1914073411yescharacteristic
808C2#1914073612yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#390C2
socle, cosocleC24×C43C24
prime radicalC2×#14582807C2
hypercenterC2×#390D43
hypocenterC43#14321
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#14582799C2semidirect
3. C2×#14582793C2semidirect
4. C2×#14582790C2semidirect
5. #19132858C2semidirect
6. #19132838C2semidirect
7. #19132837C2semidirect
8. #19132836C2semidirect
9. #19132834C2semidirect
10. C4×C43⋊#95C2semidirect
11. C2×C43×#390C2semidirect
23. #14582807C4semidirect
79. C2×C4×Dic43D4semidirect
106. C2×C42×C43D4semidirect
394. C2×#390D43semidirect
444. C43#14321semidirect
504. C2×C42C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828072
C2×#145827992
C2×#145827932
C2×#145827902
#191328582
#191328382
#191328372
#191328362
#191328342
C4×C43⋊#952
C2×C43×#3902
#1432143