Finite Group Databasebeta

← #25019116

Subgroups — #25019116

Order 11008.

4470 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621902C211yesmaximal, characteristic
2C2×#14582806C211yesmaximal, characteristic, complemented
3C2×#14582801C211yesmaximal, characteristic, complemented
4C2×#14582800C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7#19132835C214yesmaximal, complemented
8(C2×D43)⋊#95C214yesmaximal, complemented
9C2×C43×#391C211yesmaximal, characteristic, complemented
10C22×#10621902—24no—
11C22×#10621902—24no—
12C22×#10621902—24no—
13C22×#10621902—24no—
14C22×#10621902—24no—
15C22×#10621902—24no—
16C22×#10621902C418yescomplemented
17C23×D172C2212yes—
18C23×D172C2211yescharacteristic
19C23×C4×D43C2212yes—
20C23×C4×D43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2214yes—
24C22×(C2×D43)⋊C4C2214yes—
25C22×(C2×D43)⋊C4C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27#14582806—24no—
28#14582801—24no—
29#14582800—24no—
30#14582756—24no—
31C4×(C2×D43)⋊C4—24no—
32C2×C43⋊#95C2214yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C23×Q8×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#391—24no—
39C2×#95×C43C2214yes—
40C24×D43C2312yes—
41C24×D43C2311yescharacteristic
42C2×#10621902—232no—
43C2×#10621902—232no—
44C2×#10621902—232no—
45C2×#10621902—232no—
46C2×#10621902—232no—
47C2×#10621902—232no—
48C2×#10621902—232no—
49C22×D172—24no—
50C22×D172—24no—
51C22×D172—24no—
52C22×D172—24no—
53C22×D172—24no—
54C22×D172—22no—
55C22×D172—22no—
56C22×D172—22no—
57C22×D172—24no—
58C22×D172—22no—
59C22×D172C2×C418yes—
60C22×D172C2×C414yes—
61C22×D172D414yes—
62C22×D172D414yes—
63C23×Dic43C2312yes—
64C23×Dic43C2312yes—
65C23×Dic43C2311yescharacteristic
66C22×C4×D43—24no—
67C22×C4×D43—24no—
68C22×C4×D43—24no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—22no—
72C22×C4×D43—24no—
73C22×C4×D43—22no—
74C22×C4×D43—24no—
75C22×C4×D43—24no—
76C22×C4×D43C2×C418yes—
77C22×C4×D43C2×C414yes—
78C22×C4×D43D414yes—
79C22×C4×D43D414yes—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4—24no—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—28no—
87C2×(C2×D43)⋊C4—28no—
88C2×(C2×D43)⋊C4—24no—
89C2×(C2×D43)⋊C4—28no—
90C2×(C2×D43)⋊C4—28no—
91C2×(C2×D43)⋊C4—44no—
92C2×(C2×D43)⋊C4—44no—
93C2×(C2×D43)⋊C4—44no—
94C2×C4×Dic43—22no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C43⋊#95—28no—
98C43⋊#95—24no—
99C43⋊#95—24no—
100C22×Q8×C43—22no—
101C22×Q8×C43—22no—
102C22×Q8×C43—22no—
103C22×Q8×C43—22no—
104C22×Q8×C43C2×C414yes—
105C22×Q8×C43D414yes—
106C22×Q8×C43D414yes—
107C23×C4×C43C2312yes—
108C23×C4×C43C2312yes—
109C23×C4×C43C2312yes—
110C23×C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C42×C43—22no—
115C2×C42×C43—22no—
116C2×C42×C43—22no—
117#95×C43—28no—
118C24×C43C2411yescharacteristic
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—22no—
124C23×D43—21no—
125C23×D43—22no—
126C23×D43—21no—
127C23×D43—22no—
128C23×D43—22no—
129C23×D43—24no—
130C23×D43—24no—
131C23×D43—22no—
132C23×D43—24no—
133C23×D43—22no—
134C23×D43—24no—
135C23×D43C22×C414yes—
136C23×D43C22×C412yes—
137C23×D43C2×D414yes—
138C23×D43C2×D414yes—
139C23×D43C2×D412yes—
140C23×D43C2×D412yes—
141C2×Q8×C43—28no—
142C2×Q8×C43—28no—
143C2×Q8×C43—28no—
144C2×Q8×C43—28no—
145C2×Q8×C43—28no—
146C2×Q8×C43—28no—
147C2×Q8×C43C22⋊C4116yescomplemented
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—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—24no—
160C22×C4×C43—22no—
161C22×C4×C43—24no—
162C22×C4×C43—22no—
163C22×C4×C43C22×C414yes—
164C22×C4×C43C22×C412yes—
165C22×C4×C43C2×D414yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D412yes—
168C22×C4×C43C2×D412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D414yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43#4114yescomplemented
174C22×Dic43—21no—
175C22×Dic43—21no—
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—24no—
186C22×Dic43—22no—
187C22×Dic43—24no—
188C22×Dic43—22no—
189C22×Dic43C22×C412yes—
190C22×Dic43C2×D412yes—
191C22×Dic43C2×D412yes—
192C22×Dic43#4114yescomplemented
193#10621902—2256no—
194C2×D172—216no—
195C2×D172—216no—
196C2×D172—216no—
197C2×D172—216no—
198C2×D172—28no—
199C2×D172—216no—
200C2×D172—28no—
201C2×D172—28no—
202C2×D172—28no—
203C2×D172—28no—
204C2×D172—28no—
205C2×D172—216no—
206C2×D172—216no—
207C2×D172C22⋊C4116yescomplemented
208C2×C4×D43—216no—
209C2×C4×D43—216no—
210C2×C4×D43—216no—
211C2×C4×D43—216no—
212C2×C4×D43—28no—
213C2×C4×D43—216no—
214C2×C4×D43—28no—
215C2×C4×D43—28no—
216C2×C4×D43—28no—
217C2×C4×D43—28no—
218C2×C4×D43—28no—
219C2×C4×D43—216no—
220C2×C4×D43—216no—
221C2×C4×D43C22⋊C4116yescomplemented
222C4⋊C4×C43—44no—
223C42×C43—44no—
224(C2×D43)⋊C4—216no—
225(C2×D43)⋊C4—416no—
226(C2×D43)⋊C4—416no—
227(C2×D43)⋊C4—48no—
228C4⋊Dic43—44no—
229C4×Dic43—44no—
230C23×C43C23×C411yescharacteristic
231C23×C43C22×D411yescharacteristic
232C23×C43C22×D411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C23×C43C22×D411yescharacteristic
235C23×C43C22×D411yescharacteristic
236C23×C43C22×D411yescharacteristic
237C23×C43C2×#4112yes—
238C23×C43C2×#4112yes—
239C23×C43H(5,𝔽2)12yes—
240C23×C432−1+412yes—
241C22×D43—24no—
242C22×D43—22no—
243C22×D43—24no—
244C22×D43—22no—
245C22×D43—28no—
246C22×D43—24no—
247C22×D43—24no—
248C22×D43—28no—
249C22×D43—24no—
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—22no—
253C22×D43—24no—
254C22×D43—22no—
255C22×D43—24no—
256C22×D43—22no—
257C22×D43—24no—
258C22×D43—22no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—24no—
263C22×D43—28no—
264C22×D43—28no—
265C22×D43—28no—
266C22×D43—28no—
267C22×D43—44no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—44no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278C22×D43—44no—
279C22×D43—42no—
280C22×D43—44no—
281C22×D43—42no—
282C22×D43—44no—
283C22×D43—42no—
284C22×D43—44no—
285C22×D43C2×C22⋊C418yes—
286C22×D43C2×C22⋊C414yes—
287Q8×C43—232no—
288C2×C4×C43—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—24no—
296C2×C4×C43—24no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43C2×C22⋊C414yes—
307C2×C4×C43C2×C22⋊C414yes—
308C2×C4×C43C2×C22⋊C418yes—
309C2×C4×C43C2×C22⋊C414yes—
310C2×C4×C43#12014yes—
311C2×C4×C43#12014yes—
312C2×C4×C43#12014yes—
313C2×C4×C43#12014yes—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332C2×Dic43C2×C22⋊C414yes—
333D172—264no—
334D172—232no—
335C4×D43—264no—
336C4×D43—232no—
337#13937—431nomaximal, Sylow
338C22×C43C22×C22⋊C411yescharacteristic
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43C22×C22⋊C411yescharacteristic
341C22×C43C4×#4112yes—
342C22×C43#52012yes—
343C22×C43C2×#12011yescharacteristic
344C22×C43C2×#12011yescharacteristic
345C22×C43C2×#12011yescharacteristic
346C22×C43C2×#12011yescharacteristic
347C22×C43#52512yes—
348C22×C43#53211yescharacteristic
349C22×C43#53211yescharacteristic
350C22×C43#53511yescharacteristic
351C22×C43#53611yescharacteristic
352C22×C43#53712yes—
353C22×C43#54612yes—
354C22×C43#54612yes—
355C22×C43#54712yes—
356C22×C43#54712yes—
357C22×C43#54812yes—
358C22×C43#54812yes—
359C22×C43#55012yes—
360C22×C43#55012yes—
361C2×D43—24no—
362C2×D43—216no—
363C2×D43—28no—
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43—48no—
370C2×D43—44no—
371C2×D43—48no—
372C2×D43—44no—
373C2×D43—48no—
374C2×D43—42no—
375C2×D43—44no—
376C2×D43—42no—
377C2×D43—44no—
378C2×D43—42no—
379C2×D43—44no—
380C2×D43—42no—
381C2×D43—44no—
382C2×D43—44no—
383C4×C43—28no—
384C4×C43—44no—
385C4×C43—82no—
386C4×C43#37918yes—
387Dic43—24no—
388Dic43—44no—
389Dic43—82no—
390C23×#41—431no—
391C2×#391—431no—
392C2×#391D4311yescharacteristic, complemented
393C2×#390—431no—
394C2×#390—431no—
395C2×#380—431no—
396C2×C4×C22⋊C4—431no—
397#1438—434no—
398C22⋊#95—434no—
399C2×C43C2×#37911yescharacteristic
400C2×C43#229711yescharacteristic
401C2×C43#231111yescharacteristic
402C2×C43#233912yes—
403C2×C43#234112yes—
404C2×C43#240712yes—
405C2×C43#240712yes—
406C2×C43#243111yescharacteristic
407C2×C43#243111yescharacteristic
408C2×C43#243211yescharacteristic
409C2×C43#243211yescharacteristic
410D43—44no—
411D43—48no—
412C22×#41—438no—
413C22×#41—864no—
414C22×#41—864no—
415C22×#41—864no—
416C22×#41—864no—
417C22×#41—864no—
418C22×#41—864no—
419C23×Q8C2×D4311yescharacteristic
420C23×D4—431no—
421C23×D4—432no—
422C24×C4—431no—
423C24×C4—432no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—432no—
427C22×C22⋊C4—434no—
428C22×C22⋊C4—434no—
429C22×C22⋊C4—432no—
430C22×C42—431no—
431C22×C42C2×D4311yescharacteristic
432#391—24no—
433#391—864no—
434#390—864no—
435#390—864no—
436#380—864no—
437C4×C22⋊C4—864no—
438C2×#95—432no—
439C2×#95—432no—
440C2×#95—434no—
441C2×#95C2×D4314yes—
442C43#1393711yescharacteristic, complemented, Sylow
443C25—431no—
444C25—432no—
445C2×#41—8632no—
446C2×#41—8632no—
447C2×#41—8632no—
448C2×#41—8632no—
449C2×#41—8632no—
450C2×#41—8632no—
451C2×#41—8632no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—22no—
456C22×Q8C4×D4314yes—
457C22×Q8D17214yes—
458C22×Q8C22⋊D4314yes—
459C22×D4—434no—
460C22×D4—438no—
461C22×D4—434no—
462C22×D4—434no—
463C22×D4—864no—
464C22×D4—864no—
465C22×D4—864no—
466C22×D4—864no—
467C22×D4—864no—
468C22×D4—862no—
469C22×D4—862no—
470C22×D4—862no—
471C22×D4—864no—
472C22×D4—862no—
473C23×C4—431no—
474C23×C4—434no—
475C23×C4—434no—
476C23×C4—434no—
477C23×C4—432no—
478C23×C4—438no—
479C23×C4—432no—
480C23×C4—864no—
481C23×C4—864no—
482C23×C4—864no—
483C23×C4—864no—
484C23×C4—864no—
485C23×C4—862no—
486C23×C4—862no—
487C23×C4—862no—
488C23×C4—864no—
489C23×C4—862no—
490C23×C4C22×D4312yes—
491C23×C4C22×D4312yes—
492C23×C4C22×D4312yes—
493C23×C4C22×D4311yescharacteristic
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—862no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4—864no—
502C2×C22⋊C4—864no—
503C2×C22⋊C4—868no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4—868no—
506C2×C22⋊C4—868no—
507C2×C22⋊C4—868no—
508C2×C22⋊C4—1724no—
509C2×C22⋊C4—1724no—
510C2×C22⋊C4—1724no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—862no—
515C2×C42—862no—
516C2×C42—862no—
517#95—28no—
518#95—864no—
519#95—864no—
520#95—868no—
521C24—432no—
522C24—434no—
523C24—432no—
524C24—432no—
525C24—434no—
526C24—434no—
527C24—861no—
528C24—862no—
529C24—862no—
530C24—861no—
531C24—862no—
532C24—861no—
533C24—862no—
534C24—861no—
535C24—862no—
536C24—864no—
537C24—864no—
538C24—862no—
539C24—862no—
540C24—864no—
541C24—864no—
542C24—862no—
543C24C23×D4311yescharacteristic
544#41—86256no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—28no—
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8(C2×D43)⋊C4116yescomplemented
552C2×D4—4316no—
553C2×D4—8616no—
554C2×D4—8616no—
555C2×D4—8616no—
556C2×D4—8616no—
557C2×D4—8616no—
558C2×D4—8616no—
559C2×D4—868no—
560C2×D4—8616no—
561C2×D4—868no—
562C2×D4—868no—
563C2×D4—868no—
564C2×D4—868no—
565C2×D4—868no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—4316no—
585C22×C4—434no—
586C22×C4—8616no—
587C22×C4—8616no—
588C22×C4—8616no—
589C22×C4—8616no—
590C22×C4—8616no—
591C22×C4—8616no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—868no—
597C22×C4—8616no—
598C22×C4—868no—
599C22×C4—868no—
600C22×C4—868no—
601C22×C4—868no—
602C22×C4—868no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4C2×C4×D4314yes—
615C22×C4C2×C4×D4312yes—
616C22×C4C2×D17214yes—
617C22×C4C2×D17212yes—
618C22×C4D4×D4312yes—
619C22×C4D4×D4312yes—
620C22×C4D4×D4312yes—
621C22×C4D4×D4312yes—
622C22×C4#1062190214yescomplemented
623C22×C4C2×C22⋊D4314yes—
624C22×C4C2×C22⋊D4312yes—
625C4⋊C4—44no—
626C4⋊C4—1724no—
627C22⋊C4—8616no—
628C22⋊C4—17216no—
629C22⋊C4—17216no—
630C22⋊C4—1728no—
631C42—44no—
632C42—1724no—
633C23—434no—
634C23—438no—
635C23—868no—
636C23—864no—
637C23—862no—
638C23—864no—
639C23—862no—
640C23—864no—
641C23—868no—
642C23—868no—
643C23—864no—
644C23—864no—
645C23—862no—
646C23—864no—
647C23—862no—
648C23—864no—
649C23—862no—
650C23—864no—
651C23—862no—
652C23—864no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—864no—
658C23—868no—
659C23—868no—
660C23—868no—
661C23—1722no—
662C23—1722no—
663C23—1724no—
664C23—1724no—
665C23—1722no—
666C23—1722no—
667C23—1724no—
668C23—1724no—
669C23—1722no—
670C23—1724no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1724no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23C22×C4×D4311yescharacteristic
680C23C2×D4×D4311yescharacteristic
681C23C2×D4×D4311yescharacteristic
682C23C2×D4×D4311yescharacteristic
683C23C2×D4×D4311yescharacteristic
684C23C22×C22⋊D4311yescharacteristic
685C23C22×D17211yescharacteristic
686C23#41×D4312yes—
687C23C2×#1062190212yes—
688C23#1306337112yes—
689C23#1306337312yes—
690Q8—232no—
691D4—8664no—
692D4—8632no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—434no—
712C2×C4—8664no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—8632no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—1724no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1724no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4C22⋊C4×D4314yes—
733C2×C4C22⋊C4×D4314yes—
734C2×C4C2×(C2×D43)⋊C418yes—
735C2×C4C2×(C2×D43)⋊C414yes—
736C2×C4#1306329314yes—
737C2×C4#1306329314yes—
738C2×C4#1306329514yes—
739C2×C4#1306329514yes—
740C22—864no—
741C22—8616no—
742C22—864no—
743C22—868no—
744C22—864no—
745C22—1724no—
746C22—1724no—
747C22—1724no—
748C22—1728no—
749C22—1728no—
750C22—1724no—
751C22—1724no—
752C22—1728no—
753C22—1724no—
754C22—1722no—
755C22—1724no—
756C22—1722no—
757C22—1724no—
758C22—1724no—
759C22—1722no—
760C22—1722no—
761C22—1724no—
762C22C2×C22⋊C4×D4311yescharacteristic
763C22C2×C22⋊C4×D4311yescharacteristic
764C22C22×(C2×D43)⋊C411yescharacteristic
765C22C4×#1062190212yes—
766C22#1458338112yes—
767C22C2×#1306329311yescharacteristic
768C22C2×#1306329311yescharacteristic
769C22C2×#1306329511yescharacteristic
770C22C2×#1306329511yescharacteristic
771C22#1458341212yes—
772C22#1458344811yescharacteristic
773C22#1458345011yescharacteristic
774C22#1458346711yescharacteristic
775C22#1458347411yescharacteristic
776C22#1458347912yes—
777C22#1458354012yes—
778C22#1458354212yes—
779C22#1458355112yes—
780C22#1458355212yes—
781C22#1458356012yes—
782C22#1458356112yes—
783C22#1458356812yes—
784C22#1458357112yes—
785C4—28no—
786C4—44no—
787C4—82no—
788C4—864no—
789C4—3442no—
790C4—1724no—
791C4#1458275418yes—
792C2—1724no—
793C2—1728no—
794C2C2×#1458275411yescharacteristic
795C2#1913708411yescharacteristic
796C2#1913718611yescharacteristic
797C2#1913742412yes—
798C2#1913743312yes—
799C2#1913794212yes—
800C2#1913794312yes—
801C2#1913821611yescharacteristic
802C2#1913821711yescharacteristic
803C2#1913822011yescharacteristic
804C2#1913822211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#391C2
socle, cosocleC24×C43C24
prime radicalC23×#10621902C2
hypercenterC2×#391D43
hypocenterC43#13937
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#14582806C2semidirect
3. C2×#14582801C2semidirect
4. C2×#14582800C2semidirect
5. C2×#14582756C2semidirect
6. C2×C4×(C2×D43)⋊C4C2semidirect
7. #19132835C2semidirect
8. (C2×D43)⋊#95C2semidirect
9. C2×C43×#391C2semidirect
16. C22×#10621902C4semidirect
147. C2×Q8×C43C22⋊C4semidirect
173. C22×C4×C43#41semidirect
192. C22×Dic43#41semidirect
207. C2×D172C22⋊C4semidirect
221. C2×C4×D43C22⋊C4semidirect
392. C2×#391D43semidirect
442. C43#13937semidirect
551. C2×Q8(C2×D43)⋊C4semidirect
622. C22×C4#10621902semidirect

Maximal subgroups

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

subgroupindex
C23×#106219022
C2×#145828062
C2×#145828012
C2×#145828002
C2×#145827562
C2×C4×(C2×D43)⋊C42
#191328352
(C2×D43)⋊#952
C2×C43×#3912
#1393743