Finite Group Databasebeta

← #25102354

Subgroups — #25102354

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583382C211yesmaximal, characteristic
2C2×#14583061C211yesmaximal, characteristic
3C2×#14583003C211yesmaximal, characteristic, complemented
4C2×#14582990C211yesmaximal, characteristic, complemented
5#19137273C211yesmaximal, characteristic, complemented
6#19134934C211yesmaximal, characteristic, complemented
7#19134927C211yesmaximal, characteristic, complemented
8#19134900C211yesmaximal, characteristic, complemented
9#19134861C211yesmaximal, characteristic, complemented
10#19134854C211yesmaximal, characteristic, complemented
11#19134787C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19#14583382—24no—
20#14583382—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×D4×Dic43—21no—
25C2×D4×Dic43—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×#13063284—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32#14583061C418yescomplemented
33#14583003—24no—
34#14582990—24no—
35C2×#13063256C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582796—21no—
46#14582795C2211yescharacteristic
47#14582793—21no—
48#14582787—21no—
49#14582786—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C23×Dic43—21no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885C2×C414yescomplemented
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063304—22no—
77#13063304C2×C414yescomplemented
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81Q8×Dic43D414yes—
82#13063290—22no—
83#13063290—22no—
84D4×Dic43—28no—
85D4×Dic43—28no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43D414yes—
90#13063284—28no—
91#13063284—22no—
92#13063284—22no—
93C2×C4⋊Dic43—28no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43D411yescharacteristic
100C2×C4⋊Dic43D411yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×C22⋊Dic43D411yescharacteristic
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118#13063256—22no—
119#13063256—22no—
120#13063250—22no—
121#13063250—22no—
122#13063249C2×C414yescomplemented
123#13063246C2×C414yescomplemented
124C22⋊(C43⋊C8)C2×C414yescomplemented
125#13063235—22no—
126C8×Dic43—22no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C2×#41×C43—22no—
132C2×#41×C43—22no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43C2×C414yes—
137C22×Q8×C43C2311yescharacteristic
138C22×D4×C43—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—22no—
148#103×C43—22no—
149#102×C43—22no—
150#102×C43—22no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—28no—
156#41×C43—28no—
157#41×C43—28no—
158#41×C43—28no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43#4112yes—
165C2×D4×C43—24no—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—24no—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C2×D412yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—24no—
175C22×C4×C43—24no—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43C22×C412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—24no—
189C22×Dic43—24no—
190C22×Dic43—24no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—81no—
196C22×Dic43—81no—
197C22×Dic43—81no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C22×Dic43—81no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86C22×C412yes—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C22⋊C4×C43—81no—
222C22⋊Dic43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—24no—
227#10621885—28no—
228#10621883—28no—
229C4⋊Dic43—24no—
230C4⋊Dic43—24no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—22no—
235C4⋊Dic43—24no—
236C4⋊Dic43—22no—
237C4⋊Dic43C22×C412yes—
238C4⋊Dic43C2×D412yes—
239C4⋊Dic43C2×D412yes—
240Dic43⋊C4—24no—
241Dic43⋊C4—42no—
242Dic43⋊C4—81no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—24no—
247C4×Dic43—42no—
248C4×Dic43—81no—
249C4×Dic43C2×D412yes—
250C4×Dic43C2×D412yes—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256C2×C43⋊C8C22×C412yes—
257C23×C43—22no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C4×D412yes—
271C23×C43C22×D411yescharacteristic
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43C4×D414yes—
276D4×C43—216no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43C4×D414yes—
281C2×C4×C43—216no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43C4×D412yes—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43—84no—
329C2×Dic43#12012yes—
330C2×Dic43#12012yes—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
335C8×C43—41no—
336C8×C43—41no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339#21461—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—24no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43C2×C4×D411yescharacteristic
355C22×C43C2×#12011yescharacteristic
356C22×C43#52511yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57711yescharacteristic
360C22×C43#57811yescharacteristic
361C4×C43—22no—
362C4×C43—24no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52511yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—42no—
372Dic43—41no—
373Dic43—42no—
374Dic43—42no—
375Dic43—41no—
376Dic43—42no—
377C2×#520—431no—
378C2×#452—431no—
379C2×#441—431no—
380C2×C4×SD16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872—431no—
385#1865—431no—
386#1864—431no—
387#1853—431no—
388#1788D4311yescharacteristic
389#1762—431no—
390C4×#103—431no—
391#1750—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43C4×#12011yescharacteristic
395C2×C43#294711yescharacteristic
396C2×C43#295211yescharacteristic
397C2×C43#300911yescharacteristic
398C2×C43#301311yescharacteristic
399C2×C43#312011yescharacteristic
400C2×C43#312511yescharacteristic
401C22×#41C2×D4311yescharacteristic
402C22×Q16—431no—
403C22×SD16—431no—
404C2×C22⋊Q8—431no—
405#520—864no—
406#520—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×#117—431no—
415C2×#117—861no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—861no—
418#452—438no—
419#441—864no—
420C4×SD16—864no—
421C2×#106—431no—
422C2×#106—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103C2×D4311yescharacteristic
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102C2×D4311yescharacteristic
430C2×#102C2×D4311yescharacteristic
431C2×C22⋊C8—431no—
432C2×C22⋊C8C2×D4311yescharacteristic
433C2×#97—431no—
434C2×C4×C8—431no—
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380C2×D4311yescharacteristic
442C4×C4⋊C4—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2146111yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C4×D4314yes—
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×Q16—434no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×SD16—434no—
469C2×SD16—862no—
470C2×SD16—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×D4—434no—
484C4×D4—862no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—868no—
488C4×D4—862no—
489#117—862no—
490#117—862no—
491#117—868no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—868no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520#106—862no—
521#106—862no—
522#103—22no—
523#103—22no—
524#103—434no—
525#103—862no—
526#103—862no—
527#102—22no—
528#102—22no—
529#102—434no—
530C22⋊C8—22no—
531C22⋊C8—434no—
532#97—862no—
533C4×C8—862no—
534#95—21no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24D4×D4311yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—432no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8C2×C4×D4312yes—
555C2×Q8D4×D4312yes—
556C2×Q8#1062190012yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C2×C4×D4312yes—
564C2×D4D4×D4312yes—
565C2×D4#1062190012yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—3441no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4C2×C4×D4312yes—
594C22×C4D4×D4311yescharacteristic
595C22×C4#1062190012yes—
596C22×C4C23×D4311yescharacteristic
597Q16—868no—
598SD16—868no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—432no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—862no—
619C4⋊C4—862no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—3441no—
628C4⋊C4—1722no—
629C22⋊C4—81no—
630C22⋊C4—862no—
631C22⋊C4—862no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—861no—
640C42—861no—
641C42—3441no—
642C42—1722no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23(C22⋊D43)⋊C412yes—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—862no—
662Q8—862no—
663Q8—1721no—
664Q8—1721no—
665Q8(C22⋊D43)⋊C414yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4(C22⋊D43)⋊C414yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—3444no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4(C22⋊D43)⋊C412yes—
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C2×C4C2×#1062190011yescharacteristic
720C2×C4C2×#1062190011yescharacteristic
721C8—41no—
722C8—41no—
723C8—862no—
724C8—862no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×(C22⋊D43)⋊C411yescharacteristic
740C22#120×D4311yescharacteristic
741C22#1458340511yescharacteristic
742C22#1458370611yescharacteristic
743C22#1458370811yescharacteristic
744C22#1458370911yescharacteristic
745C22#1458371311yescharacteristic
746C4—22no—
747C4—24no—
748C4—81no—
749C4—81no—
750C4—862no—
751C4—862no—
752C4—1722no—
753C4—1722no—
754C4—1721no—
755C4—1722no—
756C4—1722no—
757C4—1721no—
758C4C2×(C22⋊D43)⋊C411yescharacteristic
759C4C2×(C22⋊D43)⋊C411yescharacteristic
760C4#1458340511yescharacteristic
761C4#1458340511yescharacteristic
762C2—42no—
763C2—44no—
764C2#1913709411yescharacteristic
765C2#1914344111yescharacteristic
766C2#1914347411yescharacteristic
767C2#1914386911yescharacteristic
768C2#1914390811yescharacteristic
769C2#1914481011yescharacteristic
770C2#1914487311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21461
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
3. C2×#14583003C2semidirect
4. C2×#14582990C2semidirect
5. #19137273C2semidirect
6. #19134934C2semidirect
7. #19134927C2semidirect
8. #19134900C2semidirect
9. #19134861C2semidirect
10. #19134854C2semidirect
11. #19134787C2semidirect
12. #19134422C2semidirect
13. #103×Dic43C2semidirect
14. #19134363C2semidirect
32. #14583061C4semidirect
70. C2×#10621885C2×C4semidirect
73. C2×#10621883C2×C4semidirect
77. #13063304C2×C4semidirect
122. #13063249C2×C4semidirect
123. #13063246C2×C4semidirect
124. C22⋊(C43⋊C8)C2×C4semidirect
449. C43#21461semidirect

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#145830612
C2×#145830032
C2×#145829902
#191372732
#191349342
#191349272
#191349002
#191348612
#191348542
#191347872
#191344222
#103×Dic432
#191343632
C43×#17882
#2146143