Finite Group Databasebeta

← #25097498

Subgroups — #25097498

Order 11008.

1312 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#568×D43C211yesmaximal, characteristic
2#430×D43C211yesmaximal, characteristic, complemented
3#19143157C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic
5#421×D43C211yesmaximal, characteristic
6#19134838C211yesmaximal, characteristic, complemented
7#19134837C211yesmaximal, characteristic, complemented
8#19134836C211yesmaximal, characteristic, complemented
9#19134835C211yesmaximal, characteristic, complemented
10#19134834C211yesmaximal, characteristic, complemented
11#19134833C211yesmaximal, characteristic, complemented
12#19134832C211yesmaximal, characteristic, complemented
13#344×D43C211yesmaximal, characteristic, complemented
14#19134303C211yesmaximal, characteristic, complemented
15C43×#1861C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583666C2211yescharacteristic
18#14583665—22no—
19#14583665C2211yescharacteristic
20#14583665C2211yescharacteristic
21#14583664—22no—
22#14583664—22no—
23#131×D43—22no—
24#131×D43—22no—
25C2×M16×D43—22no—
26C2×M16×D43C2211yescharacteristic
27C2×M16×D43C2211yescharacteristic
28C2×M16×D43C2211yescharacteristic
29C2×M16×D43C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31#117×D43C2211yescharacteristic
32#14582948C2211yescharacteristic, complemented
33#14582947C2211yescharacteristic, complemented
34#14582947C2211yescharacteristic, complemented
35#14582946—22no—
36#108×D43—22no—
37#14582924—22no—
38#14582924—22no—
39#14582923C2211yescharacteristic, complemented
40#14582922C2211yescharacteristic, complemented
41#14582922C2211yescharacteristic, complemented
42#14582917C2211yescharacteristic
43#14582916C2211yescharacteristic
44#14582915C2211yescharacteristic
45#14582914—22no—
46#14582914C414yescomplemented
47#14582914C414yescomplemented
48C2×#13063253C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51#104×D43—22no—
52#14582671C2211yescharacteristic, complemented
53#14582670C2211yescharacteristic, complemented
54#14582669C2211yescharacteristic, complemented
55#14582660C2211yescharacteristic, complemented
56#14582659C2211yescharacteristic, complemented
57#14582658C2211yescharacteristic, complemented
58C43×#568C2211yescharacteristic
59C43×#430C2211yescharacteristic, complemented
60C43×#423C2211yescharacteristic, complemented
61C43×#421C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#344C2211yescharacteristic, complemented
64C43×#339C2211yescharacteristic, complemented
65C2×#10621902Q811yescharacteristic
66C2×#10621898—21no—
67C2×#10621898C2311yescharacteristic
68C2×#10621900—21no—
69C2×#10621900Q811yescharacteristic
70#41×D43—21no—
71#41×D43—21no—
72#41×D43—21no—
73#41×D43—21no—
74#41×D43C2×C412yes—
75#41×D43C2×C412yes—
76#41×D43D412yes—
77#41×D43D412yes—
78C2×Q8×D43Q811yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43Q811yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83#13063333—24no—
84#13063333—24no—
85#13063333—22no—
86#13063333—22no—
87#13063332—22no—
88#13063332—22no—
89#13063331—24no—
90#13063331—24no—
91#13063331—22no—
92#13063331—22no—
93C2×#10621877—22no—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621877C2311yescharacteristic
97C2×#10621877C2311yescharacteristic
98C2×#10621872—24no—
99C2×#10621872—21no—
100C2×#10621872—21no—
101C2×#10621872—21no—
102C2×#10621872D412yes—
103M16×D43—24no—
104M16×D43—24no—
105M16×D43—21no—
106M16×D43—21no—
107M16×D43—21no—
108M16×D43—21no—
109M16×D43—21no—
110M16×D43—21no—
111M16×D43—21no—
112M16×D43—21no—
113M16×D43—22no—
114M16×D43—22no—
115M16×D43—21no—
116M16×D43—21no—
117M16×D43—21no—
118M16×D43—21no—
119M16×D43C2×C412yes—
120M16×D43C2×C412yes—
121M16×D43D412yes—
122M16×D43D412yes—
123C2×C8×D43—24no—
124C2×C8×D43—21no—
125C2×C8×D43—21no—
126C2×C8×D43—21no—
127C2×C8×D43D412yes—
128#13063284C2311yescharacteristic
129#13063283—21no—
130#13063282—21no—
131#13063282—21no—
132#13063282—21no—
133#13063282C2×C412yes—
134#13063282C2×C412yes—
135#13063281—21no—
136C2×Dic43⋊C4—21no—
137C4⋊C4×D43—21no—
138C2×(C2×D43)⋊C4—21no—
139C22⋊C4×D43—21no—
140C2×C4×Dic43C2311yescharacteristic
141C42×D43—21no—
142#13063261—22no—
143#13063260—22no—
144#13063260—22no—
145C4⋊(C43⋊C8)—22no—
146Dic43⋊C8—22no—
147Dic43⋊C8—22no—
148#13063253—22no—
149#13063253C2×C414yescomplemented
150#13063252—22no—
151#13063252C2×C414yescomplemented
152#13063251—22no—
153#13063251C2×C414yescomplemented
154C2×#41×C43C2311yescharacteristic
155#131×C43—22no—
156#131×C43—22no—
157C2×M16×C43—22no—
158C2×M16×C43C2311yescharacteristic
159C2×M16×C43C2311yescharacteristic
160C2×M16×C43C2311yescharacteristic
161C2×M16×C43C2311yescharacteristic
162#117×C43C2311yescharacteristic
163C2×C42×C43C2311yescharacteristic
164#108×C43—22no—
165C4⋊C8×C43—22no—
166#104×C43—22no—
167#104×C43C2×C414yescomplemented
168C23×D43—21no—
169C23×D43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43C22×C412yes—
173#41×C43C2×D412yes—
174C2×Q8×C43C2×Q811yescharacteristic
175C2×D4×C43—21no—
176C2×D4×C43C2×Q811yescharacteristic
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43#4111yescharacteristic
186#10621902—21no—
187#10621902—21no—
188#10621902C4⋊C412yes—
189#10621902C4⋊C412yes—
190Q8×D43—21no—
191Q8×D43—21no—
192Q8×D43C4⋊C412yes—
193Q8×D43C4⋊C412yes—
194#10621900—22no—
195#10621900—22no—
196#10621900—22no—
197#10621900—22no—
198#10621900—21no—
199#10621900—21no—
200#10621900C4⋊C412yes—
201#10621900C4⋊C412yes—
202D4×D43—21no—
203D4×D43—21no—
204D4×D43—22no—
205D4×D43—22no—
206D4×D43—22no—
207D4×D43—22no—
208D4×D43C4⋊C412yes—
209D4×D43C4⋊C412yes—
210#10621898—21no—
211#10621898—21no—
212#10621898—22no—
213#10621898—22no—
214#10621898—22no—
215#10621898—22no—
216#10621898C22×C412yes—
217#10621898C2×D412yes—
218C2×D172—21no—
219C2×D172C2×Q811yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—21no—
227C2×C4×D43—41no—
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236C2×C4×D43C2×Q811yescharacteristic
237C2×C4×D43C2×Q811yescharacteristic
238C2×C4×D43#4111yescharacteristic
239C2×C4×D43#4111yescharacteristic
240C2×Dic86—21no—
241C2×Dic86C2×Q811yescharacteristic
242M16×C43—24no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43C22×C412yes—
250M16×C43C2×D412yes—
251C2×C8×C43—24no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43C2×D412yes—
256C4⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43C22×C412yes—
261C22⋊Dic43—21no—
262(C2×D43)⋊C4—22no—
263(C2×D43)⋊C4—22no—
264(C2×D43)⋊C4—41no—
265C4⋊Dic43—21no—
266Dic43⋊C4—22no—
267Dic43⋊C4—22no—
268Dic43⋊C4—41no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—41no—
272C4×Dic43C22×C412yes—
273#10621877—24no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877—21no—
278#10621877—21no—
279#10621877—21no—
280#10621877C22×C412yes—
281#10621877C2×D412yes—
282C2×C43⋊C8—24no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8C2×D412yes—
287#10621872—24no—
288#10621872—24no—
289#10621872—22no—
290#10621872—22no—
291#10621872—22no—
292#10621872—22no—
293#10621872—22no—
294#10621872—22no—
295#10621872—41no—
296#10621872—41no—
297C8×D43—24no—
298C8×D43—24no—
299C8×D43—22no—
300C8×D43—22no—
301C8×D43—22no—
302C8×D43—22no—
303C8×D43—22no—
304C8×D43—22no—
305C8×D43—41no—
306C8×D43—41no—
307C23×C43—21no—
308C23×C43C2×#4111yescharacteristic
309C22×D43—21no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—81no—
313C22×D43—82no—
314C22×D43C4×D411yescharacteristic
315C22×D43C4×D411yescharacteristic
316C22×D43C22⋊Q811yescharacteristic
317C22×D43C22⋊Q811yescharacteristic
318C22×D43#12311yescharacteristic
319C22×D43#12311yescharacteristic
320Q8×C43—21no—
321Q8×C43C2×C4⋊C412yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—21no—
325D4×C43C2×C4⋊C412yes—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—41no—
331C2×C4×C43—81no—
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×Q811yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C22⋊D43—22no—
339C22⋊D43—22no—
340C22⋊D43—22no—
341C22⋊D43—22no—
342C22⋊D43—22no—
343C22⋊D43—22no—
344C2×Dic43—21no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—41no—
349C2×Dic43—81no—
350C2×Dic43C4×D411yescharacteristic
351C2×Dic43C4×D411yescharacteristic
352C2×Dic43C22⋊Q811yescharacteristic
353C2×Dic43C22⋊Q811yescharacteristic
354C2×Dic43#12311yescharacteristic
355C2×Dic43#12311yescharacteristic
356D172—22no—
357D172—22no—
358D172—21no—
359D172C2×C4⋊C412yes—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—82no—
367C4×D43C2×C4⋊C411yescharacteristic
368C4×D43C2×C4⋊C411yescharacteristic
369C4×D43C2×C4⋊C411yescharacteristic
370C4×D43C2×C4⋊C411yescharacteristic
371C4×D43C4×D411yescharacteristic
372C4×D43C4×D411yescharacteristic
373C4×D43C4×D411yescharacteristic
374C4×D43C4×D411yescharacteristic
375C4×D43#12011yescharacteristic
376C4×D43#12011yescharacteristic
377C4×D43#12011yescharacteristic
378C4×D43#12011yescharacteristic
379C4×D43C22⋊Q811yescharacteristic
380C4×D43C22⋊Q811yescharacteristic
381C4×D43C22⋊Q811yescharacteristic
382C4×D43C22⋊Q811yescharacteristic
383Dic86—21no—
384Dic86—22no—
385Dic86—22no—
386Dic86C2×C4⋊C412yes—
387C8×C43—22no—
388C8×C43—22no—
389C8×C43—22no—
390C8×C43—41no—
391C43⋊C8—22no—
392C43⋊C8—22no—
393C43⋊C8—22no—
394C43⋊C8—41no—
395#20867—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—41no—
398C22×C43—81no—
399C22×C43C2×C4×D411yescharacteristic
400C22×C43C2×C22⋊Q811yescharacteristic
401C22×C43C2×#12311yescharacteristic
402C2×D43—22no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—44no—
410C2×D43—82no—
411C2×D43—81no—
412C2×D43#38511yescharacteristic
413C2×D43#38511yescharacteristic
414C2×D43#38511yescharacteristic
415C2×D43#38511yescharacteristic
416C4×C43—22no—
417C4×C43—42no—
418C4×C43—81no—
419C4×C43C22×C4⋊C411yescharacteristic
420C4×C43C2×C4×D411yescharacteristic
421C4×C43C2×#12011yescharacteristic
422C4×C43C2×C22⋊Q811yescharacteristic
423Dic43—22no—
424Dic43—42no—
425Dic43—81no—
426Dic43#38511yescharacteristic
427Dic43#38511yescharacteristic
428Dic43#38511yescharacteristic
429Dic43#38511yescharacteristic
430C2×#568—431no—
431C2×#430—431no—
432#2905—431no—
433C2×#421—431no—
434C2×#421—431no—
435#1861—431no—
436#1861—431no—
437#1861—431no—
438#1861—431no—
439#1861—431no—
440#1861—431no—
441#1861—431no—
442#1861D4311yescharacteristic, complemented
443C2×#344—431no—
444#1733—431no—
445C2×C43—21no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—42no—
449C2×C43C2×#38511yescharacteristic
450D43—21no—
451D43—21no—
452D43—21no—
453D43—21no—
454D43—42no—
455C22×#41—431no—
456#568—431no—
457#568—431no—
458#568—431no—
459#568—862no—
460#568—862no—
461#568—862no—
462#568C2×D4311yescharacteristic
463C2×#131—862no—
464C2×#131—862no—
465C22×M16—431no—
466C22×M16—431no—
467C22×M16—431no—
468C22×M16—431no—
469C22×M16—862no—
470C2×#117—431no—
471C2×#117—431no—
472#430—431no—
473#430—431no—
474#430—431no—
475#430—862no—
476#430C2×D4311yescharacteristic, complemented
477C2×#108—862no—
478#424—862no—
479#424—862no—
480#423—431no—
481#423—431no—
482#423—431no—
483#423C2×D4311yescharacteristic, complemented
484#421—434no—
485#421—434no—
486#421—431no—
487#421—431no—
488#421—431no—
489#421—862no—
490#421C2×D4311yescharacteristic
491C2×#104—431no—
492C2×#104—431no—
493C2×#104—431no—
494C2×#104—862no—
495C2×#104C2×D4311yescharacteristic
496#344—431no—
497#344—431no—
498#344—431no—
499#344C2×D4311yescharacteristic, complemented
500#339—431no—
501#339—431no—
502#339—431no—
503#339C2×D4311yescharacteristic, complemented
504C43#2086711yescharacteristic, complemented, Sylow
505C2×#41—432no—
506C2×#41—432no—
507C2×#41—432no—
508C2×#41—432no—
509C2×#41—431no—
510C2×#41—431no—
511C2×#41—431no—
512C2×#41—861no—
513C2×#41—861no—
514C2×#41—861no—
515C2×#41—861no—
516C2×#41—861no—
517C2×#41—861no—
518C2×#41C22×D4311yescharacteristic
519C22×Q8—431no—
520C22×D4—431no—
521C22×D4—861no—
522C23×C4—431no—
523C23×C4—861no—
524#131—22no—
525#131—22no—
526#131—862no—
527#131—864no—
528#131—864no—
529#131—862no—
530#131—862no—
531#131—862no—
532#131—864no—
533#131—864no—
534#131—862no—
535#131—862no—
536C2×M16—22no—
537C2×M16—431no—
538C2×M16—432no—
539C2×M16—431no—
540C2×M16—431no—
541C2×M16—432no—
542C2×M16—432no—
543C2×M16—432no—
544C2×M16—432no—
545C2×M16—431no—
546C2×M16—861no—
547C2×M16—861no—
548C2×M16—864no—
549C2×M16—861no—
550C2×M16—862no—
551C2×M16—861no—
552C2×M16—861no—
553C2×M16—861no—
554C2×M16—861no—
555C2×M16—861no—
556C2×M16—861no—
557C2×M16—861no—
558C2×M16—861no—
559C2×M16—864no—
560C2×M16—864no—
561C2×M16—862no—
562C2×M16—862no—
563C2×M16—861no—
564C2×M16—861no—
565C2×M16—861no—
566C2×M16—861no—
567C2×M16C22×D4311yescharacteristic
568C2×M16C22×D4311yescharacteristic
569C2×M16C22×D4311yescharacteristic
570C2×M16C22×D4311yescharacteristic
571C22×C8—432no—
572C22×C8—861no—
573C22×C8—861no—
574C22×C8—864no—
575C22×C8—861no—
576#117—432no—
577#117—432no—
578#117—431no—
579#117—861no—
580#117—861no—
581#117—861no—
582#117—861no—
583#117—861no—
584#117C22×D4311yescharacteristic
585C2×C4⋊C4—861no—
586C2×C4⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—431no—
590C2×C42—861no—
591C2×C42C22×D4311yescharacteristic
592#108—22no—
593#108—862no—
594#108—862no—
595#108—862no—
596C4⋊C8—22no—
597C4⋊C8—862no—
598C4⋊C8—862no—
599C4⋊C8—862no—
600#104—22no—
601#104—434no—
602#104—434no—
603#104—434no—
604#104—862no—
605#104—862no—
606#104—862no—
607#104C4×D4314yescomplemented
608C24—431no—
609C24—861no—
610#41—21no—
611#41—21no—
612#41—432no—
613#41—432no—
614#41—432no—
615#41—432no—
616#41—432no—
617#41—432no—
618#41—862no—
619#41—862no—
620#41—862no—
621#41—862no—
622#41—862no—
623#41—862no—
624#41—862no—
625#41—862no—
626#41—861no—
627#41—861no—
628#41—861no—
629#41—861no—
630#41—861no—
631#41—861no—
632#41C2×C4×D4312yes—
633#41D4×D4312yes—
634C2×Q8—432no—
635C2×Q8—432no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8Q8×D4311yescharacteristic
641C2×D4—21no—
642C2×D4—432no—
643C2×D4—432no—
644C2×D4—431no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—862no—
650C2×D4—862no—
651C2×D4—862no—
652C2×D4—862no—
653C2×D4—861no—
654C2×D4—861no—
655C2×D4Q8×D4311yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—861no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—1721no—
681C22×C4C23×D4311yescharacteristic
682M16—24no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—432no—
690M16—432no—
691M16—862no—
692M16—862no—
693M16—862no—
694M16—862no—
695M16—862no—
696M16—862no—
697M16—864no—
698M16—864no—
699M16—864no—
700M16—861no—
701M16—861no—
702M16—861no—
703M16—861no—
704M16—861no—
705M16—861no—
706M16—1721no—
707M16—1721no—
708M16C2×C4×D4312yes—
709M16D4×D4312yes—
710C2×C8—24no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—432no—
715C2×C8—862no—
716C2×C8—862no—
717C2×C8—862no—
718C2×C8—862no—
719C2×C8—862no—
720C2×C8—862no—
721C2×C8—864no—
722C2×C8—864no—
723C2×C8—864no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—861no—
727C2×C8—1721no—
728C2×C8—1721no—
729C2×C8D4×D4312yes—
730C4⋊C4—21no—
731C4⋊C4—862no—
732C4⋊C4—862no—
733C4⋊C4—861no—
734C4⋊C4—1721no—
735C22⋊C4—21no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—861no—
739C22⋊C4—1721no—
740C42—21no—
741C42—21no—
742C42—432no—
743C42—861no—
744C42—861no—
745C42—1721no—
746C42C2×C4×D4312yes—
747C23—21no—
748C23—431no—
749C23—431no—
750C23—431no—
751C23—431no—
752C23—431no—
753C23—431no—
754C23—862no—
755C23—862no—
756C23—861no—
757C23—3441no—
758C23—3442no—
759C23#41×D4311yescharacteristic
760Q8—21no—
761Q8—432no—
762Q8—862no—
763Q8—862no—
764Q8—861no—
765Q8C4⋊C4×D4312yes—
766D4—22no—
767D4—22no—
768D4—21no—
769D4—432no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—862no—
776D4—862no—
777D4—862no—
778D4—861no—
779D4C4⋊C4×D4312yes—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—81no—
786C2×C4—431no—
787C2×C4—431no—
788C2×C4—431no—
789C2×C4—431no—
790C2×C4—431no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—431no—
803C2×C4—431no—
804C2×C4—431no—
805C2×C4—431no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—3442no—
819C2×C4—3441no—
820C2×C4—1721no—
821C2×C4C22×C4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×D4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×Q8×D4311yescharacteristic
826C2×C4#41×D4311yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C8—862no—
832C8—862no—
833C8—862no—
834C8—1721no—
835C22—22no—
836C22—41no—
837C22—81no—
838C22—431no—
839C22—431no—
840C22—431no—
841C22—431no—
842C22—862no—
843C22—3441no—
844C22—3442no—
845C22—1721no—
846C22—1721no—
847C22—1721no—
848C22—1721no—
849C22—1721no—
850C22—1721no—
851C22—1724no—
852C22C4×D4×D4311yescharacteristic
853C22C22⋊Q8×D4311yescharacteristic
854C22#123×D4311yescharacteristic
855C4—22no—
856C4—42no—
857C4—81no—
858C4—431no—
859C4—431no—
860C4—431no—
861C4—431no—
862C4—862no—
863C4—3441no—
864C4—1722no—
865C4C2×C4⋊C4×D4311yescharacteristic
866C4C4×D4×D4311yescharacteristic
867C4#120×D4311yescharacteristic
868C4C22⋊Q8×D4311yescharacteristic
869C2—21no—
870C2—21no—
871C2—21no—
872C2—42no—
873C2—861no—
874C2—861no—
875C2—861no—
876C2—861no—
877C2—1722no—
878C2#385×D4311yescharacteristic
subgroupG/H
centerC4#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1861C2
socleC2×C43C2×#385
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1861D43
hypocenterC43#20867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1861

Complements

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

NH ≅ G/Ntype
2. #430×D43C2semidirect
3. #19143157C2semidirect
6. #19134838C2semidirect
7. #19134837C2semidirect
8. #19134836C2semidirect
9. #19134835C2semidirect
10. #19134834C2semidirect
11. #19134833C2semidirect
12. #19134832C2semidirect
13. #344×D43C2semidirect
14. #19134303C2semidirect
15. C43×#1861C2semidirect
32. #14582948C22semidirect
33. #14582947C22semidirect
34. #14582947C22semidirect
39. #14582923C22semidirect
40. #14582922C22semidirect
41. #14582922C22semidirect
46. #14582914C4semidirect
47. #14582914C4semidirect
52. #14582671C22semidirect
53. #14582670C22semidirect
54. #14582669C22semidirect
55. #14582660C22semidirect
56. #14582659C22semidirect
57. #14582658C22semidirect
59. C43×#430C22semidirect
60. C43×#423C22semidirect
63. C43×#344C22semidirect
64. C43×#339C22semidirect
149. #13063253C2×C4semidirect
151. #13063252C2×C4semidirect
153. #13063251C2×C4semidirect
167. #104×C43C2×C4semidirect
442. #1861D43semidirect
476. #430C2×D43semidirect
483. #423C2×D43semidirect
499. #344C2×D43semidirect
503. #339C2×D43semidirect
504. C43#20867semidirect
607. #104C4×D43semidirect

Maximal subgroups

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

subgroupindex
#568×D432
#430×D432
#191431572
C2×#145829142
#421×D432
#191348382
#191348372
#191348362
#191348352
#191348342
#191348332
#191348322
#344×D432
#191343032
C43×#18612
#2086743