Finite Group Databasebeta

← C4×#14583078 #25102484

Subgroups — C4×#14583078 #25102484

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063371C211yesmaximal, characteristic
2C2×#14583078C211yesmaximal, characteristic
3C4×#13063358C211yesmaximal, characteristic, complemented
4C4×#13063355C211yesmaximal, characteristic, complemented
5C4×#13063313C211yesmaximal, characteristic, complemented
6#19134982C211yesmaximal, characteristic, complemented
7#19134965C211yesmaximal, characteristic, complemented
8#19134962C211yesmaximal, characteristic, complemented
9#19134830C211yesmaximal, characteristic, complemented
10#19134829C211yesmaximal, characteristic, complemented
11#19134806C211yesmaximal, characteristic, complemented
12#19134550C211yesmaximal, characteristic
13C4×#13063253C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#104×C43C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063358C2211yescharacteristic
18C2×#13063355C2211yescharacteristic
19C2×#13063313C2211yescharacteristic
20#14583382C2211yescharacteristic
21#14583381—21no—
22#14583379—21no—
23#14583379C2211yescharacteristic
24#14583373—21no—
25#14583373C2211yescharacteristic
26#14583371—22no—
27#14583371—21no—
28C4×#10621902—21no—
29C4×#10621898—21no—
30C4×#10621898C2211yescharacteristic
31C2×C4×Dic86C2211yescharacteristic, complemented
32C2×C4×D172—21no—
33C2×C4×D172C2211yescharacteristic
34C4×D4×D43—22no—
35C4×D4×D43—21no—
36#14583078C418yesdirect product factor
37#14583007—21no—
38#14583004—21no—
39#14583001—21no—
40#14582999—21no—
41C4×Dic172—21no—
42C4×#10621885—21no—
43C4×#10621873—21no—
44C4×#10621883—21no—
45#14582942C2211yescharacteristic, complemented
46#14582941C2211yescharacteristic, complemented
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49#14582909C2211yescharacteristic, complemented
50#14582907C2211yescharacteristic, complemented
51#14582901C2211yescharacteristic
52#14582900C2211yescharacteristic
53C2×#13063241C2211yescharacteristic
54C2×#13063241C2211yescharacteristic
55C4×#10621877C2211yescharacteristic, complemented
56#14582805C2211yescharacteristic, complemented
57#14582801C2211yescharacteristic
58#14582790—22no—
59#14582765C2211yescharacteristic, complemented
60C4×(C2×D43)⋊C4—22no—
61#14582667C2211yescharacteristic, complemented
62#14582667C2211yescharacteristic, complemented
63#14582659C2211yescharacteristic, complemented
64#14582659C2211yescharacteristic, complemented
65C4×#41×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic
68C4×M16×C43C2211yescharacteristic, complemented
69C43×C43C2211yescharacteristic, complemented
70C43×#339C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72#13063371—22no—
73#13063371—22no—
74#13063371—22no—
75#13063371C2×C414yes—
76C2×#10621902—21no—
77C2×#10621898—21no—
78C2×#10621898C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C2×D4×D43—22no—
83C2×D4×D43—21no—
84C22×C4×D43—22no—
85C22×C4×D43D412yes—
86#13063358—22no—
87#13063358C2×C414yescomplemented
88#13063355—22no—
89#13063355C2×C414yescomplemented
90C2×Dic172—21no—
91C2×#10621885—21no—
92C2×#10621873—21no—
93C2×#10621883—21no—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96#13063313—22no—
97#13063313C2×C414yescomplemented
98Q8×Dic43—21no—
99C4×Dic86—21no—
100C4×Dic86—21no—
101C4×Dic86—21no—
102C4×Dic86—21no—
103C4×Dic86—21no—
104C4×Dic86D411yescharacteristic
105C4×Dic86D411yescharacteristic
106C4×D172—22no—
107C4×D172—22no—
108C4×D172—21no—
109C4×D172—21no—
110C4×D172—21no—
111C4×D172—21no—
112C4×D172—21no—
113C4×D172—21no—
114C4×D172—21no—
115C4×D172D411yescharacteristic
116C4×D172D411yescharacteristic
117D4×Dic43—21no—
118D4×Dic43—22no—
119#13063287—22no—
120#13063287—22no—
121#13063287—21no—
122#13063287—21no—
123C4×C22⋊D43—22no—
124C4×C22⋊D43—22no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127(C22⋊D43)⋊C4—22no—
128(C22⋊D43)⋊C4—22no—
129(C22⋊D43)⋊C4—22no—
130#13063284—21no—
131#13063284C2311yescharacteristic
132#13063283—22no—
133#13063283—21no—
134#13063282—22no—
135#13063282—21no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×C4⋊Dic43C2311yescharacteristic
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43—21no—
142C2×(C2×D43)⋊C4—22no—
143C2×(C2×D43)⋊C4—22no—
144C2×(C2×D43)⋊C4—22no—
145C2×(C2×D43)⋊C4D412yes—
146C22⋊C4×D43—22no—
147C22⋊C4×D43—22no—
148C22⋊C4×D43—22no—
149C2×C4×Dic43—21no—
150C42×D43—22no—
151C42×D43—21no—
152#13063259—21no—
153#13063258—21no—
154#13063257—21no—
155#13063256—21no—
156#13063253—22no—
157#13063253C2×C414yescomplemented
158#13063250—21no—
159#13063250—21no—
160#13063250—21no—
161#13063249—21no—
162#13063248—21no—
163#13063248—21no—
164#13063247—21no—
165#13063246—21no—
166#13063241—22no—
167#13063241C2×C414yescomplemented
168#13063236—21no—
169C4×C43⋊C8—21no—
170C43⋊#95—22no—
171C43⋊#95—22no—
172C2×#41×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C4×Q8×C43D411yescharacteristic
176C4×Q8×C43D411yescharacteristic
177C4×D4×C43—21no—
178C4×D4×C43—21no—
179C4×D4×C43D411yescharacteristic
180C4×D4×C43D411yescharacteristic
181#117×C43—21no—
182#117×C43C2311yescharacteristic
183C2×C42×C43—21no—
184C2×C42×C43—21no—
185C2×C42×C43—21no—
186C2×C42×C43C2311yescharacteristic
187C2×C42×C43C2311yescharacteristic
188C2×C42×C43C2311yescharacteristic
189#104×C43—22no—
190#104×C43C2×C414yescomplemented
191#97×C43—21no—
192C4×C8×C43—21no—
193C23×D43—22no—
194C23×D43C2×D412yes—
195#41×C43—21no—
196#41×C43—21no—
197#41×C43C22×C412yes—
198#41×C43#4112yes—
199C2×Q8×C43C2×D411yescharacteristic
200C2×D4×C43—21no—
201C2×D4×C43C2×D411yescharacteristic
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—22no—
211C2×C22⋊D43—21no—
212C22×Dic43—22no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43C2×D412yes—
216#10621902—24no—
217#10621902—24no—
218D4×D43—24no—
219D4×D43—28no—
220D4×D43—24no—
221D4×D43—28no—
222#10621898—24no—
223#10621898—21no—
224#10621898—21no—
225#10621898—24no—
226#10621898C22×C412yes—
227#10621898#4112yes—
228C2×D172—22no—
229C2×D172—24no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—24no—
235C2×D172C22×C412yes—
236C2×D172C2×D411yescharacteristic
237C2×D172#4112yes—
238C2×C4×D43—22no—
239C2×C4×D43—21no—
240C2×C4×D43—22no—
241C2×C4×D43—21no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—44no—
248C2×C4×D43—84no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86C22×C412yescomplemented
255C2×Dic86C2×D411yescharacteristic
256M16×C43—21no—
257M16×C43—21no—
258M16×C43—21no—
259M16×C43C22×C412yescomplemented
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2×D411yescharacteristic
265C4⋊C4×C43C2×D411yescharacteristic
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C42×C43—21no—
270C42×C43—21no—
271C42×C43—21no—
272C42×C43—21no—
273C42×C43—21no—
274C42×C43—21no—
275C42×C43—42no—
276C42×C43—42no—
277C42×C43C22×C412yescomplemented
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C22⋊Dic43—22no—
283C22⋊Dic43—21no—
284#10621885—24no—
285#10621883—24no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—28no—
294(C2×D43)⋊C4—44no—
295C4⋊Dic43—22no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43C2×D411yescharacteristic
301C4⋊Dic43C2×D411yescharacteristic
302Dic43⋊C4—22no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—41no—
306Dic43⋊C4—41no—
307C4×Dic43—22no—
308C4×Dic43—22no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—41no—
313C4×Dic43—41no—
314#10621877—21no—
315#10621877—21no—
316#10621877—21no—
317#10621877C22×C412yescomplemented
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320Dic172—24no—
321#10621873—24no—
322C23×C43—21no—
323C23×C43C22×D411yescharacteristic
324C22×D43—22no—
325C22×D43—21no—
326C22×D43—28no—
327C22×D43—22no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—82no—
331C22×D43—82no—
332C22×D43C4×D414yes—
333Q8×C43—21no—
334Q8×C43C4×D412yes—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—21no—
338D4×C43C4×D412yes—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—42no—
353C2×C4×C43—81no—
354C2×C4×C43#12011yescharacteristic
355C2×C4×C43#12011yescharacteristic
356C2×C4×C43#12011yescharacteristic
357C2×C4×C43#12011yescharacteristic
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C2×#4111yescharacteristic
362C2×C4×C43C2×#4111yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C22⋊D43—28no—
365C22⋊D43—22no—
366C22⋊D43—22no—
367C2×Dic43—21no—
368C2×Dic43—22no—
369C2×Dic43—21no—
370C2×Dic43—22no—
371C2×Dic43—21no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—41no—
377C2×Dic43—82no—
378D172—28no—
379D172—22no—
380D172—22no—
381D172—21no—
382D172—22no—
383D172—22no—
384D172C4×D412yes—
385C4×D43—28no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—44no—
389C4×D43—42no—
390C4×D43—81no—
391C4×D43—82no—
392C4×D43—82no—
393C4×D43—82no—
394C4×D43—82no—
395Dic86—21no—
396Dic86—22no—
397Dic86—22no—
398Dic86—41no—
399Dic86—41no—
400Dic86C4×D412yes—
401C8×C43—22no—
402C8×C43—41no—
403C43⋊C8—22no—
404C43⋊C8—41no—
405C4×#455—431nomaximal, Sylow
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—22no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43C2×C4×D411yescharacteristic
412C22×C43C2×#12011yescharacteristic
413C22×C43#52511yescharacteristic
414C2×D43—22no—
415C2×D43—24no—
416C2×D43—42no—
417C2×D43—41no—
418C2×D43—42no—
419C2×D43—41no—
420C2×D43—44no—
421C2×D43—82no—
422C2×D43—88no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—22no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43#45512yescomplemented
432C4×C43C2×C4×D411yescharacteristic
433C4×C43C2×C4×D411yescharacteristic
434C4×C43#52511yescharacteristic
435C4×C43#52511yescharacteristic
436Dic43—22no—
437Dic43—42no—
438Dic43—41no—
439Dic43—41no—
440Dic43—42no—
441Dic43—81no—
442C4×H(5,𝔽2)—431no—
443C2×#455—431no—
444C4×#137—431no—
445C4×#137—431no—
446C4×#124—431no—
447#1885—431no—
448#1882—431no—
449#1882—431no—
450#1860—431no—
451#1860—431no—
452#1856—431no—
453#1792—431no—
454C4×#104—431no—
455C4×#104D4311yescharacteristic, complemented
456C4×#100—431no—
457C2×C43—21no—
458C2×C43—21no—
459C2×C43—42no—
460C2×C43C4×#12011yescharacteristic
461C2×C43C2×#45511yescharacteristic
462C2×C43#301811yescharacteristic
463D43—44no—
464D43—42no—
465C2×H(5,𝔽2)—431no—
466C2×#137—431no—
467C2×#137—431no—
468C2×#124—431no—
469#520—431no—
470#520—431no—
471#520—861no—
472#520—861no—
473#518—431no—
474#518—862no—
475#518—861no—
476#518—861no—
477C4×#41—431no—
478C4×#41—861no—
479C4×#41—861no—
480C4×#41C2×D4311yescharacteristic
481C2×C4×Q8—431no—
482C2×C4×D4—431no—
483C2×C4×D4—861no—
484C2×C4×D4—862no—
485C2×C4×D4—861no—
486#455—438no—
487#441—861no—
488#441—861no—
489#440—861no—
490#440—861no—
491C4×Q16—861no—
492C4×Q16—861no—
493C4×SD16—861no—
494C4×SD16—861no—
495#428—431no—
496#428—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104C2×D4311yescharacteristic
500C2×#104C2×D4311yescharacteristic
501#419—431no—
502#419—431no—
503#417—431no—
504#417—431no—
505C2×#100—431no—
506C2×#100—431no—
507C4×M16—431no—
508C4×M16C2×D4311yescharacteristic, complemented
509#391—431no—
510#390—431no—
511#388—862no—
512#382—431no—
513C4×C22⋊C4—862no—
514C43C2×D4311yescharacteristic, complemented
515#343—431no—
516#343—431no—
517#339—431no—
518#339—431no—
519#339C2×D4311yescharacteristic, complemented
520#339C2×D4311yescharacteristic, complemented
521C43C4×#45511yescharacteristic, complemented, Sylow
522H(5,𝔽2)—434no—
523H(5,𝔽2)—862no—
524H(5,𝔽2)—862no—
525H(5,𝔽2)—862no—
526C2×#41—431no—
527C2×#41—861no—
528C2×#41—861no—
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C22×D4—862no—
534C22×D4—861no—
535C23×C4—432no—
536C23×C4—862no—
537#137—434no—
538#137—434no—
539#137—862no—
540#137—862no—
541C2×Q16—861no—
542C2×Q16—861no—
543C2×SD16—861no—
544C2×SD16—861no—
545C2×M16—431no—
546C2×M16—431no—
547C2×M16C22×D4311yescharacteristic
548C2×M16C22×D4311yescharacteristic
549#124—434no—
550#124—862no—
551C4×Q8—431no—
552C4×Q8—431no—
553C4×Q8—861no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8—861no—
559C4×Q8D17211yescharacteristic
560C4×Q8D17211yescharacteristic
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—431no—
564C4×D4—431no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—862no—
569C4×D4—862no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C4×D4—862no—
575C4×D4—862no—
576C4×D4—862no—
577C4×D4—862no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4D17211yescharacteristic
588C4×D4D17211yescharacteristic
589#117—21no—
590#117—431no—
591#117—862no—
592#117—862no—
593#117—861no—
594#117—861no—
595#117—861no—
596#117C22×D4311yescharacteristic
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—862no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C22⋊C4—432no—
604C2×C22⋊C4—862no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—862no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—862no—
614C2×C42—861no—
615C2×C42—861no—
616C2×C42C22×D4311yescharacteristic
617C2×C42C22×D4311yescharacteristic
618C2×C42C22×D4311yescharacteristic
619#107—861no—
620#107—861no—
621#106—861no—
622#106—861no—
623#104—22no—
624#104—434no—
625#104—862no—
626#104C4×D4314yescomplemented
627#103—861no—
628#103—861no—
629#103—861no—
630#103—861no—
631#103—861no—
632#103—861no—
633#102—861no—
634#102—861no—
635#100—434no—
636#100—862no—
637#97—21no—
638#97—861no—
639C4×C8—21no—
640C4×C8—861no—
641#95—862no—
642#95—862no—
643C24—432no—
644C24—862no—
645#41—21no—
646#41—21no—
647#41—432no—
648#41—432no—
649#41—864no—
650#41—864no—
651#41—864no—
652#41—864no—
653#41—861no—
654#41—861no—
655#41C2×C4×D4312yes—
656#41#1062189812yes—
657C2×Q8—432no—
658C2×Q8—431no—
659C2×Q8—861no—
660C2×Q8—861no—
661C2×Q8—861no—
662C2×Q8—861no—
663C2×Q8—861no—
664C2×Q8C2×D17211yescharacteristic
665C2×D4—21no—
666C2×D4—432no—
667C2×D4—431no—
668C2×D4—432no—
669C2×D4—864no—
670C2×D4—862no—
671C2×D4—864no—
672C2×D4—868no—
673C2×D4—868no—
674C2×D4—864no—
675C2×D4—862no—
676C2×D4—861no—
677C2×D4—864no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4C2×D17211yescharacteristic
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—432no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—861no—
694C22×C4—862no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—862no—
698C22×C4—861no—
699C22×C4—862no—
700C22×C4—861no—
701C22×C4—3444no—
702C22×C4—1724no—
703C22×C4D4×D4311yescharacteristic
704C22×C4D4×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—864no—
707Q16—864no—
708SD16—864no—
709SD16—864no—
710M16—21no—
711M16—21no—
712M16—21no—
713M16—432no—
714M16—861no—
715M16—861no—
716M16—861no—
717M16C2×C4×D4312yescomplemented
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—861no—
721C2×C8—861no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—431no—
725C4⋊C4—431no—
726C4⋊C4—862no—
727C4⋊C4—862no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—1721no—
735C4⋊C4—1721no—
736C4⋊C4C2×D17211yescharacteristic
737C4⋊C4C2×D17211yescharacteristic
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—868no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—861no—
747C22⋊C4—862no—
748C22⋊C4—862no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—1724no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—42no—
759C42—42no—
760C42—862no—
761C42—862no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42—1721no—
766C42—1721no—
767C42C2×C4×D4312yescomplemented
768C42C2×D17211yescharacteristic
769C42C2×D17211yescharacteristic
770C42D4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C23—21no—
773C23—434no—
774C23—868no—
775C23—862no—
776C23—861no—
777C23—862no—
778C23—3442no—
779C23—3442no—
780C23—1722no—
781C23—1722no—
782C23C2×D4×D4311yescharacteristic
783Q8—21no—
784Q8—432no—
785Q8—861no—
786Q8—862no—
787Q8—862no—
788Q8—1721no—
789Q8—1721no—
790Q8C4×D17212yes—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—432no—
795D4—868no—
796D4—868no—
797D4—862no—
798D4—862no—
799D4—862no—
800D4—862no—
801D4—861no—
802D4—862no—
803D4—862no—
804D4C4×D17212yes—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—81no—
820C2×C4—868no—
821C2×C4—861no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—862no—
828C2×C4—3442no—
829C2×C4—3441no—
830C2×C4—3442no—
831C2×C4—3442no—
832C2×C4—3442no—
833C2×C4—3442no—
834C2×C4—1722no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1722no—
839C2×C4—1724no—
840C2×C4—1722no—
841C2×C4#1306329511yescharacteristic
842C2×C4#1306329511yescharacteristic
843C2×C4#1306329511yescharacteristic
844C2×C4#1306329511yescharacteristic
845C2×C4C22×C4×D4311yescharacteristic
846C2×C4C2×D4×D4311yescharacteristic
847C2×C4C22×D17211yescharacteristic
848C2×C4#41×D4311yescharacteristic
849C2×C4#41×D4311yescharacteristic
850C2×C4C2×#1062189811yescharacteristic
851C8—22no—
852C8—41no—
853C8—862no—
854C8—1721no—
855C22—21no—
856C22—21no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—862no—
861C22—864no—
862C22—3442no—
863C22—3448no—
864C22—1724no—
865C22—1721no—
866C22—1722no—
867C22—1721no—
868C22—1722no—
869C22C4×D4×D4311yescharacteristic
870C22C2×#1306329511yescharacteristic
871C22#1458340811yescharacteristic
872C4—21no—
873C4—21no—
874C4—22no—
875C4—21no—
876C4—42no—
877C4—42no—
878C4—41no—
879C4—41no—
880C4—862no—
881C4—3441no—
882C4—1721no—
883C4—1722no—
884C4—1721no—
885C4—1722no—
886C4#1458307812yesdirect product factor
887C4C4×D4×D4311yescharacteristic
888C4C2×C4×D17211yescharacteristic
889C4#1458340811yescharacteristic
890C4#1458341111yescharacteristic
891C2—21no—
892C2—21no—
893C2—42no—
894C2—1722no—
895C2—1724no—
896C2C4×#1306329511yescharacteristic
897C2C2×#1458307811yescharacteristic
898C2#1914394611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#104×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063371C22
cosocleC22×C4×C43C24
hypercenterC4×#104D43
hypocenterC43C4×#455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
3. C4×#13063358C2semidirect
4. C4×#13063355C2semidirect
5. C4×#13063313C2semidirect
6. #19134982C2semidirect
7. #19134965C2semidirect
8. #19134962C2semidirect
9. #19134830C2semidirect
10. #19134829C2semidirect
11. #19134806C2semidirect
13. C4×#13063253C2semidirect
14. C4×#13063241C2semidirect
15. C4×#104×C43C2semidirect
31. C2×C4×Dic86C22semidirect
36. #14583078C4direct (N × H)
45. #14582942C22semidirect
46. #14582941C22semidirect
49. #14582909C22semidirect
50. #14582907C22semidirect
55. C4×#10621877C22semidirect
56. #14582805C22semidirect
59. #14582765C22semidirect
61. #14582667C22semidirect
62. #14582667C22semidirect
63. #14582659C22semidirect
64. #14582659C22semidirect
68. C4×M16×C43C22semidirect
69. C43×C43C22semidirect
70. C43×#339C22semidirect
71. C43×#339C22semidirect
87. #13063358C2×C4semidirect
89. #13063355C2×C4semidirect
97. #13063313C2×C4semidirect
157. #13063253C2×C4semidirect
167. #13063241C2×C4semidirect
190. #104×C43C2×C4semidirect
254. C2×Dic86C22×C4semidirect
259. M16×C43C22×C4semidirect
277. C42×C43C22×C4semidirect
317. #10621877C22×C4semidirect
431. C4×C43#455semidirect
455. C4×#104D43semidirect
508. C4×M16C2×D43semidirect
514. C43C2×D43semidirect
519. #339C2×D43semidirect
520. #339C2×D43semidirect
521. C43C4×#455semidirect
626. #104C4×D43semidirect
717. M16C2×C4×D43semidirect
767. C42C2×C4×D43semidirect
886. C4#14583078direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633712
C2×#145830782
C4×#130633582
C4×#130633552
C4×#130633132
#191349822
#191349652
#191349622
#191348302
#191348292
#191348062
#191345502
C4×#130632532
C4×#130632412
C4×#104×C432
C4×#45543