Finite Group Databasebeta

← #30622271

Subgroups — #30622271

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462579C211yesmaximal, characteristic, complemented
2#21462577C211yesmaximal, characteristic, complemented
3#21462576C211yesmaximal, characteristic
4#21462473C211yesmaximal, characteristic, complemented
5#21461964C211yesmaximal, characteristic, complemented
6#21461936C211yesmaximal, characteristic, complemented
7#21461905C211yesmaximal, characteristic, complemented
8#21461904C211yesmaximal, characteristic, complemented
9#21461819C211yesmaximal, characteristic
10#21461818C211yesmaximal, characteristic, complemented
11#21461775C211yesmaximal, characteristic, complemented
12#21461774C211yesmaximal, characteristic, complemented
13#21461624C211yesmaximal, characteristic, complemented
14#21461593C211yesmaximal, characteristic, complemented
15#471×D61C211yesmaximal, characteristic
16#16840831C2211yescharacteristic
17#16840831C2211yescharacteristic
18#16840830C2211yescharacteristic
19#16840829C2211yescharacteristic
20#16840803—21no—
21#16840802—21no—
22#16840801—21no—
23#16840801—21no—
24#16840801—21no—
25#16840801—21no—
26Q16×#6923—21no—
27SD16×#6923—21no—
28SD16×#6923—21no—
29SD16×#6923—21no—
30SD16×#6923—21no—
31D8×#6923—21no—
32#16840773—21no—
33#16840773—21no—
34#16840773C2211yescharacteristic
35#16840773C2211yescharacteristic
36#16840773C2211yescharacteristic
37#16840773C2211yescharacteristic
38#16840772—21no—
39#16840772C2211yescharacteristic
40C2×#14519845—21no—
41C2×#14519845C2211yescharacteristic
42D61⋊#104C2211yescharacteristic
43#16840755C2211yescharacteristic
44#16840754C2211yescharacteristic
45#16840752C2211yescharacteristic
46C2×#14519840C2211yescharacteristic
47C2×#14519839C2211yescharacteristic
48#16840728C2211yescharacteristic
49#16840728C2211yescharacteristic
50#16840725C2211yescharacteristic
51C2×C8×#6923C2211yescharacteristic
52(C2×#6923)⋊Q8C2211yescharacteristic
53#16840714C2211yescharacteristic
54#16840641C2211yescharacteristic
55#16840641C2211yescharacteristic
56#16840637C2211yescharacteristic
57#16840634C2211yescharacteristic
58#16840634C2211yescharacteristic
59#16840634C2211yescharacteristic
60#137×D61C2211yescharacteristic
61AGL(1,ℤ/8)×D61C2211yescharacteristic
62C2×SD16×D61C2211yescharacteristic
63#131×D61C2211yescharacteristic
64#16840028C411yescharacteristic, complemented
65#16840027C411yescharacteristic, complemented
66#16840026C411yescharacteristic, complemented
67#16840025C411yescharacteristic, complemented
68#16840024C411yescharacteristic, complemented
69#16840023C411yescharacteristic, complemented
70#16840022C411yescharacteristic, complemented
71#108×D61C2211yescharacteristic
72#101×D61C2211yescharacteristic
73#100×D61C2211yescharacteristic
74C61×#471C411yescharacteristic, complemented
75D61⋊M16C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—21no—
78Q8×#6923—21no—
79Q8×#6923—21no—
80Q8×#6923—21no—
81Q8×#6923—21no—
82Q8×#6923—21no—
83D4×#6923—21no—
84D4×#6923—21no—
85D4×#6923—21no—
86D4×#6923—21no—
87D4×#6923—21no—
88D4×#6923—21no—
89D4×#6923—41no—
90D4×#6923—41no—
91#14519856—21no—
92#14519856—21no—
93#14519856—41no—
94#14519856C2311yescharacteristic
95#14519856C2311yescharacteristic
96#14519856C2311yescharacteristic
97C2×C4⋊#6923—21no—
98C2×C4⋊#6923—21no—
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C22⋊#6923—41no—
102C2×C22⋊#6923—41no—
103C2×C4×#6923C2311yescharacteristic
104#14519846—21no—
105#14519846—21no—
106#14519846—21no—
107#14519846—21no—
108#14519846D411yescharacteristic
109#14519846D411yescharacteristic
110#14519845—21no—
111#14519845—21no—
112#14519845—21no—
113#14519845—21no—
114#14519845—21no—
115#14519845—21no—
116#14519845D411yescharacteristic
117#14519845D411yescharacteristic
118#14519842—21no—
119#14519841—21no—
120#14519840—21no—
121#14519840—21no—
122#14519840—21no—
123#14519840—21no—
124#14519840D411yescharacteristic
125#14519840D411yescharacteristic
126#14519839—21no—
127#14519839—21no—
128#14519839—21no—
129#14519839—21no—
130#14519839D411yescharacteristic
131#14519839D411yescharacteristic
132#14519831—21no—
133#14519831—21no—
134#14519831—21no—
135C8×#6923—21no—
136C8×#6923—21no—
137C8×#6923—21no—
138C8×#6923—21no—
139C8×#6923—21no—
140(C2×#6923)⋊C4—41no—
141#41×D61C2311yescharacteristic
142C2×Q8×D61C2311yescharacteristic
143C2×D4×D61C2311yescharacteristic
144#14519810C2×C411yescharacteristic, complemented
145#14519809—21no—
146#14519808C2×C411yescharacteristic, complemented
147#14519807C2×C411yescharacteristic, complemented
148#14519806—21no—
149#14519805C2×C411yescharacteristic
150#14519804—21no—
151#14519803C2×C411yescharacteristic
152#14519802C2×C411yescharacteristic
153#14519801—21no—
154Q16×D61—21no—
155C2×#11758190C2×C411yescharacteristic, complemented
156C2×#11758200C2×C411yescharacteristic, complemented
157C2×#11758201C2×C411yescharacteristic, complemented
158SD16×D61—21no—
159SD16×D61—21no—
160SD16×D61—21no—
161SD16×D61—21no—
162SD16×D61—21no—
163SD16×D61—21no—
164D8×D61—21no—
165#14519785—21no—
166#14519785C2×C411yescharacteristic, complemented
167#14519784C2×C411yescharacteristic, complemented
168#14519783—21no—
169#14519783C2×C411yescharacteristic, complemented
170M16×D61—21no—
171M16×D61C2311yescharacteristic
172M16×D61C2311yescharacteristic
173M16×D61C2311yescharacteristic
174C2×C8×D61—21no—
175C2×C8×D61C2311yescharacteristic
176#14519713C2×C411yescharacteristic, complemented
177#14519712C2×C411yescharacteristic, complemented
178#14519712C2×C411yescharacteristic, complemented
179#14519696C2×C411yescharacteristic, complemented
180#14519695C2×C411yescharacteristic, complemented
181#14519695C2×C411yescharacteristic, complemented
182#14519694C2×C411yescharacteristic, complemented
183#14519693C2×C411yescharacteristic, complemented
184#14519693C2×C411yescharacteristic, complemented
185#137×C61C2×C411yescharacteristic, complemented
186AGL(1,ℤ/8)×C61C2×C411yescharacteristic
187C2×SD16×C61C2×C411yescharacteristic, complemented
188#131×C61C2×C411yescharacteristic, complemented
189#108×C61C2×C411yescharacteristic, complemented
190#101×C61C2×C411yescharacteristic, complemented
191#100×C61C2×C411yescharacteristic, complemented
192C23×D61—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—41no—
197C22×#6923—41no—
198C22×#6923—41no—
199C22×#6923—41no—
200#41×C61C22×C411yescharacteristic
201C2×Q8×C61C22×C411yescharacteristic
202C2×D4×C61C22×C411yescharacteristic
203C2×C22⋊D61—21no—
204#11758226#4111yescharacteristic
205Q8×D61—21no—
206Q8×D61—21no—
207Q8×D61—21no—
208Q8×D61—21no—
209Q8×D61C2×D411yescharacteristic
210#11758224—21no—
211#11758224#4111yescharacteristic
212D4×D61—21no—
213D4×D61—21no—
214D4×D61—21no—
215D4×D61—21no—
216D4×D61—21no—
217D4×D61C2×D411yescharacteristic
218#11758222—21no—
219#11758222C22×C411yescharacteristic
220C2×D244C22×C411yescharacteristic
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61C2411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122C22×C411yescharacteristic
226C22⋊#6923—21no—
227C22⋊#6923—21no—
228C22⋊#6923—21no—
229C22⋊#6923—41no—
230C22⋊#6923—41no—
231C22⋊#6923—41no—
232C22⋊#6923—41no—
233C22⋊#6923—82no—
234#11758217—21no—
235C2×#92420—21no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923—21no—
239C4⋊#6923—21no—
240C4⋊#6923—41no—
241C4⋊#6923—41no—
242C4⋊#6923—41no—
243C4⋊#6923—41no—
244C4⋊#6923C2×D411yescharacteristic
245C4⋊#6923C2×D411yescharacteristic
246C4⋊#6923C2×D411yescharacteristic
247C4⋊#6923C2×D411yescharacteristic
248C4⋊#6923C2×D411yescharacteristic
249C4⋊#6923C2×D411yescharacteristic
250C4×#6923—21no—
251C4×#6923—21no—
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923—41no—
256C4×#6923—41no—
257C4×#6923—41no—
258C4×#6923—41no—
259#11758213—21no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8C2×D411yescharacteristic
263D61⋊C8C2×D411yescharacteristic
264Q16×C61—21no—
265SD16×C61—21no—
266SD16×C61—21no—
267SD16×C61—21no—
268SD16×C61—21no—
269D8×C61—21no—
270M16×C61—21no—
271M16×C61C22×C411yescharacteristic
272M16×C61C22×C411yescharacteristic
273M16×C61C22×C411yescharacteristic
274C2×C8×C61—21no—
275C2×C8×C61C22×C411yescharacteristic
276#11758202—21no—
277#11758202—21no—
278#11758201—21no—
279#11758201—21no—
280#11758201—21no—
281#11758201—21no—
282#11758200—21no—
283#11758200—21no—
284#11758200—21no—
285#11758200—21no—
286#11758199—21no—
287#11758199—21no—
288#11758194—21no—
289#11758194C22×C411yescharacteristic
290#11758194C22×C411yescharacteristic
291#11758194C22×C411yescharacteristic
292C2×#92418—21no—
293C2×#92418C22×C411yescharacteristic
294Dic244—21no—
295D488—21no—
296#11758190—21no—
297#11758190—21no—
298#11758190—21no—
299#11758190—21no—
300#11758189—21no—
301#11758189—21no—
302#11758189—21no—
303#11758189—21no—
304#11758189—21no—
305C8×D61—21no—
306C8×D61—21no—
307C8×D61—21no—
308C8×D61—21no—
309C8×D61—21no—
310C8×D61C2×D411yescharacteristic
311C8×D61C2×D411yescharacteristic
312C8×D61#4111yescharacteristic
313C8×D61#4111yescharacteristic
314C23×C61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—81no—
320C22×D61—81no—
321C22×D61H(5,𝔽2)11yescharacteristic
322C2×#6923—22no—
323C2×#6923—21no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—21no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—81no—
334C2×#6923—81no—
335C2×#6923—161no—
336C2×#6923—161no—
337C2×#6923—161no—
338C2×#6923—161no—
339Q8×C61—21no—
340Q8×C61—21no—
341Q8×C61C4×D411yescharacteristic
342D4×C61—21no—
343D4×C61—21no—
344D4×C61—21no—
345D4×C61C4×D411yescharacteristic
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61C23×C411yescharacteristic
349C22⋊D61—21no—
350C22⋊D61—21no—
351C22⋊D61—21no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic612−1+411yescharacteristic
357D244—21no—
358D244—21no—
359D244—21no—
360D244C4×D411yescharacteristic
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61C22×D411yescharacteristic
367C4×D61C22×D411yescharacteristic
368C4×D61C2×#4111yescharacteristic
369C4×D61C2×#4111yescharacteristic
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—41no—
374Dic122—41no—
375Dic122C4×D411yescharacteristic
376#92420—21no—
377#92420—21no—
378#92420—41no—
379C8×C61—21no—
380C8×C61—21no—
381C8×C61—21no—
382C8×C61C4×D411yescharacteristic
383C8×C61C4×D411yescharacteristic
384#92418—21no—
385#92418—21no—
386#92418—21no—
387#92418C4×D411yescharacteristic
388#92418C4×D411yescharacteristic
389#23044—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—41no—
392C22×C61—81no—
393C22×C61#52011yescharacteristic
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—161no—
404C2×D61D4211yescharacteristic
405C2×D61#55311yescharacteristic
406#6923—42no—
407#6923—41no—
408#6923—41no—
409#6923—41no—
410#6923—41no—
411#6923—41no—
412#6923—41no—
413#6923—81no—
414#6923—81no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61C2×C4×D411yescharacteristic
418C4×C61C2×C4×D411yescharacteristic
419Dic61—21no—
420Dic61—41no—
421Dic61#54711yescharacteristic
422Dic61#54811yescharacteristic
423C2×#471—611no—
424#2949—611no—
425#2947—611no—
426#2946—611no—
427#2912—611no—
428#1968—611no—
429#1951—611no—
430#1931—611no—
431#1930—611no—
432#1883—611no—
433#1882—611no—
434#1857—611no—
435#1856—611no—
436#1772—611no—
437#1764—611no—
438C2×C61—21no—
439C2×C61—41no—
440C2×C61—81no—
441C2×C61#236111yescharacteristic
442D61—21no—
443D61—41no—
444D61—81no—
445D61#329011yescharacteristic
446D61#329111yescharacteristic
447C2×#137—611no—
448C2×AGL(1,ℤ/8)—611no—
449C22×SD16—611no—
450C2×#131—611no—
451#520—611no—
452#520—611no—
453#519—611no—
454#518—611no—
455#471—611no—
456#471—611no—
457#471—611no—
458#471—611no—
459#471—611no—
460#471—611no—
461#471—611no—
462#471#692311yescharacteristic, complemented
463#442—1221no—
464#441—1221no—
465#440—1221no—
466#440—1221no—
467#440—1221no—
468#440—1221no—
469C4×Q16—1221no—
470C4×SD16—1221no—
471C4×SD16—1221no—
472C4×SD16—1221no—
473C4×SD16—1221no—
474C4×D8—1221no—
475C2×#108—611no—
476#428—611no—
477#428—611no—
478#428—611no—
479#428—611no—
480#428—1221no—
481#428—1221no—
482#427—611no—
483#427—1221no—
484C2×#106—611no—
485C2×#106—1221no—
486C2×#104—611no—
487#419—611no—
488#418—611no—
489#416—611no—
490C2×#103—611no—
491C2×#102—611no—
492C2×#101—611no—
493C2×#100—611no—
494#405—611no—
495#405—611no—
496#405—611no—
497C2×C4×C8—611no—
498#391—611no—
499#390—611no—
500#343—611no—
501#343—611no—
502#341—611no—
503#339—611no—
504#339—611no—
505#339—611no—
506C61#2304411yescharacteristic, complemented, Sylow
507C2×#41—611no—
508C22×Q8—611no—
509C22×D4—611no—
510#137—611no—
511#137—611no—
512#137—611no—
513#137—1221no—
514#137—1221no—
515#137C2×#692311yescharacteristic, complemented
516AGL(1,ℤ/8)—611no—
517AGL(1,ℤ/8)—611no—
518AGL(1,ℤ/8)—611no—
519AGL(1,ℤ/8)—1221no—
520AGL(1,ℤ/8)—1221no—
521AGL(1,ℤ/8)C2×#692311yescharacteristic
522C2×Q16—1221no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×SD16—1221no—
527C2×SD16—1221no—
528C2×SD16—1221no—
529C2×SD16—1221no—
530C2×SD16—1221no—
531C2×SD16—1221no—
532C2×SD16C2×#692311yescharacteristic, complemented
533C2×D8—1221no—
534#131—611no—
535#131—611no—
536#131—611no—
537#131—1221no—
538#131—1221no—
539#131C2×#692311yescharacteristic, complemented
540C2×M16—611no—
541C2×M16—611no—
542C2×M16—611no—
543C2×M16—611no—
544C2×M16—1221no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1221no—
548C4×Q8—1221no—
549C4×Q8—1221no—
550C4×Q8—1221no—
551C4×Q8—1221no—
552C4×Q8—1221no—
553C4×Q8—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—2441no—
561C4×D4—2441no—
562#117—611no—
563#117—611no—
564#117—611no—
565#117—1221no—
566#117—1221no—
567#117—2441no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C22⋊C4—2441no—
573C2×C22⋊C4—2441no—
574C2×C42—611no—
575#108—611no—
576#108—611no—
577#108—611no—
578#108C2×#692311yescharacteristic, complemented
579#107—611no—
580#107—611no—
581#107—1221no—
582#107—1221no—
583#107—1221no—
584#107—1221no—
585#106—611no—
586#106—611no—
587#106—1221no—
588#106—1221no—
589#106—1221no—
590#106—1221no—
591#106—1221no—
592#106—1221no—
593#104—1221no—
594#104—1221no—
595#103—611no—
596#103—611no—
597#103—1221no—
598#103—1221no—
599#103—1221no—
600#103—1221no—
601#102—611no—
602#102—611no—
603#102—1221no—
604#102—1221no—
605#102—1221no—
606#102—1221no—
607#101—611no—
608#101—611no—
609#101—611no—
610#101C2×#692311yescharacteristic, complemented
611#100—611no—
612#100—611no—
613#100—611no—
614#100C2×#692311yescharacteristic, complemented
615#97—1221no—
616#97—1221no—
617#97—1221no—
618C4×C8—1221no—
619C4×C8—1221no—
620C4×C8—1221no—
621C4×C8—1221no—
622C4×C8—1221no—
623#95—2441no—
624C24—1221no—
625#41—611no—
626#41—611no—
627#41—611no—
628#41—1221no—
629#41—1221no—
630#41C22×#692311yescharacteristic
631C2×Q8—611no—
632C2×Q8—611no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8C22×#692311yescharacteristic
639C2×D4—611no—
640C2×D4—611no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4C22×#692311yescharacteristic
648C22×C4—611no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—2441no—
655C22×C4—2441no—
656C22×C4—2441no—
657C22×C4—2441no—
658Q16—21no—
659Q16—1221no—
660Q16—1221no—
661Q16—1221no—
662SD16—21no—
663SD16—21no—
664SD16—21no—
665SD16—21no—
666SD16—1221no—
667SD16—1221no—
668SD16—1221no—
669SD16—1221no—
670SD16—1221no—
671SD16—1221no—
672SD16—1221no—
673SD16—1221no—
674SD16—1221no—
675SD16—1221no—
676SD16—1221no—
677SD16—1221no—
678D8—21no—
679D8—1221no—
680D8—1221no—
681D8—1221no—
682M16—21no—
683M16—611no—
684M16—611no—
685M16—611no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—1221no—
692M16—1221no—
693M16—1221no—
694M16C22×#692311yescharacteristic
695M16C22×#692311yescharacteristic
696M16C22×#692311yescharacteristic
697C2×C8—21no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8C22×#692311yescharacteristic
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—2441no—
726C4⋊C4—2441no—
727C4⋊C4—2441no—
728C4⋊C4—2441no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—4882no—
733C22⋊C4—2441no—
734C22⋊C4—2441no—
735C22⋊C4—2441no—
736C22⋊C4—2441no—
737C42—1221no—
738C42—1221no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42—2441no—
743C42—2441no—
744C42—2441no—
745C42—2441no—
746C23—21no—
747C23—611no—
748C23—1221no—
749C23—1221no—
750C23—4881no—
751C23—4881no—
752C23—2441no—
753C23—2441no—
754Q8—21no—
755Q8—21no—
756Q8—611no—
757Q8—1221no—
758Q8—1221no—
759Q8—1221no—
760Q8—2441no—
761Q8—2441no—
762Q8D4×#692311yescharacteristic
763D4—21no—
764D4—21no—
765D4—21no—
766D4—611no—
767D4—1221no—
768D4—1221no—
769D4—1221no—
770D4—1221no—
771D4—1221no—
772D4—1221no—
773D4—2441no—
774D4—2441no—
775D4D4×#692311yescharacteristic
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—9761no—
796C2×C4—9761no—
797C2×C4—9761no—
798C2×C4—9761no—
799C2×C4—4881no—
800C2×C4—4881no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4C23×#692311yescharacteristic
808C8—21no—
809C8—21no—
810C8—21no—
811C8—611no—
812C8—611no—
813C8—1221no—
814C8—1221no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—2441no—
819C8D4×#692311yescharacteristic
820C8D4×#692311yescharacteristic
821C22—21no—
822C22—41no—
823C22—81no—
824C22—611no—
825C22—611no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—9761no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22#1684083111yescharacteristic
837C4—21no—
838C4—41no—
839C4—611no—
840C4—611no—
841C4—1221no—
842C4—4881no—
843C4—4881no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C4—2441no—
850C4—2442no—
851C4—2441no—
852C4C2×D4×#692311yescharacteristic
853C4C2×D4×#692311yescharacteristic
854C2—21no—
855C2—41no—
856C2—81no—
857C2—611no—
858C2—611no—
859C2—1221no—
860C2—4881no—
861C2—2441no—
862C2#2146234411yescharacteristic
subgroupG/H
centerC2#21462344
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#471C4
socleC2×C61#2361
prime radicalAGL(1,ℤ/8)×D61C22
cosocleC2×C4×D61C24
hypercenter#471#6923
hypocenterC61#23044
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #21462579C2semidirect
2. #21462577C2semidirect
4. #21462473C2semidirect
5. #21461964C2semidirect
6. #21461936C2semidirect
7. #21461905C2semidirect
8. #21461904C2semidirect
10. #21461818C2semidirect
11. #21461775C2semidirect
12. #21461774C2semidirect
13. #21461624C2semidirect
14. #21461593C2semidirect
64. #16840028C4semidirect
65. #16840027C4semidirect
66. #16840026C4semidirect
67. #16840025C4semidirect
68. #16840024C4semidirect
69. #16840023C4semidirect
70. #16840022C4semidirect
74. C61×#471C4semidirect
144. #14519810C2×C4semidirect
146. #14519808C2×C4semidirect
147. #14519807C2×C4semidirect
155. C2×#11758190C2×C4semidirect
156. C2×#11758200C2×C4semidirect
157. C2×#11758201C2×C4semidirect
166. #14519785C2×C4semidirect
167. #14519784C2×C4semidirect
169. #14519783C2×C4semidirect
176. #14519713C2×C4semidirect
177. #14519712C2×C4semidirect
178. #14519712C2×C4semidirect
179. #14519696C2×C4semidirect
180. #14519695C2×C4semidirect
181. #14519695C2×C4semidirect
182. #14519694C2×C4semidirect
183. #14519693C2×C4semidirect
184. #14519693C2×C4semidirect
185. #137×C61C2×C4semidirect
187. C2×SD16×C61C2×C4semidirect
188. #131×C61C2×C4semidirect
189. #108×C61C2×C4semidirect
190. #101×C61C2×C4semidirect
191. #100×C61C2×C4semidirect
462. #471#6923semidirect
506. C61#23044semidirect
515. #137C2×#6923semidirect
532. C2×SD16C2×#6923semidirect
539. #131C2×#6923semidirect
578. #108C2×#6923semidirect
610. #101C2×#6923semidirect
614. #100C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625792
#214625772
#214625762
#214624732
#214619642
#214619362
#214619052
#214619042
#214618192
#214618182
#214617752
#214617742
#214616242
#214615932
#471×D612
#2304461