Finite Group Databasebeta

← #6355484

Subgroups — #6355484

Order 512.

1736 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60966C211yesmaximal, characteristic, complemented
2#60558C211yesmaximal, characteristic
3C2×#3077C211yesmaximal, characteristic, complemented
4#60230C211yesmaximal, characteristic, complemented
5#19466C214yesmaximal, complemented
6#19460C214yesmaximal, complemented
7#19429C211yesmaximal, characteristic, complemented
8#19427C211yesmaximal, characteristic, complemented
9#19423C211yesmaximal, characteristic, complemented
10#19421C211yesmaximal, characteristic, complemented
11#19393C211yesmaximal, characteristic, complemented
12#19391C211yesmaximal, characteristic, complemented
13#19387C211yesmaximal, characteristic, complemented
14#19385C211yesmaximal, characteristic, complemented
15#19307C214yesmaximal, complemented
16#19305C214yesmaximal, complemented
17#17820C211yesmaximal, characteristic, complemented
18#17747C211yesmaximal, characteristic, complemented
19#17737C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#3252—22no—
24#3231C2212yescomplemented
25#3230C2211yescharacteristic, complemented
26#3227C2211yescharacteristic, complemented
27#3210C2212yescomplemented
28#3209C2211yescharacteristic, complemented
29#3206C2211yescharacteristic, complemented
30#3196—22no—
31#3185C2212yescomplemented
32#3182C2212yescomplemented
33#3117—22no—
34#3116—22no—
35#3114—22no—
36#3110C2212yes—
37#3109C2212yes—
38#3105—22no—
39#3101C2212yes—
40#3100C2212yes—
41#3092—21no—
42#3077—22no—
43#3077—22no—
44#3077C2214yes—
45#3077C2214yes—
46#3077C2211yescharacteristic
47#3077C2211yescharacteristic
48C2×#478—21no—
49C2×#478—21no—
50C2×#476C2211yescharacteristic
51C2×#476C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic
54#3036C2211yescharacteristic
55#3036C2211yescharacteristic
56#3003—21no—
57#2975C2211yescharacteristic
58#2975C2211yescharacteristic
59#2974—22no—
60#2974C2214yes—
61#2973—22no—
62#2972C2211yescharacteristic
63#2972C2211yescharacteristic
64C4×AGL(1,ℤ/8)—21no—
65C4×AGL(1,ℤ/8)—21no—
66D4×M16—22no—
67D4×M16C2214yes—
68#2920C2211yescharacteristic
69#2920C2211yescharacteristic
70#2920C2211yescharacteristic
71C2×#428—21no—
72C2×#423C2211yescharacteristic
73C2×#418—21no—
74C2×#407—22no—
75#1703C2214yescomplemented
76#1703C2214yescomplemented
77#1699C2214yescomplemented
78#1697C2214yescomplemented
79#1695C2214yescomplemented
80#1691C2214yescomplemented
81#1689C2214yescomplemented
82#1685C2214yescomplemented
83#1683C2214yescomplemented
84#1683C2214yescomplemented
85#1679C2214yescomplemented
86#1677C2214yescomplemented
87#1675C2214yescomplemented
88#1671C2214yescomplemented
89#1669C2214yescomplemented
90#1665C2214yescomplemented
91#1574C2214yescomplemented
92#1571C2211yescharacteristic, complemented
93#1571C2211yescharacteristic, complemented
94#1570C2211yescharacteristic, complemented
95#1570C2211yescharacteristic, complemented
96#1569C2214yescomplemented
97#1561C2212yescomplemented
98#1560C2212yescomplemented
99#1559C2212yescomplemented
100#1559C2214yescomplemented
101#1557C2212yescomplemented
102#1554C2214yescomplemented
103#1549C2211yescharacteristic, complemented
104#1549C2211yescharacteristic, complemented
105#1548C2211yescharacteristic, complemented
106#1548C2211yescharacteristic, complemented
107#1542C2211yescharacteristic, complemented
108#1542C2211yescharacteristic, complemented
109#1540C2211yescharacteristic, complemented
110#1540C2211yescharacteristic, complemented
111C23×D4D411yescharacteristic
112C24×C4—21no—
113C2×AGL(1,ℤ/8)—21no—
114C2×AGL(1,ℤ/8)—21no—
115C22×M16—21no—
116C22×M16—24no—
117#533—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533—21no—
123#533C2311yescharacteristic
124#533C2312yes—
125#533C2312yes—
126#533C2311yescharacteristic
127#533C2311yescharacteristic
128#532C2311yescharacteristic
129#532C2311yescharacteristic
130#532C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133#529—21no—
134#529—21no—
135#529—21no—
136#529—21no—
137#529—21no—
138#529—21no—
139C2×#125—21no—
140#525—21no—
141#525—21no—
142#525—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C4×#41—21no—
146C4×#41—21no—
147C4×#41—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4D411yescharacteristic
157C2×C4×D4D411yescharacteristic
158C2×C4×D4D412yes—
159C2×C4×D4D412yes—
160C2×C4×D4C2312yes—
161C2×C4×D4C2312yes—
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×#117—21no—
165C22×C4⋊C4D411yescharacteristic
166C22×C22⋊C4—21no—
167C22×C42C2311yescharacteristic
168#500C2312yescomplemented
169#498C2312yescomplemented
170#494C2312yescomplemented
171#492C2312yescomplemented
172#487C2312yescomplemented
173#487C2312yescomplemented
174#487C2312yescomplemented
175#486C2312yescomplemented
176#485—24no—
177#484—22no—
178#484—22no—
179#483—22no—
180#481—22no—
181#481—22no—
182#480—22no—
183#479—24no—
184#478—24no—
185#478—24no—
186#478—24no—
187#478—24no—
188#478—22no—
189#478—22no—
190#477—22no—
191#476—22no—
192#476—22no—
193#476—22no—
194#476C2314yes—
195#476C2314yes—
196#476C2312yes—
197#476C2312yes—
198#474—22no—
199#474—22no—
200#474C2314yes—
201#474C2314yes—
202#474C2312yes—
203#474C2312yes—
204#470—24no—
205#468—24no—
206#464—24no—
207#463—22no—
208#463—22no—
209#462—22no—
210#461—22no—
211#461C2312yes—
212#461C2312yes—
213#459C2312yes—
214#459C2312yes—
215#452—24no—
216#451—22no—
217#450—22no—
218#450—22no—
219#448—22no—
220#447—22no—
221#447—22no—
222#442—22no—
223#442—22no—
224#441—24no—
225#440—22no—
226#440—22no—
227#440—24no—
228C4×SD16—22no—
229C4×SD16—22no—
230C4×D8—22no—
231C4×D8—22no—
232#436—22no—
233#436—22no—
234#436C2314yes—
235#436C2314yes—
236#435—24no—
237#435—24no—
238#435—24no—
239#435—24no—
240C8×D4—22no—
241C8×D4—22no—
242C8×D4C2314yes—
243C8×D4C2314yes—
244#432—21no—
245#432—21no—
246#432D412yes—
247#432D412yes—
248#432C2312yes—
249#432C2312yes—
250#431—21no—
251#431—21no—
252#431C2311yescharacteristic
253#431C2311yescharacteristic
254#431C2312yes—
255#431C2311yescharacteristic
256#431C2311yescharacteristic
257#431C2312yes—
258#428—24no—
259#428—24no—
260#428—21no—
261#428—21no—
262C2×#107—21no—
263C2×#107—21no—
264C2×#106—21no—
265C2×#106—21no—
266#423—21no—
267#423—21no—
268#423D412yes—
269#423C2312yes—
270#423C2312yes—
271#423C2311yescharacteristic
272#423C2311yescharacteristic
273#423C2312yes—
274C2×C4⋊C8—21no—
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#418—24no—
278#418—24no—
279#418—21no—
280#418—21no—
281#417—21no—
282#417—21no—
283C2×#102—21no—
284C2×#102—21no—
285C2×#102—21no—
286C2×#102—21no—
287#407—21no—
288#407—21no—
289#407—24no—
290#407—22no—
291#407—22no—
292#407—24no—
293#407D412yes—
294C2×C22⋊C8—22no—
295C2×C22⋊C8—22no—
296C2×C22⋊C8—24no—
297C4×M16—21no—
298C4×M16—21no—
299C4×M16C2312yes—
300#335C2314yescomplemented
301#335C2314yescomplemented
302#334C2314yescomplemented
303#334C2314yescomplemented
304#333C2312yescomplemented
305#333C2312yescomplemented
306#333C2314yescomplemented
307#333C2314yescomplemented
308#332C2312yescomplemented
309#332C2312yescomplemented
310#332C2312yescomplemented
311#332C2312yescomplemented
312#332C2314yescomplemented
313#332C2314yescomplemented
314#331C2312yescomplemented
315#331C2312yescomplemented
316C25—21no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×D4—24no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—42no—
327C22×D4C2×D411yescharacteristic
328C22×D4C2×D412yes—
329C22×D4C2×D412yes—
330C22×D4C2×D411yescharacteristic
331C23×C4—21no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—22no—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—84no—
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4#4111yescharacteristic
344AGL(1,ℤ/8)—44no—
345AGL(1,ℤ/8)—44no—
346C2×Q16—24no—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×SD16—24no—
350C2×D8—22no—
351C2×D8—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—24no—
358C2×M16—24no—
359C2×M16—44no—
360C2×M16—88no—
361C2×M16C2×D414yes—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—24no—
365C22×C8—24no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C2412yes—
373C4⋊Q8C2412yes—
374C4⋊Q8C2411yescharacteristic
375C4⋊Q8C2411yescharacteristic
376C4⋊Q8C2411yescharacteristic
377#127C2411yescharacteristic
378#126—41no—
379#126—41no—
380#125—22no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—41no—
386#125—41no—
387#124—21no—
388#124—21no—
389#124—21no—
390#123—41no—
391#123—41no—
392#123—41no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—41no—
405C22⋊Q8—41no—
406C22⋊Q8—41no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#120—41no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—41no—
425C4×Q8—41no—
426C4×Q8—41no—
427C4×Q8—41no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—22no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—41no—
451C4×D4—41no—
452C4×D4—41no—
453C4×D4—41no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4C2×D412yes—
457C4×D4C2×D412yes—
458C4×D4C2×D412yes—
459C4×D4C2×D412yes—
460C4×D4C2×D412yes—
461C4×D4C2×D412yes—
462C4×D4C2412yes—
463C4×D4C2412yes—
464#117—22no—
465#117—22no—
466#117—21no—
467#117—21no—
468#117—21no—
469#117—41no—
470#117—41no—
471#117—41no—
472#117—41no—
473#117—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4C2×D411yescharacteristic
484C2×C4⋊C4C2×D411yescharacteristic
485C2×C4⋊C4C2×D412yes—
486C2×C4⋊C4C2×D412yes—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—41no—
496C2×C42—41no—
497C2×C42—41no—
498C2×C42C2×D411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42#4111yescharacteristic
505C2×C42#4111yescharacteristic
506C2×C42#4111yescharacteristic
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509C2×C42C2411yescharacteristic
510#107—24no—
511#107—24no—
512#107—24no—
513#107—22no—
514#107—22no—
515#106—24no—
516#106—24no—
517#106—24no—
518#106—22no—
519#106—22no—
520C4⋊C8—22no—
521C4⋊C8—22no—
522C4⋊C8—21no—
523C4⋊C8—21no—
524C4⋊C8—22no—
525C4⋊C8—21no—
526C4⋊C8—21no—
527C4⋊C8C2×D412yes—
528C4⋊C8C2×D412yes—
529C4⋊C8C2×D414yes—
530C4⋊C8C2412yes—
531C4⋊C8C2412yes—
532C4⋊C8C2412yes—
533C4⋊C8C2412yes—
534C4⋊C8C2412yes—
535C4⋊C8C2412yes—
536#103—24no—
537#103—24no—
538#103—24no—
539#103—22no—
540#103—22no—
541#102—24no—
542#102—24no—
543#102—24no—
544#102—24no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—24no—
550#102—22no—
551#102—22no—
552C22⋊C8—22no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—24no—
558C22⋊C8—24no—
559C22⋊C8—24no—
560C22⋊C8—24no—
561C22⋊C8C2×D412yes—
562C22⋊C8C2×D412yes—
563C22⋊C8C2×D414yes—
564#97—22no—
565#97—22no—
566#97C2×D414yes—
567C4×C8—21no—
568C4×C8—21no—
569C4×C8—22no—
570C4×C8C2412yes—
571C4×C8C2412yes—
572C24—21no—
573C24—22no—
574C24—22no—
575C24—21no—
576C24—44no—
577C24—82no—
578C24—82no—
579C24#12111yescharacteristic
580#41—42no—
581#41—42no—
582#41—82no—
583#41—82no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—41no—
590C2×Q8—41no—
591C2×Q8—82no—
592C2×Q8—82no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4#13714yes—
614C2×D4C22×D412yes—
615C2×D4C22×D412yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—42no—
631C22×C4—48no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—82no—
638C22×C4—82no—
639C22×C4—84no—
640C22×C4—81no—
641C22×C4—82no—
642C22×C4—82no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—82no—
646C22×C4#12111yescharacteristic
647C22×C4#12111yescharacteristic
648C22×C4#12111yescharacteristic
649C22×C4#12111yescharacteristic
650C22×C4#12111yescharacteristic
651C22×C4#12111yescharacteristic
652C22×C4#12111yescharacteristic
653C22×C4#12111yescharacteristic
654C22×C4#12111yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C2×#4111yescharacteristic
662C22×C4C2×#4111yescharacteristic
663C22×C4C2×#4111yescharacteristic
664Q16—84no—
665SD16—44no—
666SD16—44no—
667SD16—84no—
668D8—44no—
669D8—44no—
670M16—44no—
671M16—44no—
672M16—44no—
673M16—44no—
674M16—42no—
675M16—42no—
676M16—84no—
677M16—84no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—42no—
685C2×C8—42no—
686C2×C8—84no—
687C2×C8—84no—
688C2×C8C22×D414yes—
689C2×C8C22×D414yes—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—41no—
705C4⋊C4—41no—
706C4⋊C4—41no—
707C4⋊C4—41no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—41no—
716C4⋊C4—41no—
717C4⋊C4—41no—
718C4⋊C4C22×D412yes—
719C4⋊C4C22×D412yes—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C22⋊C4—41no—
733C22⋊C4—41no—
734C22⋊C4—41no—
735C22⋊C4—41no—
736C22⋊C4—41no—
737C22⋊C4—41no—
738C22⋊C4—41no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—42no—
743C42—42no—
744C42#12111yescharacteristic
745C42#12111yescharacteristic
746C42#12111yescharacteristic
747C42#12111yescharacteristic
748C42#12111yescharacteristic
749C42#12111yescharacteristic
750C42C22×D411yescharacteristic
751C42C22×D411yescharacteristic
752C42C22×D411yescharacteristic
753C42C22×D411yescharacteristic
754C42C22×D411yescharacteristic
755C42C22×D411yescharacteristic
756C42C2×#4111yescharacteristic
757C42C2×#4111yescharacteristic
758C42C2×#4111yescharacteristic
759C42C2511yescharacteristic
760C23—22no—
761C23—22no—
762C23—24no—
763C23—22no—
764C23—41no—
765C23—41no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—42no—
771C23—41no—
772C23—81no—
773C23—81no—
774C23—82no—
775C23—81no—
776C23—81no—
777C23—82no—
778C23—816no—
779C23C2×#12111yescharacteristic
780C23C2×#12111yescharacteristic
781C23C2×#12111yescharacteristic
782Q8—44no—
783Q8—42no—
784Q8—41no—
785Q8—41no—
786Q8—82no—
787Q8—81no—
788Q8—82no—
789Q8—82no—
790D4—24no—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—44no—
795D4—44no—
796D4—42no—
797D4—42no—
798D4—41no—
799D4—41no—
800D4—81no—
801D4—82no—
802D4—82no—
803D4—82no—
804D4C2×#13714yes—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—82no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—82no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—82no—
848C2×C4C2×#12111yescharacteristic
849C2×C4C2×#12111yescharacteristic
850C2×C4C2×#12111yescharacteristic
851C2×C4C2×#12111yescharacteristic
852C2×C4C2×#12111yescharacteristic
853C2×C4C2×#12111yescharacteristic
854C2×C4C2×#12111yescharacteristic
855C2×C4C2×#12111yescharacteristic
856C2×C4C2×#12111yescharacteristic
857C2×C4C2×#13712yes—
858C2×C4#57512yes—
859C2×C4C23×D411yescharacteristic
860C2×C4C23×D411yescharacteristic
861C2×C4C22×#4111yescharacteristic
862C8—24no—
863C8—24no—
864C8—42no—
865C8—42no—
866C8—42no—
867C8—42no—
868C8—42no—
869C8—42no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—21no—
878C22—21no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—84no—
886C22—84no—
887C22—88no—
888C22—88no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22#305612yes—
893C22C22×#12111yescharacteristic
894C4—21no—
895C4—21no—
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—21no—
903C4—42no—
904C4—42no—
905C4—81no—
906C4—82no—
907C4—81no—
908C4—81no—
909C4—82no—
910C4#305612yes—
911C4C22×#13711yescharacteristic
912C4C2×#57511yescharacteristic
913C4#358512yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—44no—
918C2—82no—
919C2—161no—
920C2#6042311yescharacteristic
921C2C2×#305611yescharacteristic
922C2#6046911yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#60558C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60966C2semidirect
3. C2×#3077C2semidirect
4. #60230C2semidirect
5. #19466C2semidirect
6. #19460C2semidirect
7. #19429C2semidirect
8. #19427C2semidirect
9. #19423C2semidirect
10. #19421C2semidirect
11. #19393C2semidirect
12. #19391C2semidirect
13. #19387C2semidirect
14. #19385C2semidirect
15. #19307C2semidirect
16. #19305C2semidirect
17. #17820C2semidirect
18. #17747C2semidirect
19. #17737C2semidirect
24. #3231C22semidirect
25. #3230C22semidirect
26. #3227C22semidirect
27. #3210C22semidirect
28. #3209C22semidirect
29. #3206C22semidirect
31. #3185C22semidirect
32. #3182C22semidirect
75. #1703C22semidirect
76. #1703C22semidirect
77. #1699C22semidirect
78. #1697C22semidirect
79. #1695C22semidirect
80. #1691C22semidirect
81. #1689C22semidirect
82. #1685C22semidirect
83. #1683C22semidirect
84. #1683C22semidirect
85. #1679C22semidirect
86. #1677C22semidirect
87. #1675C22semidirect
88. #1671C22semidirect
89. #1669C22semidirect
90. #1665C22semidirect
91. #1574C22semidirect
92. #1571C22semidirect
93. #1571C22semidirect
94. #1570C22semidirect
95. #1570C22semidirect
96. #1569C22semidirect
97. #1561C22semidirect
98. #1560C22semidirect
99. #1559C22semidirect
100. #1559C22semidirect
101. #1557C22semidirect
102. #1554C22semidirect
103. #1549C22semidirect
104. #1549C22semidirect
105. #1548C22semidirect
106. #1548C22semidirect
107. #1542C22semidirect
108. #1542C22semidirect
109. #1540C22semidirect
110. #1540C22semidirect
168. #500C23semidirect
169. #498C23semidirect
170. #494C23semidirect
171. #492C23semidirect
172. #487C23semidirect
173. #487C23semidirect
174. #487C23semidirect
175. #486C23semidirect
300. #335C23semidirect
301. #335C23semidirect
302. #334C23semidirect
303. #334C23semidirect
304. #333C23semidirect
305. #333C23semidirect
306. #333C23semidirect
307. #333C23semidirect
308. #332C23semidirect
309. #332C23semidirect
310. #332C23semidirect
311. #332C23semidirect
312. #332C23semidirect
313. #332C23semidirect
314. #331C23semidirect
315. #331C23semidirect

Maximal subgroups

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

subgroupindex
#609662
#605582
C2×#30772
#602302
#194662
#194602
#194292
#194272
#194232
#194212
#193932
#193912
#193872
#193852
#193072
#193052
#178202
#177472
#177372