Finite Group Databasebeta

← #6345199

Subgroups — #6345199

Order 512.

1599 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60953C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3#60204C211yesmaximal, characteristic, complemented
4#17986C212yesmaximal, complemented
5#17985C212yesmaximal, complemented
6#17965C212yesmaximal, complemented
7#17964C212yesmaximal, complemented
8#17941C212yesmaximal, complemented
9#17940C212yesmaximal, complemented
10#17937C214yesmaximal, complemented
11#17913C212yesmaximal, complemented
12#17912C212yesmaximal, complemented
13#17904C214yesmaximal, complemented
14#17823C211yesmaximal, characteristic, complemented
15#17499C211yesmaximal, characteristic, complemented
16#17493C211yesmaximal, characteristic, complemented
17#17323C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19#3444C2211yescharacteristic
20#3252C412yes—
21#3251C412yes—
22#3240C412yes—
23#3237C411yescharacteristic
24#3235C411yescharacteristic
25#3219C412yes—
26#3216C411yescharacteristic
27#3214C411yescharacteristic
28#3197C414yes—
29#3172C2212yes—
30#3171C2212yes—
31#3107C2212yes—
32#3106C2212yes—
33#3102C2214yes—
34#2966—21no—
35#2966—21no—
36#2966—21no—
37#2966—21no—
38#2966C2212yes—
39#2966C2212yes—
40#2966C2212yes—
41#2966C2212yes—
42#2965—21no—
43#2965—21no—
44#2965C2212yes—
45#2965C2212yes—
46C8×#41—21no—
47C8×#41—21no—
48C8×#41C2212yes—
49C8×#41C2212yes—
50#2960C2211yescharacteristic
51#2960C2211yescharacteristic
52#2960C2211yescharacteristic
53#2960C2211yescharacteristic
54#2931C2211yescharacteristic
55#2931C2211yescharacteristic
56#2931C2211yescharacteristic
57#2931C2211yescharacteristic
58#2929—21no—
59#2929—21no—
60#2929—21no—
61#2929—21no—
62#2922—21no—
63#2922—21no—
64#2920C2211yescharacteristic
65#2920C2211yescharacteristic
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68C4×#131—21no—
69C4×#131—21no—
70C22×C4×C8C2211yescharacteristic
71#1594C2214yescomplemented
72#1593C2214yescomplemented
73#1592C2214yescomplemented
74#1592C2214yescomplemented
75#1588C2214yescomplemented
76#1587C2214yescomplemented
77#1586C2214yescomplemented
78#1585C2214yescomplemented
79#1584C2214yescomplemented
80#1583C2214yescomplemented
81#1582C2214yescomplemented
82#1581C2214yescomplemented
83C8×Q16C2214yescomplemented
84C8×SD16C2214yescomplemented
85C8×SD16C2214yescomplemented
86C8×D8C2214yescomplemented
87#1574C2212yes—
88#1574C2212yes—
89#1572C2214yes—
90#1569C2212yes—
91#1569C2212yes—
92#1497C2212yes—
93#1496C2212yes—
94#1495C2212yes—
95#1495C2212yes—
96#1489C2212yes—
97#1489C2212yes—
98#1488C2214yes—
99#1485C2212yes—
100#1484C2212yes—
101#1482C2214yes—
102#1452C2212yes—
103#1451C2212yes—
104#1451C2212yes—
105#1450C2212yes—
106C8×M16C2212yes—
107C8×M16C2212yes—
108C2×#131—21no—
109C2×#131—21no—
110C2×#131—21no—
111C2×#131—21no—
112C23×C8D411yescharacteristic
113C23×C8D411yescharacteristic
114#533C2×C411yescharacteristic
115#533C2×C411yescharacteristic
116#533C2×C411yescharacteristic
117#533C2×C411yescharacteristic
118#533C2311yescharacteristic
119#533C2311yescharacteristic
120#532C2×C411yescharacteristic
121#532C2×C411yescharacteristic
122#532C2×C411yescharacteristic
123#532C2×C411yescharacteristic
124#532C2311yescharacteristic
125#532C2311yescharacteristic
126#529—21no—
127#529—21no—
128#529—21no—
129#529—21no—
130#529—21no—
131#529—21no—
132#529—21no—
133#529—21no—
134#529C2×C412yes—
135#529C2×C412yes—
136#529C2312yes—
137#529C2312yes—
138#525—21no—
139#525—21no—
140#525—21no—
141#525—21no—
142#525C2×C412yes—
143#525C2×C412yes—
144C4×#41—21no—
145C4×#41—21no—
146C4×#41—21no—
147C4×#41—21no—
148C4×#41C2312yes—
149C4×#41C2312yes—
150C22×C42C2311yescharacteristic
151#501C2×C412yes—
152#501C2×C412yes—
153#497C2×C412yes—
154#496C2×C412yes—
155#491C2×C412yes—
156#490C2×C412yes—
157#489C2×C412yes—
158#489C2×C412yes—
159#485C2×C414yes—
160#485C2×C414yes—
161#482C2×C414yes—
162#482C2×C414yes—
163#479C2×C414yes—
164#478C2×C414yes—
165#477C2×C412yes—
166#476C2×C412yes—
167#475C2×C412yes—
168#474C2×C412yes—
169#470C2×C414yes—
170#469C2×C414yes—
171#468C2×C414yes—
172#468C2×C414yes—
173#464C2×C414yes—
174#463C2×C414yes—
175#462C2×C412yes—
176#461C2×C412yes—
177#460C2×C412yes—
178#459C2×C412yes—
179#452C2×C414yes—
180#452C2×C414yes—
181#449C2×C414yes—
182#449C2×C414yes—
183#446—21no—
184#446—21no—
185#446—21no—
186#446—21no—
187#446C2312yes—
188#446C2312yes—
189#446C2312yes—
190#446C2312yes—
191C8×Q8—21no—
192C8×Q8—21no—
193C8×Q8—21no—
194C8×Q8—21no—
195C8×Q8C2312yes—
196C8×Q8C2312yes—
197C8×Q8C2312yes—
198C8×Q8C2312yes—
199C4×Q16C2314yes—
200C4×SD16C2314yes—
201C4×SD16C2314yes—
202C4×D8C2314yes—
203#436—21no—
204#436—21no—
205#436—21no—
206#436—21no—
207#436C2312yes—
208#436C2312yes—
209#436C2312yes—
210#436C2312yes—
211#435—22no—
212#435—22no—
213#435—22no—
214#435—22no—
215#435—22no—
216#435—22no—
217#435—22no—
218#435—22no—
219C8×D4—22no—
220C8×D4—22no—
221C8×D4—22no—
222C8×D4—22no—
223C8×D4—22no—
224C8×D4—22no—
225C8×D4—22no—
226C8×D4—22no—
227C8×D4—21no—
228C8×D4—21no—
229C8×D4—21no—
230C8×D4—21no—
231C8×D4C2312yes—
232C8×D4C2312yes—
233C8×D4C2312yes—
234C8×D4C2312yes—
235#433—22no—
236#433—22no—
237#433—22no—
238#433—22no—
239#432—21no—
240#432—21no—
241#432—21no—
242#432—21no—
243#432C2×C411yescharacteristic
244#432C2×C411yescharacteristic
245#432C2×C412yes—
246#432C2312yes—
247#432C2312yes—
248#431—21no—
249#431—21no—
250#431—22no—
251#431—22no—
252#431—22no—
253#431—22no—
254#431C2312yes—
255#431C2312yes—
256#431C2312yes—
257#431C2312yes—
258#431C2312yes—
259#431C2312yes—
260#424—21no—
261#424—21no—
262#424—21no—
263#424—21no—
264#423—21no—
265#423C2×C412yes—
266#423C2311yescharacteristic
267#423C2311yescharacteristic
268#423C2311yescharacteristic
269#423C2311yescharacteristic
270#408—21no—
271#408—21no—
272#408—21no—
273#408—21no—
274#407—21no—
275#407—21no—
276#407—21no—
277#407C2×C412yes—
278#405—21no—
279#405—21no—
280#405—21no—
281#405—21no—
282#405—22no—
283#405—22no—
284#405—22no—
285#405—22no—
286C4×M16—21no—
287C4×M16—21no—
288C4×M16—22no—
289C4×M16—22no—
290C4×M16C2312yes—
291C4×M16C2312yes—
292C2×C4×C8—22no—
293C2×C4×C8—22no—
294C2×C4×C8D411yescharacteristic
295C2×C4×C8D411yescharacteristic
296C2×C4×C8D411yescharacteristic
297C2×C4×C8D411yescharacteristic
298C2×C4×C8D411yescharacteristic
299C2×C4×C8D411yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#335C2314yes—
307#335C2314yes—
308#334C2314yes—
309#334C2314yes—
310Q8⋊C8C2314yes—
311Q8⋊C8C2314yes—
312Q8⋊C8C2314yes—
313Q8⋊C8C2314yes—
314D4⋊C8C2314yes—
315D4⋊C8C2314yes—
316D4⋊C8C2314yes—
317D4⋊C8C2314yes—
318#322C2314yes—
319#322C2314yes—
320#322C2314yes—
321C82C2314yes—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41C22×C412yes—
327C2×#41C22×C412yes—
328C23×C4C22×C411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4#4111yescharacteristic
331C2×Q16C22×C414yes—
332C2×SD16C22×C414yes—
333C2×SD16C22×C414yes—
334C2×D8C22×C414yes—
335#131—44no—
336#131—44no—
337#131—44no—
338#131—44no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16C22×C414yes—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8C2×D411yescharacteristic
356C22×C8C2×D411yescharacteristic
357C22×C8C2×D411yescharacteristic
358C22×C8C2×D411yescharacteristic
359C22×C8C2×D411yescharacteristic
360C22×C8C2×D411yescharacteristic
361C22×C8C2×D411yescharacteristic
362C22×C8C2×D411yescharacteristic
363C22×C8C2×D411yescharacteristic
364C22×C8C2×D411yescharacteristic
365C22×C8C2×D411yescharacteristic
366C22×C8C2×D411yescharacteristic
367C4⋊Q8C22×C411yescharacteristic
368C4⋊Q8C22×C411yescharacteristic
369C4⋊Q8C22×C411yescharacteristic
370C4⋊Q8C22×C411yescharacteristic
371C4⋊Q8C22×C411yescharacteristic
372C4⋊Q8C22×C411yescharacteristic
373#127C22×C411yescharacteristic
374#127C22×C411yescharacteristic
375#126—22no—
376#126—22no—
377#126—22no—
378#126—22no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125C22×C412yes—
384#125C22×C412yes—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124C22×C412yes—
390#124C22×C412yes—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8C22×C412yes—
406C22⋊Q8C22×C412yes—
407C22⋊Q8C22×C412yes—
408C22⋊Q8C22×C412yes—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121C22×C412yes—
418#121C22×C412yes—
419#121C22×C412yes—
420#121C22×C412yes—
421#120—22no—
422#120—22no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8C22×C412yes—
432C4×Q8C22×C412yes—
433C4×Q8C2412yes—
434C4×Q8C2412yes—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4C22×C412yes—
456C4×D4C22×C412yes—
457C4×D4C2412yes—
458C4×D4C2412yes—
459#117—21no—
460#117—21no—
461#117—21no—
462#117—21no—
463#117—22no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117C22×C412yes—
470#117C22×C412yes—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42C22×C411yescharacteristic
474C2×C42C22×C411yescharacteristic
475C2×C42C22×C411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42#4111yescharacteristic
480C2×C42#4111yescharacteristic
481C2×C42#4111yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107C22×C414yes—
486#107C22×C414yes—
487#106C22×C414yes—
488#106C22×C414yes—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8—22no—
497C4⋊C8—21no—
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8C22×C412yes—
504C4⋊C8C22×C412yes—
505C4⋊C8C22×C414yes—
506C4⋊C8C2412yes—
507C4⋊C8C2412yes—
508C4⋊C8C2412yes—
509C4⋊C8C2412yes—
510#103C22×C414yes—
511#103C22×C414yes—
512#103C22×C414yes—
513#103C22×C414yes—
514#102C22×C414yes—
515#102C22×C414yes—
516#102C22×C414yes—
517#102C22×C414yes—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8C22×C412yes—
533C22⋊C8C22×C414yes—
534C22⋊C8C22×C412yes—
535#97—22no—
536#97—22no—
537#97—22no—
538#97—22no—
539#97—22no—
540#97—22no—
541#97—22no—
542#97C22×C412yes—
543#97C22×C412yes—
544C4×C8—22no—
545C4×C8—22no—
546C4×C8—22no—
547C4×C8—22no—
548C4×C8—22no—
549C4×C8—22no—
550C4×C8C2×D411yescharacteristic
551C4×C8C2×D411yescharacteristic
552C4×C8C2×D411yescharacteristic
553C4×C8C2×D411yescharacteristic
554C4×C8C2×D411yescharacteristic
555C4×C8C2×D411yescharacteristic
556C4×C8C2×D411yescharacteristic
557C4×C8C2×D411yescharacteristic
558C4×C8C2×D411yescharacteristic
559C4×C8C2×D411yescharacteristic
560C4×C8C2×D411yescharacteristic
561C4×C8C2×D411yescharacteristic
562C4×C8C2414yes—
563C4×C8C2414yes—
564C4×C8C2411yescharacteristic
565C4×C8C2411yescharacteristic
566C4×C8C2411yescharacteristic
567C4×C8C2411yescharacteristic
568C24C4×D411yescharacteristic
569#41—42no—
570#41—44no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8C23×C412yes—
583C2×Q8C23×C412yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4C23×C412yes—
595C2×D4C23×C412yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C4×D411yescharacteristic
607C22×C4C4×D411yescharacteristic
608C22×C4C4×D411yescharacteristic
609C22×C4C4×D411yescharacteristic
610C22×C4C4×D411yescharacteristic
611C22×C4C4×D411yescharacteristic
612C22×C4C4×D411yescharacteristic
613C22×C4C4×D411yescharacteristic
614C22×C4C4×D411yescharacteristic
615C22×C4C23×C411yescharacteristic
616C22×C4C23×C411yescharacteristic
617C22×C4C23×C411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624Q16—44no—
625SD16—44no—
626SD16—44no—
627D8—44no—
628M16—44no—
629M16—44no—
630M16—44no—
631M16—44no—
632M16—44no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637M16—44no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—24no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—44no—
656C2×C8—44no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8C23×C414yes—
660C2×C8C23×C414yes—
661C2×C8C22×D411yescharacteristic
662C2×C8C22×D411yescharacteristic
663C2×C8C22×D411yescharacteristic
664C2×C8C22×D411yescharacteristic
665C2×C8C22×D411yescharacteristic
666C2×C8C22×D411yescharacteristic
667C2×C8C22×D411yescharacteristic
668C2×C8C22×D411yescharacteristic
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4C23×C412yes—
690C4⋊C4C23×C412yes—
691C4⋊C4C23×C412yes—
692C4⋊C4C23×C412yes—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42C4×D411yescharacteristic
718C42C4×D411yescharacteristic
719C42C4×D411yescharacteristic
720C42C4×D411yescharacteristic
721C42C4×D411yescharacteristic
722C42C4×D411yescharacteristic
723C42C23×C411yescharacteristic
724C42C23×C411yescharacteristic
725C42C23×C411yescharacteristic
726C42C22×D411yescharacteristic
727C42C22×D411yescharacteristic
728C42C22×D411yescharacteristic
729C42C2×#4111yescharacteristic
730C42C2×#4111yescharacteristic
731C42C2×#4111yescharacteristic
732C42C2511yescharacteristic
733C23—22no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23C2×C4×D411yescharacteristic
739C23C2×C4×D411yescharacteristic
740C23C2×C4×D411yescharacteristic
741Q8—22no—
742Q8—24no—
743Q8—22no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748D4—22no—
749D4—24no—
750D4—22no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—44no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—44no—
759D4—44no—
760D4—42no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4C2×C4×D411yescharacteristic
797C2×C4C2×C4×D411yescharacteristic
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C2×C4×D411yescharacteristic
800C2×C4C2×C4×D411yescharacteristic
801C2×C4C2×C4×D411yescharacteristic
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C2×C4×D411yescharacteristic
804C2×C4C2×C4×D411yescharacteristic
805C2×C4C24×C411yescharacteristic
806C2×C4C23×D411yescharacteristic
807C2×C4C22×#4111yescharacteristic
808C8—24no—
809C8—24no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—44no—
817C8—42no—
818C8—42no—
819C8—42no—
820C8—42no—
821C8#57512yes—
822C8#57512yes—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—44no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22C22×C4×D411yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4#295512yes—
856C4#357312yes—
857C4C2×#57511yescharacteristic
858C4C2×#57511yescharacteristic
859C2—41no—
860C2—41no—
861C2—41no—
862C2—82no—
863C2—82no—
864C2#6014011yescharacteristic
865C2C4×#57511yescharacteristic
866C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C8C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60953C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C22×C4×C8 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. #60204C2semidirect
4. #17986C2semidirect
5. #17985C2semidirect
6. #17965C2semidirect
7. #17964C2semidirect
8. #17941C2semidirect
9. #17940C2semidirect
10. #17937C2semidirect
11. #17913C2semidirect
12. #17912C2semidirect
13. #17904C2semidirect
14. #17823C2semidirect
15. #17499C2semidirect
16. #17493C2semidirect
17. #17323C2semidirect
71. #1594C22semidirect
72. #1593C22semidirect
73. #1592C22semidirect
74. #1592C22semidirect
75. #1588C22semidirect
76. #1587C22semidirect
77. #1586C22semidirect
78. #1585C22semidirect
79. #1584C22semidirect
80. #1583C22semidirect
81. #1582C22semidirect
82. #1581C22semidirect
83. C8×Q16C22semidirect
84. C8×SD16C22semidirect
85. C8×SD16C22semidirect
86. C8×D8C22semidirect

Maximal subgroups

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

subgroupindex
#609532
#602042
#179862
#179852
#179652
#179642
#179412
#179402
#179372
#179132
#179122
#179042
#178232
#174992
#174932
#173232