Finite Group Databasebeta

← #6395798

Subgroups — #6395798

Order 512.

1841 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60782C211yesmaximal, characteristic
2#60237C211yesmaximal, characteristic, complemented
3#60211C211yesmaximal, characteristic, complemented
4#23235C212yesmaximal, complemented
5#23234C212yesmaximal, complemented
6#23180C212yesmaximal, complemented
7#23179C212yesmaximal, complemented
8#22889C214yesmaximal, complemented
9#22887C214yesmaximal, complemented
10#22167C214yesmaximal, complemented
11#21900C211yesmaximal, characteristic, complemented
12#21519C214yesmaximal, complemented
13#21370C211yesmaximal, characteristic, complemented
14#21252C211yesmaximal, characteristic, complemented
15#20537C211yesmaximal, characteristic, complemented
16#3444C2211yescharacteristic
17C2×#532C2211yescharacteristic
18#3212C414yescomplemented
19#3211C414yescomplemented
20#3210C411yescharacteristic, complemented
21#3210C411yescharacteristic, complemented
22#3209C411yescharacteristic, complemented
23#3208C411yescharacteristic, complemented
24#3207C411yescharacteristic, complemented
25#3207C411yescharacteristic, complemented
26#3206C411yescharacteristic, complemented
27#3205C411yescharacteristic, complemented
28#3147C2211yescharacteristic
29#3147C2211yescharacteristic
30#3131C2211yescharacteristic
31#3131C2211yescharacteristic
32#3035C2214yes—
33#3002C2214yes—
34#2981—22no—
35#2980—22no—
36#2974—21no—
37#2974—21no—
38#2973—22no—
39#2971—21no—
40#2970—22no—
41#2970—21no—
42#2967—22no—
43#2966—22no—
44#2962C2212yescomplemented
45C2×#444C2214yescomplemented
46C2×#443C2214yescomplemented
47#2935C2212yes—
48#2935C2212yes—
49#2935C2212yescomplemented
50#2933C2214yes—
51#2932C2214yes—
52#2923C2212yescomplemented
53#2920C2211yescharacteristic
54C2×#432C2211yescharacteristic
55C2×#431C2211yescharacteristic
56C2×#421C2214yes—
57#2880C2212yes—
58#2880C2212yes—
59#2875C2212yescomplemented
60C2×C4×M16C2211yescharacteristic
61#2285C2211yescharacteristic
62#1986C2212yescomplemented
63#1980C2212yes—
64#1980C2212yes—
65#1980C2212yes—
66#1980C2212yes—
67#1980C2212yescomplemented
68#1975C2214yescomplemented
69#1974C2214yescomplemented
70#1950C2212yescomplemented
71#1950C2212yescomplemented
72#1938C2214yescomplemented
73#1937C2214yescomplemented
74#1929C2214yescomplemented
75#1929C2214yescomplemented
76#1897C2212yes—
77#1897C2212yes—
78#1876C2214yescomplemented
79#1876C2214yescomplemented
80#1876C2214yescomplemented
81#1876C2214yescomplemented
82#1866C2214yescomplemented
83#1866C2214yescomplemented
84#1855C2212yes—
85#1855C2212yes—
86#1806C2214yescomplemented
87C4×#108C2212yescomplemented
88C4×#108C2212yescomplemented
89#1771C2214yescomplemented
90#1770C2212yescomplemented
91C8×C4⋊C4C2212yescomplemented
92#1765C2214yescomplemented
93#1764C2214yescomplemented
94#1750C2214yes—
95C22×#41C2312yes—
96C2×#135C2314yes—
97C2×#135C2314yes—
98C2×#131C2314yes—
99C2×#131C2314yes—
100C2×#131C2314yes—
101C22×M16C2312yes—
102#533C2×C411yescharacteristic
103#533C2×C411yescharacteristic
104#533C2311yescharacteristic
105#532—21no—
106#532—21no—
107#532—21no—
108#532—21no—
109#532C2×C411yescharacteristic
110#532C2×C411yescharacteristic
111#532C2×C412yes—
112#532C2×C411yescharacteristic
113#532C2×C411yescharacteristic
114#532C2311yescharacteristic
115#532C2311yescharacteristic
116#532C2311yescharacteristic
117#532C2312yes—
118C2×C4⋊Q8C2×C411yescharacteristic
119C2×#127C2×C411yescharacteristic
120#529—21no—
121#529—21no—
122#529—21no—
123#529—21no—
124#529C2×C412yes—
125#529C2×C412yes—
126C2×#124C2×C412yes—
127#525—21no—
128#525—21no—
129#525C2312yes—
130C2×#121—21no—
131C2×#121—21no—
132C4×#41—21no—
133C4×#41—21no—
134C4×#41C2312yes—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×#117C2312yes—
138C22×C42C2311yescharacteristic
139#495C2×C414yes—
140#495C2×C414yes—
141#494C2×C411yescharacteristic
142#494C2×C411yescharacteristic
143#493C2×C411yescharacteristic
144#493C2×C411yescharacteristic
145#492C2×C411yescharacteristic
146#492C2×C411yescharacteristic
147#492C2×C411yescharacteristic
148#492C2×C411yescharacteristic
149#488C2×C414yes—
150#488C2×C414yes—
151#487C2×C411yescharacteristic
152#487C2×C411yescharacteristic
153#487C2×C411yescharacteristic
154#487C2×C411yescharacteristic
155#486C2×C411yescharacteristic
156#486C2×C411yescharacteristic
157#486C2×C411yescharacteristic
158#486C2×C411yescharacteristic
159#464C2×C414yes—
160#464C2×C414yes—
161#463C2×C414yes—
162#463C2×C414yes—
163#462C2×C414yes—
164#461C2×C414yes—
165#460C2×C414yes—
166#459C2×C414yes—
167#452C2×C414yes—
168#452C2×C414yes—
169#451C2×C414yes—
170#450C2×C414yes—
171#449C2×C414yes—
172#449C2×C414yes—
173#448C2×C414yes—
174#447C2×C414yes—
175#446—22no—
176#446—24no—
177C8×Q8—22no—
178#444—48no—
179#443—48no—
180#436—22no—
181#436—22no—
182#436—22no—
183#436—24no—
184#435—24no—
185#435—24no—
186#435—24no—
187#435—24no—
188#435—24no—
189#435—24no—
190#435—24no—
191#435—24no—
192#435—24no—
193C8×D4—22no—
194C8×D4—22no—
195C8×D4—22no—
196C8×D4—24no—
197#433—24no—
198#432—21no—
199#432—21no—
200#432—22no—
201#432—22no—
202#432D412yes—
203#432D412yes—
204#432D411yescharacteristic
205#432D412yes—
206#432D411yescharacteristic
207#431—21no—
208#431—21no—
209#431C2×C411yescharacteristic
210#431C2×C411yescharacteristic
211#431C2×C411yescharacteristic
212#431C2×C411yescharacteristic
213#431C2×C412yes—
214#431C2×C412yes—
215C2×#108C2312yes—
216C2×#108C2312yes—
217C2×#108C2312yes—
218C2×#108C2312yes—
219#424C2314yes—
220#423C2312yes—
221C2×C4⋊C8C2312yes—
222C2×C4⋊C8C2312yes—
223#421—48no—
224C2×#104C2314yes—
225C2×#104C2314yes—
226C2×#104C2314yes—
227C2×#104C2314yes—
228C2×#104C2314yes—
229C2×#104C2314yes—
230#416C2314yes—
231#416C2314yes—
232#408—24no—
233#408—24no—
234#408C2314yes—
235#408C2314yes—
236#408C2314yes—
237#407—22no—
238#407—22no—
239#407C2311yescharacteristic
240#407C2311yescharacteristic
241C2×C22⋊C8—22no—
242C2×C22⋊C8—22no—
243C2×C22⋊C8C2312yes—
244C2×C22⋊C8C2312yes—
245#405—24no—
246#405C2314yes—
247C4×M16—21no—
248C4×M16—21no—
249C4×M16—22no—
250C4×M16C2311yescharacteristic
251C4×M16C2311yescharacteristic
252C4×M16C2312yes—
253C4×M16C2312yes—
254C2×#97—21no—
255C2×#97—22no—
256C2×#97C2314yes—
257C2×#97C2312yes—
258C2×C4×C8—21no—
259C2×C4×C8C2314yes—
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262#384—21no—
263#382—21no—
264#380—21no—
265#380—21no—
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268#341C2312yes—
269#341C2312yes—
270#341C2312yes—
271#341C2312yes—
272#339C2314yes—
273#339C2314yes—
274#336C2314yes—
275#336C2314yes—
276C2×#41—21no—
277C2×#41—21no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—44no—
281C2×#41—44no—
282C2×#41C22×C412yes—
283C2×#41C22×C412yes—
284C2×#41C2412yes—
285C2×#41C2412yes—
286C2×#41C2412yes—
287C22×Q8C22×C412yes—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C22×C412yes—
292C23×C4—22no—
293C23×C4#4111yescharacteristic
294C23×C4#4111yescharacteristic
295C23×C4C2411yescharacteristic
296#135—44no—
297#135—44no—
298#135—44no—
299#135—44no—
300C2×Q16C22×C414yes—
301C2×Q16C22×C414yes—
302C2×SD16C22×C414yes—
303C2×SD16C22×C414yes—
304C2×SD16C22×C414yes—
305C2×SD16C22×C414yes—
306C2×D8C22×C414yes—
307C2×D8C22×C414yes—
308#131—28no—
309#131—44no—
310#131—44no—
311#131—44no—
312#131—44no—
313#131—44no—
314C2×M16—22no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—42no—
320C2×M16C2412yes—
321C2×M16C2412yes—
322C2×M16C2412yes—
323C2×M16C2412yes—
324C22×C8—22no—
325C22×C8—24no—
326C22×C8—24no—
327C22×C8—24no—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2414yes—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8C22×C412yes—
334C4⋊Q8C22×C411yescharacteristic
335C4⋊Q8C22×C411yescharacteristic
336C4⋊Q8C22×C411yescharacteristic
337C4⋊Q8C22×C411yescharacteristic
338C4⋊Q8C22×C411yescharacteristic
339#127—21no—
340#127—21no—
341#127C22×C412yes—
342#127C22×C411yescharacteristic
343#127C22×C411yescharacteristic
344#127C22×C411yescharacteristic
345#126—22no—
346#126—22no—
347#125—21no—
348#125—21no—
349#125C22×C412yes—
350#124—22no—
351#124—22no—
352#124—21no—
353#124—21no—
354#124C22×C412yes—
355#124C22×C412yes—
356#124C22×C412yes—
357#124C22×C412yes—
358#124C22×C412yes—
359#123—22no—
360#123—22no—
361#123—22no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8C22×C412yes—
367C22⋊Q8C22×C412yes—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—22no—
373#121—22no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121—21no—
378#121—22no—
379#121—21no—
380#121—21no—
381#121—22no—
382#121—21no—
383#121—21no—
384#121C22×C412yes—
385#121C22×C412yes—
386#120—22no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C22×C412yes—
392C4×Q8C22×C412yes—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C22×C412yes—
416C4×D4C22×C412yes—
417#117—21no—
418#117—21no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117—44no—
423#117C2412yes—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C42—22no—
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C411yescharacteristic
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42#4111yescharacteristic
442C2×C42#4111yescharacteristic
443C2×C42C2414yes—
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446#108—24no—
447#108—24no—
448#108—42no—
449#108—42no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454C4⋊C8C22×C412yes—
455C4⋊C8C22×C412yes—
456C4⋊C8C22×C412yes—
457C4⋊C8C22×C412yes—
458C4⋊C8C2×D412yes—
459C4⋊C8C2×D412yes—
460C4⋊C8C2×D414yes—
461#104—28no—
462#104—28no—
463#104—44no—
464#104—44no—
465#104—44no—
466#104—44no—
467#103C22×C414yes—
468#103C22×C414yes—
469#103C22×C414yes—
470#103C22×C414yes—
471#102C22×C414yes—
472#102C22×C414yes—
473#102C22×C414yes—
474#102C22×C414yes—
475C22⋊C8—21no—
476C22⋊C8—21no—
477C22⋊C8—21no—
478C22⋊C8—21no—
479C22⋊C8—24no—
480C22⋊C8—24no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C22⋊C8C22×C412yes—
486C22⋊C8C22×C412yes—
487C22⋊C8C22×C412yes—
488C22⋊C8C22×C412yes—
489C22⋊C8C2×D412yes—
490C22⋊C8C2×D412yes—
491C22⋊C8C2×D414yes—
492#97—24no—
493#97—21no—
494#97—21no—
495#97—22no—
496#97—22no—
497#97—44no—
498#97C2×D412yes—
499#97C2×D412yes—
500#97C2×D414yes—
501C4×C8—24no—
502C4×C8—21no—
503C4×C8—21no—
504C4×C8—22no—
505C4×C8—22no—
506C4×C8—44no—
507C4×C8C22×C411yescharacteristic
508C4×C8C22×C411yescharacteristic
509C4×C8C22×C411yescharacteristic
510C4×C8C22×C411yescharacteristic
511C4×C8C22×C412yes—
512C4×C8C22×C412yes—
513#95—22no—
514#95—22no—
515C24—22no—
516C24C2×#4111yescharacteristic
517#41—24no—
518#41—24no—
519#41—24no—
520#41—24no—
521#41—24no—
522#41—24no—
523#41—44no—
524#41—44no—
525#41—84no—
526#41—82no—
527#41—82no—
528#41—82no—
529#41—82no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—44no—
534C2×Q8C23×C412yes—
535C2×Q8C23×C412yes—
536C2×Q8C23×C412yes—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—44no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4C23×C412yes—
559C2×D4C23×C412yes—
560C2×D4C23×C412yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—84no—
574C22×C4—81no—
575C22×C4C4×D411yescharacteristic
576C22×C4C4×D411yescharacteristic
577C22×C4C4×D411yescharacteristic
578C22×C4C4×D411yescharacteristic
579C22×C4C4×D411yescharacteristic
580C22×C4C4×D411yescharacteristic
581C22×C4C4×D411yescharacteristic
582C22×C4C4×D411yescharacteristic
583C22×C4C23×C411yescharacteristic
584C22×C4C23×C411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2511yescharacteristic
593Q16—44no—
594Q16—44no—
595SD16—44no—
596SD16—44no—
597SD16—44no—
598SD16—44no—
599D8—44no—
600D8—44no—
601M16—22no—
602M16—22no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—48no—
609M16—44no—
610M16—84no—
611M16—84no—
612M16H(5,𝔽2)14yes—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—24no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—24no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—48no—
624C2×C8—44no—
625C2×C8—84no—
626C2×C8—84no—
627C2×C8C23×C412yes—
628C2×C8C23×C412yes—
629C2×C8C23×C412yes—
630C2×C8C23×C412yes—
631C2×C8C22×D414yes—
632C2×C8C22×D414yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—44no—
650C4⋊C4—82no—
651C4⋊C4—82no—
652C4⋊C4C23×C412yes—
653C4⋊C4C23×C412yes—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—82no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—24no—
676C42—24no—
677C42C4×D411yescharacteristic
678C42C4×D411yescharacteristic
679C42C4×D411yescharacteristic
680C42C4×D411yescharacteristic
681C42C4×D411yescharacteristic
682C42C4×D411yescharacteristic
683C42C4×D411yescharacteristic
684C42C4×D411yescharacteristic
685C42C23×C411yescharacteristic
686C42C23×C411yescharacteristic
687C42C23×C411yescharacteristic
688C42C23×C411yescharacteristic
689C42C22×D411yescharacteristic
690C42C22×D411yescharacteristic
691C42C22×D411yescharacteristic
692C42C22×D411yescharacteristic
693C23—21no—
694C23—21no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—44no—
701C23—82no—
702C23—82no—
703C23C2×C4×D411yescharacteristic
704C23C2×C4×D411yescharacteristic
705C23C22×#4111yescharacteristic
706Q8—24no—
707Q8—24no—
708Q8—24no—
709Q8—42no—
710Q8—82no—
711Q8—81no—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—44no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—82no—
732D4—82no—
733D4—82no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—82no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—82no—
767C2×C4—82no—
768C2×C4C2×C4×D411yescharacteristic
769C2×C4C2×C4×D411yescharacteristic
770C2×C4C2×C4×D411yescharacteristic
771C2×C4C2×C4×D411yescharacteristic
772C2×C4C2×C4×D411yescharacteristic
773C2×C4C2×C4×D411yescharacteristic
774C2×C4C2×C4×D411yescharacteristic
775C2×C4C2×C4×D411yescharacteristic
776C2×C4C2×C4×D411yescharacteristic
777C2×C4C2×C4×D411yescharacteristic
778C2×C4C24×C411yescharacteristic
779C2×C4C23×D411yescharacteristic
780C2×C4C2×H(5,𝔽2)12yes—
781C2×C4#58512yes—
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—24no—
787C8—24no—
788C8—24no—
789C8—42no—
790C8—42no—
791C8—42no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—81no—
810C22—81no—
811C22—164no—
812C22C22×C4×D411yescharacteristic
813C22#350811yescharacteristic
814C22#351011yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—84no—
830C4#295712yes—
831C4C4×H(5,𝔽2)12yes—
832C4#348812yes—
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2#3426911yescharacteristic
841C2C2×#295711yescharacteristic
842C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#60782C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#432 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60237C2semidirect
3. #60211C2semidirect
4. #23235C2semidirect
5. #23234C2semidirect
6. #23180C2semidirect
7. #23179C2semidirect
8. #22889C2semidirect
9. #22887C2semidirect
10. #22167C2semidirect
11. #21900C2semidirect
12. #21519C2semidirect
13. #21370C2semidirect
14. #21252C2semidirect
15. #20537C2semidirect
18. #3212C4semidirect
19. #3211C4semidirect
20. #3210C4semidirect
21. #3210C4semidirect
22. #3209C4semidirect
23. #3208C4semidirect
24. #3207C4semidirect
25. #3207C4semidirect
26. #3206C4semidirect
27. #3205C4semidirect
44. #2962C22semidirect
45. C2×#444C22semidirect
46. C2×#443C22semidirect
49. #2935C22semidirect
52. #2923C22semidirect
59. #2875C22semidirect
62. #1986C22semidirect
67. #1980C22semidirect
68. #1975C22semidirect
69. #1974C22semidirect
70. #1950C22semidirect
71. #1950C22semidirect
72. #1938C22semidirect
73. #1937C22semidirect
74. #1929C22semidirect
75. #1929C22semidirect
78. #1876C22semidirect
79. #1876C22semidirect
80. #1876C22semidirect
81. #1876C22semidirect
82. #1866C22semidirect
83. #1866C22semidirect
86. #1806C22semidirect
87. C4×#108C22semidirect
88. C4×#108C22semidirect
89. #1771C22semidirect
90. #1770C22semidirect
91. C8×C4⋊C4C22semidirect
92. #1765C22semidirect
93. #1764C22semidirect

Maximal subgroups

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

subgroupindex
#607822
#602372
#602112
#232352
#232342
#231802
#231792
#228892
#228872
#221672
#219002
#215192
#213702
#212522
#205372