Finite Group Databasebeta

← #6395315

Subgroups — #6395315

Order 512.

1736 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60907C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic, complemented
3#60210C211yesmaximal, characteristic, complemented
4#23148C214yesmaximal, complemented
5#23114C212yesmaximal, complemented
6#23081C212yesmaximal, complemented
7#23020C214yesmaximal, complemented
8#23015C212yesmaximal, complemented
9#22982C212yesmaximal, complemented
10#22166C212yesmaximal, complemented
11#22130C212yesmaximal, complemented
12#21856C211yesmaximal, characteristic, complemented
13#21628C212yesmaximal, complemented
14#21517C212yesmaximal, complemented
15#21382C211yesmaximal, characteristic, complemented
16#21177C211yesmaximal, characteristic, complemented
17#20550C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19#3444C2211yescharacteristic
20#3256C414yescomplemented
21#3255C411yescharacteristic, complemented
22#3254C411yescharacteristic, complemented
23#3254C411yescharacteristic, complemented
24#3253C411yescharacteristic, complemented
25#3252C412yescomplemented
26#3252C412yescomplemented
27#3251C412yescomplemented
28#3251C412yescomplemented
29#3076C2212yes—
30#3076C2212yes—
31#3054C2214yes—
32#3035C2212yes—
33#3035C2212yes—
34#2994—22no—
35#2993—22no—
36#2991—21no—
37#2990—21no—
38#2989—21no—
39#2988—21no—
40#2969—21no—
41#2969—21no—
42#2968—22no—
43#2965—21no—
44#2965—22no—
45C8×#41—21no—
46#2962C2211yescharacteristic
47#2962C2211yescharacteristic
48#2960C2212yes—
49C2×#443C2214yes—
50#2935C2211yescharacteristic
51#2935C2211yescharacteristic
52#2933C2212yes—
53#2933C2212yes—
54#2933C2214yes—
55#2931C2212yes—
56#2925C2212yes—
57#2922C2212yes—
58C2×#431C2211yescharacteristic
59C2×#430C2212yes—
60#2906C2212yes—
61C2×#423C2211yescharacteristic
62C2×#423C2211yescharacteristic
63C4×#131C2212yes—
64C2×C4×M16C2211yescharacteristic
65C4×#117C2211yescharacteristic
66#1994C2212yes—
67#1986C2211yescharacteristic
68#1986C2211yescharacteristic
69#1980C2211yescharacteristic
70#1980C2211yescharacteristic
71#1975C2214yes—
72#1962C2212yes—
73#1950C2212yes—
74#1950C2212yes—
75#1950C2212yes—
76#1950C2212yes—
77#1945C2214yes—
78#1938C2214yes—
79#1937C2214yes—
80#1929C2214yes—
81#1929C2214yes—
82#1922C2214yes—
83#1922C2214yes—
84#1876C2214yes—
85#1876C2214yes—
86#1871C2214yes—
87#1871C2212yes—
88#1871C2212yes—
89#1866C2214yes—
90#1866C2214yes—
91#1806C2212yes—
92#1806C2212yes—
93#1773C2214yes—
94#1770C2212yes—
95C8×C4⋊C4C2212yes—
96#1767C2212yes—
97C4×C4⋊C8C2212yes—
98#1765C2214yes—
99#1764C2214yes—
100C4×#104C2212yes—
101C4×#104C2212yes—
102#1753C2214yes—
103#1738C2212yes—
104C2×#135C2314yes—
105C2×#131C2312yes—
106C2×#131C2312yes—
107C2×#131C2314yes—
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2312yes—
111C22×M16C2312yes—
112#533C2×C411yescharacteristic
113#533C2×C411yescharacteristic
114#533C2×C411yescharacteristic
115#533C2×C411yescharacteristic
116#533C2311yescharacteristic
117#533C2311yescharacteristic
118#532C2×C411yescharacteristic
119#532C2×C411yescharacteristic
120#532C2×C411yescharacteristic
121#532C2×C411yescharacteristic
122#532C2311yescharacteristic
123#532C2311yescharacteristic
124#529—21no—
125#529—21no—
126#529—21no—
127#529—21no—
128#529—21no—
129#529—21no—
130#529—21no—
131#529—21no—
132#529C2×C412yes—
133#529C2×C412yes—
134#529C2×C412yes—
135#529C2×C412yes—
136#525—21no—
137#525—21no—
138#525—21no—
139#525—21no—
140#525C2312yes—
141#525C2312yes—
142C4×#41—21no—
143C4×#41—21no—
144C4×#41—21no—
145C4×#41—21no—
146C4×#41C2312yes—
147C4×#41C2312yes—
148C2×#117—21no—
149C22×C42C2311yescharacteristic
150#479C2×C414yes—
151#479C2×C414yes—
152#478C2×C414yes—
153#478C2×C414yes—
154#477C2×C412yes—
155#477C2×C412yes—
156#476C2×C412yes—
157#476C2×C412yes—
158#475C2×C412yes—
159#475C2×C412yes—
160#474C2×C412yes—
161#474C2×C412yes—
162#470C2×C414yes—
163#470C2×C414yes—
164#469C2×C414yes—
165#469C2×C414yes—
166#468C2×C414yes—
167#468C2×C414yes—
168#468C2×C414yes—
169#468C2×C414yes—
170#464C2×C414yes—
171#464C2×C414yes—
172#463C2×C414yes—
173#463C2×C414yes—
174#462C2×C412yes—
175#462C2×C412yes—
176#461C2×C412yes—
177#461C2×C412yes—
178#460C2×C412yes—
179#460C2×C412yes—
180#459C2×C412yes—
181#459C2×C412yes—
182#446—22no—
183#446—22no—
184#446—21no—
185#446—21no—
186#446—22no—
187#446—22no—
188C8×Q8—21no—
189C8×Q8—21no—
190C8×Q8—22no—
191C8×Q8—22no—
192#443—48no—
193#436—21no—
194#436—21no—
195#436—22no—
196#436—22no—
197#436—24no—
198#436—22no—
199#436—22no—
200#435—22no—
201#435—22no—
202#435—22no—
203#435—22no—
204#435—22no—
205#435—22no—
206#435—24no—
207#435—24no—
208C8×D4—21no—
209C8×D4—21no—
210C8×D4—22no—
211C8×D4—22no—
212C8×D4—24no—
213C8×D4—22no—
214C8×D4—22no—
215#433—24no—
216#433—22no—
217#433—22no—
218#432—22no—
219#431—22no—
220#431—22no—
221#431—22no—
222#431D411yescharacteristic
223#431D411yescharacteristic
224#431D412yes—
225#431D412yes—
226#431D411yescharacteristic
227#431D411yescharacteristic
228#430—44no—
229C2×#108C2314yes—
230C2×#108C2314yes—
231#427C2314yes—
232#424—24no—
233#424C2312yes—
234#424C2314yes—
235#424C2312yes—
236#423—21no—
237#423—21no—
238#423—22no—
239#423C2×C412yes—
240#423C2×C412yes—
241#423C2×C411yescharacteristic
242#423C2×C411yescharacteristic
243#423C2×C412yes—
244#423C2312yes—
245#423C2312yes—
246C2×C4⋊C8—21no—
247C2×C4⋊C8—21no—
248C2×C4⋊C8—22no—
249C2×C4⋊C8C2312yes—
250C2×C4⋊C8C2312yes—
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×#104C2312yes—
254C2×#104C2312yes—
255C2×#104C2314yes—
256C2×#104C2314yes—
257C2×#104C2312yes—
258C2×#104C2312yes—
259#416C2314yes—
260#416C2314yes—
261#408C2312yes—
262#408C2314yes—
263#408C2312yes—
264C2×C22⋊C8C2312yes—
265#405—22no—
266#405—22no—
267#405C2312yes—
268#405C2312yes—
269#405C2314yes—
270C4×M16—21no—
271C4×M16—21no—
272C4×M16—22no—
273C4×M16C2311yescharacteristic
274C4×M16C2311yescharacteristic
275C4×M16C2311yescharacteristic
276C4×M16C2311yescharacteristic
277C2×#97—21no—
278C2×#97C2314yes—
279C2×C4×C8—21no—
280C2×C4×C8—22no—
281C2×C4×C8C2314yes—
282C2×C4×C8C2312yes—
283C4×C4⋊C4—21no—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C22⋊C4—21no—
287C4×C22⋊C4C2312yes—
288#376—21no—
289C43C2312yes—
290#341C2314yes—
291#341C2314yes—
292#339C2314yes—
293#339C2314yes—
294#339C2312yes—
295#339C2312yes—
296#339C2312yes—
297#339C2312yes—
298#336C2314yes—
299#336C2314yes—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41C2412yes—
305C2×#41C2412yes—
306C23×C4#4111yescharacteristic
307C23×C4#4111yescharacteristic
308C23×C4C2411yescharacteristic
309#135—44no—
310#135—44no—
311C2×Q16C22×C414yes—
312C2×SD16C22×C414yes—
313C2×SD16C22×C414yes—
314C2×D8C22×C414yes—
315#131—24no—
316#131—24no—
317#131—42no—
318#131—42no—
319#131—44no—
320#131—44no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—24no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—41no—
332C2×M16—41no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16C22×C412yes—
336C2×M16C22×C414yes—
337C2×M16C22×C412yes—
338C2×M16C2414yes—
339C2×M16C2411yescharacteristic
340C2×M16C2411yescharacteristic
341C2×M16C2411yescharacteristic
342C2×M16C2411yescharacteristic
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—24no—
349C22×C8C2414yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C4⋊Q8C22×C411yescharacteristic
353C4⋊Q8C22×C411yescharacteristic
354C4⋊Q8C22×C411yescharacteristic
355C4⋊Q8C22×C411yescharacteristic
356C4⋊Q8C22×C411yescharacteristic
357C4⋊Q8C22×C411yescharacteristic
358#127C22×C411yescharacteristic
359#127C22×C411yescharacteristic
360#126—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125—21no—
368#125C22×C412yes—
369#125C22×C412yes—
370#124—21no—
371#124—21no—
372#124—21no—
373#124—21no—
374#124C22×C412yes—
375#124C22×C412yes—
376#123—22no—
377#123—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8C22×C412yes—
391C22⋊Q8C22×C412yes—
392C22⋊Q8C22×C412yes—
393C22⋊Q8C22×C412yes—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121C22×C412yes—
403#121C22×C412yes—
404#121C22×C412yes—
405#121C22×C412yes—
406#120—22no—
407#120—22no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C22×C412yes—
417C4×Q8C22×C412yes—
418C4×Q8C22×C412yes—
419C4×Q8C22×C412yes—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4C22×C412yes—
441C4×D4C22×C412yes—
442C4×D4C22×C412yes—
443C4×D4C22×C412yes—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—22no—
449#117—22no—
450#117—22no—
451#117—22no—
452#117—22no—
453#117—22no—
454#117—44no—
455#117C2412yes—
456#117C2412yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42C22×C411yescharacteristic
465C2×C42C22×C411yescharacteristic
466C2×C42C22×C411yescharacteristic
467C2×C42C22×C411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42#4111yescharacteristic
473C2×C42#4111yescharacteristic
474C2×C42C2412yes—
475C2×C42C2412yes—
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478#108—28no—
479#108—44no—
480#107C22×C414yes—
481#107C22×C414yes—
482#106C22×C414yes—
483#106C22×C414yes—
484C4⋊C8—24no—
485C4⋊C8—24no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8C22×C412yes—
495C4⋊C8C22×C412yes—
496C4⋊C8C22×C412yes—
497C4⋊C8C22×C412yes—
498C4⋊C8C22×C414yes—
499C4⋊C8C22×C414yes—
500C4⋊C8C2×D411yescharacteristic
501C4⋊C8C2×D411yescharacteristic
502C4⋊C8C2×D412yes—
503C4⋊C8C2×D411yescharacteristic
504C4⋊C8C2×D411yescharacteristic
505C4⋊C8C2×D412yes—
506#104—24no—
507#104—24no—
508#104—42no—
509#104—42no—
510#104—44no—
511#104—44no—
512#103C22×C414yes—
513#103C22×C414yes—
514#103C22×C414yes—
515#103C22×C414yes—
516#102C22×C414yes—
517#102C22×C414yes—
518#102C22×C414yes—
519#102C22×C414yes—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—24no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C22⋊C8—24no—
526C22⋊C8C2×D412yes—
527C22⋊C8C2×D412yes—
528C22⋊C8C2×D412yes—
529C22⋊C8C2×D412yes—
530#97—22no—
531#97—22no—
532#97—24no—
533#97—21no—
534#97—21no—
535#97—21no—
536#97—21no—
537#97—44no—
538C4×C8—22no—
539C4×C8—22no—
540C4×C8—24no—
541C4×C8—21no—
542C4×C8—21no—
543C4×C8—21no—
544C4×C8—21no—
545C4×C8—44no—
546C4×C8C2×D412yes—
547C4×C8C2×D412yes—
548C4×C8C2×D412yes—
549C4×C8C2×D412yes—
550#95—21no—
551#95—21no—
552#95—22no—
553C24C2×#4111yescharacteristic
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—44no—
563#41—44no—
564#41—82no—
565#41—82no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8C23×C412yes—
571C2×Q8C23×C412yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4C23×C412yes—
583C2×D4C23×C412yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4C4×D411yescharacteristic
599C22×C4C4×D411yescharacteristic
600C22×C4C4×D411yescharacteristic
601C22×C4C4×D411yescharacteristic
602C22×C4C4×D411yescharacteristic
603C22×C4C4×D411yescharacteristic
604C22×C4C4×D411yescharacteristic
605C22×C4C4×D411yescharacteristic
606C22×C4C23×C411yescharacteristic
607C22×C4C23×C411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2511yescharacteristic
616Q16—44no—
617SD16—44no—
618SD16—44no—
619D8—44no—
620M16—21no—
621M16—21no—
622M16—24no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—24no—
628M16—42no—
629M16—44no—
630M16—42no—
631M16—44no—
632M16—44no—
633M16—42no—
634M16—42no—
635M16—84no—
636M16—82no—
637M16H(5,𝔽2)12yes—
638M162−1+412yes—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—24no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—24no—
646C2×C8—22no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—24no—
650C2×C8—44no—
651C2×C8—44no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—84no—
655C2×C8—82no—
656C2×C8C23×C414yes—
657C2×C8C23×C414yes—
658C2×C8C22×D412yes—
659C2×C8C22×D412yes—
660C2×C8C22×D412yes—
661C2×C8C22×D412yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—42no—
684C4⋊C4C23×C412yes—
685C4⋊C4C23×C412yes—
686C4⋊C4C23×C412yes—
687C4⋊C4C23×C412yes—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
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—44no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—44no—
718C42—44no—
719C42C4×D411yescharacteristic
720C42C4×D411yescharacteristic
721C42C4×D411yescharacteristic
722C42C4×D411yescharacteristic
723C42C4×D411yescharacteristic
724C42C4×D411yescharacteristic
725C42C4×D411yescharacteristic
726C42C4×D411yescharacteristic
727C42C23×C411yescharacteristic
728C42C23×C411yescharacteristic
729C42C23×C411yescharacteristic
730C42C23×C411yescharacteristic
731C42C22×D411yescharacteristic
732C42C22×D411yescharacteristic
733C42C22×D411yescharacteristic
734C42C22×D411yescharacteristic
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—41no—
741C23C2×C4×D411yescharacteristic
742C23C2×C4×D411yescharacteristic
743C23C22×#4111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—42no—
749Q8—42no—
750Q8—42no—
751Q8—81no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—22no—
756D4—42no—
757D4—44no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—81no—
766D4—82no—
767D4—82no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—82no—
810C2×C4C2×C4×D411yescharacteristic
811C2×C4C2×C4×D411yescharacteristic
812C2×C4C2×C4×D411yescharacteristic
813C2×C4C2×C4×D411yescharacteristic
814C2×C4C2×C4×D411yescharacteristic
815C2×C4C2×C4×D411yescharacteristic
816C2×C4C2×C4×D411yescharacteristic
817C2×C4C2×C4×D411yescharacteristic
818C2×C4C2×C4×D411yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C24×C411yescharacteristic
821C2×C4C23×D411yescharacteristic
822C2×C4C2×H(5,𝔽2)11yescharacteristic
823C2×C4C2×2−1+411yescharacteristic
824C2×C4#58511yescharacteristic
825C2×C4#58511yescharacteristic
826C8—24no—
827C8—24no—
828C8—22no—
829C8—22no—
830C8—22no—
831C8—22no—
832C8—22no—
833C8—22no—
834C8—41no—
835C8—44no—
836C8—41no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—81no—
852C22—81no—
853C22C22×C4×D411yescharacteristic
854C22#351111yescharacteristic
855C22#351211yescharacteristic
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—44no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—82no—
872C4#295512yes—
873C4#295612yes—
874C4C4×H(5,𝔽2)11yescharacteristic
875C4C4×2−1+411yescharacteristic
876C4#348811yescharacteristic
877C4#348911yescharacteristic
878C2—21no—
879C2—21no—
880C2—41no—
881C2—41no—
882C2—82no—
883C2—82no—
884C2#3426711yescharacteristic
885C2C2×#295511yescharacteristic
886C2C2×#295611yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#60907C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60268C2semidirect
3. #60210C2semidirect
4. #23148C2semidirect
5. #23114C2semidirect
6. #23081C2semidirect
7. #23020C2semidirect
8. #23015C2semidirect
9. #22982C2semidirect
10. #22166C2semidirect
11. #22130C2semidirect
12. #21856C2semidirect
13. #21628C2semidirect
14. #21517C2semidirect
15. #21382C2semidirect
16. #21177C2semidirect
17. #20550C2semidirect
20. #3256C4semidirect
21. #3255C4semidirect
22. #3254C4semidirect
23. #3254C4semidirect
24. #3253C4semidirect
25. #3252C4semidirect
26. #3252C4semidirect
27. #3251C4semidirect
28. #3251C4semidirect

Maximal subgroups

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

subgroupindex
#609072
#602682
#602102
#231482
#231142
#230812
#230202
#230152
#229822
#221662
#221302
#218562
#216282
#215172
#213822
#211772
#205502