Finite Group Databasebeta

← #6396757

Subgroups — #6396757

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60854C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic
3#60250C211yesmaximal, characteristic, complemented
4#23082C214yesmaximal, complemented
5#22984C214yesmaximal, complemented
6#22950C214yesmaximal, complemented
7#22948C214yesmaximal, complemented
8#22257C211yesmaximal, characteristic, complemented
9#22257C211yesmaximal, characteristic, complemented
10#22235C211yesmaximal, characteristic, complemented
11#22235C211yesmaximal, characteristic, complemented
12#21994C211yesmaximal, characteristic, complemented
13#21737C211yesmaximal, characteristic, complemented
14#21735C211yesmaximal, characteristic, complemented
15#21663C211yesmaximal, characteristic, complemented
16#21661C211yesmaximal, characteristic, complemented
17#21417C211yesmaximal, characteristic
18C2×#1995C211yesmaximal, characteristic, complemented
19#20469C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#533C2211yescharacteristic
22#3240C412yescomplemented
23#3240C412yescomplemented
24#3239C412yescomplemented
25#3238C412yescomplemented
26#3237C412yescomplemented
27#3236C412yescomplemented
28#3235C412yescomplemented
29#3234C412yescomplemented
30#3162C2211yescharacteristic
31#3162C2211yescharacteristic
32#3135C2211yescharacteristic
33#3135C2211yescharacteristic
34#3091C2214yes—
35#3076C2214yes—
36#2994—21no—
37#2994—21no—
38#2993—21no—
39#2993—21no—
40#2991—21no—
41#2990—21no—
42#2989—21no—
43#2988—21no—
44#2986—21no—
45#2986—21no—
46#2985—21no—
47#2985—21no—
48#2984—21no—
49#2984—21no—
50#2983—21no—
51#2982—21no—
52#2962C2212yes—
53#2962C2212yes—
54#2960C2211yescharacteristic
55#2960C2211yescharacteristic
56#2960C2211yescharacteristic
57#2960C2211yescharacteristic
58#2960C2211yescharacteristic
59#2960C2211yescharacteristic
60#2933C2212yes—
61#2933C2212yes—
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic
64#2925C2212yes—
65#2924C2212yes—
66#2924C2212yes—
67#2920C2211yescharacteristic
68C2×#432C2211yescharacteristic
69C2×#431C2211yescharacteristic
70#2906C2212yes—
71C2×#423C2211yescharacteristic
72C2×#376C2211yescharacteristic
73#1995C2214yes—
74#1995C2211yescharacteristic
75#1995C2211yescharacteristic
76#1995C2211yescharacteristic
77#1995C2211yescharacteristic
78#1995C2211yescharacteristic
79#1995C2211yescharacteristic
80#1963C2211yescharacteristic
81#1963C2211yescharacteristic
82#1950C2214yes—
83#1946C2214yes—
84#1945C2214yes—
85#1938C2214yes—
86#1937C2214yes—
87#1929C2214yes—
88#1929C2214yes—
89#1922C2214yes—
90#1922C2214yes—
91#1922C2214yes—
92#1922C2214yes—
93#1896C2214yes—
94#1866C2214yes—
95#1866C2214yes—
96#1855C2214yes—
97#1849C2211yescharacteristic
98#1849C2211yescharacteristic
99#1838C2211yescharacteristic
100#1838C2211yescharacteristic
101#1773C2214yes—
102#1772C2214yes—
103#1768C2212yes—
104#1768C2212yes—
105#1765C2214yes—
106#1764C2214yes—
107#1759C2214yes—
108#1749C2212yes—
109C4×C22⋊C8C2212yes—
110#1746C2211yescharacteristic
111#1746C2211yescharacteristic
112C2×#339C2214yes—
113#1726C2211yescharacteristic
114#1726C2211yescharacteristic
115C2×#131C2312yes—
116C2×#131C2312yes—
117C22×M16C2312yes—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533C2×C411yescharacteristic
123#533C2×C411yescharacteristic
124#533C2×C412yes—
125#533C2×C411yescharacteristic
126#533C2×C411yescharacteristic
127#533C2312yes—
128#533C2311yescharacteristic
129#533C2311yescharacteristic
130#533C2311yescharacteristic
131#532C2×C411yescharacteristic
132#532C2×C411yescharacteristic
133#532C2311yescharacteristic
134C2×C4⋊Q8C2×C411yescharacteristic
135C2×C4⋊Q8C2×C411yescharacteristic
136#529—21no—
137#529—21no—
138#529—21no—
139#529—21no—
140#529C2×C412yes—
141#529C2×C412yes—
142C2×#125C2×C412yes—
143#525—21no—
144#525—21no—
145#525C2312yes—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C4×#41—21no—
149C4×#41—21no—
150C4×#41C2312yes—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×#117C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156#501C2×C412yescomplemented
157#501C2×C412yescomplemented
158#501C2×C412yescomplemented
159#501C2×C412yescomplemented
160#501C2×C412yescomplemented
161#501C2×C412yescomplemented
162#501C2×C412yescomplemented
163#501C2×C412yescomplemented
164#491C2×C412yescomplemented
165#491C2×C412yescomplemented
166#490C2×C412yescomplemented
167#490C2×C412yescomplemented
168#489C2×C412yescomplemented
169#489C2×C412yescomplemented
170#489C2×C412yescomplemented
171#489C2×C412yescomplemented
172#485C2×C414yes—
173#485C2×C414yes—
174#484C2×C414yes—
175#483C2×C414yes—
176#482C2×C414yes—
177#482C2×C414yes—
178#481C2×C414yes—
179#480C2×C414yes—
180#479C2×C414yescomplemented
181#479C2×C414yescomplemented
182#478C2×C414yescomplemented
183#478C2×C414yescomplemented
184#477C2×C414yescomplemented
185#476C2×C414yescomplemented
186#475C2×C414yescomplemented
187#474C2×C414yescomplemented
188#446—22no—
189#446—22no—
190#446—22no—
191#446—22no—
192#446—22no—
193#446—22no—
194#446—21no—
195#446—21no—
196#446—21no—
197#446—21no—
198#446—21no—
199#446—21no—
200#446—21no—
201#446—21no—
202#446—21no—
203#446—21no—
204#446—21no—
205#446—21no—
206C8×Q8—22no—
207C8×Q8—22no—
208C8×Q8—21no—
209C8×Q8—21no—
210C8×Q8—21no—
211C8×Q8—21no—
212C8×Q8—21no—
213C8×Q8—21no—
214C8×Q8—21no—
215C8×Q8—21no—
216C8×Q8—21no—
217C8×Q8—21no—
218C8×Q8—21no—
219C8×Q8—21no—
220#436—22no—
221#436—22no—
222#436—21no—
223#436—21no—
224#436—21no—
225#436—21no—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230C8×D4—22no—
231C8×D4—22no—
232C8×D4—21no—
233C8×D4—21no—
234C8×D4—21no—
235C8×D4—21no—
236#433—22no—
237#433—22no—
238#433—22no—
239#433—22no—
240#433—22no—
241#433—22no—
242#432—21no—
243#432—21no—
244#432—22no—
245#432—22no—
246#432—22no—
247#432C2×C412yes—
248#432C2×C412yes—
249#432C2×C412yes—
250#432C2×C412yes—
251#431—21no—
252#431—21no—
253#431—22no—
254#431—22no—
255#431—22no—
256#431D411yescharacteristic
257#431D411yescharacteristic
258#431D411yescharacteristic
259#431D411yescharacteristic
260#431D411yescharacteristic
261#431D411yescharacteristic
262#431D411yescharacteristic
263#431D411yescharacteristic
264C2×#108C2314yes—
265C2×#108C2314yes—
266#427C2314yes—
267#427C2314yes—
268#424—22no—
269#424—22no—
270#424C2312yes—
271#424C2312yes—
272#424C2312yes—
273#424C2312yes—
274#424C2312yes—
275#424C2312yes—
276#423—21no—
277#423—21no—
278#423—22no—
279#423C2311yescharacteristic
280#423C2311yescharacteristic
281#423C2311yescharacteristic
282#423C2311yescharacteristic
283#423C2312yes—
284C2×C4⋊C8—21no—
285C2×C4⋊C8—21no—
286C2×C4⋊C8—22no—
287C2×C4⋊C8C2312yes—
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×#104C2314yes—
291C2×#104C2314yes—
292#416C2314yes—
293#416C2314yes—
294#408C2312yes—
295#408C2312yes—
296#407C2312yes—
297C2×C22⋊C8C2312yes—
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300#405C2312yes—
301#405C2312yes—
302#405C2312yes—
303#405C2312yes—
304#405C2312yes—
305#405C2312yes—
306C4×M16C2312yes—
307C2×#97C2312yes—
308C2×#97C2312yes—
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2312yes—
312C2×C4×C8C2312yes—
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#376—21no—
316#376—21no—
317#376C2311yescharacteristic
318#376C2311yescharacteristic
319#376C2312yes—
320C2×#95—21no—
321C2×#95—21no—
322#341C2314yes—
323#341C2314yes—
324#339C2314yes—
325#339C2314yes—
326#339C2314yes—
327#339C2314yes—
328#339C2314yes—
329#339C2314yes—
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C2412yes—
337C22×Q8—21no—
338C22×Q8—21no—
339C23×C4—22no—
340C23×C4#4111yescharacteristic
341C23×C4#4111yescharacteristic
342C23×C4C2411yescharacteristic
343#131—44no—
344#131—44no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—44no—
349C2×M16C2412yes—
350C2×M16C2412yes—
351C2×M16C2412yes—
352C2×M16C2412yes—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C22×C411yescharacteristic
367C4⋊Q8C22×C412yes—
368C4⋊Q8C22×C412yes—
369C4⋊Q8C22×C411yescharacteristic
370C4⋊Q8C22×C411yescharacteristic
371C4⋊Q8C22×C411yescharacteristic
372C4⋊Q8C22×C411yescharacteristic
373C4⋊Q8C22×C411yescharacteristic
374C4⋊Q8C22×C411yescharacteristic
375#127C22×C411yescharacteristic
376#126—22no—
377#126—22no—
378#125—22no—
379#125—22no—
380#125—21no—
381#125—21no—
382#125C22×C412yes—
383#125C22×C412yes—
384#125C22×C412yes—
385#125C22×C412yes—
386#125C22×C412yes—
387#124—21no—
388#124—21no—
389#124C22×C412yes—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8C22×C412yes—
410C22⋊Q8C22×C412yes—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121C22×C412yes—
416#121C22×C412yes—
417#120—22no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—22no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—22no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8C22×C412yes—
435C4×Q8C22×C412yes—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4C22×C412yes—
447C4×D4C22×C412yes—
448#117—21no—
449#117—21no—
450#117—22no—
451#117—22no—
452#117—22no—
453#117—22no—
454#117—22no—
455#117C22×C412yes—
456#117C22×C412yes—
457#117C2412yes—
458#117C2412yes—
459#117C2412yes—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C22×C412yes—
465C2×C4⋊C4C22×C412yes—
466C2×C22⋊C4—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—24no—
470C2×C42—22no—
471C2×C42—42no—
472C2×C42C22×C411yescharacteristic
473C2×C42C22×C411yescharacteristic
474C2×C42C22×C411yescharacteristic
475C2×C42C22×C411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42#4111yescharacteristic
481C2×C42#4111yescharacteristic
482C2×C42C2412yes—
483C2×C42C2412yes—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486#108—44no—
487#108—44no—
488#107C22×C414yes—
489#107C22×C414yes—
490#107C22×C414yes—
491#107C22×C414yes—
492#106C22×C414yes—
493#106C22×C414yes—
494#106C22×C414yes—
495#106C22×C414yes—
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518C4⋊C8C22×C414yes—
519C4⋊C8C22×C414yes—
520C4⋊C8C2×D411yescharacteristic
521C4⋊C8C2×D411yescharacteristic
522C4⋊C8C2×D411yescharacteristic
523C4⋊C8C2×D411yescharacteristic
524C4⋊C8C2×D411yescharacteristic
525C4⋊C8C2×D411yescharacteristic
526C4⋊C8C2×D411yescharacteristic
527C4⋊C8C2×D411yescharacteristic
528#104—28no—
529#104—44no—
530#103C22×C414yes—
531#103C22×C414yes—
532#103C22×C414yes—
533#103C22×C414yes—
534#102C22×C414yes—
535#102C22×C414yes—
536#102C22×C414yes—
537#102C22×C414yes—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8C22×C414yes—
545C22⋊C8C22×C414yes—
546C22⋊C8C2×D411yescharacteristic
547C22⋊C8C2×D411yescharacteristic
548C22⋊C8C2×D411yescharacteristic
549C22⋊C8C2×D411yescharacteristic
550C22⋊C8C2×D411yescharacteristic
551C22⋊C8C2×D411yescharacteristic
552C22⋊C8C2×D411yescharacteristic
553C22⋊C8C2×D411yescharacteristic
554#97—22no—
555#97—22no—
556#97—22no—
557#97—22no—
558#97—22no—
559#97—22no—
560#97—22no—
561#97—24no—
562#97—42no—
563#97C22×C412yes—
564#97C22×C412yes—
565#97C22×C412yes—
566#97C22×C412yes—
567C4×C8—22no—
568C4×C8—22no—
569C4×C8—22no—
570C4×C8—22no—
571C4×C8—22no—
572C4×C8—22no—
573C4×C8—22no—
574C4×C8—24no—
575C4×C8—42no—
576C4×C8C2×D411yescharacteristic
577C4×C8C2×D411yescharacteristic
578C4×C8C2×D411yescharacteristic
579C4×C8C2×D411yescharacteristic
580C4×C8C2×D411yescharacteristic
581C4×C8C2×D411yescharacteristic
582C4×C8C2×D411yescharacteristic
583C4×C8C2×D411yescharacteristic
584#95—21no—
585#95—21no—
586#95—22no—
587#95—22no—
588#95—21no—
589#95—21no—
590C24C2×#4111yescharacteristic
591#41—24no—
592#41—24no—
593#41—44no—
594#41—82no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—44no—
604C2×Q8—82no—
605C2×Q8C23×C412yes—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4C23×C412yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—81no—
625C22×C4—82no—
626C22×C4C4×D411yescharacteristic
627C22×C4C4×D411yescharacteristic
628C22×C4C4×D411yescharacteristic
629C22×C4C4×D411yescharacteristic
630C22×C4C4×D411yescharacteristic
631C22×C4C4×D411yescharacteristic
632C22×C4C4×D411yescharacteristic
633C22×C4C4×D411yescharacteristic
634C22×C4C23×C411yescharacteristic
635C22×C4C23×C411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C2×#4111yescharacteristic
639C22×C4C2×#4111yescharacteristic
640C22×C4C2×#4111yescharacteristic
641C22×C4C2×#4111yescharacteristic
642C22×C4C2×#4111yescharacteristic
643C22×C4C2511yescharacteristic
644M16—24no—
645M16—24no—
646M16—24no—
647M16—24no—
648M16—82no—
649M16—82no—
650M16—82no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—82no—
664C2×C8—82no—
665C2×C8—82no—
666C2×C8C23×C414yes—
667C2×C8C23×C414yes—
668C2×C8C22×D411yescharacteristic
669C2×C8C22×D411yescharacteristic
670C2×C8C22×D411yescharacteristic
671C2×C8C22×D411yescharacteristic
672C2×C8C22×D411yescharacteristic
673C2×C8C22×D411yescharacteristic
674C2×C8C22×D411yescharacteristic
675C2×C8C22×D411yescharacteristic
676C4⋊C4—22no—
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—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4C23×C412yes—
703C4⋊C4C23×C412yes—
704C4⋊C4C23×C412yes—
705C4⋊C4C23×C412yes—
706C4⋊C4C23×C412yes—
707C4⋊C4C23×C412yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—44no—
732C42C4×D411yescharacteristic
733C42C4×D411yescharacteristic
734C42C4×D411yescharacteristic
735C42C4×D411yescharacteristic
736C42C4×D411yescharacteristic
737C42C4×D411yescharacteristic
738C42C4×D411yescharacteristic
739C42C4×D411yescharacteristic
740C42C23×C411yescharacteristic
741C42C23×C411yescharacteristic
742C42C23×C411yescharacteristic
743C42C23×C411yescharacteristic
744C42C22×D411yescharacteristic
745C42C22×D411yescharacteristic
746C42C22×D411yescharacteristic
747C42C22×D411yescharacteristic
748C422−1+414yes—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23C2×C4×D411yescharacteristic
754C23C2×C4×D411yescharacteristic
755C23C22×#4111yescharacteristic
756Q8—24no—
757Q8—44no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—82no—
765D4—24no—
766D4—42no—
767D4—42no—
768D4—44no—
769D4—44no—
770D4—82no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—88no—
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×C4C2×2−1+412yes—
823C2×C4#58512yes—
824C8—24no—
825C8—24no—
826C8—21no—
827C8—21no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—21no—
832C8—21no—
833C8—21no—
834C8—42no—
835C8—42no—
836C8—42no—
837C8—42no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22#295512yes—
850C22C22×C4×D411yescharacteristic
851C22#349512yes—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—82no—
871C4C4×2−1+412yes—
872C4#349911yescharacteristic
873C4#350011yescharacteristic
874C2—22no—
875C2—22no—
876C2—41no—
877C2—82no—
878C2#3427611yescharacteristic
879C2C2×#295511yescharacteristic
880C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#3444C22
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
3. #60250C2semidirect
4. #23082C2semidirect
5. #22984C2semidirect
6. #22950C2semidirect
7. #22948C2semidirect
8. #22257C2semidirect
9. #22257C2semidirect
10. #22235C2semidirect
11. #22235C2semidirect
12. #21994C2semidirect
13. #21737C2semidirect
14. #21735C2semidirect
15. #21663C2semidirect
16. #21661C2semidirect
18. C2×#1995C2semidirect
19. #20469C2semidirect
22. #3240C4semidirect
23. #3240C4semidirect
24. #3239C4semidirect
25. #3238C4semidirect
26. #3237C4semidirect
27. #3236C4semidirect
28. #3235C4semidirect
29. #3234C4semidirect
156. #501C2×C4semidirect
157. #501C2×C4semidirect
158. #501C2×C4semidirect
159. #501C2×C4semidirect
160. #501C2×C4semidirect
161. #501C2×C4semidirect
162. #501C2×C4semidirect
163. #501C2×C4semidirect
164. #491C2×C4semidirect
165. #491C2×C4semidirect
166. #490C2×C4semidirect
167. #490C2×C4semidirect
168. #489C2×C4semidirect
169. #489C2×C4semidirect
170. #489C2×C4semidirect
171. #489C2×C4semidirect
180. #479C2×C4semidirect
181. #479C2×C4semidirect
182. #478C2×C4semidirect
183. #478C2×C4semidirect
184. #477C2×C4semidirect
185. #476C2×C4semidirect
186. #475C2×C4semidirect
187. #474C2×C4semidirect

Maximal subgroups

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

subgroupindex
#608542
#602682
#602502
#230822
#229842
#229502
#229482
#222572
#222352
#219942
#217372
#217352
#216632
#216612
#214172
C2×#19952
#204692