Finite Group Databasebeta

← #6404340

Subgroups — #6404340

Order 512.

1528 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61365C211yesmaximal, characteristic
2#60254C212yesmaximal, complemented
3#23172C211yesmaximal, characteristic, complemented
4#23172C211yesmaximal, characteristic, complemented
5#23171C211yesmaximal, characteristic, complemented
6#23082C212yesmaximal, complemented
7#23082C212yesmaximal, complemented
8#23081C212yesmaximal, complemented
9#22804C211yesmaximal, characteristic
10#22804C211yesmaximal, characteristic
11#22803C211yesmaximal, characteristic
12#22733C211yesmaximal, characteristic, complemented
13#22529C212yesmaximal, complemented
14#22132C212yesmaximal, complemented
15#22132C212yesmaximal, complemented
16#22131C212yesmaximal, complemented
17#21737C211yesmaximal, characteristic, complemented
18#21736C211yesmaximal, characteristic, complemented
19#21733C211yesmaximal, characteristic, complemented
20#21297C211yesmaximal, characteristic
21#21296C211yesmaximal, characteristic
22#21294C211yesmaximal, characteristic
23#20518C211yesmaximal, characteristic, complemented
24Q8×#41C2212yes—
25#3390C412yescomplemented
26#3389C412yescomplemented
27#3388C412yescomplemented
28#3388C412yescomplemented
29#3387C412yescomplemented
30#3386C412yescomplemented
31#3385C412yescomplemented
32#3384C412yescomplemented
33#3162C2211yescharacteristic
34#3162C2211yescharacteristic
35#3160C2211yescharacteristic
36#3076C2212yes—
37#3076C2212yes—
38#3076C2212yes—
39#2987—22no—
40#2987—22no—
41#2986—22no—
42#2985—22no—
43#2985—22no—
44#2985—22no—
45#2984—22no—
46#2983—22no—
47Q8×M16C2212yes—
48#2962C2212yes—
49#2962C2212yes—
50#2962C2212yes—
51#2961C2212yes—
52#2961C2212yes—
53#2960C2212yes—
54C2×#446C2211yescharacteristic
55C2×#446C2211yescharacteristic
56#2943C2211yescharacteristic
57#2943C2211yescharacteristic
58C4×#135C2211yescharacteristic
59#2925C2212yes—
60#2925C2212yes—
61#2925C2212yes—
62#2923C2212yes—
63#2923C2212yes—
64#2922C2212yes—
65#2295C2211yescharacteristic
66#1995C2212yes—
67#1995C2212yes—
68#1994C2212yes—
69#1986C2212yes—
70#1986C2212yes—
71#1986C2212yes—
72#1975C2211yescharacteristic
73#1975C2211yescharacteristic
74#1974C2211yescharacteristic
75#1974C2211yescharacteristic
76#1950C2212yes—
77#1950C2212yes—
78#1950C2212yes—
79#1946C2211yescharacteristic
80#1946C2211yescharacteristic
81#1946C2212yes—
82#1946C2212yes—
83#1945C2211yescharacteristic
84#1945C2211yescharacteristic
85#1945C2211yescharacteristic
86#1945C2211yescharacteristic
87#1945C2212yes—
88#1938C2212yes—
89#1938C2212yes—
90#1938C2212yes—
91#1938C2212yes—
92#1937C2212yes—
93#1937C2212yes—
94#1929C2212yes—
95#1929C2212yes—
96#1929C2212yes—
97#1929C2212yes—
98#1929C2212yes—
99#1929C2212yes—
100#1922C2212yes—
101#1922C2212yes—
102#1922C2212yes—
103#1922C2212yes—
104#1922C2212yes—
105#1922C2212yes—
106#1849C2211yescharacteristic
107#1849C2211yescharacteristic
108#1848C2211yescharacteristic
109#1806C2212yes—
110#1806C2212yes—
111#1806C2212yes—
112#1778C2211yescharacteristic
113#1778C2211yescharacteristic
114C4×#108C2211yescharacteristic
115#1773C2211yescharacteristic
116#1773C2211yescharacteristic
117#1773C2211yescharacteristic
118#1773C2211yescharacteristic
119#1773C2212yes—
120#1773C2212yes—
121#1772C2211yescharacteristic
122#1772C2211yescharacteristic
123#1772C2212yes—
124#1771C2211yescharacteristic
125#1771C2211yescharacteristic
126#1771C2211yescharacteristic
127#1771C2211yescharacteristic
128#1770C2211yescharacteristic
129#1770C2211yescharacteristic
130#1768C2211yescharacteristic
131#1768C2211yescharacteristic
132#1767C2211yescharacteristic
133#1759C2212yes—
134#1759C2212yes—
135C4×#104C2212yes—
136#1726C2211yescharacteristic
137#1726C2211yescharacteristic
138C4×#97C2211yescharacteristic
139C2×#135C2311yescharacteristic
140Q82C2×C412yes—
141#557C2×C412yes—
142#557C2×C412yes—
143#557C2×C412yes—
144#554—22no—
145#554—22no—
146#554—22no—
147#554C2×C412yes—
148#554C2×C412yes—
149#554C2×C412yes—
150D4×Q8—22no—
151D4×Q8C2×C412yes—
152#533—22no—
153#533—22no—
154#533—22no—
155#533C2312yes—
156#533C2312yes—
157#533C2312yes—
158C4×#41C2312yes—
159C4×#41C2312yes—
160C4×#41C2312yes—
161C2×C4×Q8—22no—
162C2×C4×Q8C2311yescharacteristic
163#501C2×C412yes—
164#501C2×C412yes—
165#501C2×C412yes—
166#501C2×C412yes—
167#501C2×C412yes—
168#501C2×C412yes—
169#501C2×C412yes—
170#501C2×C412yes—
171#500C2×C411yescharacteristic
172#500C2×C411yescharacteristic
173#499C2×C411yescharacteristic
174#499C2×C411yescharacteristic
175#499C2×C412yes—
176#498C2×C412yes—
177#479C2×C412yes—
178#479C2×C412yes—
179#479C2×C412yes—
180#479C2×C412yes—
181#479C2×C412yes—
182#479C2×C412yes—
183#478C2×C412yes—
184#478C2×C412yes—
185#478C2×C412yes—
186#478C2×C412yes—
187#478C2×C412yes—
188#478C2×C412yes—
189#477C2×C412yes—
190#477C2×C412yes—
191#477C2×C412yes—
192#476C2×C412yes—
193#476C2×C412yes—
194#476C2×C412yes—
195#475C2×C412yes—
196#475C2×C412yes—
197#475C2×C412yes—
198#474C2×C412yes—
199#474C2×C412yes—
200#474C2×C412yes—
201#446—22no—
202#446—22no—
203#446—22no—
204#446—22no—
205#446—22no—
206#446—22no—
207#446—22no—
208#446—22no—
209#446—22no—
210#446—22no—
211#446—22no—
212#446—22no—
213#446—22no—
214#446—22no—
215#446—22no—
216#446—22no—
217#446—22no—
218#446—22no—
219#446—22no—
220#446—22no—
221#446—22no—
222#446—22no—
223#446C2×C412yes—
224#446C2×C412yes—
225#446C2×C412yes—
226#446C2×C412yes—
227#446D412yes—
228#446D412yes—
229#446D412yes—
230#446D412yes—
231C8×Q8—22no—
232C8×Q8—22no—
233C8×Q8—22no—
234C8×Q8—22no—
235C8×Q8—22no—
236C8×Q8—22no—
237#442C2×C412yes—
238#442C2×C412yes—
239#441C2×C412yes—
240#441C2×C412yes—
241#440C2×C412yes—
242#440C2×C412yes—
243#440C2×C412yes—
244#440C2×C412yes—
245C4×Q16C2×C411yescharacteristic
246C4×Q16C2×C411yescharacteristic
247C4×SD16C2×C412yes—
248C4×SD16C2×C412yes—
249C4×D8C2×C411yescharacteristic
250C4×D8C2×C411yescharacteristic
251#433—22no—
252#433—22no—
253#433—22no—
254#433—22no—
255#433—22no—
256#433—22no—
257#433—22no—
258#433—22no—
259#433—22no—
260#433—22no—
261#433—22no—
262#433—22no—
263#432—22no—
264#432—22no—
265#432—22no—
266#432—22no—
267#432—22no—
268#432—22no—
269#432—22no—
270#431—22no—
271#431—22no—
272#431—22no—
273#431—22no—
274#431—22no—
275C2×#108C2311yescharacteristic
276C2×#108C2311yescharacteristic
277C2×#108C2311yescharacteristic
278C2×#108C2311yescharacteristic
279C2×#108C2312yes—
280C2×#108C2312yes—
281C2×#108C2312yes—
282#427C2312yes—
283#427C2312yes—
284#427C2312yes—
285#427C2311yescharacteristic
286#427C2311yescharacteristic
287#427C2311yescharacteristic
288#424C2312yes—
289#424C2312yes—
290#424C2312yes—
291#424C2312yes—
292#424C2312yes—
293#424C2312yes—
294#423C2312yes—
295#423C2312yes—
296#423C2312yes—
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×#104C2312yes—
304C2×#104C2312yes—
305C2×#104C2312yes—
306C2×#104C2312yes—
307#416C2312yes—
308#416C2312yes—
309#416C2312yes—
310#408C2312yes—
311#408C2312yes—
312#408C2312yes—
313#408C2312yes—
314#405C2312yes—
315#405C2312yes—
316#405C2312yes—
317#405C2312yes—
318#405C2312yes—
319#405C2312yes—
320C4×M16C2312yes—
321C4×M16C2312yes—
322C4×M16C2312yes—
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#391—21no—
340#389—21no—
341#387—21no—
342#387—21no—
343C4×C4⋊C4C2311yescharacteristic
344C4×C4⋊C4C2311yescharacteristic
345C4×C4⋊C4C2311yescharacteristic
346#376C2311yescharacteristic
347#376C2311yescharacteristic
348C43C2311yescharacteristic
349#341C2312yes—
350#341C2312yes—
351#341C2312yes—
352#339C2312yes—
353#339C2312yes—
354#339C2312yes—
355#339C2312yes—
356#339C2312yes—
357#339C2312yes—
358#339C2312yes—
359#339C2312yes—
360#339C2312yes—
361#339C2312yes—
362#339C2312yes—
363#339C2312yes—
364#336C2311yescharacteristic
365#336C2311yescharacteristic
366#336C2311yescharacteristic
367#336C2311yescharacteristic
368#336C2311yescharacteristic
369#336C2311yescharacteristic
370C2×#41C2412yes—
371C22×Q8—22no—
372C22×Q8#4111yescharacteristic
373#135—22no—
374#135—22no—
375C2×Q16C22×C411yescharacteristic
376C2×SD16C22×C412yes—
377C2×D8C22×C411yescharacteristic
378C2×M16C2412yes—
379C2×M16C2412yes—
380C2×M16C2412yes—
381C2×M16C2412yes—
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C22×C8C2411yescharacteristic
387C22×C8C2411yescharacteristic
388C22×C8C2411yescharacteristic
389C22×C8C2411yescharacteristic
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396C4⋊Q8C22×C412yes—
397C4⋊Q8C22×C412yes—
398C4⋊Q8C22×C412yes—
399C4⋊Q8C22×C412yes—
400C4⋊Q8C22×C412yes—
401C4⋊Q8C22×C412yes—
402#125—22no—
403#125—22no—
404#125—22no—
405#125—22no—
406#125—22no—
407#125—22no—
408#125C22×C412yes—
409#125C22×C412yes—
410#125C22×C412yes—
411#125C22×C412yes—
412#125C22×C412yes—
413#125C22×C412yes—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×Q8—22no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×Q8C22×C412yes—
443C4×Q8C22×C412yes—
444C4×Q8C22×C412yes—
445C4×Q8C22×C412yes—
446C4×Q8C22×C412yes—
447C4×Q8C22×C412yes—
448C4×Q8C22×C412yes—
449C4×Q8C22×C412yes—
450C4×Q8C2×D412yes—
451C4×Q8C2×D412yes—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4C22×C412yes—
459C4×D4C22×C412yes—
460C4×D4C22×C412yes—
461C4×D4C22×C412yes—
462C4×D4C22×C412yes—
463C4×D4C22×C412yes—
464#117—22no—
465#117—22no—
466#117—22no—
467#117C2412yes—
468#117C2412yes—
469#117C2412yes—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4#4111yescharacteristic
477C2×C4⋊C4#4111yescharacteristic
478C2×C4⋊C4#4111yescharacteristic
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491#108—22no—
492#108—22no—
493#108—22no—
494#108—22no—
495#108—42no—
496#108—42no—
497#108—42no—
498#107C22×C411yescharacteristic
499#107C22×C411yescharacteristic
500#107C22×C411yescharacteristic
501#107C22×C411yescharacteristic
502#107C22×C411yescharacteristic
503#107C22×C411yescharacteristic
504#107C22×C412yes—
505#107C22×C412yes—
506#107C22×C412yes—
507#107C22×C412yes—
508#107C22×C412yes—
509#107C22×C412yes—
510#106C22×C412yes—
511#106C22×C412yes—
512#106C22×C412yes—
513#106C22×C412yes—
514#106C22×C412yes—
515#106C22×C412yes—
516#106C22×C412yes—
517#106C22×C412yes—
518#106C22×C412yes—
519C4⋊C8—22no—
520C4⋊C8—22no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523C4⋊C8—22no—
524C4⋊C8—22no—
525C4⋊C8—22no—
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8—22no—
531C4⋊C8—22no—
532C4⋊C8—22no—
533C4⋊C8—22no—
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537C4⋊C8C22×C412yes—
538C4⋊C8C22×C412yes—
539C4⋊C8C22×C412yes—
540C4⋊C8C22×C412yes—
541C4⋊C8C22×C412yes—
542C4⋊C8C22×C412yes—
543C4⋊C8C2×D412yes—
544C4⋊C8C2×D412yes—
545C4⋊C8C2×D412yes—
546C4⋊C8C2×D412yes—
547C4⋊C8C2×D412yes—
548C4⋊C8C2×D412yes—
549#104—24no—
550#104—42no—
551#104—42no—
552#104—42no—
553#103C22×C412yes—
554#103C22×C412yes—
555#103C22×C412yes—
556#103C22×C412yes—
557#103C22×C412yes—
558#103C22×C412yes—
559#102C22×C412yes—
560#102C22×C412yes—
561#102C22×C412yes—
562#102C22×C412yes—
563#102C22×C412yes—
564#102C22×C412yes—
565C22⋊C8—22no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—22no—
570C22⋊C8—22no—
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#97—22no—
575#97—22no—
576#97—22no—
577#97—22no—
578#97—22no—
579#97—22no—
580#97—22no—
581#97—22no—
582#97—22no—
583#97—22no—
584#97—22no—
585#97—22no—
586#97—41no—
587#97—41no—
588#97C22×C412yes—
589#97C22×C412yes—
590#97C22×C412yes—
591#97C22×C412yes—
592#97C2×D411yescharacteristic
593#97C2×D411yescharacteristic
594#97C2×D412yes—
595#97C2×D412yes—
596#97C2×D411yescharacteristic
597#97C2×D411yescharacteristic
598C4×C8—22no—
599C4×C8—22no—
600C4×C8—22no—
601C4×C8—22no—
602C4×C8—22no—
603C4×C8—22no—
604C4×C8—22no—
605C4×C8—22no—
606C4×C8—22no—
607C4×C8—22no—
608C4×C8—22no—
609C4×C8—22no—
610C4×C8—41no—
611C4×C8C22×C411yescharacteristic
612C4×C8C22×C411yescharacteristic
613C4×C8C22×C411yescharacteristic
614C4×C8C22×C411yescharacteristic
615C4×C8C2×D412yes—
616C4×C8C2×D412yes—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622#95—21no—
623#95—21no—
624#41—22no—
625#41—22no—
626#41—22no—
627#41—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—81no—
635C2×Q8—84no—
636C2×Q8C4×D412yes—
637C2×Q8C4×D412yes—
638C2×Q8C23×C412yes—
639C2×D4—22no—
640C2×D4C23×C412yes—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4C2×#4111yescharacteristic
653C22×C4C2×#4111yescharacteristic
654C22×C4C2×#4111yescharacteristic
655C22×C4C2×#4111yescharacteristic
656C22×C4C2×#4111yescharacteristic
657C22×C4C2×#4111yescharacteristic
658C22×C4C2511yescharacteristic
659Q16—22no—
660SD16—24no—
661D8—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—22no—
668M16—22no—
669M16—22no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8C23×C411yescharacteristic
689C2×C8C23×C411yescharacteristic
690C2×C8C23×C412yes—
691C2×C8C23×C412yes—
692C2×C8C23×C411yescharacteristic
693C2×C8C23×C411yescharacteristic
694C2×C8C22×D412yes—
695C2×C8C22×D411yescharacteristic
696C2×C8C22×D411yescharacteristic
697C2×C8C22×D412yes—
698C2×C8C22×D411yescharacteristic
699C2×C8C22×D411yescharacteristic
700C2×C82−1+412yes—
701C2×C82−1+412yes—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—81no—
727C4⋊C4—81no—
728C4⋊C4—81no—
729C4⋊C4C4×D412yes—
730C4⋊C4C4×D412yes—
731C4⋊C4C4×D412yes—
732C4⋊C4C4×D412yes—
733C4⋊C4C4×D412yes—
734C4⋊C4C4×D412yes—
735C4⋊C4C23×C412yes—
736C4⋊C4C23×C412yes—
737C4⋊C4C23×C412yes—
738C4⋊C4C23×C412yes—
739C4⋊C4C23×C412yes—
740C4⋊C4C23×C412yes—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—22no—
758C42—22no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—81no—
767C42—81no—
768C42C23×C411yescharacteristic
769C42C23×C411yescharacteristic
770C42C23×C412yes—
771C42C23×C412yes—
772C42C22×D411yescharacteristic
773C42C22×D412yes—
774C42C22×D412yes—
775C42C22×D411yescharacteristic
776C422−1+412yes—
777C23—22no—
778C23C22×#4111yescharacteristic
779Q8—22no—
780Q8—22no—
781Q8—42no—
782Q8—42no—
783Q8—44no—
784Q8—82no—
785Q8—82no—
786Q8—82no—
787Q8—82no—
788Q8—82no—
789D4—22no—
790D4—22no—
791D4—42no—
792D4—42no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—44no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—82no—
824C2×C4—82no—
825C2×C4—82no—
826C2×C4C2×C4×D411yescharacteristic
827C2×C4C2×C4×D411yescharacteristic
828C2×C4C2×C4×D412yes—
829C2×C4C2×C4×D412yes—
830C2×C4C2×C4×D412yes—
831C2×C4C2×C4×D412yes—
832C2×C4C2×C4×D411yescharacteristic
833C2×C4C2×C4×D411yescharacteristic
834C2×C4C24×C411yescharacteristic
835C2×C4C23×D411yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4C2×2−1+411yescharacteristic
839C2×C4#58511yescharacteristic
840C8—22no—
841C8—22no—
842C8—21no—
843C8—21no—
844C8—21no—
845C8—21no—
846C8—21no—
847C8—21no—
848C8—22no—
849C8—22no—
850C8—42no—
851C8—42no—
852C8—42no—
853C8—42no—
854C8#51912yes—
855C8#51912yes—
856C22—21no—
857C22—21no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22C22×C4×D411yescharacteristic
862C22#351811yescharacteristic
863C22#352311yescharacteristic
864C4—22no—
865C4—21no—
866C4—22no—
867C4—21no—
868C4—21no—
869C4—22no—
870C4—22no—
871C4—21no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4C2×#51911yescharacteristic
884C4C4×2−1+411yescharacteristic
885C4#349711yescharacteristic
886C4#349911yescharacteristic
887C2—21no—
888C2—21no—
889C2—82no—
890C2#3431111yescharacteristic
891C2#6018211yescharacteristic
892C2#6018411yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radicalC2×#135C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#446 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60254C2semidirect
3. #23172C2semidirect
4. #23172C2semidirect
5. #23171C2semidirect
6. #23082C2semidirect
7. #23082C2semidirect
8. #23081C2semidirect
12. #22733C2semidirect
13. #22529C2semidirect
14. #22132C2semidirect
15. #22132C2semidirect
16. #22131C2semidirect
17. #21737C2semidirect
18. #21736C2semidirect
19. #21733C2semidirect
23. #20518C2semidirect
25. #3390C4semidirect
26. #3389C4semidirect
27. #3388C4semidirect
28. #3388C4semidirect
29. #3387C4semidirect
30. #3386C4semidirect
31. #3385C4semidirect
32. #3384C4semidirect

Maximal subgroups

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

subgroupindex
#613652
#602542
#231722
#231712
#230822
#230812
#228042
#228032
#227332
#225292
#221322
#221312
#217372
#217362
#217332
#212972
#212962
#212942
#205182