Finite Group Databasebeta

← #6498880

Subgroups — #6498880

Order 512.

2057 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3211C211yesmaximal, characteristic
3C2×#3172C211yesmaximal, characteristic, complemented
4C2×#3140C211yesmaximal, characteristic, complemented
5#37545C211yesmaximal, characteristic, complemented
6#37537C211yesmaximal, characteristic, complemented
7#33247C211yesmaximal, characteristic, complemented
8#33245C211yesmaximal, characteristic, complemented
9#33229C211yesmaximal, characteristic, complemented
10#33229C211yesmaximal, characteristic, complemented
11#30290C211yesmaximal, characteristic, complemented
12#30289C211yesmaximal, characteristic, complemented
13#30275C211yesmaximal, characteristic, complemented
14#30275C211yesmaximal, characteristic, complemented
15#28411C212yesmaximal, complemented
16#28410C212yesmaximal, complemented
17#28407C212yesmaximal, complemented
18#28406C212yesmaximal, complemented
19#28367C212yesmaximal, complemented
20#28361C212yesmaximal, complemented
21#28357C212yesmaximal
22#28355C212yesmaximal, complemented
23#20482C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C22×#124C2211yescharacteristic
28#3231—28no—
29#3211—28no—
30#3172—28no—
31C2×#501C2211yescharacteristic, complemented
32C2×#500C2211yescharacteristic, complemented
33C2×#498C2211yescharacteristic, complemented
34C2×#497C2211yescharacteristic, complemented
35C2×#495C2211yescharacteristic
36C2×#495C2211yescharacteristic
37#3140—28no—
38C2×#491C2211yescharacteristic, complemented
39C2×#489C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#489C2211yescharacteristic, complemented
44C2×#488C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#488C2212yes—
47C2×#488C2212yes—
48C2×#487C2211yescharacteristic, complemented
49C2×#487C2211yescharacteristic, complemented
50C2×#485C2212yes—
51C2×#485C2212yes—
52C2×#479C2212yescomplemented
53C2×#479C2212yescomplemented
54C2×#470C2212yes—
55C2×#468C2212yes—
56C2×#464C2211yescharacteristic
57C2×#464C2211yescharacteristic
58C2×#463C2211yescharacteristic
59C2×#463C2211yescharacteristic
60C2×#451C2211yescharacteristic
61C2×#448C2211yescharacteristic
62C2×#450C2211yescharacteristic
63C2×#447C2211yescharacteristic
64C2×C4×Q16C2212yescomplemented
65C2×C4×SD16C2212yescomplemented
66C2×#431C2211yescharacteristic
67C2×#419C2212yes—
68C2×#418C2212yes—
69C2×C4×M16C2211yescharacteristic
70#2820—22no—
71#2814—22no—
72#2660C2211yescharacteristic, complemented
73#2660C2211yescharacteristic, complemented
74#2658C2211yescharacteristic
75#2658C2211yescharacteristic
76#2640C2211yescharacteristic
77#2640C2211yescharacteristic
78#2640C2211yescharacteristic, complemented
79#2640C2211yescharacteristic, complemented
80#2638—22no—
81#2637—22no—
82#2632—22no—
83#2626—22no—
84#2599—22no—
85#2566C2212yescomplemented
86#2565C2212yescomplemented
87#2545C2212yes—
88#2545C2212yes—
89#2500C2212yes—
90#2499C2212yes—
91#2482—22no—
92#2435C2212yes—
93#2434C2212yes—
94#2283C2211yescharacteristic
95#2097C2212yescomplemented
96#2097C2212yescomplemented
97#2096C2212yescomplemented
98#2095C2212yescomplemented
99#2094C2212yes—
100#2093C2212yes—
101#2092C2212yes—
102#2092C2212yes—
103#2016C2212yescomplemented
104#2016C2212yescomplemented
105#2015C2212yes—
106#2015C2212yes—
107#2013C2212yescomplemented
108#2013C2212yescomplemented
109#2012C2212yes—
110#2012C2212yes—
111#1973C2212yes—
112#1973C2212yescomplemented
113#1972C2212yes—
114#1971C2212yescomplemented
115#1970C2212yes—
116#1969C2212yescomplemented
117#1968C2212yes—
118#1968C2212yescomplemented
119#1960C2212yescomplemented
120#1960C2212yescomplemented
121#1959C2212yes—
122#1959C2212yes—
123#1958C2212yes—
124#1958C2212yes—
125#1956C2212yescomplemented
126#1956C2212yescomplemented
127#1770C2212yescomplemented
128C8×C4⋊C4C2212yescomplemented
129#1753C2212yes—
130#1753C2212yes—
131#1746C2211yescharacteristic, complemented
132#1746C2211yescharacteristic, complemented
133#1726C2211yescharacteristic, complemented
134#1726C2211yescharacteristic, complemented
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C22×Q16C2311yescharacteristic
138C22×Q16C2311yescharacteristic
139C22×Q16C2312yes—
140C22×SD16C2311yescharacteristic
141C22×SD16C2311yescharacteristic
142C22×SD16C2311yescharacteristic
143C22×SD16C2311yescharacteristic
144C22×SD16C2312yes—
145C22×D8C2311yescharacteristic
146C22×D8C2311yescharacteristic
147C22×M16C2312yes—
148#533—24no—
149#533—24no—
150#533—24no—
151#533—24no—
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2312yes—
155C2×C4⋊Q8C2311yescharacteristic
156C2×C4⋊Q8C2311yescharacteristic
157C2×C4⋊Q8C2311yescharacteristic
158#529—24no—
159#529—24no—
160C2×#126—21no—
161C2×#125—21no—
162C2×#125C2312yes—
163C2×#125C2311yescharacteristic
164C2×#124—21no—
165C2×#124—21no—
166C2×#124—24no—
167C2×#124—24no—
168C2×#124C2311yescharacteristic
169C2×#124C2311yescharacteristic
170C2×#124C2311yescharacteristic
171C2×#124C2311yescharacteristic
172C2×#124C2311yescharacteristic
173C2×#124C2312yes—
174C2×#124C2312yes—
175C2×#123—21no—
176C2×C22⋊Q8—21no—
177C2×C22⋊Q8—21no—
178C2×C22⋊Q8—21no—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2311yescharacteristic
181C2×#121C2311yescharacteristic
182C2×C4×Q8—21no—
183C2×C4×Q8—21no—
184C2×C4×Q8—21no—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×D4—21no—
188C2×C4×D4C2311yescharacteristic
189C2×#117—21no—
190C2×#117—21no—
191C2×#117C2312yes—
192C22×C22⋊C4—21no—
193C22×C22⋊C4—21no—
194C22×C42C2311yescharacteristic
195#501—24no—
196#500—24no—
197#498—24no—
198#497—24no—
199#495—24no—
200#495—24no—
201#491—24no—
202#489—24no—
203#489—24no—
204#489—24no—
205#489—24no—
206#489—24no—
207#488—28no—
208#488—28no—
209#488—24no—
210#488—24no—
211#487—24no—
212#487—24no—
213#485—28no—
214#485—28no—
215#479—28no—
216#479—28no—
217#470—28no—
218#468—28no—
219#464—24no—
220#464—24no—
221#463—24no—
222#463—24no—
223#451—24no—
224#450—24no—
225#448—24no—
226#447—24no—
227C4×Q16—28no—
228C4×SD16—28no—
229#431D418yes—
230C2×#107C2312yes—
231C2×#107C2312yes—
232C2×#107C2312yes—
233C2×#106C2312yes—
234C2×#106C2312yes—
235C2×#106C2312yes—
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238#419—28no—
239#418—28no—
240C2×#103C2312yes—
241C2×#103C2312yes—
242C2×#103C2312yes—
243C2×#103C2312yes—
244C2×#103C2311yescharacteristic
245C2×#103C2312yes—
246C2×#103C2311yescharacteristic
247C2×#103C2312yes—
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2312yes—
251C2×#103C2312yes—
252C2×#103C2312yes—
253C2×#103C2312yes—
254C2×#103C2312yes—
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2312yes—
258C2×#102C2312yes—
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2312yes—
262C2×#102C2312yes—
263C2×#102C2312yes—
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C4×M16D418yes—
267C2×#97C2312yes—
268C2×#97C2312yes—
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×C4×C8C2312yes—
272C2×C4×C8C2312yes—
273C2×C4×C8C2312yes—
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276#399—22no—
277#399—22no—
278#399—22no—
279#399—22no—
280#398—24no—
281#398—22no—
282#398—22no—
283#397—24no—
284#397—22no—
285#397—22no—
286#397—22no—
287#397—22no—
288#396—24no—
289#396—24no—
290#396—24no—
291#395—24no—
292#395—22no—
293#395—22no—
294#394—24no—
295#394—24no—
296#393—22no—
297#393—22no—
298#393—22no—
299#393—22no—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#390C2312yes—
305#390C2312yes—
306#390C2312yes—
307#390C2312yes—
308#388—24no—
309#388—24no—
310#388—24no—
311#387—24no—
312#387—24no—
313#385—24no—
314#385—24no—
315#384C2312yes—
316#384C2312yes—
317#383D412yes—
318#382D412yes—
319#382C2312yes—
320#382C2312yes—
321#381D412yes—
322#380D412yes—
323#379—24no—
324C4×C4⋊C4C2312yes—
325C4×C22⋊C4C2312yes—
326#376C2311yescharacteristic
327#376C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331#336C2312yes—
332C25—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8C2412yes—
342C22×Q8C2411yescharacteristic
343C22×Q8C2411yescharacteristic
344C22×Q8C2411yescharacteristic
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4C2411yescharacteristic
352C22×D4C2411yescharacteristic
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2411yescharacteristic
359C2×Q16—24no—
360C2×Q16—22no—
361C2×Q16—22no—
362C2×Q16—42no—
363C2×Q16—42no—
364C2×Q16—42no—
365C2×Q16—42no—
366C2×SD16—24no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—42no—
372C2×SD16—42no—
373C2×SD16—42no—
374C2×SD16—42no—
375C2×SD16—42no—
376C2×SD16—42no—
377C2×D8—22no—
378C2×D8—22no—
379C2×D8—42no—
380C2×D8—42no—
381C2×M16—42no—
382C2×M16—42no—
383C2×M16C2×D418yes—
384C22×C8C2412yes—
385C22×C8C2412yes—
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⋊Q8—22no—
397C4⋊Q8—22no—
398C4⋊Q8—42no—
399C4⋊Q8—42no—
400C4⋊Q8—42no—
401C4⋊Q8—42no—
402#126—44no—
403#125—22no—
404#125—22no—
405#125—24no—
406#125—24no—
407#125—44no—
408#124—22no—
409#124—22no—
410#124—22no—
411#124—22no—
412#124—22no—
413#124—22no—
414#124—22no—
415#124—22no—
416#124—22no—
417#124—22no—
418#124—42no—
419#124—42no—
420#124—42no—
421#124—42no—
422#124—44no—
423#124—44no—
424#123—44no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—24no—
428C22⋊Q8—24no—
429C22⋊Q8—44no—
430C22⋊Q8—44no—
431C22⋊Q8—44no—
432#121—22no—
433#121—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—24no—
437C4×Q8—24no—
438C4×Q8—44no—
439C4×Q8—44no—
440C4×Q8—44no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—44no—
444#117—24no—
445#117—24no—
446#117—44no—
447#117—44no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2412yes—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—44no—
493C2×C22⋊C4—44no—
494C2×C22⋊C4C2×D414yes—
495C2×C42—21no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42C2×D411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D414yes—
501C2×C42C2×D414yes—
502C2×C42C2412yes—
503C2×C42C2412yes—
504C2×C42C2411yescharacteristic
505C2×C42C2411yescharacteristic
506#107—24no—
507#107—24no—
508#107—24no—
509#106—24no—
510#106—24no—
511#106—24no—
512C4⋊C8C2×D414yes—
513C4⋊C8C2×D414yes—
514#103—24no—
515#103—24no—
516#103—24no—
517#103—24no—
518#103—24no—
519#103—24no—
520#103—24no—
521#103—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#103—24no—
526#103—24no—
527#103—24no—
528#103—24no—
529#102—24no—
530#102—24no—
531#102—24no—
532#102—24no—
533#102—24no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538C22⋊C8C2×D414yes—
539C22⋊C8C2×D414yes—
540#97—42no—
541#97—42no—
542#97C2×D414yes—
543#97C2×D414yes—
544C4×C8—42no—
545C4×C8—42no—
546C4×C8C2×D418yes—
547C4×C8C2×D414yes—
548C4×C8C2×D414yes—
549#95—24no—
550#95—24no—
551#95—24no—
552#95—24no—
553#95—24no—
554#95—24no—
555#95C2×D412yes—
556#95C2×D412yes—
557#95C2×D412yes—
558#95C2×D412yes—
559#95C2×D414yes—
560#95C2×D414yes—
561C24—21no—
562C24—21no—
563C24—21no—
564C24—44no—
565C24—42no—
566C24—82no—
567C24—82no—
568C24C22×D411yescharacteristic
569C2×Q8—22no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—48no—
588C2×Q8—42no—
589C2×Q8—42no—
590C2×Q8—42no—
591C2×Q8—42no—
592C2×Q8—82no—
593C2×Q8—82no—
594C2×Q8—82no—
595C2×Q8—82no—
596C2×Q8—82no—
597C2×Q8—82no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—48no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—82no—
614C2×D4—82no—
615C2×D4—82no—
616C2×D4—82no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—82no—
633C22×C4—82no—
634C22×C4#12714yes—
635C22×C4#12714yes—
636C22×C4C22×D414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C2511yescharacteristic
646Q16—48no—
647Q16—82no—
648Q16—82no—
649SD16—48no—
650SD16—82no—
651SD16—82no—
652SD16—82no—
653SD16—82no—
654D8—82no—
655D8—82no—
656M16—48no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8C22×D414yes—
666C2×C8C22×D414yes—
667C2×C8C22×D412yes—
668C2×C8C22×D412yes—
669C2×C8C22×D412yes—
670C2×C8C22×D412yes—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—44no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—84no—
696C4⋊C4—84no—
697C4⋊C4—84no—
698C4⋊C4—84no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—84no—
716C22⋊C4—84no—
717C22⋊C4—84no—
718C22⋊C4—84no—
719C22⋊C4—84no—
720C22⋊C4—84no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—44no—
726C42—42no—
727C42—44no—
728C42#12714yes—
729C42#12714yes—
730C42C22×D412yes—
731C42C22×D412yes—
732C42C22×D412yes—
733C42C22×D412yes—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—168no—
753C23C2×#12712yes—
754C23C23×D411yescharacteristic
755Q8—42no—
756Q8—42no—
757Q8—42no—
758Q8—42no—
759Q8—42no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—42no—
767Q8—42no—
768Q8—84no—
769Q8—84no—
770Q8—84no—
771Q8—84no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4C2×#12712yes—
821C2×C4C2×#12712yes—
822C2×C4C2×#12712yes—
823C2×C4C2×#12712yes—
824C2×C4C2×#12712yes—
825C2×C4C23×D411yescharacteristic
826C2×C4C23×D411yescharacteristic
827C2×C4#58512yes—
828C2×C4#58512yes—
829C8—24no—
830C8—24no—
831C8—22no—
832C8—22no—
833C8—22no—
834C8—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22—84no—
844C22—84no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—168no—
852C22C22×#12711yescharacteristic
853C22#350012yes—
854C22#358412yes—
855C22#358612yes—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—44no—
862C4—44no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4—82no—
869C4—82no—
870C4—81no—
871C4—82no—
872C4#344912yes—
873C4#350011yescharacteristic
874C4#350011yescharacteristic
875C2—42no—
876C2—161no—
877C2—161no—
878C2—161no—
879C2#3532911yescharacteristic
880C2#6064311yescharacteristic
881C2#6064511yescharacteristic
882C2#6261514yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3231C2semidirect
3. C2×#3172C2semidirect
4. C2×#3140C2semidirect
5. #37545C2semidirect
6. #37537C2semidirect
7. #33247C2semidirect
8. #33245C2semidirect
9. #33229C2semidirect
10. #33229C2semidirect
11. #30290C2semidirect
12. #30289C2semidirect
13. #30275C2semidirect
14. #30275C2semidirect
15. #28411C2semidirect
16. #28410C2semidirect
17. #28407C2semidirect
18. #28406C2semidirect
19. #28367C2semidirect
20. #28361C2semidirect
22. #28355C2semidirect
23. #20482C2semidirect
31. C2×#501C22semidirect
32. C2×#500C22semidirect
33. C2×#498C22semidirect
34. C2×#497C22semidirect
38. C2×#491C22semidirect
43. C2×#489C22semidirect
48. C2×#487C22semidirect
49. C2×#487C22semidirect
52. C2×#479C22semidirect
53. C2×#479C22semidirect
64. C2×C4×Q16C22semidirect
65. C2×C4×SD16C22semidirect
72. #2660C22semidirect
73. #2660C22semidirect
78. #2640C22semidirect
79. #2640C22semidirect
85. #2566C22semidirect
86. #2565C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
97. #2096C22semidirect
98. #2095C22semidirect
103. #2016C22semidirect
104. #2016C22semidirect
107. #2013C22semidirect
108. #2013C22semidirect
112. #1973C22semidirect
114. #1971C22semidirect
116. #1969C22semidirect
118. #1968C22semidirect
119. #1960C22semidirect
120. #1960C22semidirect
125. #1956C22semidirect
126. #1956C22semidirect
127. #1770C22semidirect
128. C8×C4⋊C4C22semidirect
131. #1746C22semidirect
132. #1746C22semidirect
133. #1726C22semidirect
134. #1726C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32112
C2×#31722
C2×#31402
#375452
#375372
#332472
#332452
#332292
#302902
#302892
#302752
#284112
#284102
#284072
#284062
#283672
#283612
#283572
#283552
#204822