Finite Group Databasebeta

← #6569539

Subgroups — #6569539

Order 512.

2220 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3337C212yesmaximal, complemented
2C2×#3296C212yesmaximal, complemented
3#36362C211yesmaximal, characteristic
4#36181C211yesmaximal, characteristic, complemented
5#30282C211yesmaximal, characteristic, complemented
6#30244C211yesmaximal, characteristic, complemented
7#30240C211yesmaximal, characteristic, complemented
8#28537C212yesmaximal, complemented
9#28516C211yesmaximal, characteristic, complemented
10#28412C212yesmaximal, complemented
11#28380C211yesmaximal, characteristic, complemented
12#28352C212yesmaximal, complemented
13#28344C212yesmaximal, complemented
14#28317C211yesmaximal, characteristic, complemented
15#28311C211yesmaximal, characteristic, complemented
16#27937C212yesmaximal, complemented
17#27933C212yesmaximal, complemented
18#27917C211yesmaximal, characteristic, complemented
19#27914C211yesmaximal, characteristic, complemented
20#23799C211yesmaximal, characteristic, complemented
21#23730C211yesmaximal, characteristic, complemented
22C2×#2094C211yesmaximal, characteristic, complemented
23#20558C211yesmaximal, characteristic, complemented
24C2×#553C2211yescharacteristic
25C2×#552C2212yes—
26C2×#546C2211yescharacteristic
27#3337—216no—
28#3296—216no—
29C2×#499C2212yescomplemented
30C2×#488C2212yes—
31C2×#484C2212yes—
32C2×#485C2212yescomplemented
33C2×#482C2212yes—
34C2×#482C2212yescomplemented
35C2×#483C2212yes—
36C2×#480C2212yes—
37C2×#479C2212yescomplemented
38C2×#478C2212yes—
39C2×#478C2212yescomplemented
40C2×#467C2212yes—
41C2×#465C2212yes—
42C2×#465C2212yes—
43C2×#465C2212yescomplemented
44C2×#464C2212yes—
45C2×#452C2212yes—
46C2×#450C2212yes—
47C2×C4×SD16C2212yes—
48C2×C4×SD16C2212yescomplemented
49C2×C8×D4C2212yes—
50C2×#427C2212yescomplemented
51C22×#106C2212yes—
52C2×#416C2212yes—
53C22×#102C2212yes—
54#2861C2211yescharacteristic
55#2859C2211yescharacteristic, complemented
56#2857C2211yescharacteristic
57#2857C2211yescharacteristic, complemented
58#2856C2211yescharacteristic
59#2850C2211yescharacteristic
60#2566C2211yescharacteristic
61#2565C2212yescomplemented
62#2554—22no—
63#2544C2211yescharacteristic
64#2506—22no—
65#2503C2212yes—
66#2502C2211yescharacteristic
67#2500C2211yescharacteristic
68#2499C2212yescomplemented
69#2496—22no—
70#2486—22no—
71#2464—22no—
72#2433C2211yescharacteristic
73#2431C2211yescharacteristic
74#2424—22no—
75#2358—22no—
76#2344—22no—
77C4×C4⋊Q8C2211yescharacteristic, complemented
78C4×#127C2211yescharacteristic
79#2297C2211yescharacteristic
80C2×#390C2211yescharacteristic
81#2285C2211yescharacteristic, complemented
82C2×#384C2211yescharacteristic
83C42×D4C2211yescharacteristic
84#2097C2212yescomplemented
85#2097C2212yescomplemented
86#2097C2212yescomplemented
87#2096C2212yescomplemented
88#2096C2212yescomplemented
89#2096C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2095C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2094C2211yescharacteristic
94#2094C2212yes—
95#2094C2211yescharacteristic
96#2094C2212yes—
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic, complemented
99#2094C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic, complemented
103#2092C2212yes—
104#2092C2212yes—
105#2016C2211yescharacteristic, complemented
106#2015C2212yescomplemented
107#2014C2212yes—
108#2014C2212yes—
109#2013C2211yescharacteristic
110#2013C2211yescharacteristic
111#2013C2211yescharacteristic, complemented
112#1973C2212yes—
113#1973C2212yes—
114#1973C2212yes—
115#1973C2212yes—
116#1971C2212yescomplemented
117#1971C2212yescomplemented
118#1961C2212yes—
119#1961C2212yes—
120#1959C2212yescomplemented
121#1847C2212yescomplemented
122#1847C2212yescomplemented
123#1847C2212yescomplemented
124#1770C2212yescomplemented
125#1767C2211yescharacteristic, complemented
126#1752C2212yes—
127#1752C2212yescomplemented
128#1749C2211yescharacteristic
129#1749C2211yescharacteristic, complemented
130#1744C2211yescharacteristic, complemented
131C2×#336C2211yescharacteristic
132C2×#336C2211yescharacteristic, complemented
133C22×#41C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C22×Q16C2312yes—
136C22×SD16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C23×C8C2312yes—
140C23×C8C2312yes—
141#553—28no—
142#552—28no—
143#552—28no—
144#546—28no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#127C2311yescharacteristic
148C2×#126—21no—
149C2×#126—22no—
150C2×#125—22no—
151C2×#125C2312yes—
152C2×#125C2311yescharacteristic
153C2×#124C2311yescharacteristic
154C2×#124C2311yescharacteristic
155C2×#123—22no—
156C2×#123—21no—
157C2×#123—21no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2312yes—
161C2×#121—21no—
162C2×#121—22no—
163C2×#121—21no—
164C2×#121C2311yescharacteristic
165C2×#121C2311yescharacteristic
166C2×#121C2311yescharacteristic
167C2×#120—21no—
168C2×#120—22no—
169C2×C4×Q8C2312yes—
170C2×C4×D4—21no—
171C2×C4×D4—22no—
172C2×C4×D4D412yes—
173C2×C4×D4C2311yescharacteristic
174C2×C4×D4C2311yescharacteristic
175C2×C4×D4C2311yescharacteristic
176C2×#117—22no—
177C2×#117C2312yes—
178C2×#117C2311yescharacteristic
179C22×C4⋊C4—22no—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4—22no—
183C22×C22⋊C4—21no—
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186#499—28no—
187#488—28no—
188#485—28no—
189#484—28no—
190#483—28no—
191#482—28no—
192#482—28no—
193#480—28no—
194#479—28no—
195#478—28no—
196#478—28no—
197#467—28no—
198#465—28no—
199#465—28no—
200#465—28no—
201#464—28no—
202#452—28no—
203#450—28no—
204C4×SD16—28no—
205C4×SD16—28no—
206C8×D4D4116yescomplemented
207#427—28no—
208C2×#107C2312yes—
209C2×#107C2312yes—
210C2×#107C2312yes—
211C2×#107C2312yes—
212C2×#107C2312yes—
213C2×#106—28no—
214C2×#106C2312yes—
215C2×#106C2312yes—
216C2×#106C2312yes—
217C2×#106C2312yes—
218C2×#106C2312yes—
219C2×#106C2312yes—
220C2×#106C2312yes—
221C2×C4⋊C8C2312yes—
222#416—28no—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×#103C2312yes—
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×#103C2312yes—
229C2×#103C2312yes—
230C2×#102—28no—
231C2×#102C2312yes—
232C2×#102C2312yes—
233C2×#102C2312yes—
234C2×#102C2312yes—
235C2×#102C2312yes—
236C2×#102C2312yes—
237C2×#102C2312yes—
238C2×#102C2312yes—
239C2×#102C2312yes—
240C2×C22⋊C8C2312yes—
241C2×C22⋊C8C2312yes—
242C2×#97C2312yes—
243C2×#97C2312yes—
244C2×#97C2312yes—
245C2×C4×C8C2312yes—
246#400—24no—
247#398—24no—
248#398—22no—
249#397—24no—
250#396—22no—
251#394—22no—
252#394—22no—
253#392—22no—
254#392—22no—
255#391C2312yes—
256#391C2312yes—
257#391C2312yes—
258#391C2311yescharacteristic
259#391C2311yescharacteristic
260#391C2311yescharacteristic
261#390—22no—
262#390—22no—
263#390—22no—
264#390C2311yescharacteristic
265#390C2311yescharacteristic
266#390C2311yescharacteristic
267#390C2311yescharacteristic
268#390C2311yescharacteristic
269#390C2311yescharacteristic
270#390C2311yescharacteristic
271#389—22no—
272#389—22no—
273#389—22no—
274#389—22no—
275#389—22no—
276#388—22no—
277#388—22no—
278#388—22no—
279#388—22no—
280#387—24no—
281#387—24no—
282#386—22no—
283#386—22no—
284#386—22no—
285#386—22no—
286#385—22no—
287#385—22no—
288#384—22no—
289#384C2311yescharacteristic
290#384C2311yescharacteristic
291#384C2312yes—
292#384C2311yescharacteristic
293#384C2311yescharacteristic
294#384C2311yescharacteristic
295#382C2312yes—
296#382C2311yescharacteristic
297#382C2312yes—
298#381—24no—
299#380—22no—
300#380—22no—
301#380—22no—
302C4×C4⋊C4—22no—
303C4×C4⋊C4—22no—
304C4×C4⋊C4D412yes—
305C4×C4⋊C4C2311yescharacteristic
306C4×C22⋊C4—22no—
307C4×C22⋊C4D412yes—
308C4×C22⋊C4D412yes—
309C4×C22⋊C4C2311yescharacteristic
310C4×C22⋊C4C2311yescharacteristic
311C43C2311yescharacteristic
312#336C2312yes—
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2311yescharacteristic
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318#336C2312yes—
319C25—21no—
320C2×#41—22no—
321C2×#41—24no—
322C2×#41—41no—
323C2×#41—42no—
324C22×Q8C2412yes—
325C22×Q8C2411yescharacteristic
326C22×D4—22no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4—41no—
337C22×D4C2×D411yescharacteristic
338C22×D4C2411yescharacteristic
339C22×D4C2411yescharacteristic
340C22×D4C2411yescharacteristic
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4C2×D412yes—
347C23×C4C2×D412yes—
348C23×C4C2411yescharacteristic
349C23×C4C2411yescharacteristic
350C2×Q16—24no—
351C2×Q16—42no—
352C2×Q16—42no—
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16—24no—
356C2×SD16—24no—
357C2×SD16—42no—
358C2×SD16—42no—
359C2×SD16—42no—
360C2×SD16—42no—
361C2×SD16—42no—
362C22×C8—42no—
363C22×C8—42no—
364C22×C8—42no—
365C22×C8—42no—
366C22×C8C2×D418yes—
367C22×C8C2×D418yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C4⋊Q8—42no—
373#127—22no—
374#127—41no—
375#127—42no—
376#126—44no—
377#126—48no—
378#125—24no—
379#125—24no—
380#125—24no—
381#125—48no—
382#124—24no—
383#124—42no—
384#123—48no—
385#123—44no—
386#123—44no—
387C22⋊Q8—24no—
388C22⋊Q8—24no—
389C22⋊Q8—24no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392#121—24no—
393#121—24no—
394#121—24no—
395#121—44no—
396#121—44no—
397#121—84no—
398#120—48no—
399#120—44no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×D4—24no—
403C4×D4—24no—
404C4×D4—44no—
405C4×D4—44no—
406C4×D4—84no—
407C4×D4C2×D418yes—
408#117—24no—
409#117—24no—
410#117—24no—
411#117—48no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—48no—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—44no—
463C2×C22⋊C4—84no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—42no—
472C2×C42—42no—
473C2×C42C2×D412yes—
474C2×C42C2×D412yes—
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—24no—
483#107—24no—
484#107—24no—
485#107—24no—
486#107—24no—
487#106—24no—
488#106—24no—
489#106—24no—
490#106—24no—
491#106—24no—
492#106—24no—
493#106—24no—
494C4⋊C8C2×D418yes—
495#103—24no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#102—24no—
503#102—24no—
504#102—24no—
505#102—24no—
506#102—24no—
507#102—24no—
508#102—24no—
509#102—24no—
510#102—24no—
511C22⋊C8C2×D418yes—
512C22⋊C8C2×D418yes—
513#97—42no—
514#97—42no—
515#97—42no—
516C4×C8C2×D418yes—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—22no—
525#95—22no—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—42no—
533C24—42no—
534C24—44no—
535C24—82no—
536C24—81no—
537C24C22×D411yescharacteristic
538C24C22×D411yescharacteristic
539#41—48no—
540#41—84no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4—82no—
577C2×D4—81no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4—81no—
581C2×D4—82no—
582C2×D4—82no—
583C2×D4#12714yes—
584C2×D42−1+412yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D414yes—
625C22×C4C22×D414yes—
626C22×C4C22×D412yes—
627C22×C4C2511yescharacteristic
628Q16—84no—
629SD16—48no—
630SD16—48no—
631SD16—84no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—48no—
641C2×C8—48no—
642C2×C8C22×D414yes—
643C2×C8C22×D414yes—
644C2×C8C22×D414yes—
645C2×C8C22×D414yes—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4#12714yes—
675C22⋊C4—24no—
676C22⋊C4—42no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4#12714yes—
698C22⋊C4#12714yes—
699C42—24no—
700C42—21no—
701C42—21no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—44no—
709C42—42no—
710C42—44no—
711C42C22×D414yes—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—84no—
735C23—88no—
736C23—84no—
737C23—164no—
738C23—162no—
739C23C2×#12712yes—
740C23C2×#12712yes—
741C23#57514yes—
742C23C23×D411yescharacteristic
743Q8—42no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749D4—28no—
750D4—24no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—84no—
757D4—88no—
758D4—84no—
759D4—84no—
760D4—164no—
761D4—162no—
762D4—162no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—88no—
808C2×C4—162no—
809C2×C4—162no—
810C2×C4—162no—
811C2×C4C2×#12712yes—
812C2×C4C2×#12712yes—
813C2×C4C2×#12712yes—
814C2×C4C2×#12712yes—
815C2×C4#57714yes—
816C2×C4C23×D412yes—
817C2×C4C2×2−1+411yescharacteristic
818C2×C4#58511yescharacteristic
819C2×C4#58512yes—
820C8—24no—
821C8—24no—
822C8—24no—
823C8—24no—
824C22—24no—
825C22—24no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—82no—
836C22—81no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—168no—
849C22#315014yes—
850C22C22×#12711yescharacteristic
851C22#348511yescharacteristic
852C22#348911yescharacteristic
853C22C2×#57512yes—
854C22C2×#57712yes—
855C4—24no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4#348512yes—
873C4#348912yes—
874C2—24no—
875C2—42no—
876C2—82no—
877C2—161no—
878C2—161no—
879C2#3606011yescharacteristic
880C2C2×#315011yescharacteristic
881C2#6064611yescharacteristic
882C2#6172912yes—
883C2#6212612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36362C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3337C2semidirect
2. C2×#3296C2semidirect
4. #36181C2semidirect
5. #30282C2semidirect
6. #30244C2semidirect
7. #30240C2semidirect
8. #28537C2semidirect
9. #28516C2semidirect
10. #28412C2semidirect
11. #28380C2semidirect
12. #28352C2semidirect
13. #28344C2semidirect
14. #28317C2semidirect
15. #28311C2semidirect
16. #27937C2semidirect
17. #27933C2semidirect
18. #27917C2semidirect
19. #27914C2semidirect
20. #23799C2semidirect
21. #23730C2semidirect
22. C2×#2094C2semidirect
23. #20558C2semidirect
29. C2×#499C22semidirect
32. C2×#485C22semidirect
34. C2×#482C22semidirect
37. C2×#479C22semidirect
39. C2×#478C22semidirect
43. C2×#465C22semidirect
48. C2×C4×SD16C22semidirect
50. C2×#427C22semidirect
55. #2859C22semidirect
57. #2857C22semidirect
61. #2565C22semidirect
68. #2499C22semidirect
77. C4×C4⋊Q8C22semidirect
81. #2285C22semidirect
84. #2097C22semidirect
85. #2097C22semidirect
86. #2097C22semidirect
87. #2096C22semidirect
88. #2096C22semidirect
89. #2096C22semidirect
90. #2095C22semidirect
91. #2095C22semidirect
98. #2094C22semidirect
99. #2094C22semidirect
102. #2093C22semidirect
105. #2016C22semidirect
106. #2015C22semidirect
111. #2013C22semidirect
116. #1971C22semidirect
117. #1971C22semidirect
120. #1959C22semidirect
121. #1847C22semidirect
122. #1847C22semidirect
123. #1847C22semidirect
124. #1770C22semidirect
125. #1767C22semidirect
127. #1752C22semidirect
129. #1749C22semidirect
130. #1744C22semidirect
132. C2×#336C22semidirect
206. C8×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33372
C2×#32962
#363622
#361812
#302822
#302442
#302402
#285372
#285162
#284122
#283802
#283522
#283442
#283172
#283112
#279372
#279332
#279172
#279142
#237992
#237302
C2×#20942
#205582