Finite Group Databasebeta

← #7613509

Subgroups — #7613509

Order 512.

2200 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×#3297C212yesmaximal, complemented
2#59812C212yesmaximal, complemented
3#31238C211yesmaximal, characteristic, complemented
4#31210C211yesmaximal, characteristic, complemented
5#31190C211yesmaximal, characteristic, complemented
6#31056C211yesmaximal, characteristic, complemented
7#28908C212yesmaximal, complemented
8#28116C212yesmaximal, complemented
9#28096C212yesmaximal, complemented
10#26819C212yesmaximal, complemented
11#26785C212yesmaximal, complemented
12#25160C212yesmaximal, complemented
13#25112C212yesmaximal, complemented
14#24090C212yesmaximal, complemented
15#23850C212yesmaximal, complemented
16#22870C212yesmaximal, complemented
17C4×#466C211yesmaximal, characteristic, complemented
18C8×#121C211yesmaximal, characteristic, complemented
19#21224C211yesmaximal, characteristic, complemented
20C22×#135C2211yescharacteristic
21C2×#553C2212yes—
22C2×#546C2212yescomplemented
23#3297—216no—
24C2×#488C2212yescomplemented
25C2×#484C2212yescomplemented
26C2×#482C2212yescomplemented
27C2×#478C2212yescomplemented
28C2×#466C2211yescharacteristic
29C2×#465C2212yes—
30C2×#463C2212yes—
31C2×#449C2212yes—
32C2×#450C2212yescomplemented
33C2×#447C2212yes—
34C2×#447C2212yes—
35C2×C4×D8C2212yes—
36C2×C4×D8C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×C8×D4C2212yescomplemented
39C2×#427C2211yescharacteristic, complemented
40C2×#416C2212yescomplemented
41C22×#102C2212yescomplemented
42C22×C4×C8C2211yescharacteristic, complemented
43#2708—22no—
44#2668—22no—
45#2553—22no—
46#2535—22no—
47#2534—22no—
48#2489C2212yescomplemented
49#2485C2212yescomplemented
50#2480—22no—
51#2457—22no—
52#2454C2212yescomplemented
53#2447C2212yescomplemented
54#2427C2212yes—
55#2417C2212yes—
56#2408C2212yes—
57#2407C2212yes—
58#2361C2212yes—
59#2358—22no—
60D4×C22⋊C4C2212yescomplemented
61C4×#121C2211yescharacteristic
62C4×#121C2212yescomplemented
63#2297C2212yescomplemented
64#2068C2212yescomplemented
65#2068C2212yescomplemented
66#2067C2212yescomplemented
67#2065C2212yescomplemented
68#2059C2212yescomplemented
69#2059C2212yescomplemented
70#2055C2212yescomplemented
71#2054C2212yes—
72#2036C2212yescomplemented
73#2034C2212yes—
74#2033C2212yes—
75#2033C2212yes—
76#2015C2212yescomplemented
77#2012C2212yes—
78#2001C2212yescomplemented
79#2000C2212yes—
80#1970C2211yescharacteristic
81#1970C2211yescharacteristic
82#1970C2211yescharacteristic
83#1969C2211yescharacteristic, complemented
84#1969C2211yescharacteristic, complemented
85#1968C2212yescomplemented
86#1968C2212yescomplemented
87#1954C2211yescharacteristic
88#1942C2211yescharacteristic, complemented
89#1939C2211yescharacteristic, complemented
90#1934C2212yescomplemented
91#1934C2212yescomplemented
92#1933C2212yescomplemented
93#1927C2212yescomplemented
94#1925C2212yescomplemented
95#1923C2212yescomplemented
96#1893C2212yes—
97#1893C2212yescomplemented
98#1892C2212yescomplemented
99#1879C2212yes—
100#1879C2212yes—
101#1877C2212yescomplemented
102#1877C2212yescomplemented
103#1869C2212yescomplemented
104#1864C2212yescomplemented
105#1862C2212yescomplemented
106#1853C2212yescomplemented
107#1852C2212yescomplemented
108#1825C2212yescomplemented
109#1808C2211yescharacteristic, complemented
110#1797C2211yescharacteristic, complemented
111#1788C2212yescomplemented
112C4×#107C2211yescharacteristic, complemented
113C8×C4⋊C4C2211yescharacteristic, complemented
114C4×#102C2212yescomplemented
115C8×C22⋊C4C2212yescomplemented
116C22×#41C2312yes—
117C23×D4C2312yes—
118C2×#135—24no—
119C2×#135—42no—
120C2×#135—42no—
121C22×Q16C2311yescharacteristic
122C22×SD16C2312yes—
123C22×SD16C2312yes—
124C22×D8C2312yes—
125C22×D8C2311yescharacteristic
126C22×D8C2311yescharacteristic
127C23×C8C2311yescharacteristic
128C23×C8C2312yes—
129C23×C8C2311yescharacteristic
130#553—28no—
131#553—44no—
132#546—28no—
133#546—44no—
134C2×#126—22no—
135C2×#125C2312yes—
136C2×#124C2312yes—
137C2×#123—22no—
138C2×#123—22no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×#121—22no—
142C2×#121—22no—
143C2×#121D411yescharacteristic
144C2×#121C2312yes—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×#120—22no—
148C2×#120—22no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—22no—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×#117C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C22⋊C4—22no—
160C22×C22⋊C4—22no—
161C22×C42C2311yescharacteristic
162#488—28no—
163#484—28no—
164#482—28no—
165#478—28no—
166#466D418yescomplemented
167#465—28no—
168#463—28no—
169#450—44no—
170#449—28no—
171#447—28no—
172#447—28no—
173C4×D8—28no—
174C4×D8—42no—
175C8×D4—28no—
176C8×D4—42no—
177#427—42no—
178C2×#107C2312yes—
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189#416—28no—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102—28no—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C4×C8—42no—
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216#400—22no—
217#399—22no—
218#398—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#397—22no—
224#396—22no—
225#396—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#394—22no—
230#392—22no—
231#392—22no—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#390D411yescharacteristic
236#390C2312yes—
237#390C2312yes—
238#390C2312yes—
239#390C2312yes—
240#389D411yescharacteristic
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388D412yes—
249#387—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386D412yes—
260#385—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#382—22no—
265#381—22no—
266#380—22no—
267#380—22no—
268#380—22no—
269#380D411yescharacteristic
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#379—22no—
274#379—22no—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C25—22no—
292C2×#41—24no—
293C2×#41—24no—
294C2×#41—24no—
295C2×#41—42no—
296C2×#41—42no—
297C2×#41—42no—
298C22×Q8C2412yes—
299C22×D4—22no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—42no—
307C22×D4—42no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4C2×D412yes—
311C22×D4C2×D411yescharacteristic
312C22×D4C2412yes—
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323#135—416no—
324C2×Q16—22no—
325C2×Q16—41no—
326C2×Q16—41no—
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—42no—
331C2×SD16—42no—
332C2×SD16—42no—
333C2×D8—24no—
334C2×D8—24no—
335C2×D8—41no—
336C2×D8—42no—
337C2×D8—41no—
338C2×D8—41no—
339C2×D8—41no—
340C2×D8C2×D414yes—
341C2×D8#4114yes—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—24no—
346C22×C8—41no—
347C22×C8—41no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8C2×D414yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357#126—48no—
358#125—24no—
359#125—42no—
360#124—24no—
361#124—42no—
362#123—48no—
363#123—48no—
364C22⋊Q8—24no—
365C22⋊Q8—42no—
366C22⋊Q8—42no—
367C22⋊Q8—42no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—48no—
373#121—42no—
374#121—42no—
375#121—48no—
376#121C2×D418yes—
377#120—48no—
378#120—48no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—42no—
388C4×D4—42no—
389C4×D4—48no—
390C4×D4—84no—
391C4×D4—84no—
392#117—24no—
393#117—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4C2×D412yes—
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—48no—
436C2×C22⋊C4—84no—
437C2×C22⋊C4C2×D412yes—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2412yes—
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451#107—24no—
452#107—41no—
453#107—41no—
454#107—41no—
455#107—41no—
456#107C2×D414yes—
457#106—24no—
458#106—42no—
459C4⋊C8—24no—
460C4⋊C8—41no—
461C4⋊C8—41no—
462#103—24no—
463#103—24no—
464#103—24no—
465#103—42no—
466#103—42no—
467#102—24no—
468#102—24no—
469#102—24no—
470#102—24no—
471#102—24no—
472#102—24no—
473#102—24no—
474#102—24no—
475#102—42no—
476#102C2×D418yes—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C22⋊C8—24no—
480C22⋊C8—24no—
481C4×C8—24no—
482C4×C8—22no—
483C4×C8—22no—
484C4×C8—41no—
485C4×C8—41no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95C2×D412yes—
500#95C2×D412yes—
501#95C2×D412yes—
502C24—22no—
503C24—22no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—82no—
508C24—82no—
509C24—82no—
510C24—82no—
511C24C22×D411yescharacteristic
512C24C22×D412yes—
513#41—48no—
514#41—48no—
515#41—84no—
516#41—84no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—28no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—48no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—82no—
549C2×D4—84no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4#13514yescomplemented
558C2×D4C22×D414yes—
559C2×D4C2×#4114yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4H(5,𝔽2)12yes—
607C22×C4C2511yescharacteristic
608Q16—44no—
609SD16—48no—
610SD16—84no—
611D8—44no—
612D8—44no—
613D8—48no—
614C2×C8—28no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—44no—
630C2×C8—84no—
631C2×C8C22×D412yes—
632C2×C8C22×D412yes—
633C2×C8C2×#4112yes—
634C2×C8H(5,𝔽2)12yes—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—82no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4C22×D414yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—28no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—42no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—22no—
688C42—21no—
689C42—21no—
690C42—41no—
691C42—41no—
692C42—44no—
693C42—44no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—21no—
706C23—24no—
707C23—24no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—88no—
721C23—88no—
722C23—88no—
723C23—164no—
724C23—164no—
725C23—164no—
726C23—164no—
727C23D4212yes—
728C23C2×#13514yes—
729C23C23×D411yescharacteristic
730Q8—42no—
731Q8—42no—
732Q8—42no—
733Q8—42no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—24no—
738D4—44no—
739D4—48no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—88no—
745D4—88no—
746D4—88no—
747D4—88no—
748D4—88no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—88no—
799C2×C4—164no—
800C2×C4—164no—
801C2×C4—164no—
802C2×C4—164no—
803C2×C4D4212yes—
804C2×C4C2×#13512yes—
805C2×C4#57612yes—
806C2×C4C23×D411yescharacteristic
807C2×C4C22×#4111yescharacteristic
808C2×C4C2×H(5,𝔽2)11yescharacteristic
809C2×C4C2×H(5,𝔽2)11yescharacteristic
810C2×C4#58511yescharacteristic
811C2×C4#58511yescharacteristic
812C8—22no—
813C8—22no—
814C8—22no—
815C8—22no—
816C8—42no—
817C8—42no—
818C22—24no—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—22no—
823C22—24no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—1616no—
847C22C2×D4211yescharacteristic
848C22D4×#4111yescharacteristic
849C22#349611yescharacteristic
850C22C22×#13511yescharacteristic
851C22C2×#57611yescharacteristic
852C22#358411yescharacteristic
853C22#358411yescharacteristic
854C4—22no—
855C4—22no—
856C4—22no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—42no—
861C4—44no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4D4×#4111yescharacteristic
869C4#349011yescharacteristic
870C4#349611yescharacteristic
871C4#354511yescharacteristic
872C2—42no—
873C2—44no—
874C2—84no—
875C2—84no—
876C2#5981411yescharacteristic
877C2D4×#13511yescharacteristic
878C2#6108411yescharacteristic
879C2#6143111yescharacteristic
880C2#6150111yescharacteristic
881C2#6224411yescharacteristic
882C2#6227811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3297C2semidirect
2. #59812C2semidirect
3. #31238C2semidirect
4. #31210C2semidirect
5. #31190C2semidirect
6. #31056C2semidirect
7. #28908C2semidirect
8. #28116C2semidirect
9. #28096C2semidirect
10. #26819C2semidirect
11. #26785C2semidirect
12. #25160C2semidirect
13. #25112C2semidirect
14. #24090C2semidirect
15. #23850C2semidirect
16. #22870C2semidirect
17. C4×#466C2semidirect
18. C8×#121C2semidirect
19. #21224C2semidirect
22. C2×#546C22semidirect
24. C2×#488C22semidirect
25. C2×#484C22semidirect
26. C2×#482C22semidirect
27. C2×#478C22semidirect
32. C2×#450C22semidirect
38. C2×C8×D4C22semidirect
39. C2×#427C22semidirect
40. C2×#416C22semidirect
41. C22×#102C22semidirect
42. C22×C4×C8C22semidirect
48. #2489C22semidirect
49. #2485C22semidirect
52. #2454C22semidirect
53. #2447C22semidirect
60. D4×C22⋊C4C22semidirect
62. C4×#121C22semidirect
63. #2297C22semidirect
64. #2068C22semidirect
65. #2068C22semidirect
66. #2067C22semidirect
67. #2065C22semidirect
68. #2059C22semidirect
69. #2059C22semidirect
70. #2055C22semidirect
72. #2036C22semidirect
76. #2015C22semidirect
78. #2001C22semidirect
83. #1969C22semidirect
84. #1969C22semidirect
85. #1968C22semidirect
86. #1968C22semidirect
88. #1942C22semidirect
89. #1939C22semidirect
90. #1934C22semidirect
91. #1934C22semidirect
92. #1933C22semidirect
93. #1927C22semidirect
94. #1925C22semidirect
95. #1923C22semidirect
97. #1893C22semidirect
98. #1892C22semidirect
101. #1877C22semidirect
102. #1877C22semidirect
103. #1869C22semidirect
104. #1864C22semidirect
105. #1862C22semidirect
106. #1853C22semidirect
107. #1852C22semidirect
108. #1825C22semidirect
109. #1808C22semidirect
110. #1797C22semidirect
111. #1788C22semidirect
112. C4×#107C22semidirect
113. C8×C4⋊C4C22semidirect
114. C4×#102C22semidirect
115. C8×C22⋊C4C22semidirect
166. #466D4semidirect
557. C2×D4#135semidirect

Maximal subgroups

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

subgroupindex
C2×#32972
#598122
#312382
#312102
#311902
#310562
#289082
#281162
#280962
#268192
#267852
#251602
#251122
#240902
#238502
#228702
C4×#4662
C8×#1212
#212242