Finite Group Databasebeta

← #6687960

Subgroups — #6687960

Order 512.

1866 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39752C211yesmaximal, characteristic, complemented
2D4×C22⋊Q8C211yesmaximal, characteristic
3#32953C211yesmaximal, characteristic
4#32661C212yesmaximal, complemented
5#31546C212yesmaximal, complemented
6#31540C212yesmaximal, complemented
7#31252C212yesmaximal, complemented
8#30291C211yesmaximal, characteristic, complemented
9#29951C211yesmaximal, characteristic, complemented
10#28775C212yesmaximal, complemented
11#26398C212yesmaximal, complemented
12#26384C212yesmaximal, complemented
13#25963C212yesmaximal, complemented
14#25952C212yesmaximal
15#24825C212yesmaximal, complemented
16#24342C212yesmaximal, complemented
17#22437C212yesmaximal
18#22295C211yesmaximal, characteristic, complemented
19C2×#1877C211yesmaximal, characteristic
20C23×SD16C2211yescharacteristic
21C2×D4×Q8C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C22×C4×D4C2211yescharacteristic
24C2×#477C2212yescomplemented
25C2×#478C2212yes—
26C2×#474C2211yescharacteristic
27C2×#474C2211yescharacteristic
28C2×#440C2212yes—
29C2×#440C2212yes—
30C22×#103C2211yescharacteristic
31C22×#102C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2848—21no—
35#2809—21no—
36#2806—21no—
37#2799—22no—
38#2659—21no—
39#2581C2212yescomplemented
40#2569—22no—
41#2565C2212yescomplemented
42#2542C2211yescharacteristic
43#2538C2211yescharacteristic
44#2453C2212yescomplemented
45#2452C2212yes—
46#2451C2212yescomplemented
47#2449—22no—
48#2442C2212yes—
49#2440C2212yes—
50#2437—22no—
51#2417—21no—
52#2409—21no—
53D4×C4⋊C4C2212yes—
54D4×C4⋊C4C2211yescharacteristic
55Q8×C22⋊C4C2212yes—
56D4×C22⋊C4C2212yes—
57#2329—21no—
58C4×C22⋊Q8C2211yescharacteristic
59C2×#391C2211yescharacteristic
60#2096C2212yescomplemented
61#2095C2212yescomplemented
62#2092C2212yes—
63#2085C2212yescomplemented
64#2083C2212yescomplemented
65#2083C2212yescomplemented
66#2083C2212yescomplemented
67#2068C2212yescomplemented
68#2068C2212yescomplemented
69#2067C2212yes—
70#2066C2212yescomplemented
71#2066C2212yescomplemented
72#2065C2212yes—
73#2059C2212yescomplemented
74#2057C2212yescomplemented
75#2057C2212yescomplemented
76#2057C2212yescomplemented
77#2025C2212yes—
78#2024C2212yescomplemented
79#2024C2212yescomplemented
80#1993C2212yescomplemented
81#1992C2212yescomplemented
82#1985C2212yescomplemented
83#1973C2212yes—
84#1973C2212yes—
85#1944C2212yescomplemented
86#1943C2212yescomplemented
87#1940C2212yescomplemented
88#1917C2212yescomplemented
89#1917C2212yescomplemented
90#1880C2212yes—
91#1880C2212yes—
92#1877C2212yes—
93#1877C2212yes—
94#1877C2212yes—
95#1877C2212yes—
96#1877C2212yes—
97#1877C2212yes—
98#1864C2212yes—
99#1863C2212yescomplemented
100#1863C2212yescomplemented
101#1862C2212yes—
102#1862C2212yes—
103#1862C2212yes—
104#1853C2212yes—
105#1852C2212yes—
106#1850C2212yes—
107#1808C2212yes—
108#1808C2212yes—
109#1804C2212yes—
110#1803C2212yescomplemented
111#1802C2211yescharacteristic
112#1802C2211yescharacteristic
113#1797C2211yescharacteristic
114#1787C2212yes—
115#1786C2212yes—
116#1752C2212yes—
117C2×#340C2211yescharacteristic
118C2×#336C2211yescharacteristic
119C23×Q8—21no—
120C23×Q8C2311yescharacteristic
121C23×D4C2311yescharacteristic
122C24×C4—21no—
123C22×SD16—42no—
124C22×SD16—42no—
125C22×SD16Q818yescomplemented
126C22×SD16C2312yes—
127C22×SD16C2312yes—
128C23×C8C2311yescharacteristic
129C23×C8C2311yescharacteristic
130D4×Q8—42no—
131D4×Q8—42no—
132C2×C4⋊Q8C2312yes—
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2311yescharacteristic
135C2×#125C2312yes—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8—22no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—22no—
145C2×C22⋊Q8—48no—
146C2×C22⋊Q8D411yescharacteristic
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2311yescharacteristic
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—42no—
153C2×C4×D4—42no—
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2312yes—
159C2×C4×D4C2311yescharacteristic
160C22×C4⋊C4—21no—
161C22×C4⋊C4—22no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4—21no—
165C22×C22⋊C4—22no—
166C22×C42C2311yescharacteristic
167#478—44no—
168#477—44no—
169#474—42no—
170#474—42no—
171#440—44no—
172#440—44no—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×#103—42no—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#102—42no—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×C22⋊C8C2312yes—
200C2×#97C2312yes—
201C2×#97C2312yes—
202#400—22no—
203#400—22no—
204#400—22no—
205#399—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#398—22no—
210#398—22no—
211#398—22no—
212#396—22no—
213#396—22no—
214#395—22no—
215#395—22no—
216#395—22no—
217#393—22no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—22no—
223#391—22no—
224#391—22no—
225#391D411yescharacteristic
226#391C2312yes—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#390C2312yes—
231#390C2312yes—
232#389—22no—
233#389—21no—
234#389—21no—
235#389D411yescharacteristic
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387D412yes—
249#386—22no—
250#386—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385D412yes—
258#384C2311yescharacteristic
259#384C2312yes—
260#384C2311yescharacteristic
261#382C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—22no—
267#380—22no—
268#380—22no—
269#380D411yescharacteristic
270#380C2312yes—
271#380C2312yes—
272#379—22no—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4C2312yes—
277C2×#95—21no—
278C2×#95—21no—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296C25—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—21no—
301C22×Q8—22no—
302C22×Q8—44no—
303C22×Q8—41no—
304C22×Q8—41no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8—44no—
308C22×Q8—82no—
309C22×Q8C2×D411yescharacteristic
310C22×Q8C2×Q814yescomplemented
311C22×Q8C2412yes—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—22no—
316C22×D4—41no—
317C22×D4—41no—
318C22×D4C2×Q814yes—
319C22×D4C2411yescharacteristic
320C22×D4C2411yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—44no—
331C23×C4—44no—
332C23×C4—82no—
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D411yescharacteristic
335C23×C4C2411yescharacteristic
336C2×SD16—24no—
337C2×SD16—24no—
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16—416no—
341C2×SD16C2×Q818yes—
342C2×SD16C2×Q818yescomplemented
343C22×C8—22no—
344C22×C8—41no—
345C22×C8—41no—
346C22×C8—41no—
347C22×C8—41no—
348C22×C8C2×Q814yescomplemented
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C4⋊Q8—24no—
354C4⋊Q8—42no—
355C4⋊Q8—41no—
356C4⋊Q8—41no—
357C4⋊Q8—41no—
358C4⋊Q8—41no—
359#125—42no—
360#125—42no—
361C22⋊Q8—24no—
362C22⋊Q8—48no—
363C22⋊Q8—48no—
364C22⋊Q8—44no—
365C22⋊Q8—48no—
366C22⋊Q8—44no—
367C22⋊Q8—44no—
368C22⋊Q8—44no—
369C22⋊Q8—44no—
370C22⋊Q8—82no—
371C4×Q8—41no—
372C4×Q8—41no—
373C4×Q8—42no—
374C4×Q8—42no—
375C4×Q8—42no—
376C4×Q8—42no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—22no—
383C4×D4—41no—
384C4×D4—41no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—42no—
388C4×D4—42no—
389C4×D4—44no—
390C4×D4—44no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—48no—
418C2×C4⋊C4C2×D412yes—
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D412yes—
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4C2×D412yes—
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2411yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—48no—
445C2×C22⋊C4C2×D412yes—
446C2×C22⋊C4C2×D412yes—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—41no—
450C2×C42—41no—
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2412yes—
456C2×C42C2412yes—
457#107—24no—
458#107—42no—
459#107—42no—
460#107—42no—
461#107—42no—
462#107—42no—
463#106—42no—
464#106—42no—
465C4⋊C8—41no—
466C4⋊C8—41no—
467C4⋊C8—42no—
468C4⋊C8—42no—
469#103—24no—
470#103—42no—
471#103—42no—
472#103—42no—
473#103—42no—
474#103—42no—
475#102—24no—
476#102—24no—
477#102—24no—
478#102—42no—
479#102—42no—
480#102—42no—
481C22⋊C8—24no—
482#97—42no—
483#97—42no—
484#95—22no—
485#95—22no—
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#95—22no—
500#95—22no—
501#95—22no—
502#95C2×D412yes—
503#95C2×D412yes—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507C24—21no—
508C24—21no—
509C24—24no—
510C24—42no—
511C24—42no—
512C24—42no—
513C24—42no—
514C24—81no—
515C24—81no—
516C24C22×D411yescharacteristic
517C2×Q8—24no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—41no—
525C2×Q8—41no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—44no—
531C2×Q8—44no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—81no—
535C2×Q8—81no—
536C2×Q8—82no—
537C2×Q8—81no—
538C2×Q8—81no—
539C2×Q8—82no—
540C2×Q8—82no—
541C2×Q8—816no—
542C2×Q8C22×Q814yes—
543C2×D4—28no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4C22×Q812yes—
559C2×D4C22×Q812yes—
560C2×D4H(5,𝔽2)12yes—
561C2×D4H(5,𝔽2)12yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—82no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4—82no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—816no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4AGL(1,ℤ/8)14yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×Q812yes—
618C22×C42−1+412yes—
619C22×C4C2511yescharacteristic
620SD16—216no—
621SD16—48no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8—82no—
635C2×C8C22×Q814yes—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—42no—
652C4⋊C4—41no—
653C4⋊C4—42no—
654C4⋊C4—41no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—81no—
669C4⋊C4—81no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—81no—
676C4⋊C4H(5,𝔽2)12yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—22no—
699C42—41no—
700C42—41no—
701C42—82no—
702C42—82no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—48no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—48no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23D4×Q812yes—
729C23C2×AGL(1,ℤ/8)12yes—
730C23#57812yes—
731C23C23×D411yescharacteristic
732Q8—24no—
733Q8—24no—
734Q8—44no—
735Q8—42no—
736Q8—42no—
737Q8—84no—
738Q8—84no—
739Q8—88no—
740Q8—162no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4#54314yes—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—82no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—88no—
811C2×C4—88no—
812C2×C4—162no—
813C2×C4D4×Q812yes—
814C2×C4C2×AGL(1,ℤ/8)12yes—
815C2×C4C2×AGL(1,ℤ/8)12yes—
816C2×C4C23×Q811yescharacteristic
817C2×C4C2×H(5,𝔽2)11yescharacteristic
818C2×C4C2×H(5,𝔽2)11yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C2×C4#58511yescharacteristic
822C8—24no—
823C8—42no—
824C8—42no—
825C8—42no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22#338614yes—
848C22C2×D4×Q811yescharacteristic
849C22#348411yescharacteristic
850C22#348811yescharacteristic
851C22C22×AGL(1,ℤ/8)11yescharacteristic
852C22C2×#57811yescharacteristic
853C22#358511yescharacteristic
854C22#358611yescharacteristic
855C4—22no—
856C4—22no—
857C4—22no—
858C4—42no—
859C4—44no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—41no—
865C4—41no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4C2×#54311yescharacteristic
873C4#350111yescharacteristic
874C4#353511yescharacteristic
875C4#353611yescharacteristic
876C2—24no—
877C2—44no—
878C2—82no—
879C2#3768411yescharacteristic
880C2C2×#338611yescharacteristic
881C2#6137711yescharacteristic
882C2#6157111yescharacteristic
883C2#6162211yescharacteristic
884C2#6196211yescharacteristic
885C2#6201711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39752C2semidirect
4. #32661C2semidirect
5. #31546C2semidirect
6. #31540C2semidirect
7. #31252C2semidirect
8. #30291C2semidirect
9. #29951C2semidirect
10. #28775C2semidirect
11. #26398C2semidirect
12. #26384C2semidirect
13. #25963C2semidirect
15. #24825C2semidirect
16. #24342C2semidirect
18. #22295C2semidirect
24. C2×#477C22semidirect
39. #2581C22semidirect
41. #2565C22semidirect
44. #2453C22semidirect
46. #2451C22semidirect
60. #2096C22semidirect
61. #2095C22semidirect
63. #2085C22semidirect
64. #2083C22semidirect
65. #2083C22semidirect
66. #2083C22semidirect
67. #2068C22semidirect
68. #2068C22semidirect
70. #2066C22semidirect
71. #2066C22semidirect
73. #2059C22semidirect
74. #2057C22semidirect
75. #2057C22semidirect
76. #2057C22semidirect
78. #2024C22semidirect
79. #2024C22semidirect
80. #1993C22semidirect
81. #1992C22semidirect
82. #1985C22semidirect
85. #1944C22semidirect
86. #1943C22semidirect
87. #1940C22semidirect
88. #1917C22semidirect
89. #1917C22semidirect
99. #1863C22semidirect
100. #1863C22semidirect
110. #1803C22semidirect
125. C22×SD16Q8semidirect
310. C22×Q8C2×Q8semidirect
342. C2×SD16C2×Q8semidirect
348. C22×C8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#397522
D4×C22⋊Q82
#329532
#326612
#315462
#315402
#312522
#302912
#299512
#287752
#263982
#263842
#259632
#259522
#248252
#243422
#224372
#222952
C2×#18772