Finite Group Databasebeta

← #6629084

Subgroups — #6629084

Order 512.

4296 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#520C211yesmaximal, characteristic
2C2×#3083C212yesmaximal, complemented
3#35253C211yesmaximal, characteristic, complemented
4#32968C214yesmaximal, complemented
5#32963C214yesmaximal, complemented
6#32960C212yesmaximal, complemented
7#32959C212yesmaximal, complemented
8#32957C212yesmaximal, complemented
9#32953C212yesmaximal, complemented
10#20881C212yesmaximal, complemented
11#20878C212yesmaximal, complemented
12#20844C211yesmaximal, characteristic, complemented
13C2×#1852C211yesmaximal, characteristic, complemented
14#20652C212yesmaximal, complemented
15#20628C211yesmaximal, characteristic, complemented
16#20601C211yesmaximal, characteristic
17#20597C211yesmaximal, characteristic
18C23×#41C2211yescharacteristic
19C2×#544C2211yescharacteristic, complemented
20C2×#520—216no—
21C2×#520—22no—
22C2×#520—21no—
23C2×#520—21no—
24C2×#520C2212yes—
25C2×#520C2214yes—
26C2×#520C2212yes—
27C22×C4×Q8C2212yes—
28C22×C4×D4—22no—
29C22×C4×D4C2212yes—
30C22×#117—21no—
31C22×#117C2211yescharacteristic
32C23×C4⋊C4—21no—
33C23×C4⋊C4C2211yescharacteristic
34#3083—216no—
35C2×#479C2214yescomplemented
36C2×#477C2214yescomplemented
37C2×#478C2214yescomplemented
38C2×#474C2214yescomplemented
39C2×#428C2212yescomplemented
40C22×#107C2212yescomplemented
41C2×#424C2212yescomplemented
42C2×#417C2212yes—
43C2×#417C2212yes—
44C2×#416C2212yes—
45C2×#416C2212yes—
46C2×#407C2211yescharacteristic
47C22×C22⋊C8C2211yescharacteristic
48#2857C2212yes—
49#2851C2212yes—
50#2629C2212yescomplemented
51#2628C2212yescomplemented
52#2442—21no—
53#2441—21no—
54#2440—21no—
55#2439—21no—
56#2438—22no—
57#2437—22no—
58#2317C2211yescharacteristic, complemented
59#2317C2211yescharacteristic, complemented
60#2316C2211yescharacteristic, complemented
61#2280C2211yescharacteristic
62C2×#380C2211yescharacteristic
63#1865C2214yescomplemented
64#1864C2214yescomplemented
65#1863C2214yescomplemented
66#1863C2214yescomplemented
67#1863C2214yescomplemented
68#1862C2214yescomplemented
69#1862C2214yescomplemented
70#1862C2214yescomplemented
71#1853C2212yes—
72#1853C2212yescomplemented
73#1852C2212yes—
74#1852C2212yes—
75#1852C2212yes—
76#1852C2214yescomplemented
77#1852C2212yescomplemented
78#1805C2214yescomplemented
79#1804C2214yescomplemented
80#1803C2214yescomplemented
81#1802C2214yescomplemented
82#1798C2214yescomplemented
83#1797C2212yes—
84#1797C2212yes—
85#1788C2212yes—
86#1788C2212yes—
87#1788C2214yes—
88#1787C2211yescharacteristic
89#1787C2211yescharacteristic
90#1787C2212yes—
91#1786C2211yescharacteristic
92#1786C2211yescharacteristic
93#1786C2212yes—
94#1736C2212yescomplemented
95C2×#340C2212yescomplemented
96#1729C2212yescomplemented
97C22×#41—28no—
98C22×#41—28no—
99C22×#41—21no—
100C22×#41—21no—
101C22×#41—24no—
102C22×#41Q818yescomplemented
103C22×#41C2312yes—
104C22×#41C2312yes—
105C23×Q8C2311yescharacteristic
106C23×D4—21no—
107C23×D4C2311yescharacteristic
108C24×C4—21no—
109C24×C4—21no—
110C24×C4—22no—
111C24×C4C2311yescharacteristic
112C22×M16C2312yes—
113C23×C8C2312yes—
114#544—28no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8C2312yes—
117C2×#125—21no—
118C2×#125C2312yes—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121#520—232no—
122#520—216no—
123#520—216no—
124#520—28no—
125#520—216no—
126#520—216no—
127#520—28no—
128#520—28no—
129#520D4116yes—
130C2×C4×Q8—216no—
131C2×C4×Q8—22no—
132C2×C4×Q8—22no—
133C2×C4×Q8C2314yes—
134C2×C4×Q8C2314yes—
135C2×C4×D4—232no—
136C2×C4×D4—216no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—22no—
142C2×C4×D4—22no—
143C2×C4×D4C2314yes—
144C2×C4×D4C2314yes—
145C2×#117—216no—
146C2×#117—28no—
147C2×#117—22no—
148C2×#117—24no—
149C2×#117—22no—
150C2×#117D412yes—
151C2×#117D411yescharacteristic
152C2×#117D411yescharacteristic
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2312yes—
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C22×C4⋊C4—216no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—22no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—22no—
164C22×C4⋊C4—24no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4—28no—
167C22×C4⋊C4D411yescharacteristic
168C22×C4⋊C4D411yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—22no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4D412yes—
177C22×C42—22no—
178C22×C42C2312yes—
179#479—216no—
180#478—216no—
181#477—216no—
182#474—216no—
183#428—28no—
184C2×#107—28no—
185C2×#107C2314yes—
186C2×#107C2314yes—
187C2×#107C2314yes—
188C2×#106C2314yes—
189#424—28no—
190C2×C4⋊C8C2314yes—
191C2×C4⋊C8C2314yes—
192#417—28no—
193#417—28no—
194#416—28no—
195#416—28no—
196C2×#103C2312yes—
197C2×#103C2314yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2314yes—
201C2×#103C2312yes—
202C2×#102C2312yes—
203C2×#102C2314yes—
204C2×#102C2312yes—
205C2×#102C2314yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208#407—24no—
209C2×C22⋊C8—24no—
210C2×C22⋊C8C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215#400—22no—
216#399—22no—
217#398—22no—
218#398—22no—
219#396—22no—
220#396—22no—
221#395—22no—
222#393—22no—
223#391—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—22no—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#387—22no—
234#387—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#385—22no—
239#384—21no—
240#384C2312yes—
241#382—21no—
242#382C2312yes—
243#381—21no—
244#380—22no—
245#380—21no—
246#380—21no—
247#380—22no—
248#380C2311yescharacteristic
249#380C2312yes—
250#380C2311yescharacteristic
251#380C2311yescharacteristic
252#380C2312yes—
253#380C2311yescharacteristic
254#379—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C2×#95—21no—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#336C2314yes—
263#336C2314yes—
264C25—21no—
265C25C2×D411yescharacteristic
266C2×#41—28no—
267C2×#41—28no—
268C2×#41—28no—
269C2×#41—264no—
270C2×#41—28no—
271C2×#41—264no—
272C2×#41—24no—
273C2×#41—24no—
274C2×#41—24no—
275C2×#41—24no—
276C2×#41—28no—
277C2×#41—28no—
278C2×#41—24no—
279C2×#41—24no—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41C2×D418yes—
283C2×#41C2×Q818yes—
284C2×#41C2×Q818yes—
285C2×#41#4118yes—
286C22×Q8—24no—
287C22×Q8—24no—
288C22×Q8—21no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8C2×Q814yes—
292C22×Q8C2412yes—
293C22×D4—28no—
294C22×D4—28no—
295C22×D4—28no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—21no—
301C22×D4—22no—
302C22×D4C2×Q814yes—
303C22×D4C2412yes—
304C23×C4—28no—
305C23×C4—28no—
306C23×C4—21no—
307C23×C4—28no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—24no—
311C23×C4—24no—
312C23×C4—22no—
313C23×C4—28no—
314C23×C4—216no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—24no—
318C23×C4—24no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—84no—
322C23×C4—82no—
323C23×C4—84no—
324C23×C4—82no—
325C23×C4C2×D412yes—
326C23×C4C2×D412yes—
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2×Q814yes—
331C23×C4#4114yes—
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2411yescharacteristic
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—24no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—24no—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C22×C8C2414yes—
344C4⋊Q8—28no—
345C4⋊Q8—44no—
346#125—28no—
347#125—44no—
348C22⋊Q8—48no—
349C22⋊Q8—84no—
350C4×Q8—216no—
351C4×Q8—216no—
352C4×Q8—28no—
353C4×Q8—28no—
354C4×Q8—28no—
355C4×Q8C2×D4116yes—
356C4×D4—232no—
357C4×D4—232no—
358C4×D4—232no—
359C4×D4—216no—
360C4×D4—216no—
361C4×D4—28no—
362C4×D4—28no—
363C4×D4—232no—
364C4×D4—28no—
365C4×D4C2×D4116yes—
366#117—216no—
367#117—232no—
368#117—24no—
369#117—216no—
370#117—24no—
371#117—24no—
372#117—28no—
373#117—28no—
374#117—24no—
375#117—24no—
376#117C2×D418yes—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—216no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—232no—
381C2×C4⋊C4—216no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—216no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D412yes—
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D418yes—
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2414yes—
421C2×C22⋊C4—216no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—82no—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C22⋊C4C2×D412yes—
438C2×C42—216no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—28no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C2×D412yes—
445C2×C42C2×D412yes—
446C2×C42C2412yes—
447C2×C42C2412yes—
448#107—28no—
449#107—28no—
450#107—28no—
451#106—28no—
452C4⋊C8—28no—
453C4⋊C8—28no—
454#103—24no—
455#103—24no—
456#103—28no—
457#103—24no—
458#103—24no—
459#103—28no—
460#102—24no—
461#102—24no—
462#102—28no—
463#102—24no—
464#102—24no—
465#102—28no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471#95—22no—
472#95—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483C24—24no—
484C24—24no—
485C24—22no—
486C24—24no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—41no—
492C24—41no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24C22⋊Q814yes—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501#41—264no—
502#41—216no—
503#41—216no—
504#41—264no—
505#41—216no—
506#41—216no—
507#41—216no—
508#41—216no—
509#41—216no—
510#41C22⋊Q8132yescomplemented
511C2×Q8—24no—
512C2×Q8—216no—
513C2×Q8—24no—
514C2×Q8—216no—
515C2×Q8—24no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—44no—
520C2×Q8—82no—
521C2×Q8—82no—
522C2×Q8C22×D414yes—
523C2×Q8C22×Q814yes—
524C2×Q8C2×#4114yes—
525C2×D4—28no—
526C2×D4—24no—
527C2×D4—264no—
528C2×D4—28no—
529C2×D4—24no—
530C2×D4—216no—
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—216no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4C22×D414yes—
541C2×D4C22×Q814yes—
542C2×D4C2×#4114yes—
543C22×C4—24no—
544C22×C4—28no—
545C22×C4—24no—
546C22×C4—264no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—216no—
558C22×C4—22no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—216no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—216no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—216no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—832no—
597C22×C4—816no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4C22⋊Q814yes—
603C22×C4C22⋊Q814yes—
604C22×C4C22⋊Q814yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D414yes—
613C22×C4C22×Q812yes—
614C22×C4C22×Q812yes—
615C22×C4C22×Q812yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4112yes—
620C22×C4C2511yescharacteristic
621M16—48no—
622C2×C8—24no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—24no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—24no—
631C2×C8—48no—
632C4⋊C4—28no—
633C4⋊C4—216no—
634C4⋊C4—28no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—28no—
638C4⋊C4—216no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4#12014yes—
660C4⋊C4#12014yes—
661C4⋊C4C22×D418yes—
662C22⋊C4—216no—
663C22⋊C4—24no—
664C22⋊C4—216no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—44no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C22⋊C4—82no—
675C22⋊C4#12018yes—
676C42—216no—
677C42—216no—
678C42—24no—
679C42—24no—
680C42—24no—
681C42—42no—
682C42—42no—
683C42C22×D418yes—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—216no—
693C23—21no—
694C23—21no—
695C23—28no—
696C23—28no—
697C23—21no—
698C23—24no—
699C23—24no—
700C23—21no—
701C23—24no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—48no—
710C23—48no—
711C23—48no—
712C23—48no—
713C23—48no—
714C23—42no—
715C23—42no—
716C23—48no—
717C23—42no—
718C23—42no—
719C23C2×#12012yes—
720C23C2×C22⋊Q812yes—
721C23C2×C22⋊Q812yes—
722C23C2×C22⋊Q812yes—
723C23#52512yes—
724C23#57612yes—
725C23#57812yes—
726C23C23×D411yescharacteristic
727Q8—216no—
728Q8—24no—
729Q8—24no—
730Q8—24no—
731Q8—164no—
732Q8C2×C22⋊Q818yes—
733D4—232no—
734D4—216no—
735D4—232no—
736D4—24no—
737D4—24no—
738D4—24no—
739D4C2×C22⋊Q818yes—
740C2×C4—216no—
741C2×C4—232no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—24no—
749C2×C4—21no—
750C2×C4—24no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—28no—
755C2×C4—232no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—416no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—816no—
792C2×C4—88no—
793C2×C4—816no—
794C2×C4—88no—
795C2×C4—162no—
796C2×C4—162no—
797C2×C4C2×#12014yes—
798C2×C4C2×#12014yes—
799C2×C4C2×#12012yes—
800C2×C4C2×C22⋊Q812yes—
801C2×C4C2×C22⋊Q812yes—
802C2×C4C2×C22⋊Q812yes—
803C2×C4C2×C22⋊Q818yes—
804C2×C4#52512yes—
805C2×C4#52518yes—
806C2×C4C23×D412yes—
807C2×C4C23×Q811yescharacteristic
808C2×C4C22×#4112yes—
809C2×C4C22×#4111yescharacteristic
810C8—42no—
811C8—42no—
812C8—44no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—28no—
827C22—22no—
828C22—22no—
829C22—416no—
830C22—432no—
831C22—44no—
832C22—44no—
833C22—41no—
834C22—44no—
835C22—41no—
836C22—44no—
837C22—41no—
838C22—44no—
839C22—41no—
840C22—44no—
841C22#284814yes—
842C22#308314yescomplemented
843C22C22×#12011yescharacteristic
844C22C22×C22⋊Q811yescharacteristic
845C22C2×#52511yescharacteristic
846C22C2×#57611yescharacteristic
847C22C2×#57811yescharacteristic
848C22#358511yescharacteristic
849C22#358611yescharacteristic
850C4—22no—
851C4—28no—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—48no—
857C4—42no—
858C4—81no—
859C4—82no—
860C4—81no—
861C4—82no—
862C4—81no—
863C4—81no—
864C4#284814yes—
865C4C22×C22⋊Q812yes—
866C4C2×#52512yes—
867C2—24no—
868C2—24no—
869C2—42no—
870C2—48no—
871C2C2×#284811yescharacteristic
872C2#6037211yescharacteristic
873C2#6037511yescharacteristic
874C2C2×#308311yescharacteristic
875C2#6049211yescharacteristic
876C2#6058411yescharacteristic
877C2#6058911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3083C2semidirect
3. #35253C2semidirect
4. #32968C2semidirect
5. #32963C2semidirect
6. #32960C2semidirect
7. #32959C2semidirect
8. #32957C2semidirect
9. #32953C2semidirect
10. #20881C2semidirect
11. #20878C2semidirect
12. #20844C2semidirect
13. C2×#1852C2semidirect
14. #20652C2semidirect
15. #20628C2semidirect
19. C2×#544C22semidirect
35. C2×#479C22semidirect
36. C2×#477C22semidirect
37. C2×#478C22semidirect
38. C2×#474C22semidirect
39. C2×#428C22semidirect
40. C22×#107C22semidirect
41. C2×#424C22semidirect
50. #2629C22semidirect
51. #2628C22semidirect
58. #2317C22semidirect
59. #2317C22semidirect
60. #2316C22semidirect
63. #1865C22semidirect
64. #1864C22semidirect
65. #1863C22semidirect
66. #1863C22semidirect
67. #1863C22semidirect
68. #1862C22semidirect
69. #1862C22semidirect
70. #1862C22semidirect
72. #1853C22semidirect
76. #1852C22semidirect
77. #1852C22semidirect
78. #1805C22semidirect
79. #1804C22semidirect
80. #1803C22semidirect
81. #1802C22semidirect
82. #1798C22semidirect
94. #1736C22semidirect
95. C2×#340C22semidirect
96. #1729C22semidirect
102. C22×#41Q8semidirect
510. #41C22⋊Q8semidirect
842. C22#3083semidirect

Maximal subgroups

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

subgroupindex
C22×#5202
C2×#30832
#352532
#329682
#329632
#329602
#329592
#329572
#329532
#208812
#208782
#208442
C2×#18522
#206522
#206282
#206012
#205972