Finite Group Databasebeta

← Q8×#529 #7630260

Subgroups — Q8×#529 #7630260

Order 512.

5350 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36635C213yesmaximal, complemented
2#36556C213yesmaximal, complemented
3#36555C213yesmaximal, complemented
4#36554C216yesmaximal, complemented
5#36553C216yesmaximal, complemented
6#36552C213yesmaximal, complemented
7#36551C213yesmaximal
8Q8×#126C212yesmaximal, complemented
9Q8×#125C211yesmaximal, characteristic, complemented
10Q8×#124C211yesmaximal, characteristic, complemented
11Q8×#123C212yesmaximal, complemented
12Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
13Q8×#121C211yesmaximal, characteristic
14#34951C213yesmaximal, complemented
15#34941C213yesmaximal, complemented
16#34916C216yesmaximal, complemented
17#34772C216yesmaximal, complemented
18C4×Q82C211yesmaximal, characteristic, complemented
19C4×D4×Q8C211yesmaximal, characteristic, complemented
20C4×D4×Q8C212yesmaximal, complemented
21Q8×#117C212yesmaximal, complemented
22C4×#529C213yesmaximal
23C2×C42×Q8C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×D4×Q8C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C22×C4×Q8C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2864C2216yes—
33#2863C2216yes—
34#2863C2216yes—
35#2862C2213yes—
36#2859C2213yes—
37#2857C2213yes—
38#2857C2213yes—
39#2855C2216yes—
40#2855C2216yes—
41#2851C2216yes—
42#2590C22112yes—
43#2589C22112yes—
44#2588C22112yes—
45#2587C22112yes—
46#2585C22112yes—
47#2582C2213yes—
48#2574C22112yes—
49#2568C2213yes—
50#2567C2213yes—
51#2563C2213yes—
52#2552C2213yes—
53#2552C2213yes—
54#2546C2213yes—
55#2538C2213yes—
56#2522C22112yes—
57#2520C22112yes—
58#2511C2216yes—
59#2511C2216yes—
60#2511C2216yes—
61#2509C2216yes—
62#2508C2216yes—
63#2507C2216yes—
64#2507C2216yes—
65#2505C22112yes—
66#2502C2216yes—
67#2497C2216yes—
68#2497C2216yes—
69#2497C2216yes—
70#2492C2216yes—
71#2492C2216yes—
72#2487C2216yes—
73#2454C2216yes—
74#2453C2216yes—
75#2451C2216yes—
76#2450C22112yes—
77#2446C2216yes—
78#2446C2216yes—
79#2440C2216yes—
80#2429C2216yes—
81#2423C2216yes—
82#2423C2216yes—
83#2417C2216yes—
84#2402C22112yes—
85#2396C22112yes—
86#2369C2213yes—
87#2369C2216yes—
88#2365C2213yes—
89#2365C2216yes—
90#2360C2216yes—
91#2360C2216yes—
92#2360C2216yes—
93#2355C2216yes—
94#2355C2216yes—
95Q8×C4⋊C4C2212yes—
96Q8×C4⋊C4C2212yes—
97Q8×C4⋊C4C2211yescharacteristic
98Q8×C4⋊C4C2212yes—
99Q8×C4⋊C4C2211yescharacteristic
100Q8×C4⋊C4C2212yes—
101Q8×C4⋊C4C2213yes—
102D4×C4⋊C4C2216yes—
103D4×C4⋊C4C2213yes—
104#2345C2216yes—
105#2345C2216yes—
106Q8×C22⋊C4C2212yes—
107Q8×C22⋊C4C2212yes—
108Q8×C22⋊C4C2212yes—
109Q8×C22⋊C4C2212yes—
110Q8×C22⋊C4C2212yes—
111C4×C4⋊Q8C2213yes—
112C4×C4⋊Q8C2213yes—
113C4×C4⋊Q8C2216yes—
114C4×C4⋊Q8C2216yes—
115C4×#125C2216yes—
116C4×#125C2213yes—
117C4×#125C2213yes—
118C4×#126C2216yes—
119C4×#126C2216yes—
120C4×#124C2213yes—
121C4×#124C2213yes—
122C4×C22⋊Q8C2216yes—
123C4×C22⋊Q8C2216yes—
124C4×C22⋊Q8C2216yes—
125C4×C22⋊Q8C2216yes—
126C4×C22⋊Q8C2213yes—
127C4×C22⋊Q8C2213yes—
128C4×#123C2216yes—
129C4×#123C2216yes—
130C4×#121C2213yes—
131C4×#121C2213yes—
132#2298C2216yes—
133#2295C2216yes—
134#2295C2216yes—
135#2295C2216yes—
136#2295C2213yes—
137#2293C2213yes—
138#2290C2216yes—
139#2285C2216yes—
140#2283C2213yes—
141C42×Q8C2211yescharacteristic
142C42×Q8C2212yes—
143C42×Q8C2213yes—
144C42×Q8C2211yescharacteristic
145C42×Q8C2213yes—
146C42×Q8C2213yes—
147C42×Q8C2211yescharacteristic
148C42×Q8C2211yescharacteristic
149C42×Q8C2213yes—
150C42×Q8C2213yes—
151C42×D4C2213yes—
152C42×D4C2216yes—
153C4×#117C2216yes—
154C2×C4×C4⋊C4C2213yes—
155C2×C4×C4⋊C4C2213yes—
156C2×C4×C4⋊C4C2213yes—
157C2×C43C2213yes—
158C23×Q8C2312yes—
159C23×Q8C2311yescharacteristic
160Q82—28no—
161D4×Q8—216no—
162D4×Q8—28no—
163C2×C4⋊Q8C2313yes—
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×C4⋊Q8C2316yes—
167#529Q8116yesdirect product factor
168C2×#126C2312yes—
169C2×#125C2316yes—
170C2×#125C2311yescharacteristic
171C2×#124C2311yescharacteristic
172C2×#123C2312yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2316yes—
177C2×C22⋊Q8C2311yescharacteristic
178C2×#121C2311yescharacteristic
179C2×C4×Q8—28no—
180C2×C4×Q8—28no—
181C2×C4×Q8—216no—
182C2×C4×Q8—28no—
183C2×C4×Q8C2313yes—
184C2×C4×Q8C2316yes—
185C2×C4×Q8C2313yes—
186C2×C4×Q8C2313yes—
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2311yescharacteristic
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2316yes—
195C2×C4×Q8C2313yes—
196C2×C4×Q8C2313yes—
197C2×C4×Q8C2313yes—
198C2×C4×Q8C2313yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2313yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2311yescharacteristic
203C2×C4×Q8C2311yescharacteristic
204C2×C4×D4C2313yes—
205C2×C4×D4C2316yes—
206C2×C4×D4C2316yes—
207C2×C4×D4C2313yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×#117C2316yes—
211C2×#117C2312yes—
212C22×C4⋊C4C2316yes—
213C22×C4⋊C4C2313yes—
214C22×C4⋊C4C2313yes—
215C22×C4⋊C4C2313yes—
216C22×C42C2313yes—
217C22×C42C2313yes—
218C22×C42C2313yes—
219C22×C42C2316yes—
220C22×C42C2313yes—
221C22×C42C2313yes—
222C22×C42C2313yes—
223C22×C42C2311yescharacteristic
224#400C23112yes—
225#400C23112yes—
226#400C23112yes—
227#400C23112yes—
228#400C23112yes—
229#399C23112yes—
230#398C23112yes—
231#398C23112yes—
232#398C23112yes—
233#398C23112yes—
234#398C23112yes—
235#398C23112yes—
236#396C23112yes—
237#396C23112yes—
238#395C23112yes—
239#393C23112yes—
240#391C2316yes—
241#391C2316yes—
242#391C2316yes—
243#391C23112yes—
244#391C2316yes—
245#391C2316yes—
246#391C2313yes—
247#391C2316yes—
248#391C2313yes—
249#391C2316yes—
250#391C2316yes—
251#391C2316yes—
252#391C2316yes—
253#391C2316yes—
254#391C2316yes—
255#391C2316yes—
256#391C2316yes—
257#390C2313yes—
258#390C2313yes—
259#389C2313yes—
260#389C2316yes—
261#389C2316yes—
262#389C2313yes—
263#389C2313yes—
264#389C2313yes—
265#389C2316yes—
266#389C23112yes—
267#389C23112yes—
268#389C23112yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C2316yes—
283#389C2316yes—
284#388C2316yes—
285#388C2316yes—
286#388C2316yes—
287#388C2316yes—
288#388C2316yes—
289#388C2316yes—
290#388C2316yes—
291#388C2316yes—
292#387C2316yes—
293#387C2316yes—
294#387C2316yes—
295#387C2316yes—
296#387C2316yes—
297#387C2316yes—
298#387C23112yes—
299#387C23112yes—
300#387C2316yes—
301#387C2316yes—
302#387C23112yes—
303#387C23112yes—
304#387C23112yes—
305#387C23112yes—
306#387C23112yes—
307#387C23112yes—
308#387C23112yes—
309#387C23112yes—
310#387C23112yes—
311#387C23112yes—
312#386C2316yes—
313#386C2316yes—
314#385C23112yes—
315#385C23112yes—
316#385C23112yes—
317#385C23112yes—
318#385C2316yes—
319#385C2316yes—
320#384C2313yes—
321#384C2313yes—
322#384C2316yes—
323#384C2316yes—
324#384C2316yes—
325#384C2316yes—
326#383C2316yes—
327#382C2316yes—
328#382C2313yes—
329#382C2313yes—
330#382C23112yes—
331#381C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C23112yes—
335#380C2313yes—
336#380C2313yes—
337#380C2316yes—
338#380C2316yes—
339#380C2316yes—
340#380C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2313yes—
348C4×C4⋊C4C2313yes—
349C4×C4⋊C4C23112yes—
350C4×C4⋊C4C2313yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2316yes—
353C4×C4⋊C4C2313yes—
354C4×C4⋊C4C2313yes—
355C4×C4⋊C4C2313yes—
356C4×C4⋊C4C23112yes—
357C4×C4⋊C4C2316yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2313yes—
360C4×C4⋊C4C2316yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2313yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2313yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2313yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2313yes—
381C4×C22⋊C4C2316yes—
382C4×C22⋊C4C2316yes—
383C4×C22⋊C4C2316yes—
384C4×C22⋊C4C2316yes—
385C4×C22⋊C4C2316yes—
386C4×C22⋊C4C2316yes—
387C4×C22⋊C4C2316yes—
388C4×C22⋊C4C2316yes—
389C4×C22⋊C4C2316yes—
390C4×C22⋊C4C2316yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2316yes—
394#376C2316yes—
395#376C2316yes—
396C2×#95C2316yes—
397C43C2313yes—
398C43C2313yes—
399C43C2313yes—
400C43C2313yes—
401C43C2313yes—
402C43C2313yes—
403C43C2316yes—
404C43C2313yes—
405C43C2313yes—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—28no—
409C22×Q8—28no—
410C22×Q8—28no—
411C22×Q8#4118yes—
412C22×Q8C2416yes—
413C22×Q8C2411yescharacteristic
414C22×Q8C2413yes—
415C22×Q8C2416yes—
416C22×Q8C2411yescharacteristic
417C22×D4C2412yes—
418C22×D4C2411yescharacteristic
419C23×C4C2416yes—
420C23×C4C2413yes—
421C23×C4C2413yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2413yes—
427C23×C4C2416yes—
428C23×C4C2413yes—
429C4⋊Q8—224no—
430C4⋊Q8—224no—
431C4⋊Q8—212no—
432C4⋊Q8—212no—
433#126C2×Q8116yescomplemented
434#125—412no—
435#125C2×Q818yescomplemented
436#124C2×Q818yescomplemented
437#123C2×Q8116yescomplemented
438C22⋊Q8—224no—
439C22⋊Q8—224no—
440C22⋊Q8—224no—
441C22⋊Q8—412no—
442C22⋊Q8C2×Q818yescomplemented
443#121C2×Q818yes—
444C4×Q8—212no—
445C4×Q8—212no—
446C4×Q8—24no—
447C4×Q8—24no—
448C4×Q8—28no—
449C4×Q8—24no—
450C4×Q8—24no—
451C4×Q8—28no—
452C4×Q8—28no—
453C4×Q8—212no—
454C4×Q8—224no—
455C4×Q8—212no—
456C4×Q8—212no—
457C4×Q8—224no—
458C4×Q8—212no—
459C4×Q8—212no—
460C4×Q8—412no—
461C4×Q8—46no—
462C4×Q8C2×Q818yescomplemented
463C4×Q8#4118yes—
464C4×Q8#4118yes—
465C4×D4—224no—
466C4×D4—212no—
467C4×D4—46no—
468C4×D4—412no—
469C4×D4C2×Q818yescomplemented
470C4×D4C2×Q8116yescomplemented
471#117—412no—
472#117C2×Q8116yescomplemented
473C2×C4⋊C4—212no—
474C2×C4⋊C4—212no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—212no—
477C2×C4⋊C4C2413yes—
478C2×C4⋊C4C2413yes—
479C2×C4⋊C4C2413yes—
480C2×C4⋊C4C2413yes—
481C2×C4⋊C4C2416yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C24112yes—
486C2×C4⋊C4C2413yes—
487C2×C4⋊C4C2413yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2416yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C24112yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C24112yes—
502C2×C4⋊C4C24112yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C24112yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2413yes—
513C2×C4⋊C4C2413yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C2416yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2412yes—
523C2×C22⋊C4C2412yes—
524C2×C22⋊C4C2412yes—
525C2×C22⋊C4C2412yes—
526C2×C22⋊C4C2412yes—
527C2×C42—212no—
528C2×C42—212no—
529C2×C42—224no—
530C2×C42—212no—
531C2×C42—46no—
532C2×C42—46no—
533C2×C42—46no—
534C2×C42C2×Q818yescomplemented
535C2×C42C2416yes—
536C2×C42C2413yes—
537C2×C42C2416yes—
538C2×C42C2413yes—
539C2×C42C2413yes—
540C2×C42C2413yes—
541C2×C42C2413yes—
542C2×C42C2413yes—
543C2×C42C2413yes—
544C2×C42C2413yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2416yes—
548C2×C42C2416yes—
549C2×C42C2413yes—
550C2×C42C2413yes—
551C2×C42C2416yes—
552C2×C42C2413yes—
553C2×C42C2413yes—
554C2×C42C2416yes—
555C2×C42C2416yes—
556C2×C42C2416yes—
557C2×C42C2413yes—
558C2×C42C2413yes—
559C2×C42C2413yes—
560C2×C42C2413yes—
561C2×C42C2413yes—
562C2×C42C2413yes—
563C2×C42C2413yes—
564C2×C42C2413yes—
565C2×C42C2411yescharacteristic
566C2×C42C2411yescharacteristic
567C2×C42C2411yescharacteristic
568C2×C42C2412yes—
569C2×C42C2411yescharacteristic
570C2×C42C2413yes—
571C2×C42C2413yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2416yes—
583#95C2416yes—
584#95C2416yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C24112yes—
594#95C2416yes—
595#95C2416yes—
596#95C2416yes—
597#95C24112yes—
598#95C24112yes—
599#95C24112yes—
600#95C24112yes—
601#95C24112yes—
602C24C2512yes—
603C24C2511yescharacteristic
604C2×Q8—232no—
605C2×Q8—22no—
606C2×Q8—26no—
607C2×Q8—26no—
608C2×Q8—212no—
609C2×Q8—212no—
610C2×Q8—212no—
611C2×Q8—212no—
612C2×Q8—22no—
613C2×Q8—46no—
614C2×Q8—46no—
615C2×Q8—432no—
616C2×Q8C22×Q814yes—
617C2×Q8C2×#41112yes—
618C2×Q8C2×#4114yes—
619C2×Q8C2×#4114yes—
620C2×Q8C2×#4114yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4C22×Q818yes—
626C2×D4C22×Q814yes—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—26no—
633C22×C4—26no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—26no—
638C22×C4—26no—
639C22×C4—26no—
640C22×C4—26no—
641C22×C4—26no—
642C22×C4—212no—
643C22×C4—212no—
644C22×C4—212no—
645C22×C4—212no—
646C22×C4—43no—
647C22×C4—43no—
648C22×C4—43no—
649C22×C4—43no—
650C22×C4—46no—
651C22×C4—46no—
652C22×C4C22×Q814yes—
653C22×C4C22×Q814yes—
654C22×C4C22×Q814yes—
655C22×C4C22×Q818yes—
656C22×C4C2×#41112yes—
657C22×C4C2516yes—
658C22×C4C2516yes—
659C22×C4C2513yes—
660C22×C4C2513yes—
661C22×C4C2513yes—
662C22×C4C2513yes—
663C22×C4C2516yes—
664C22×C4C2516yes—
665C22×C4C2511yescharacteristic
666C22×C4C2511yescharacteristic
667C22×C4C2511yescharacteristic
668C22×C4C2511yescharacteristic
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2512yes—
672C22×C4C2513yes—
673C22×C4C2513yes—
674C22×C4C2513yes—
675C22×C4C2511yescharacteristic
676C22×C4C2513yes—
677C22×C4C2511yescharacteristic
678C4⋊C4—212no—
679C4⋊C4—212no—
680C4⋊C4—212no—
681C4⋊C4—26no—
682C4⋊C4—26no—
683C4⋊C4—26no—
684C4⋊C4—26no—
685C4⋊C4—212no—
686C4⋊C4—224no—
687C4⋊C4—212no—
688C4⋊C4—26no—
689C4⋊C4—212no—
690C4⋊C4—212no—
691C4⋊C4—212no—
692C4⋊C4—26no—
693C4⋊C4—224no—
694C4⋊C4—212no—
695C4⋊C4—26no—
696C4⋊C4—26no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—46no—
700C4⋊C4—46no—
701C4⋊C4—46no—
702C4⋊C4—412no—
703C4⋊C4—46no—
704C4⋊C4—412no—
705C4⋊C4—412no—
706C4⋊C4—412no—
707C4⋊C4C22×Q818yes—
708C4⋊C4C22×Q818yes—
709C4⋊C4C22×Q814yes—
710C4⋊C4C22×Q818yes—
711C4⋊C4C22×Q814yes—
712C4⋊C4C22×Q818yes—
713C4⋊C4C2×#41112yes—
714C4⋊C4C2×#41112yes—
715C22⋊C4—212no—
716C22⋊C4—212no—
717C22⋊C4—212no—
718C22⋊C4—212no—
719C22⋊C4—46no—
720C22⋊C4—46no—
721C22⋊C4—46no—
722C22⋊C4—46no—
723C22⋊C4C22×Q818yes—
724C22⋊C4C22×Q818yes—
725C22⋊C4C22×Q818yes—
726C22⋊C4C22×Q818yes—
727C22⋊C4C22×Q818yes—
728C42—26no—
729C42—26no—
730C42—26no—
731C42—26no—
732C42—26no—
733C42—26no—
734C42—26no—
735C42—26no—
736C42—212no—
737C42—212no—
738C42—26no—
739C42—26no—
740C42—212no—
741C42—212no—
742C42—212no—
743C42—26no—
744C42—26no—
745C42—26no—
746C42—26no—
747C42—212no—
748C42—43no—
749C42—43no—
750C42—43no—
751C42—43no—
752C42—43no—
753C42—43no—
754C42—43no—
755C42—43no—
756C42—46no—
757C42—46no—
758C42C22×Q814yes—
759C42C22×Q814yes—
760C42C22×Q814yes—
761C42C22×Q814yes—
762C42C22×Q818yes—
763C42C2×#41112yes—
764C42C2×#41112yes—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23C23×Q814yes—
776C23C23×Q812yes—
777C23C22×#4112yes—
778C23#58512yes—
779C23C2611yescharacteristic
780Q8—224no—
781Q8—28no—
782Q8—424no—
783Q8—812no—
784Q8#529116yesdirect product factor
785D4—216no—
786D4—28no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—23no—
795C2×C4—23no—
796C2×C4—23no—
797C2×C4—23no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—23no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—23no—
806C2×C4—22no—
807C2×C4—28no—
808C2×C4—224no—
809C2×C4—28no—
810C2×C4—216no—
811C2×C4—28no—
812C2×C4—23no—
813C2×C4—23no—
814C2×C4—23no—
815C2×C4—23no—
816C2×C4—26no—
817C2×C4—26no—
818C2×C4—26no—
819C2×C4—26no—
820C2×C4—26no—
821C2×C4—26no—
822C2×C4—23no—
823C2×C4—23no—
824C2×C4—23no—
825C2×C4—23no—
826C2×C4—23no—
827C2×C4—23no—
828C2×C4—26no—
829C2×C4—26no—
830C2×C4—23no—
831C2×C4—23no—
832C2×C4—26no—
833C2×C4—26no—
834C2×C4—26no—
835C2×C4—26no—
836C2×C4—412no—
837C2×C4—412no—
838C2×C4—412no—
839C2×C4—424no—
840C2×C4—812no—
841C2×C4C23×Q812yes—
842C2×C4C23×Q812yes—
843C2×C4C23×Q812yes—
844C2×C4C23×Q812yes—
845C2×C4C23×Q814yes—
846C2×C4C23×Q814yes—
847C2×C4C23×Q814yes—
848C2×C4C23×Q812yes—
849C2×C4C23×Q812yes—
850C2×C4C22×#4116yes—
851C2×C4C22×#4116yes—
852C2×C4C22×#4116yes—
853C2×C4C22×#4116yes—
854C2×C4C22×#4116yes—
855C2×C4C22×#4116yes—
856C2×C4C22×#4112yes—
857C2×C4C22×#4112yes—
858C2×C4#58512yes—
859C2×C4#58512yes—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22Q8×#4114yes—
874C22C24×Q811yescharacteristic
875C22C23×#4111yescharacteristic
876C22C23×#4111yescharacteristic
877C22C23×#4111yescharacteristic
878C22C2×#58511yescharacteristic
879C22C2×#58511yescharacteristic
880C22C2×#58511yescharacteristic
881C4—26no—
882C4—26no—
883C4—26no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—24no—
890C4—24no—
891C4—46no—
892C4—43no—
893C4—43no—
894C4—43no—
895C4—46no—
896C4—43no—
897C4—46no—
898C4—46no—
899C4C2×#529112yes—
900C4Q8×#4114yes—
901C4Q8×#4114yes—
902C2—24no—
903C2—44no—
904C2C22×#52911yescharacteristic
905C2C2×Q8×#4111yescharacteristic
906C2C2×Q8×#4111yescharacteristic
907C2C2×Q8×#4111yescharacteristic
908C2#6279311yescharacteristic
909C2#6281011yescharacteristic
910C2#6281611yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36635C2semidirect
2. #36556C2semidirect
3. #36555C2semidirect
4. #36554C2semidirect
5. #36553C2semidirect
6. #36552C2semidirect
8. Q8×#126C2semidirect
9. Q8×#125C2semidirect
10. Q8×#124C2semidirect
11. Q8×#123C2semidirect
12. Q8×C22⋊Q8C2semidirect
14. #34951C2semidirect
15. #34941C2semidirect
16. #34916C2semidirect
17. #34772C2semidirect
18. C4×Q82C2semidirect
19. C4×D4×Q8C2semidirect
20. C4×D4×Q8C2semidirect
21. Q8×#117C2semidirect
23. C2×C42×Q8C2semidirect
167. #529Q8direct (N × H)
433. #126C2×Q8semidirect
435. #125C2×Q8semidirect
436. #124C2×Q8semidirect
437. #123C2×Q8semidirect
442. C22⋊Q8C2×Q8semidirect
462. C4×Q8C2×Q8semidirect
469. C4×D4C2×Q8semidirect
470. C4×D4C2×Q8semidirect
472. #117C2×Q8semidirect
534. C2×C42C2×Q8semidirect
784. Q8#529direct (N × H)

Maximal subgroups

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

subgroupindex
#366352
#365562
#365552
#365542
#365532
#365522
#365512
Q8×#1262
Q8×#1252
Q8×#1242
Q8×#1232
Q8×C22⋊Q82
Q8×#1212
#349512
#349412
#349162
#347722
C4×Q822
C4×D4×Q82
Q8×#1172
C4×#5292
C2×C42×Q82