Finite Group Databasebeta

← #10578288

Subgroups — #10578288

Order 512.

6147 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#61842C216yesmaximal, complemented
4#61841C216yesmaximal, complemented
5#61838C212yesmaximal, complemented
6#61837C212yesmaximal, complemented
7#61834C2112yesmaximal, complemented
8#61824C214yesmaximal, complemented
9#61369C216yesmaximal, complemented
10Q8×AGL(1,ℤ/8)C212yesmaximal, complemented
11#61323C216yesmaximal, complemented
12#61322C212yesmaximal, complemented
13#60866C213yesmaximal, complemented
14#60865C213yesmaximal, complemented
15#60563C213yesmaximal
16#60562C213yesmaximal, complemented
17#60248C211yesmaximal, characteristic, complemented
18#3523—21no—
19#3523—23no—
20#3523—21no—
21#3523—23no—
22#3523C2212yes—
23#3523C2216yes—
24#3523C2212yescomplemented
25#3523C2216yescomplemented
26Q8×#41—21no—
27Q8×#41—23no—
28Q8×#41—21no—
29Q8×#41—23no—
30Q8×#41C2212yes—
31Q8×#41C2216yes—
32Q8×#41C2212yescomplemented
33Q8×#41C2216yescomplemented
34C2×Q82C2211yescharacteristic, complemented
35C2×#557C2211yescharacteristic, complemented
36C2×#557C2213yescomplemented
37C2×#557C2213yescomplemented
38C2×#556C2213yescomplemented
39C2×#554—23no—
40C2×#554C2213yescomplemented
41C2×#552—23no—
42C2×D4×Q8—21no—
43C2×D4×Q8—21no—
44C2×D4×Q8C2211yescharacteristic, complemented
45C2×D4×Q8C2211yescharacteristic, complemented
46C2×#541—23no—
47C2×#533—23no—
48C2×#533C2213yes—
49C2×#533C2213yes—
50C2×#529C2213yes—
51C2×#519—21no—
52C2×C4×#41C2213yes—
53C22×C4×Q8—21no—
54C22×C4×Q8C2211yescharacteristic
55#3390C22124yescomplemented
56#3388C22124yescomplemented
57#3387C22112yescomplemented
58#3386C22112yescomplemented
59#3386C22112yescomplemented
60#3384C22112yescomplemented
61#3383C22112yescomplemented
62#3381C22112yescomplemented
63Q8×SD16C2214yescomplemented
64Q8×D8C2214yescomplemented
65#3377C22124yescomplemented
66#3376C22124yescomplemented
67#3374C22112yescomplemented
68#3372C22112yescomplemented
69#3369C22112yescomplemented
70#3367C22112yescomplemented
71#3364C22112yescomplemented
72#3363C2214yescomplemented
73#3360C22112yescomplemented
74#3359C2214yescomplemented
75#3240C22112yescomplemented
76#3239C2216yes—
77#3238C2216yes—
78#3237C22112yescomplemented
79#3236C22112yescomplemented
80#3233C22112yescomplemented
81#3232C22112yes—
82#3231C22112yescomplemented
83#3230C2216yescomplemented
84#3229C2216yescomplemented
85#3166C2216yescomplemented
86#3165C2216yescomplemented
87#3140C2216yescomplemented
88#3139C2216yescomplemented
89#3117C2216yes—
90#3116C22112yescomplemented
91#3114C2216yes—
92#3113C2216yescomplemented
93#3111C22112yes—
94#3110C2216yescomplemented
95#3108C2216yes—
96#3107C22112yescomplemented
97#3105C2216yes—
98#3104C2216yescomplemented
99#3102C22112yes—
100#3101C2216yescomplemented
101#3095C2216yes—
102#3095C2213yes—
103#3094C2213yes—
104#3080C2216yes—
105#3079C2216yes—
106#3078C2216yescomplemented
107#3078C22112yescomplemented
108#3077C2216yescomplemented
109#3040C2216yes—
110#3039C2216yes—
111#3007C2213yes—
112#3006C2211yescharacteristic
113#2984C2212yescomplemented
114#2984C2216yescomplemented
115#2983C2216yescomplemented
116#2982C2212yescomplemented
117Q8×M16C2212yescomplemented
118Q8×M16C2216yescomplemented
119C4×#137C2216yes—
120C4×#137C22112yes—
121C4×AGL(1,ℤ/8)C2216yes—
122#2920C2213yes—
123#2920C2213yes—
124C22×#41C2311yescharacteristic
125C23×Q8—21no—
126C23×Q8—21no—
127C23×Q8D411yescharacteristic
128C2×#137C2316yes—
129C2×AGL(1,ℤ/8)C2312yes—
130Q82—21no—
131Q82—23no—
132Q82C2312yes—
133Q82C2316yes—
134#557—23no—
135#557—23no—
136#557—26no—
137#557—21no—
138#557—23no—
139#557—23no—
140#557—26no—
141#557—23no—
142#557C2312yes—
143#557C2316yes—
144#557C2316yes—
145#557C2316yes—
146#557C23112yes—
147#557C2316yes—
148#557C2316yes—
149#557C23112yes—
150#556—23no—
151#556—26no—
152#556—23no—
153#556C2316yes—
154#556C2316yes—
155#556C23112yes—
156#554—23no—
157#554—23no—
158#554—26no—
159#554—26no—
160#554—26no—
161#554—212no—
162#554—26no—
163#554—26no—
164#554—212no—
165#554C2316yes—
166#554C2316yes—
167#554C23112yes—
168#552—26no—
169#552—212no—
170#552—26no—
171#552—26no—
172#552—26no—
173#552—212no—
174D4×Q8—22no—
175D4×Q8—26no—
176D4×Q8—22no—
177D4×Q8—26no—
178D4×Q8—22no—
179D4×Q8—26no—
180D4×Q8—22no—
181D4×Q8—26no—
182D4×Q8—21no—
183D4×Q8—23no—
184D4×Q8—21no—
185D4×Q8—23no—
186D4×Q8C2312yes—
187D4×Q8C2316yes—
188D4×Q8C2312yes—
189D4×Q8C2316yes—
190#541—26no—
191#541—212no—
192#541—26no—
193#541—26no—
194#541—26no—
195#541—212no—
196#533—26no—
197#533—26no—
198#533—212no—
199#533—26no—
200#533—26no—
201#533—212no—
202#533—23no—
203#533—23no—
204#533—23no—
205#533—23no—
206#533—23no—
207#533—23no—
208#533—23no—
209#533—23no—
210#533C2316yes—
211#533C2316yes—
212#533C2316yes—
213#533C2316yes—
214#533C2316yes—
215#533C2316yes—
216#533C2316yes—
217#533C2316yes—
218C2×C4⋊Q8—23no—
219C2×C4⋊Q8—23no—
220C2×C4⋊Q8—23no—
221C2×C4⋊Q8C2313yes—
222C2×C4⋊Q8C2313yes—
223C2×C4⋊Q8C2313yes—
224C2×C4⋊Q8C2313yes—
225#529—23no—
226#529—23no—
227#529—23no—
228#529—23no—
229#529C2316yes—
230#529C2316yes—
231#529C2316yes—
232#529C2316yes—
233C2×#126—26no—
234C2×#126—23no—
235C2×#125—26no—
236C2×#125—26no—
237C2×#125—23no—
238C2×#125—23no—
239C2×#125C2313yes—
240C2×#125C2316yes—
241C2×#124C2313yes—
242C2×#123—23no—
243C2×C22⋊Q8—23no—
244C2×C22⋊Q8—23no—
245C2×C22⋊Q8—23no—
246C2×C22⋊Q8—23no—
247C2×C22⋊Q8—23no—
248C2×C22⋊Q8—23no—
249C2×C22⋊Q8—26no—
250C2×C22⋊Q8—23no—
251C2×C22⋊Q8C2313yes—
252C2×#121C2311yescharacteristic
253#519—22no—
254#519—26no—
255#519—22no—
256#519—26no—
257C4×#41—23no—
258C4×#41—23no—
259C4×#41—23no—
260C4×#41—23no—
261C4×#41C2316yes—
262C4×#41C2316yes—
263C4×#41C2316yes—
264C4×#41C2316yes—
265C2×C4×Q8—21no—
266C2×C4×Q8—21no—
267C2×C4×Q8—22no—
268C2×C4×Q8—26no—
269C2×C4×Q8—22no—
270C2×C4×Q8—26no—
271C2×C4×Q8—23no—
272C2×C4×Q8—23no—
273C2×C4×Q8—23no—
274C2×C4×Q8—23no—
275C2×C4×Q8—23no—
276C2×C4×Q8D411yescharacteristic
277C2×C4×Q8D411yescharacteristic
278C2×C4×Q8D413yes—
279C2×C4×Q8D413yes—
280C2×C4×Q8D411yescharacteristic
281C2×C4×Q8D413yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2316yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×D4—23no—
293C2×C4×D4—23no—
294C2×C4×D4—23no—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×#117—23no—
299C2×#117—23no—
300C2×#117—23no—
301C2×#117—23no—
302C2×#117C2313yes—
303C22×C4⋊C4—23no—
304C22×C4⋊C4D413yes—
305C22×C42—23no—
306C22×C42C2313yes—
307#501C23124yes—
308#501C23112yes—
309#501C23112yes—
310#500C23112yes—
311#499C23124yes—
312#498C23112yes—
313#491C23124yes—
314#489C23112yes—
315#489C23112yes—
316#488C23124yes—
317#487C23112yes—
318#487C23112yes—
319#485C23112yes—
320#485C23124yes—
321#484C23112yes—
322#484C2316yes—
323#483C23112yes—
324#483C2316yes—
325#482C23112yes—
326#481C2316yes—
327#480C2316yes—
328#479C23124yes—
329#479C23124yes—
330#479C23124yes—
331#479C23112yes—
332#479C23112yes—
333#478C23124yes—
334#478C23112yes—
335#478C23112yes—
336#477C23112yes—
337#477C23124yes—
338#477C23112yes—
339#476C23112yes—
340#476C23112yes—
341#475C23112yes—
342#475C23124yes—
343#475C23112yes—
344#474C23112yes—
345#474C23112yes—
346#464C23112yes—
347#464C23112yes—
348#463C23112yes—
349#463C23112yes—
350#462C23112yes—
351#462C23112yes—
352#461C23112yes—
353#461C23112yes—
354#452C23112yes—
355#451C2316yes—
356#450C2316yes—
357#449C2314yes—
358#448C2312yes—
359#447C2312yes—
360#446C23112yes—
361#446C23112yes—
362#446C23124yes—
363C8×Q8C2314yes—
364C8×Q8C23112yes—
365#442C23112yes—
366#441C23112yes—
367#441C23124yes—
368#440C23124yes—
369#440C23112yes—
370#440C23112yes—
371C4×Q16C23112yes—
372C4×Q16C23124yes—
373C4×SD16C23124yes—
374C4×SD16C23112yes—
375C4×SD16C23112yes—
376C4×D8C23112yes—
377#432C2316yes—
378#432C2316yes—
379#432C2316yes—
380#432C2316yes—
381#431C2316yes—
382#431C2316yes—
383#431C2316yes—
384#431C2316yes—
385#428C23112yes—
386#428C2316yes—
387#428C2316yes—
388#423C2316yes—
389#423C2316yes—
390#419C2316yes—
391#419C23112yes—
392#418C2316yes—
393#417C2316yes—
394#417C2312yes—
395#407C2313yes—
396#407C2311yescharacteristic
397C4×M16C2316yes—
398C4×M16C2316yes—
399C2×#41—28no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41C2412yes—
403C2×#41C2412yes—
404C22×Q8—26no—
405C22×Q8—22no—
406C22×Q8—26no—
407C22×Q8—22no—
408C22×Q8—23no—
409C22×Q8—23no—
410C22×Q8—23no—
411C22×Q8—44no—
412C22×Q8—48no—
413C22×Q8—48no—
414C22×Q8C2×D411yescharacteristic
415C22×Q8C2×D411yescharacteristic
416C22×Q8C2×D411yescharacteristic
417C22×Q8C2×D413yes—
418C22×Q8C2×D413yes—
419C22×Q8C2×D413yes—
420C22×Q8C2411yescharacteristic
421C22×Q8C2413yes—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C2411yescharacteristic
425C22×D4C2411yescharacteristic
426C23×C4—21no—
427C23×C4—23no—
428C23×C4—23no—
429C23×C4—23no—
430C23×C4C2×D413yes—
431C23×C4C2×D413yes—
432C23×C4C2411yescharacteristic
433#137—224no—
434AGL(1,ℤ/8)—28no—
435C2×Q16C24112yes—
436C2×SD16C2414yes—
437C2×SD16C24112yes—
438C2×D8C2414yes—
439C2×M16C2412yes—
440C2×M16C2416yes—
441C4⋊Q8—26no—
442C4⋊Q8—26no—
443C4⋊Q8—212no—
444C4⋊Q8—26no—
445C4⋊Q8—26no—
446C4⋊Q8—212no—
447C4⋊Q8—26no—
448C4⋊Q8—26no—
449C4⋊Q8—212no—
450C4⋊Q8—23no—
451C4⋊Q8—23no—
452C4⋊Q8—23no—
453C4⋊Q8—23no—
454C4⋊Q8—23no—
455C4⋊Q8—23no—
456C4⋊Q8—23no—
457C4⋊Q8—23no—
458C4⋊Q8C2416yes—
459C4⋊Q8C2416yes—
460C4⋊Q8C2416yes—
461C4⋊Q8C2416yes—
462C4⋊Q8C2416yes—
463C4⋊Q8C2416yes—
464C4⋊Q8C2416yes—
465C4⋊Q8C2416yes—
466#126—212no—
467#126—212no—
468#126—212no—
469#126—212no—
470#126—26no—
471#126—26no—
472#126—26no—
473#126—26no—
474#125—212no—
475#125—212no—
476#125—212no—
477#125—212no—
478#125—212no—
479#125—212no—
480#125—212no—
481#125—212no—
482#125—26no—
483#125—212no—
484#125—26no—
485#125—26no—
486#125—26no—
487#125—26no—
488#125—26no—
489#125—23no—
490#125—23no—
491#125—26no—
492#125—26no—
493#125C2416yes—
494#125C2416yes—
495#125C24112yes—
496#125C24112yes—
497#124—23no—
498#124—23no—
499#124C2416yes—
500#124C2416yes—
501#123—26no—
502#123—26no—
503#123—26no—
504#123—26no—
505C22⋊Q8—26no—
506C22⋊Q8—26no—
507C22⋊Q8—212no—
508C22⋊Q8—26no—
509C22⋊Q8—26no—
510C22⋊Q8—212no—
511C22⋊Q8—26no—
512C22⋊Q8—26no—
513C22⋊Q8—26no—
514C22⋊Q8—26no—
515C22⋊Q8—26no—
516C22⋊Q8—26no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—26no—
523C22⋊Q8—23no—
524C22⋊Q8—23no—
525C22⋊Q8—26no—
526C22⋊Q8—26no—
527C22⋊Q8—212no—
528C22⋊Q8—212no—
529C22⋊Q8—212no—
530C22⋊Q8—212no—
531C22⋊Q8—212no—
532C22⋊Q8—26no—
533C22⋊Q8—212no—
534C22⋊Q8—26no—
535C22⋊Q8C2416yes—
536C22⋊Q8C2416yes—
537#121—21no—
538#121—21no—
539#121C2412yes—
540#121C2412yes—
541C4×Q8—26no—
542C4×Q8—22no—
543C4×Q8—26no—
544C4×Q8—22no—
545C4×Q8—26no—
546C4×Q8—26no—
547C4×Q8—212no—
548C4×Q8—26no—
549C4×Q8—212no—
550C4×Q8—26no—
551C4×Q8—26no—
552C4×Q8—26no—
553C4×Q8—26no—
554C4×Q8—26no—
555C4×Q8—26no—
556C4×Q8—26no—
557C4×Q8—26no—
558C4×Q8—26no—
559C4×Q8—26no—
560C4×Q8—26no—
561C4×Q8—26no—
562C4×Q8—26no—
563C4×Q8—23no—
564C4×Q8—23no—
565C4×Q8—23no—
566C4×Q8—23no—
567C4×Q8—23no—
568C4×Q8—23no—
569C4×Q8—26no—
570C4×Q8—26no—
571C4×Q8C2×D411yescharacteristic
572C4×Q8C2×D413yes—
573C4×Q8C2×D411yescharacteristic
574C4×Q8C2×D413yes—
575C4×Q8C2×D413yes—
576C4×Q8C2×D411yescharacteristic
577C4×Q8C2×D413yes—
578C4×Q8C2×D413yes—
579C4×Q8C2×D416yes—
580C4×Q8C2×D413yes—
581C4×Q8C2×D413yes—
582C4×Q8C2×D416yes—
583C4×Q8C2×D413yes—
584C4×Q8C2×D416yes—
585C4×Q8C2×D413yes—
586C4×Q8C2416yes—
587C4×Q8C2416yes—
588C4×Q8C2416yes—
589C4×Q8C2416yes—
590C4×Q8C2416yes—
591C4×Q8C2416yes—
592C4×Q8C24112yes—
593C4×Q8C24112yes—
594C4×Q8C2411yescharacteristic
595C4×Q8C2413yes—
596C4×Q8C2413yes—
597C4×Q8C2413yes—
598C4×Q8C2416yes—
599C4×D4—26no—
600C4×D4—26no—
601C4×D4—26no—
602C4×D4—26no—
603C4×D4—26no—
604C4×D4—26no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—26no—
608C4×D4—26no—
609C4×D4—26no—
610C4×D4—26no—
611C4×D4—23no—
612C4×D4—23no—
613C4×D4—23no—
614C4×D4—23no—
615C4×D4—23no—
616C4×D4—23no—
617C4×D4C2416yes—
618C4×D4C2416yes—
619C4×D4C2416yes—
620C4×D4C2416yes—
621C4×D4C2416yes—
622C4×D4C2416yes—
623#117—26no—
624#117—26no—
625#117—26no—
626#117—26no—
627#117—23no—
628#117—23no—
629#117—26no—
630#117—212no—
631#117—26no—
632#117—26no—
633#117—26no—
634#117—26no—
635#117—26no—
636#117—26no—
637#117—26no—
638#117—26no—
639#117—26no—
640#117C2416yes—
641#117C2416yes—
642C2×C4⋊C4—26no—
643C2×C4⋊C4—23no—
644C2×C4⋊C4—23no—
645C2×C4⋊C4—23no—
646C2×C4⋊C4—23no—
647C2×C4⋊C4—23no—
648C2×C4⋊C4—23no—
649C2×C4⋊C4—23no—
650C2×C4⋊C4—23no—
651C2×C4⋊C4—23no—
652C2×C4⋊C4—23no—
653C2×C4⋊C4—26no—
654C2×C4⋊C4—26no—
655C2×C4⋊C4—23no—
656C2×C4⋊C4—26no—
657C2×C4⋊C4—26no—
658C2×C4⋊C4—212no—
659C2×C4⋊C4C2×D413yes—
660C2×C4⋊C4C2×D413yes—
661C2×C4⋊C4C2×D416yes—
662C2×C4⋊C4C2×D413yes—
663C2×C4⋊C4C2×D413yes—
664C2×C4⋊C4C2×D416yes—
665C2×C4⋊C4C2×D413yes—
666C2×C4⋊C4C2×D413yes—
667C2×C4⋊C4C2×D416yes—
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C22⋊C4—23no—
673C2×C22⋊C4—23no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—23no—
676C2×C22⋊C4—23no—
677C2×C22⋊C4—23no—
678C2×C22⋊C4—23no—
679C2×C22⋊C4—23no—
680C2×C42—26no—
681C2×C42—23no—
682C2×C42—23no—
683C2×C42—23no—
684C2×C42—23no—
685C2×C42—26no—
686C2×C42—26no—
687C2×C42—26no—
688C2×C42—26no—
689C2×C42C2×D413yes—
690C2×C42C2×D413yes—
691C2×C42C2×D413yes—
692C2×C42C2×D413yes—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2413yes—
696C2×C42C2413yes—
697C2×C42C2413yes—
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701#107C24112yes—
702#107C24124yes—
703#107C24112yes—
704#106C24124yes—
705#106C24112yes—
706#106C24112yes—
707C4⋊C8C24112yes—
708C4⋊C8C24112yes—
709C4⋊C8C24112yes—
710C4⋊C8C24112yes—
711#103C24112yes—
712#103C2414yes—
713#103C24124yes—
714#103C24112yes—
715#103C24124yes—
716#103C24112yes—
717#102C24112yes—
718#102C2414yes—
719#102C24112yes—
720#102C24112yes—
721C22⋊C8C2412yes—
722C22⋊C8C2412yes—
723C22⋊C8C2416yes—
724C22⋊C8C2416yes—
725#97C24112yes—
726#97C24112yes—
727C4×C8C24112yes—
728C4×C8C24112yes—
729C24—21no—
730C24—21no—
731C24C22×D411yescharacteristic
732#41—28no—
733#41—28no—
734#41—24no—
735#41—24no—
736#41—24no—
737#412−1+418yes—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—21no—
743C2×Q8—23no—
744C2×Q8—26no—
745C2×Q8—26no—
746C2×Q8—26no—
747C2×Q8—26no—
748C2×Q8—26no—
749C2×Q8—26no—
750C2×Q8—212no—
751C2×Q8—46no—
752C2×Q8—46no—
753C2×Q8—46no—
754C2×Q8—412no—
755C2×Q8—412no—
756C2×Q8—424no—
757C2×Q8—424no—
758C2×Q8—48no—
759C2×Q8—48no—
760C2×Q8—86no—
761C2×Q8C22×D413yes—
762C2×Q8C22×D413yes—
763C2×Q8C22×D413yes—
764C2×Q8C22×D416yes—
765C2×Q8C22×D411yescharacteristic
766C2×Q8C2516yes—
767C2×Q8C2512yes—
768C2×D4—28no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—44no—
778C2×D4C2512yes—
779C2×D4C2512yes—
780C22×C4—28no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—23no—
786C22×C4—21no—
787C22×C4—23no—
788C22×C4—23no—
789C22×C4—23no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—26no—
793C22×C4—26no—
794C22×C4—26no—
795C22×C4—26no—
796C22×C4—46no—
797C22×C4—46no—
798C22×C4—412no—
799C22×C4—412no—
800C22×C4—86no—
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D413yes—
803C22×C4C22×D413yes—
804C22×C4C22×D413yes—
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D413yes—
810C22×C4C22×D413yes—
811C22×C4C22×D413yes—
812C22×C4C22×D413yes—
813C22×C4C22×D413yes—
814C22×C4C22×D413yes—
815C22×C4C22×D413yes—
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819Q16—224no—
820SD16—28no—
821SD16—224no—
822D8—28no—
823M16—24no—
824M16—212no—
825C2×C8C25112yes—
826C2×C8C2514yes—
827C4⋊C4—212no—
828C4⋊C4—212no—
829C4⋊C4—26no—
830C4⋊C4—26no—
831C4⋊C4—26no—
832C4⋊C4—26no—
833C4⋊C4—26no—
834C4⋊C4—26no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—26no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4—26no—
849C4⋊C4—212no—
850C4⋊C4—212no—
851C4⋊C4—212no—
852C4⋊C4—212no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—23no—
856C4⋊C4—23no—
857C4⋊C4—23no—
858C4⋊C4—21no—
859C4⋊C4C22×D413yes—
860C4⋊C4C22×D413yes—
861C4⋊C4C22×D416yes—
862C4⋊C4C22×D416yes—
863C4⋊C4C22×D413yes—
864C4⋊C4C22×D416yes—
865C4⋊C4C22×D413yes—
866C4⋊C4C22×D416yes—
867C4⋊C4C22×D416yes—
868C4⋊C4C22×D416yes—
869C4⋊C4C2516yes—
870C4⋊C4C2516yes—
871C4⋊C4C2516yes—
872C4⋊C4C2512yes—
873C22⋊C4—26no—
874C22⋊C4—26no—
875C22⋊C4—26no—
876C22⋊C4—26no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—26no—
882C22⋊C4—26no—
883C22⋊C4—26no—
884C22⋊C4—26no—
885C22⋊C4—26no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4—26no—
889C42—26no—
890C42—26no—
891C42—26no—
892C42—26no—
893C42—26no—
894C42—26no—
895C42—212no—
896C42—212no—
897C42—26no—
898C42—26no—
899C42C22×D413yes—
900C42C22×D413yes—
901C42C22×D413yes—
902C42C22×D413yes—
903C42C22×D413yes—
904C42C22×D413yes—
905C42C22×D413yes—
906C42C22×D413yes—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C22×D413yes—
910C42C22×D413yes—
911C42C2513yes—
912C42C2513yes—
913C42C2513yes—
914C42C2513yes—
915C23—24no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23C23×D411yescharacteristic
927C23C23×D411yescharacteristic
928C23C23×D411yescharacteristic
929Q8—24no—
930Q8—22no—
931Q8—26no—
932Q8—26no—
933Q8—26no—
934Q8—212no—
935Q8—46no—
936Q8—412no—
937Q8—412no—
938Q8—46no—
939Q8—412no—
940Q8—412no—
941Q8—86no—
942Q8—86no—
943Q8#57514yes—
944Q8C2×2−1+414yes—
945D4—28no—
946D4—24no—
947D4—28no—
948D4—22no—
949D4—24no—
950D4—44no—
951D4—44no—
952D4—42no—
953D4C2×2−1+414yes—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—28no—
964C2×C4—22no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—26no—
969C2×C4—22no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—26no—
973C2×C4—43no—
974C2×C4—43no—
975C2×C4—43no—
976C2×C4—43no—
977C2×C4—43no—
978C2×C4—43no—
979C2×C4—43no—
980C2×C4—412no—
981C2×C4—412no—
982C2×C4—46no—
983C2×C4—46no—
984C2×C4—42no—
985C2×C4—46no—
986C2×C4—46no—
987C2×C4—412no—
988C2×C4—412no—
989C2×C4—86no—
990C2×C4—86no—
991C2×C4C23×D411yescharacteristic
992C2×C4C23×D413yes—
993C2×C4C23×D413yes—
994C2×C4C23×D413yes—
995C2×C4C23×D413yes—
996C2×C4C23×D413yes—
997C2×C4C23×D411yescharacteristic
998C2×C4C23×D413yes—
999C2×C4C23×D413yes—
1000C2×C4C23×D411yescharacteristic
1001C2×C4C23×D413yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4C2611yescharacteristic
1004C8—24no—
1005C8—212no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—24no—
1012C22—21no—
1013C22—21no—
1014C22—44no—
1015C22—48no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—84no—
1022C22#348612yes—
1023C22#358612yes—
1024C22C24×D411yescharacteristic
1025C4—21no—
1026C4—24no—
1027C4—21no—
1028C4—23no—
1029C4—23no—
1030C4—23no—
1031C4—23no—
1032C4—23no—
1033C4—23no—
1034C4—23no—
1035C4—46no—
1036C4—46no—
1037C4—46no—
1038C4—46no—
1039C4—42no—
1040C4#348612yes—
1041C4C2×#57516yes—
1042C4C22×2−1+412yes—
1043C2—22no—
1044C2—22no—
1045C2—41no—
1046C2—44no—
1047C2—82no—
1048C2C2×#348611yescharacteristic
1049C2C22×#57511yescharacteristic
1050C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#3006C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. C2×Q8×#41C2semidirect
3. #61842C2semidirect
4. #61841C2semidirect
5. #61838C2semidirect
6. #61837C2semidirect
7. #61834C2semidirect
8. #61824C2semidirect
9. #61369C2semidirect
10. Q8×AGL(1,ℤ/8)C2semidirect
11. #61323C2semidirect
12. #61322C2semidirect
13. #60866C2semidirect
14. #60865C2semidirect
16. #60562C2semidirect
17. #60248C2semidirect
24. #3523C22semidirect
25. #3523C22semidirect
32. Q8×#41C22semidirect
33. Q8×#41C22semidirect
34. C2×Q82C22semidirect
35. C2×#557C22semidirect
36. C2×#557C22semidirect
37. C2×#557C22semidirect
38. C2×#556C22semidirect
40. C2×#554C22semidirect
44. C2×D4×Q8C22semidirect
45. C2×D4×Q8C22semidirect
55. #3390C22semidirect
56. #3388C22semidirect
57. #3387C22semidirect
58. #3386C22semidirect
59. #3386C22semidirect
60. #3384C22semidirect
61. #3383C22semidirect
62. #3381C22semidirect
63. Q8×SD16C22semidirect
64. Q8×D8C22semidirect
65. #3377C22semidirect
66. #3376C22semidirect
67. #3374C22semidirect
68. #3372C22semidirect
69. #3369C22semidirect
70. #3367C22semidirect
71. #3364C22semidirect
72. #3363C22semidirect
73. #3360C22semidirect
74. #3359C22semidirect
75. #3240C22semidirect
78. #3237C22semidirect
79. #3236C22semidirect
80. #3233C22semidirect
82. #3231C22semidirect
83. #3230C22semidirect
84. #3229C22semidirect
85. #3166C22semidirect
86. #3165C22semidirect
87. #3140C22semidirect
88. #3139C22semidirect
90. #3116C22semidirect
92. #3113C22semidirect
94. #3110C22semidirect
96. #3107C22semidirect
98. #3104C22semidirect
100. #3101C22semidirect
106. #3078C22semidirect
107. #3078C22semidirect
108. #3077C22semidirect
113. #2984C22semidirect
114. #2984C22semidirect
115. #2983C22semidirect
116. #2982C22semidirect
117. Q8×M16C22semidirect
118. Q8×M16C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×Q8×#412
#618422
#618412
#618382
#618372
#618342
#618242
#613692
Q8×AGL(1,ℤ/8)2
#613232
#613222
#608662
#608652
#605632
#605622
#602482