Finite Group Databasebeta

← #10574207

Subgroups — #10574207

Order 512.

10412 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3573C211yesmaximal, characteristic, complemented
2C22×#568C211yesmaximal, characteristic, complemented
3#62811C211yesmaximal, characteristic
4#60147C218yesmaximal, complemented
5#60146C218yesmaximal, complemented
6#60146C218yesmaximal, complemented
7D4×#131C218yesmaximal, complemented
8#60143C216yesmaximal, complemented
9#60142C216yesmaximal, complemented
10#60141C216yesmaximal, complemented
11C2×#2933C216yesmaximal, complemented
12#60100C211yesmaximal, characteristic, complemented
13#60065C211yesmaximal, characteristic, complemented
14C2×#2880C211yesmaximal, characteristic, complemented
15#60058C211yesmaximal, characteristic, complemented
16C2×#585C2211yescharacteristic
17C23×#41C2211yescharacteristic
18#3573—216no—
19C2×#568—216no—
20C2×#568C2211yescharacteristic
21C2×#568C2211yescharacteristic
22C2×#568C2216yescomplemented
23C2×#568C2218yescomplemented
24C2×#568C2216yescomplemented
25C2×#568C2218yescomplemented
26C22×#131C2211yescharacteristic
27C22×#131C2211yescharacteristic
28C22×#131C2218yescomplemented
29C22×#131C2216yescomplemented
30C22×#131C2218yescomplemented
31C23×M16C2216yescomplemented
32#3489C414yes—
33#3489C414yes—
34#3488C414yes—
35#3488C414yes—
36#3487C412yes—
37#3486C412yes—
38#3485C416yes—
39#3484C416yes—
40D4×#41C2218yes—
41D4×#41C2218yes—
42#3449C2216yes—
43C2×#525C2216yes—
44#3428C2211yescharacteristic
45#2935C22124yescomplemented
46#2935C22124yescomplemented
47D4×M16C22124yescomplemented
48D4×M16C22124yescomplemented
49#2933C2214yescomplemented
50#2933C22112yescomplemented
51#2933C22112yescomplemented
52#2933C22112yescomplemented
53#2933C22124yescomplemented
54#2933C22112yescomplemented
55#2933C22112yescomplemented
56#2933C22112yescomplemented
57#2933C22112yescomplemented
58#2933C22124yescomplemented
59#2933C22124yescomplemented
60#2932C22124yescomplemented
61#2931C22124yescomplemented
62#2930C22124yescomplemented
63#2930C22124yescomplemented
64#2929C22124yescomplemented
65#2929C22124yescomplemented
66C2×#436C22112yescomplemented
67C2×#435C22112yescomplemented
68C2×#435C22112yescomplemented
69C2×C8×D4C22112yescomplemented
70#2906C2218yescomplemented
71#2906C2218yescomplemented
72#2905C2216yescomplemented
73C2×#424C2216yescomplemented
74#2880C2214yescomplemented
75#2880C2214yescomplemented
76#2880C2214yescomplemented
77#2880C2214yescomplemented
78#2880C2218yescomplemented
79#2880C2218yescomplemented
80#2879C2216yescomplemented
81C2×#408C2213yescomplemented
82C2×#408C2213yescomplemented
83C2×#408C2216yescomplemented
84C2×#407C2213yescomplemented
85C22×C22⋊C8C2213yescomplemented
86#2875C2218yescomplemented
87C4×#131C2218yescomplemented
88#2873C2216yescomplemented
89C2×#405C2216yescomplemented
90#585—28no—
91#585—28no—
92C2×2−1+4C2×C412yes—
93C2×2−1+4C2×C414yes—
94C2×H(5,𝔽2)C2×C416yes—
95C2×H(5,𝔽2)C2×C414yes—
96C22×#41—28no—
97C22×#41—28no—
98C22×#41C2×C413yes—
99C22×#41C2×C411yescharacteristic
100C22×#41C2×C414yes—
101C22×#41C2×C414yes—
102C22×#41C2313yes—
103C22×#41C2314yes—
104C22×#41C2314yes—
105C22×#41C2316yes—
106C22×#41C2318yes—
107C22×#41C2311yescharacteristic
108C23×Q8C2×C411yescharacteristic
109C23×D4C2×C413yes—
110C24×C4C2313yes—
111#568—28no—
112#568—264no—
113#568—264no—
114#568—248no—
115#568—248no—
116#568D4116yescomplemented
117C2×#131—28no—
118C2×#131—28no—
119C2×#131—264no—
120C2×#131—264no—
121C2×#131—248no—
122C2×#131C2314yes—
123C2×#131C2314yes—
124C2×#131C2314yes—
125C2×#131C2314yes—
126C2×#131C2318yes—
127C2×#131C23124yes—
128C2×#131C2314yes—
129C2×#131C23112yes—
130C2×#131C23124yes—
131C2×#131C2318yes—
132C2×#131C23124yescomplemented
133C2×#131C23112yescomplemented
134C2×#131C23112yescomplemented
135C22×M16—248no—
136C22×M16C2313yes—
137C22×M16C2313yes—
138C22×M16C2316yes—
139C22×M16C23112yes—
140C22×M16C2314yes—
141C22×M16C23112yes—
142C22×M16C23112yes—
143C22×M16C23112yes—
144C22×M16C2316yes—
145C22×M16C23112yescomplemented
146C22×M16C23124yescomplemented
147C23×C8C2313yes—
148C23×C8C2313yes—
149C23×C8C23112yes—
150C23×C8C23112yescomplemented
151#550C2×C418yes—
152#550C2×C418yes—
153D4×Q8C2×C418yes—
154D4×Q8C2×C418yes—
155#548C2×C418yes—
156#548C2×C418yes—
157#548C2×C418yes—
158#548C2×C418yes—
159#547C2×C4124yes—
160#547C2×C4124yes—
161#546C2×C4124yes—
162#546C2×C4124yes—
163#546C2×C4124yes—
164#546C2×C4124yes—
165D42C2×C4124yes—
166D42C2×C4124yes—
167#537C2×C4112yes—
168#537C2×C4112yes—
169#536C2×C4112yes—
170#536C2×C4112yes—
171#535C2×C4112yes—
172#535C2×C4112yes—
173#534C2×C4124yes—
174#532C23124yes—
175#525C2×C4112yes—
176#525C2×C4112yes—
177#525C2×C4112yes—
178#525C2×C4112yes—
179#525C2314yes—
180#525C23112yes—
181#525C23112yes—
182#525C23112yes—
183#525C23124yes—
184C2×#123C2×C4112yes—
185C2×C22⋊Q8C2×C416yes—
186C2×C22⋊Q8C2×C416yes—
187C2×#121C2×C416yes—
188C2×#121C2×C416yes—
189C2×#120C2×C4112yes—
190#520C2×C414yes—
191#520C2×C414yes—
192#519C2×C412yes—
193#518C2×C416yes—
194C4×#41C2318yes—
195C2×C4×D4C23112yes—
196C2×C4×D4C23112yes—
197C2×#117C2316yes—
198#436C2318yes—
199#436C23124yes—
200#436C23124yescomplemented
201#436C23124yescomplemented
202#436C23148yescomplemented
203#435C2318yes—
204#435C2318yes—
205#435C23124yes—
206#435C23124yes—
207#435C23124yescomplemented
208#435C23124yescomplemented
209#435C23124yescomplemented
210#435C23124yescomplemented
211#435C23148yescomplemented
212#435C23148yescomplemented
213C8×D4C2318yes—
214C8×D4C23124yes—
215C8×D4C23124yescomplemented
216C8×D4C23124yescomplemented
217C8×D4C23148yescomplemented
218#424C2314yes—
219#424C23112yes—
220#424C23112yescomplemented
221#424C23112yescomplemented
222#424C23124yescomplemented
223#423C23124yescomplemented
224C2×C4⋊C8C23112yescomplemented
225C2×C4⋊C8C23112yescomplemented
226#408C2314yes—
227#408C23112yes—
228#408C23112yes—
229#408C23112yes—
230#408C23112yes—
231#408C23112yes—
232#408C23112yescomplemented
233#408C23112yescomplemented
234#408C23124yescomplemented
235#407C23112yes—
236#407C23112yes—
237#407C23124yescomplemented
238C2×C22⋊C8C2311yescharacteristic
239C2×C22⋊C8C2313yes—
240C2×C22⋊C8C2313yes—
241C2×C22⋊C8C2313yes—
242C2×C22⋊C8C2316yes—
243C2×C22⋊C8C2316yes—
244C2×C22⋊C8C2316yes—
245C2×C22⋊C8C2316yes—
246C2×C22⋊C8C2316yes—
247C2×C22⋊C8C23112yescomplemented
248C2×C22⋊C8C23112yescomplemented
249#405C2314yes—
250#405C23112yes—
251#405C23112yescomplemented
252#405C23112yescomplemented
253#405C23124yescomplemented
254C4×M16C23124yescomplemented
255C2×#97C23112yescomplemented
256C2×C4×C8C23112yescomplemented
257C25C22×C413yes—
2582−1+4—232no—
2592−1+4—216no—
260H(5,𝔽2)—232no—
261H(5,𝔽2)—248no—
262C2×#41—232no—
263C2×#41—232no—
264C2×#41—216no—
265C2×#41—232no—
266C2×#41—216no—
267C2×#41—216no—
268C2×#41—216no—
269C2×#41—232no—
270C2×#41—28no—
271C2×#41—224no—
272C2×#41—224no—
273C2×#41—212no—
274C2×#41—212no—
275C2×#41—224no—
276C2×#41C22×C4112yes—
277C2×#41C22×C4112yes—
278C2×#41C22×C4112yes—
279C2×#41C22×C4112yes—
280C2×#41C22×C4112yes—
281C2×#41C22×C4124yes—
282C2×#41C22×C414yes—
283C2×#41C22×C414yes—
284C2×#41C22×C418yes—
285C2×#41C22×C414yes—
286C2×#41C2×D418yes—
287C2×#41#4118yes—
288C2×#41C2414yes—
289C2×#41C24112yes—
290C2×#41C24112yes—
291C2×#41C2414yes—
292C22×Q8—28no—
293C22×Q8C22×C416yes—
294C22×Q8C22×C413yes—
295C22×Q8C22×C414yes—
296C22×Q8C22×C414yes—
297C22×Q8C22×C418yes—
298C22×Q8C22×C411yescharacteristic
299C22×D4—224no—
300C22×D4C22×C4112yes—
301C22×D4C22×C416yes—
302C22×D4C22×C416yes—
303C22×D4C22×C413yes—
304C22×D4C22×C4112yes—
305C22×D4C22×C4112yes—
306C22×D4C22×C4124yes—
307C22×D4C22×C4112yes—
308C22×D4C22×C4112yes—
309C22×D4C22×C413yes—
310C23×C4—212no—
311C23×C4—212no—
312C23×C4C22×C416yes—
313C23×C4C22×C416yes—
314C23×C4C22×C413yes—
315C23×C4C22×C413yes—
316C23×C4C22×C413yes—
317C23×C4C2416yes—
318C23×C4C24112yes—
319C23×C4C2416yes—
320C23×C4C2411yescharacteristic
321C23×C4C2413yes—
322C23×C4C2413yes—
323#131—216no—
324#131—216no—
325#131—232no—
326#131—216no—
327#131—216no—
328#131—216no—
329#131—248no—
330#131—248no—
331#131—296no—
332#131—248no—
333#131—296no—
334#131—296no—
335#131C2×D4164yescomplemented
336C2×M16—224no—
337C2×M16—212no—
338C2×M16—212no—
339C2×M16—216no—
340C2×M16—248no—
341C2×M16—248no—
342C2×M16—248no—
343C2×M16—296no—
344C2×M16—248no—
345C2×M16—248no—
346C2×M16C2×D4148yescomplemented
347C2×M16C2414yes—
348C2×M16C2418yes—
349C2×M16C24112yes—
350C2×M16C24124yes—
351C2×M16C24112yes—
352C2×M16C24112yes—
353C2×M16C2418yes—
354C2×M16C24124yes—
355C2×M16C2414yes—
356C2×M16C24112yes—
357C22×C8—212no—
358C22×C8—212no—
359C22×C8—248no—
360C22×C8—248no—
361C22×C8C2418yes—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2416yes—
365C22×C8C2413yes—
366C22×C8C24112yes—
367C22×C8C24124yes—
368C22×C8C2413yes—
369C22×C8C2416yes—
370C22×C8C2416yes—
371C22×C8C2416yes—
372C22×C8C2418yes—
373C22×C8C24124yes—
374C22×C8C24112yes—
375C4⋊Q8C22×C4124yes—
376#127C22×C4124yes—
377#124C22×C4124yes—
378#124C22×C4124yes—
379#123C22×C418yes—
380#123C22×C4124yes—
381#123C22×C4124yes—
382#123C22×C4124yes—
383#123C22×C4148yes—
384C22⋊Q8C22×C414yes—
385C22⋊Q8C22×C414yes—
386C22⋊Q8C22×C4112yes—
387C22⋊Q8C22×C4112yes—
388C22⋊Q8C22×C4112yes—
389C22⋊Q8C22×C4112yes—
390C22⋊Q8C22×C4112yes—
391C22⋊Q8C22×C4112yes—
392C22⋊Q8C22×C4124yes—
393C22⋊Q8C22×C4124yes—
394#121C22×C414yes—
395#121C22×C414yes—
396#121C22×C4112yes—
397#121C22×C4112yes—
398#121C22×C4112yes—
399#121C22×C4112yes—
400#121C22×C4112yes—
401#121C22×C4112yes—
402#121C22×C4124yes—
403#121C22×C4124yes—
404#121C22×C4148yes—
405#121C22×C4148yes—
406#120C22×C418yes—
407#120C22×C4124yes—
408#120C22×C4124yes—
409#120C22×C4124yes—
410#120C22×C4148yes—
411C4×Q8C22×C418yes—
412C4×Q8C22×C418yes—
413C4×D4C22×C4124yes—
414C4×D4C22×C4124yes—
415C4×D4C22×C4124yes—
416C4×D4C22×C4124yes—
417C4×D4C22×C4124yes—
418C4×D4C22×C4124yes—
419C4×D4C2418yes—
420C4×D4C2418yes—
421C4×D4C24124yes—
422C4×D4C24124yes—
423#117C22×C4112yes—
424#117C22×C4112yes—
425#117C2414yes—
426#117C24112yes—
427C2×C4⋊C4C22×C416yes—
428C2×C4⋊C4C22×C416yes—
429C2×C4⋊C4C22×C4112yes—
430C2×C4⋊C4C22×C4112yes—
431C2×C22⋊C4C22×C4112yes—
432C2×C22⋊C4C22×C4112yes—
433C2×C22⋊C4C22×C4112yes—
434C2×C22⋊C4C22×C4112yes—
435C2×C22⋊C4C22×C4112yes—
436C2×C42C24112yes—
437C4⋊C8C2418yes—
438C4⋊C8C2418yes—
439C4⋊C8C24124yes—
440C4⋊C8C24124yes—
441C22⋊C8C2411yescharacteristic
442C22⋊C8C2411yescharacteristic
443C22⋊C8C2411yescharacteristic
444C22⋊C8C2411yescharacteristic
445C22⋊C8C2416yes—
446C22⋊C8C2416yes—
447C22⋊C8C2416yes—
448C22⋊C8C2416yes—
449C22⋊C8C2416yes—
450C22⋊C8C2416yes—
451C22⋊C8C24124yes—
452C22⋊C8C2418yes—
453C22⋊C8C2418yes—
454C22⋊C8C24124yes—
455C22⋊C8C24124yes—
456#97C2418yes—
457#97C24124yes—
458C4×C8C2418yes—
459C4×C8C24124yes—
460C24—212no—
461C24—46no—
462C24—83no—
463C24C23×C416yes—
464C24C23×C411yescharacteristic
465C24C23×C416yes—
466C24C23×C4112yes—
467C24C23×C413yes—
468C24C23×C413yes—
469#41—216no—
470#41—216no—
471#41—232no—
472#41—248no—
473#41—248no—
474#41—296no—
475#41—248no—
476#41—248no—
477#41—248no—
478#41—224no—
479#41—224no—
480#41—28no—
481#41—28no—
482#41—224no—
483#41—224no—
484#41C4×D4132yes—
485#41C22×D4116yes—
486#41C2×#41116yes—
487C2×Q8—216no—
488C2×Q8—216no—
489C2×Q8—232no—
490C2×Q8—212no—
491C2×Q8—224no—
492C2×Q8C4×D418yes—
493C2×Q8C23×C414yes—
494C2×Q8C23×C4112yes—
495C2×Q8C23×C4112yes—
496C2×Q8C23×C414yes—
497C2×D4—224no—
498C2×D4—248no—
499C2×D4—248no—
500C2×D4—248no—
501C2×D4—296no—
502C2×D4—212no—
503C2×D4—224no—
504C2×D4—424no—
505C2×D4—812no—
506C2×D4C4×D4124yes—
507C2×D4C23×C418yes—
508C2×D4C23×C418yes—
509C2×D4C23×C4124yes—
510C2×D4C23×C4124yes—
511C2×D4C23×C414yes—
512C2×D4C23×C4112yes—
513C2×D4C23×C4112yes—
514C2×D4C23×C418yes—
515C2×D4C23×C4124yes—
516C2×D4C23×C4124yes—
517C2×D4C23×C4112yes—
518C22×C4—212no—
519C22×C4—212no—
520C22×C4—212no—
521C22×C4—224no—
522C22×C4—224no—
523C22×C4—212no—
524C22×C4—224no—
525C22×C4—22no—
526C22×C4—26no—
527C22×C4—212no—
528C22×C4—22no—
529C22×C4—26no—
530C22×C4—212no—
531C22×C4—212no—
532C22×C4—224no—
533C22×C4C23×C416yes—
534C22×C4C23×C416yes—
535C22×C4C23×C4112yes—
536C22×C4C23×C416yes—
537C22×C4C23×C416yes—
538C22×C4C23×C416yes—
539C22×C4C23×C416yes—
540C22×C4C23×C4124yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C416yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C413yes—
546C22×C4C23×C4112yes—
547C22×C4C23×C4112yes—
548C22×C4C23×C416yes—
549C22×C4C23×C413yes—
550C22×C4C22×D4112yes—
551C22×C4C2×#41112yes—
552C22×C4C2511yescharacteristic
553C22×C4C2516yes—
554C22×C4C2518yes—
555C22×C4C2511yescharacteristic
556C22×C4C2516yes—
557C22×C4C2511yescharacteristic
558M16—28no—
559M16—224no—
560M16—224no—
561M16—224no—
562M16—216no—
563M16—248no—
564M16—248no—
565M16—216no—
566M16C22×D4116yes—
567M16C22×D4148yes—
568C2×C8—212no—
569C2×C8—22no—
570C2×C8—212no—
571C2×C8—224no—
572C2×C8—26no—
573C2×C8—22no—
574C2×C8—26no—
575C2×C8—212no—
576C2×C8—212no—
577C2×C8—216no—
578C2×C8—216no—
579C2×C8—248no—
580C2×C8—248no—
581C2×C8C22×D4148yes—
582C2×C8C2511yescharacteristic
583C2×C8C2516yes—
584C2×C8C2511yescharacteristic
585C2×C8C2511yescharacteristic
586C2×C8C2511yescharacteristic
587C2×C8C2516yes—
588C2×C8C2518yes—
589C2×C8C2518yes—
590C4⋊C4C23×C414yes—
591C4⋊C4C23×C414yes—
592C4⋊C4C23×C418yes—
593C4⋊C4C23×C418yes—
594C4⋊C4C23×C4112yes—
595C4⋊C4C23×C4112yes—
596C4⋊C4C23×C4124yes—
597C4⋊C4C23×C4124yes—
598C22⋊C4C23×C418yes—
599C22⋊C4C23×C418yes—
600C22⋊C4C23×C418yes—
601C22⋊C4C23×C418yes—
602C22⋊C4C23×C418yes—
603C22⋊C4C23×C4124yes—
604C22⋊C4C23×C4124yes—
605C22⋊C4C23×C4124yes—
606C22⋊C4C23×C4124yes—
607C22⋊C4C23×C4124yes—
608C42C23×C4124yes—
609C42C2518yes—
610C23—22no—
611C23—212no—
612C23—212no—
613C23—22no—
614C23—212no—
615C23—26no—
616C23—224no—
617C23—43no—
618C23—41no—
619C23—43no—
620C23—46no—
621C23—412no—
622C23—46no—
623C23—412no—
624C23—46no—
625C23—43no—
626C23—43no—
627C23—824no—
628C23C2×C4×D4112yes—
629C23C24×C411yescharacteristic
630C23C24×C418yes—
631C23C24×C416yes—
632C23C24×C411yescharacteristic
633C23C24×C416yes—
634C23C24×C411yescharacteristic
635Q8—28no—
636Q8—224no—
637Q8—224no—
638Q8C2×C4×D4116yes—
639D4—216no—
640D4—248no—
641D4—248no—
642D4—216no—
643D4—28no—
644D4—224no—
645D4—224no—
646D4—424no—
647D4—48no—
648D4—424no—
649D4C2×C4×D4148yes—
650C2×C4—22no—
651C2×C4—26no—
652C2×C4—212no—
653C2×C4—212no—
654C2×C4—224no—
655C2×C4—21no—
656C2×C4—28no—
657C2×C4—26no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—26no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—212no—
666C2×C4—212no—
667C2×C4—212no—
668C2×C4—212no—
669C2×C4—212no—
670C2×C4—248no—
671C2×C4—412no—
672C2×C4—412no—
673C2×C4C2×C4×D4112yes—
674C2×C4C2×C4×D4124yes—
675C2×C4C24×C418yes—
676C2×C4C24×C418yes—
677C2×C4C24×C411yescharacteristic
678C2×C4C24×C411yescharacteristic
679C2×C4C24×C418yes—
680C2×C4C24×C416yes—
681C2×C4C24×C416yes—
682C2×C4C24×C411yescharacteristic
683C2×C4C23×D4112yes—
684C2×C4C23×D412yes—
685C2×C4C22×#4112yes—
686C2×C4C22×#41112yes—
687C2×C4C2611yescharacteristic
688C8—21no—
689C8—21no—
690C8—26no—
691C8—28no—
692C8—21no—
693C8—21no—
694C8—26no—
695C8C23×D4116yes—
696C22—26no—
697C22—21no—
698C22—26no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—28no—
703C22—26no—
704C22—21no—
705C22—21no—
706C22—26no—
707C22—28no—
708C22—21no—
709C22—26no—
710C22—28no—
711C22—412no—
712C22—424no—
713C22—44no—
714C22—824no—
715C22—86no—
716C22—812no—
717C22C22×C4×D412yes—
718C22C22×C4×D4112yes—
719C22#357312yescomplemented
720C22C25×C411yescharacteristic
721C4—28no—
722C4—28no—
723C4—21no—
724C4—21no—
725C4—26no—
726C4—28no—
727C4C22×C4×D412yes—
728C4C22×C4×D4112yes—
729C4C24×D411yescharacteristic
730C4C23×#4111yescharacteristic
731C2—22no—
732C2—22no—
733C2—212no—
734C2—46no—
735C2—41no—
736C2—48no—
737C2C23×C4×D411yescharacteristic
738C2C2×#357311yescharacteristic
739C2#6307611yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62811C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3573C2semidirect
2. C22×#568C2semidirect
4. #60147C2semidirect
5. #60146C2semidirect
6. #60146C2semidirect
7. D4×#131C2semidirect
8. #60143C2semidirect
9. #60142C2semidirect
10. #60141C2semidirect
11. C2×#2933C2semidirect
12. #60100C2semidirect
13. #60065C2semidirect
14. C2×#2880C2semidirect
15. #60058C2semidirect
22. C2×#568C22semidirect
23. C2×#568C22semidirect
24. C2×#568C22semidirect
25. C2×#568C22semidirect
28. C22×#131C22semidirect
29. C22×#131C22semidirect
30. C22×#131C22semidirect
31. C23×M16C22semidirect
45. #2935C22semidirect
46. #2935C22semidirect
47. D4×M16C22semidirect
48. D4×M16C22semidirect
49. #2933C22semidirect
50. #2933C22semidirect
51. #2933C22semidirect
52. #2933C22semidirect
53. #2933C22semidirect
54. #2933C22semidirect
55. #2933C22semidirect
56. #2933C22semidirect
57. #2933C22semidirect
58. #2933C22semidirect
59. #2933C22semidirect
60. #2932C22semidirect
61. #2931C22semidirect
62. #2930C22semidirect
63. #2930C22semidirect
64. #2929C22semidirect
65. #2929C22semidirect
66. C2×#436C22semidirect
67. C2×#435C22semidirect
68. C2×#435C22semidirect
69. C2×C8×D4C22semidirect
70. #2906C22semidirect
71. #2906C22semidirect
72. #2905C22semidirect
73. C2×#424C22semidirect
74. #2880C22semidirect
75. #2880C22semidirect
76. #2880C22semidirect
77. #2880C22semidirect
78. #2880C22semidirect
79. #2880C22semidirect
80. #2879C22semidirect
81. C2×#408C22semidirect
82. C2×#408C22semidirect
83. C2×#408C22semidirect
84. C2×#407C22semidirect
85. C22×C22⋊C8C22semidirect
86. #2875C22semidirect
87. C4×#131C22semidirect
88. #2873C22semidirect
89. C2×#405C22semidirect
116. #568D4semidirect
132. C2×#131C23semidirect
133. C2×#131C23semidirect
134. C2×#131C23semidirect
145. C22×M16C23semidirect
146. C22×M16C23semidirect
150. C23×C8C23semidirect
200. #436C23semidirect
201. #436C23semidirect
202. #436C23semidirect
207. #435C23semidirect
208. #435C23semidirect
209. #435C23semidirect
210. #435C23semidirect
211. #435C23semidirect
212. #435C23semidirect
215. C8×D4C23semidirect
216. C8×D4C23semidirect
217. C8×D4C23semidirect
220. #424C23semidirect
221. #424C23semidirect
222. #424C23semidirect
223. #423C23semidirect
224. C2×C4⋊C8C23semidirect
225. C2×C4⋊C8C23semidirect
232. #408C23semidirect
233. #408C23semidirect
234. #408C23semidirect
237. #407C23semidirect
247. C2×C22⋊C8C23semidirect
248. C2×C22⋊C8C23semidirect
251. #405C23semidirect
252. #405C23semidirect
253. #405C23semidirect
254. C4×M16C23semidirect
255. C2×#97C23semidirect
256. C2×C4×C8C23semidirect
335. #131C2×D4semidirect
346. C2×M16C2×D4semidirect
719. C22#3573semidirect

Maximal subgroups

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

subgroupindex
C2×#35732
C22×#5682
#628112
#601472
#601462
D4×#1312
#601432
#601422
#601412
C2×#29332
#601002
#600652
C2×#28802
#600582