Finite Group Databasebeta

← #7654780

Subgroups — #7654780

Order 512.

8280 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42443C2112yesmaximal, complemented
4#39863C2112yesmaximal, complemented
5#39491C213yesmaximal, complemented
6#39488C213yesmaximal, complemented
7#38957C213yesmaximal, complemented
8#38953C213yesmaximal, complemented
9#37616C213yesmaximal, complemented
10Q8×#127C211yesmaximal, characteristic, complemented
11Q8×#124C211yesmaximal, characteristic, complemented
12#36465C211yesmaximal, characteristic, complemented
13#36457C211yesmaximal, characteristic, complemented
14#36428C214yesmaximal, complemented
15#35771C214yesmaximal, complemented
16#35298C213yesmaximal, complemented
17#35172C213yesmaximal, complemented
18#34965C213yesmaximal, complemented
19#34129C211yesmaximal, characteristic, complemented
20C23×#41C2212yes—
21#3518—216no—
22C2×Q82C2211yescharacteristic, complemented
23C2×#556C2213yescomplemented
24C2×#556C2216yescomplemented
25C2×#555C2213yescomplemented
26D4×#41—216no—
27C2×#550C2211yescharacteristic
28C2×D4×Q8C2211yescharacteristic
29C2×D4×Q8C2211yescharacteristic, complemented
30C2×D4×Q8C2214yescomplemented
31C2×#548C2212yes—
32C2×#548C2212yes—
33C2×#548C2214yescomplemented
34C2×#547C2213yes—
35C2×#546C2216yes—
36C2×D42C2213yes—
37C2×#542C2216yescomplemented
38C2×#533C2213yescomplemented
39C2×#532C2213yes—
40C2×#529C2213yescomplemented
41C2×#525C2216yes—
42C2×#519C2212yescomplemented
43C2×C4×#41C2211yescharacteristic
44C22×C4×D4C2213yes—
45#2868C2213yescomplemented
46#2862C2213yescomplemented
47#2858C2213yescomplemented
48#2858C2213yescomplemented
49#2848C22112yescomplemented
50#2813C22112yescomplemented
51#2718C22124yescomplemented
52#2710C22124yescomplemented
53#2685C22124yescomplemented
54#2670C22124yescomplemented
55#2636C22112yescomplemented
56#2626C22112yescomplemented
57#2620C2216yescomplemented
58#2620C22112yescomplemented
59#2620C22112yescomplemented
60#2619C2216yescomplemented
61#2603C22112yescomplemented
62#2580C22112yescomplemented
63#2568C2213yescomplemented
64#2566C2213yes—
65#2566C2216yescomplemented
66#2566C2213yescomplemented
67#2563C2213yes—
68#2563C2213yescomplemented
69#2548C2213yescomplemented
70#2545C22112yescomplemented
71#2544C2211yescharacteristic
72#2544C2213yescomplemented
73#2542C2213yes—
74#2542C2213yescomplemented
75#2542C2213yescomplemented
76#2542C22112yescomplemented
77#2541C2213yescomplemented
78#2540C22112yescomplemented
79#2538C22112yescomplemented
80#2504C2213yescomplemented
81#2502C2213yescomplemented
82#2500C2216yescomplemented
83#2500C2216yescomplemented
84#2492C22112yescomplemented
85#2491C22112yescomplemented
86#2435C2213yes—
87#2435C22112yescomplemented
88#2433C2213yes—
89#2432C22112yescomplemented
90#2432C22112yescomplemented
91#2429C22112yescomplemented
92#2426C22112yescomplemented
93#2415C22112yescomplemented
94#2414C22112yescomplemented
95#2411C22112yescomplemented
96#2408C22112yescomplemented
97#2407C22112yescomplemented
98#2407C22112yescomplemented
99#2392C22112yescomplemented
100#2354C2216yescomplemented
101Q8×C4⋊C4C2212yescomplemented
102#2346C2216yescomplemented
103#2341C2212yes—
104#2341C2214yescomplemented
105Q8×C22⋊C4C2214yescomplemented
106#2326C22112yescomplemented
107#2317C2216yescomplemented
108#2309C2216yes—
109C4×#127C2213yes—
110C4×#127C2213yescomplemented
111C4×#124C2213yes—
112C4×#124C2213yescomplemented
113C4×#120C22112yescomplemented
114#2293C2213yescomplemented
115#2293C2213yescomplemented
116#2285C2213yescomplemented
117C42×Q8C2211yescharacteristic, complemented
118C42×Q8C2211yescharacteristic, complemented
119C4×#117C2213yescomplemented
120C22×#41—216no—
121C22×#41—416no—
122C22×#41C2312yes—
123C22×#41C2311yescharacteristic
124C22×#41C2316yes—
125C22×#41C2316yes—
126C23×Q8C2312yes—
127C23×Q8C2312yes—
128C23×D4C2313yes—
129C23×D4C2316yes—
130C24×C4C2316yes—
131Q82—28no—
132#556—224no—
133#556—248no—
134#555—224no—
135#550—28no—
136D4×Q8—28no—
137D4×Q8—28no—
138D4×Q8—416no—
139#548—216no—
140#548—216no—
141#548—416no—
142#547—224no—
143#546—248no—
144D42—224no—
145#542—248no—
146#533—224no—
147#532—224no—
148C2×C4⋊Q8C2313yes—
149C2×C4⋊Q8C2313yes—
150C2×C4⋊Q8C2313yes—
151C2×C4⋊Q8C2316yes—
152C2×C4⋊Q8C23112yes—
153C2×#127C2311yescharacteristic
154C2×#127C2313yes—
155C2×#127C2313yes—
156#529—224no—
157C2×#126C2316yes—
158C2×#126C23112yes—
159C2×#125C2313yes—
160C2×#124C2316yes—
161C2×#124C23112yes—
162C2×#124C2311yescharacteristic
163C2×#124C2316yes—
164C2×#124C2311yescharacteristic
165C2×#124C23112yes—
166C2×#124C23112yes—
167C2×#124C2313yes—
168#525—248no—
169C2×#123C2316yes—
170C2×#123C23112yes—
171C2×C22⋊Q8C2316yes—
172C2×C22⋊Q8C2316yes—
173C2×C22⋊Q8C2313yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2316yes—
177C2×C22⋊Q8C23112yes—
178C2×C22⋊Q8C23112yes—
179C2×C22⋊Q8C23112yes—
180C2×#121C2313yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#121C2316yes—
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C23112yes—
187C2×#120C23112yes—
188C2×#120C23112yes—
189#519—216no—
190C4×#41D4116yescomplemented
191C2×C4×Q8C2313yes—
192C2×C4×Q8C2316yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2316yes—
197C2×C4×Q8C2316yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×D4—224no—
201C2×C4×D4C2313yes—
202C2×C4×D4C2313yes—
203C2×C4×D4C2313yes—
204C2×C4×D4C2311yescharacteristic
205C2×C4×D4C2313yes—
206C2×C4×D4C2316yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C23112yes—
211C2×C4×D4C23112yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2313yes—
214C2×#117C2316yes—
215C2×#117C2316yes—
216C2×#117C2316yes—
217C2×#117C2316yes—
218C2×#117C2316yes—
219C2×#117C2313yes—
220C22×C4⋊C4C2313yes—
221C22×C22⋊C4C2316yes—
222C22×C42C2313yes—
223#400C23112yes—
224#399C23112yes—
225#399C23112yes—
226#399C23112yes—
227#398C23112yes—
228#397C23112yes—
229#396C23112yes—
230#396C23124yes—
231#396C23112yes—
232#396C23124yes—
233#394C23112yes—
234#394C23124yes—
235#394C23112yes—
236#394C23124yes—
237#394C23124yes—
238#394C23124yes—
239#394C23112yes—
240#394C2314yes—
241#393C23112yes—
242#393C23112yes—
243#392C23112yes—
244#392C23124yes—
245#392C23112yes—
246#391C2313yes—
247#391C23112yes—
248#391C23112yes—
249#391C23112yes—
250#391C2311yescharacteristic
251#390C2313yes—
252#390C23112yes—
253#390C2313yes—
254#390C2311yescharacteristic
255#390C2313yes—
256#390C23112yes—
257#390C2313yes—
258#390C2316yes—
259#390C2316yes—
260#390C23124yes—
261#390C2313yes—
262#390C23112yes—
263#390C2316yes—
264#390C2316yes—
265#390C23112yes—
266#390C23112yes—
267#389C23124yes—
268#389C2316yes—
269#389C2316yes—
270#388C23124yes—
271#388C23124yes—
272#388C23112yes—
273#388C23112yes—
274#388C23112yes—
275#388C23112yes—
276#386C2314yes—
277#386C23112yes—
278#386C23112yes—
279#385C23112yes—
280#385C23124yes—
281#385C23112yes—
282#385C23124yes—
283#385C23112yes—
284#384C2313yes—
285#384C2313yes—
286#384C2316yes—
287#384C23112yes—
288#384C2316yes—
289#382C2316yes—
290#382C2313yes—
291#382C2313yes—
292#382C2316yes—
293#380C23112yes—
294#380C23112yes—
295#380C2316yes—
296#380C2316yes—
297#379C23124yes—
298#379C23112yes—
299C4×C4⋊C4C2313yes—
300C4×C4⋊C4C2313yes—
301C4×C4⋊C4C2313yes—
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2316yes—
304C4×C4⋊C4C2316yes—
305C4×C4⋊C4C2316yes—
306C4×C22⋊C4C23112yes—
307C4×C22⋊C4C2316yes—
308C4×C22⋊C4C23112yes—
309C4×C22⋊C4C2313yes—
310C4×C22⋊C4C2313yes—
311#376C2316yes—
312C43C2313yes—
313C43C2313yes—
314C25C2416yes—
315C2×#41—28no—
316C2×#41—28no—
317C2×#41—216no—
318C2×#41—224no—
319C2×#41—224no—
320C2×#41—424no—
321C2×#41—424no—
322C2×#41—4128no—
323C2×#41C2×D418yes—
324C22×Q8—28no—
325C22×Q8—28no—
326C22×Q8—216no—
327C22×Q8—216no—
328C22×Q8C2411yescharacteristic
329C22×Q8C2416yes—
330C22×Q8C2416yes—
331C22×Q8C2416yes—
332C22×Q8C2411yescharacteristic
333C22×D4—224no—
334C22×D4—212no—
335C22×D4—212no—
336C22×D4—46no—
337C22×D4—424no—
338C22×D4C2411yescharacteristic
339C22×D4C2413yes—
340C22×D4C2416yes—
341C22×D4C2414yes—
342C22×D4C2416yes—
343C22×D4C2413yes—
344C22×D4C2411yescharacteristic
345C22×D4C2416yes—
346C22×D4C2416yes—
347C22×D4C24112yes—
348C22×D4C24112yes—
349C23×C4—224no—
350C23×C4—424no—
351C23×C4C2416yes—
352C23×C4C2416yes—
353C23×C4C2416yes—
354C23×C4C2413yes—
355C23×C4C2413yes—
356C23×C4C2416yes—
357C23×C4C2412yes—
358C23×C4C2416yes—
359C23×C4C2413yes—
360C4⋊Q8—224no—
361C4⋊Q8—212no—
362C4⋊Q8—212no—
363C4⋊Q8—212no—
364C4⋊Q8—424no—
365#127—24no—
366#127—212no—
367#127—46no—
368#126—248no—
369#126—224no—
370#125—212no—
371#124—224no—
372#124—24no—
373#124—248no—
374#124—24no—
375#124—224no—
376#124—424no—
377#124—46no—
378#124—424no—
379#123—224no—
380#123—248no—
381C22⋊Q8—212no—
382C22⋊Q8—224no—
383C22⋊Q8—224no—
384C22⋊Q8—224no—
385C22⋊Q8—224no—
386C22⋊Q8—224no—
387C22⋊Q8—424no—
388C22⋊Q8—424no—
389C22⋊Q8—424no—
390#121—224no—
391#121—212no—
392#121—224no—
393#121—224no—
394#121—224no—
395#121—224no—
396#121—424no—
397#120—248no—
398#120—424no—
399C4×Q8—28no—
400C4×Q8—28no—
401C4×Q8—28no—
402C4×Q8—224no—
403C4×Q8—224no—
404C4×Q8—212no—
405C4×Q8—224no—
406C4×Q8C2×D418yes—
407C4×Q8C2×D418yes—
408C4×D4—224no—
409C4×D4—24no—
410C4×D4—224no—
411C4×D4—212no—
412C4×D4—212no—
413C4×D4—224no—
414C4×D4—212no—
415C4×D4—224no—
416C4×D4—212no—
417C4×D4—424no—
418C4×D4—424no—
419C4×D4C2×D4124yes—
420C4×D4C2×D4124yes—
421#117—224no—
422#117—224no—
423#117—224no—
424#117—412no—
425#117—412no—
426#117C2×D4124yes—
427C2×C4⋊C4—212no—
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2413yes—
430C2×C4⋊C4C2416yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2413yes—
433C2×C4⋊C4C2413yes—
434C2×C4⋊C4C2416yes—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C24112yes—
445C2×C4⋊C4C24112yes—
446C2×C4⋊C4C24112yes—
447C2×C4⋊C4C24124yes—
448C2×C4⋊C4C2413yes—
449C2×C4⋊C4C2413yes—
450C2×C22⋊C4—224no—
451C2×C22⋊C4C2412yes—
452C2×C22⋊C4C2416yes—
453C2×C22⋊C4C2416yes—
454C2×C22⋊C4C2416yes—
455C2×C22⋊C4C2416yes—
456C2×C22⋊C4C2412yes—
457C2×C22⋊C4C2416yes—
458C2×C22⋊C4C24112yes—
459C2×C22⋊C4C2412yes—
460C2×C22⋊C4C24112yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C24112yes—
467C2×C22⋊C4C2414yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C24112yes—
472C2×C22⋊C4C24124yes—
473C2×C22⋊C4C24112yes—
474C2×C22⋊C4C24124yes—
475C2×C22⋊C4C2416yes—
476C2×C42C2×D4124yes—
477C2×C42C24112yes—
478C2×C42C2413yes—
479C2×C42C2413yes—
480C2×C42C2416yes—
481C2×C42C2416yes—
482C2×C42C2416yes—
483C2×C42C2416yes—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2416yes—
487C2×C42C2413yes—
488C2×C42C2413yes—
489C2×C42C2413yes—
490C2×C42C2411yescharacteristic
491#95C2412yes—
492#95C2416yes—
493#95C2416yes—
494#95C2416yes—
495#95C2414yes—
496#95C24112yes—
497#95C24112yes—
498#95C24112yes—
499#95C2416yes—
500#95C2416yes—
501#95C24124yes—
502C24—212no—
503C24—212no—
504C24—412no—
505C24—46no—
506C24—412no—
507C24C2516yes—
508C24C2512yes—
509C24C2513yes—
510C24C2512yes—
511#41—232no—
512#41—496no—
513#41—496no—
514#41—432no—
515C2×Q8—22no—
516C2×Q8—212no—
517C2×Q8—212no—
518C2×Q8—212no—
519C2×Q8—224no—
520C2×Q8—224no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—412no—
524C2×Q8—432no—
525C2×Q8—432no—
526C2×Q8C22×D414yes—
527C2×Q8H(5,𝔽2)18yes—
528C2×D4—224no—
529C2×D4—28no—
530C2×D4—212no—
531C2×D4—212no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—212no—
535C2×D4—26no—
536C2×D4—212no—
537C2×D4—212no—
538C2×D4—212no—
539C2×D4—224no—
540C2×D4—22no—
541C2×D4—26no—
542C2×D4—22no—
543C2×D4—28no—
544C2×D4—26no—
545C2×D4—22no—
546C2×D4—448no—
547C2×D4—44no—
548C2×D4—46no—
549C2×D4—424no—
550C2×D4—412no—
551C2×D4—412no—
552C2×D4—412no—
553C2×D4—412no—
554C2×D4—412no—
555C2×D4—496no—
556C2×D4C22×D4112yes—
557C2×D42−1+414yes—
558C22×C4—212no—
559C22×C4—26no—
560C22×C4—26no—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—24no—
564C22×C4—212no—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—224no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4—46no—
571C22×C4—44no—
572C22×C4—412no—
573C22×C4—412no—
574C22×C4—496no—
575C22×C4C22×D4112yes—
576C22×C4C22×D4112yes—
577C22×C4C22×D4112yes—
578C22×C4C2512yes—
579C22×C4C2516yes—
580C22×C4C2512yes—
581C22×C4C2516yes—
582C22×C4C2512yes—
583C22×C4C2516yes—
584C22×C4C2516yes—
585C22×C4C2516yes—
586C22×C4C2511yescharacteristic
587C22×C4C2513yes—
588C22×C4C2513yes—
589C22×C4C2511yescharacteristic
590C22×C4C2512yes—
591C22×C4C2513yes—
592C22×C4C2511yescharacteristic
593C4⋊C4—22no—
594C4⋊C4—26no—
595C4⋊C4—212no—
596C4⋊C4—26no—
597C4⋊C4—26no—
598C4⋊C4—212no—
599C4⋊C4—212no—
600C4⋊C4—212no—
601C4⋊C4—212no—
602C4⋊C4—212no—
603C4⋊C4—212no—
604C4⋊C4—212no—
605C4⋊C4—212no—
606C4⋊C4—212no—
607C4⋊C4—24no—
608C4⋊C4—46no—
609C4⋊C4—412no—
610C4⋊C4—412no—
611C4⋊C4—412no—
612C4⋊C4—424no—
613C4⋊C4C22×D4112yes—
614C4⋊C4C22×D4112yes—
615C22⋊C4—224no—
616C22⋊C4—212no—
617C22⋊C4—28no—
618C22⋊C4—24no—
619C22⋊C4—212no—
620C22⋊C4—212no—
621C22⋊C4—212no—
622C22⋊C4—212no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—224no—
626C22⋊C4—212no—
627C22⋊C4—212no—
628C22⋊C4—224no—
629C22⋊C4—46no—
630C22⋊C4—412no—
631C22⋊C4—44no—
632C22⋊C4—412no—
633C22⋊C4—412no—
634C22⋊C4—412no—
635C22⋊C4—412no—
636C22⋊C4—424no—
637C22⋊C4—424no—
638C22⋊C4—412no—
639C22⋊C4C22×D4124yes—
640C42—224no—
641C42—212no—
642C42—212no—
643C42—212no—
644C42—22no—
645C42—22no—
646C42—26no—
647C42—26no—
648C42—212no—
649C42—46no—
650C42C22×D414yes—
651C42C22×D4112yes—
652C42C22×D4112yes—
653C42C22×D4112yes—
654C23—22no—
655C23—24no—
656C23—26no—
657C23—23no—
658C23—26no—
659C23—23no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—26no—
664C23—24no—
665C23—212no—
666C23—22no—
667C23—26no—
668C23—212no—
669C23—26no—
670C23—24no—
671C23—22no—
672C23—424no—
673C23—424no—
674C23—824no—
675C23—812no—
676C23—824no—
677C23C23×D416yes—
678C23C2×2−1+414yes—
679C23C2611yescharacteristic
680Q8—424no—
681Q8—424no—
682Q8—44no—
683Q8—812no—
684Q8#535116yes—
685D4—224no—
686D4—28no—
687D4—416no—
688D4—424no—
689D4—448no—
690D4—424no—
691D4—44no—
692D4—412no—
693D4—812no—
694D4—812no—
695D4—824no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—23no—
700C2×C4—26no—
701C2×C4—22no—
702C2×C4—23no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—22no—
706C2×C4—26no—
707C2×C4—26no—
708C2×C4—22no—
709C2×C4—26no—
710C2×C4—22no—
711C2×C4—26no—
712C2×C4—26no—
713C2×C4—212no—
714C2×C4—24no—
715C2×C4—212no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—26no—
719C2×C4—26no—
720C2×C4—26no—
721C2×C4—22no—
722C2×C4—26no—
723C2×C4—212no—
724C2×C4—22no—
725C2×C4—412no—
726C2×C4—48no—
727C2×C4—424no—
728C2×C4—424no—
729C2×C4—424no—
730C2×C4—424no—
731C2×C4—424no—
732C2×C4C23×D416yes—
733C2×C4C23×D412yes—
734C2×C4C23×D412yes—
735C2×C4C23×D416yes—
736C2×C4C23×D416yes—
737C2×C4C23×D412yes—
738C2×C4C2×H(5,𝔽2)112yes—
739C2×C4C2×2−1+412yes—
740C2×C4#58514yes—
741C2×C4#58512yes—
742C22—28no—
743C22—26no—
744C22—24no—
745C22—26no—
746C22—26no—
747C22—46no—
748C22—46no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—412no—
754C22—44no—
755C22—412no—
756C22—46no—
757C22—42no—
758C22—42no—
759C22—46no—
760C22—42no—
761C22—46no—
762C22—848no—
763C22C24×D411yescharacteristic
764C22C22×H(5,𝔽2)12yes—
765C22C22×2−1+411yescharacteristic
766C22C2×#58512yes—
767C22C2×#58511yescharacteristic
768C4—24no—
769C4—26no—
770C4—22no—
771C4—26no—
772C4—22no—
773C4—42no—
774C4—46no—
775C4—46no—
776C4—42no—
777C4—46no—
778C4—42no—
779C4—46no—
780C4—46no—
781C4C2×#535112yes—
782C4#348914yes—
783C2—46no—
784C2—44no—
785C2—82no—
786C2—86no—
787C2C22×#53511yescharacteristic
788C2C2×#348911yescharacteristic
789C2#6281211yescharacteristic
790C2#6301512yes—
791C2#6302212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3518C2semidirect
2. C2×D4×#41C2semidirect
3. #42443C2semidirect
4. #39863C2semidirect
5. #39491C2semidirect
6. #39488C2semidirect
7. #38957C2semidirect
8. #38953C2semidirect
9. #37616C2semidirect
10. Q8×#127C2semidirect
11. Q8×#124C2semidirect
12. #36465C2semidirect
13. #36457C2semidirect
14. #36428C2semidirect
15. #35771C2semidirect
16. #35298C2semidirect
17. #35172C2semidirect
18. #34965C2semidirect
19. #34129C2semidirect
22. C2×Q82C22semidirect
23. C2×#556C22semidirect
24. C2×#556C22semidirect
25. C2×#555C22semidirect
29. C2×D4×Q8C22semidirect
30. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
37. C2×#542C22semidirect
38. C2×#533C22semidirect
40. C2×#529C22semidirect
42. C2×#519C22semidirect
45. #2868C22semidirect
46. #2862C22semidirect
47. #2858C22semidirect
48. #2858C22semidirect
49. #2848C22semidirect
50. #2813C22semidirect
51. #2718C22semidirect
52. #2710C22semidirect
53. #2685C22semidirect
54. #2670C22semidirect
55. #2636C22semidirect
56. #2626C22semidirect
57. #2620C22semidirect
58. #2620C22semidirect
59. #2620C22semidirect
60. #2619C22semidirect
61. #2603C22semidirect
62. #2580C22semidirect
63. #2568C22semidirect
65. #2566C22semidirect
66. #2566C22semidirect
68. #2563C22semidirect
69. #2548C22semidirect
70. #2545C22semidirect
72. #2544C22semidirect
74. #2542C22semidirect
75. #2542C22semidirect
76. #2542C22semidirect
77. #2541C22semidirect
78. #2540C22semidirect
79. #2538C22semidirect
80. #2504C22semidirect
81. #2502C22semidirect
82. #2500C22semidirect
83. #2500C22semidirect
84. #2492C22semidirect
85. #2491C22semidirect
87. #2435C22semidirect
89. #2432C22semidirect
90. #2432C22semidirect
91. #2429C22semidirect
92. #2426C22semidirect
93. #2415C22semidirect
94. #2414C22semidirect
95. #2411C22semidirect
96. #2408C22semidirect
97. #2407C22semidirect
98. #2407C22semidirect
99. #2392C22semidirect
100. #2354C22semidirect
101. Q8×C4⋊C4C22semidirect
102. #2346C22semidirect
104. #2341C22semidirect
105. Q8×C22⋊C4C22semidirect
106. #2326C22semidirect
107. #2317C22semidirect
110. C4×#127C22semidirect
112. C4×#124C22semidirect
113. C4×#120C22semidirect
114. #2293C22semidirect
115. #2293C22semidirect
116. #2285C22semidirect
117. C42×Q8C22semidirect
118. C42×Q8C22semidirect
119. C4×#117C22semidirect
190. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×D4×#412
#424432
#398632
#394912
#394882
#389572
#389532
#376162
Q8×#1272
Q8×#1242
#364652
#364572
#364282
#357712
#352982
#351722
#349652
#341292