Finite Group Databasebeta

← #32905999

Subgroups — #32905999

Order 18176.

11346 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986836C212yesmaximal, complemented
2#22602131C218yesmaximal, complemented
3#22602124C214yesmaximal, complemented
4#22602117C214yesmaximal, complemented
5#22602111C211yesmaximal, characteristic, complemented
6#22602107C212yesmaximal, complemented
7#22602103C216yesmaximal, complemented
8#22602102C216yesmaximal, complemented
9D4×#11765866C214yesmaximal, complemented
10#22601830C214yesmaximal, complemented
11#22601829C218yesmaximal, complemented
12#22601668C216yesmaximal, complemented
13#532×D71C216yesmaximal, complemented
14C2×C4×#11765866C211yesmaximal, characteristic, complemented
15C71×#3497C211yesmaximal, characteristic, complemented
16#17986836—232no—
17C2×#14556176C2212yescomplemented
18C2×#14556176C2218yescomplemented
19C2×#14556174C22112yescomplemented
20C2×#14556174C2218yescomplemented
21C22×#11765866C2211yescharacteristic
22C22×#11765866C2218yescomplemented
23C2×#41×D71C2218yescomplemented
24C2×#41×D71C22112yescomplemented
25#17986671C2214yescomplemented
26#17986668C2218yescomplemented
27Q8×D284C2214yescomplemented
28Q8×C22⋊D71C2218yescomplemented
29#17986661C2218yescomplemented
30#17986660C2218yescomplemented
31#17986656C2218yescomplemented
32#17986654C22112yescomplemented
33#17986652C22112yescomplemented
34#17986651C22124yescomplemented
35#17986646C22124yescomplemented
36#17986645C22124yescomplemented
37#17986642C22124yescomplemented
38#17986640C22124yescomplemented
39D4×D284C22112yescomplemented
40#17986634C22112yescomplemented
41#17986633C22124yescomplemented
42#17986580C2216yescomplemented
43#17986577C22112yescomplemented
44#17986572C22124yescomplemented
45#17986565C22124yescomplemented
46#17986557C22124yescomplemented
47#17986550C2216yescomplemented
48#17986549C2216yescomplemented
49#17986548C22112yescomplemented
50#17986547C2216yescomplemented
51#17986546C22112yescomplemented
52#17986546C22112yescomplemented
53#17986545C22112yescomplemented
54#17986544C2214yescomplemented
55#17986544C22112yescomplemented
56C4⋊Q8×D71C2216yescomplemented
57#127×D71C2216yescomplemented
58#124×D71C22112yescomplemented
59#17986512C22124yescomplemented
60#17986509C22124yescomplemented
61#121×D71C22112yescomplemented
62#121×D71C22112yescomplemented
63C4×#11765866C2214yescomplemented
64C4×#11765866C2214yescomplemented
65C4×#11765866C2214yescomplemented
66C4×#11765866C2214yescomplemented
67C2×Q8×Dic71C2211yescharacteristic, complemented
68C2×C4×D284C2213yescomplemented
69C2×#14556090C2213yescomplemented
70C4×D4×D71C22112yescomplemented
71C4×D4×D71C22112yescomplemented
72C2×#14556086C2213yescomplemented
73C2×C42×D71C2213yescomplemented
74C2×2−1+4×C71C2212yescomplemented
75#550×C71C2214yescomplemented
76D4×Q8×C71C2214yescomplemented
77#548×C71C2218yescomplemented
78#537×C71C2216yescomplemented
79#532×C71C2216yescomplemented
80C2×C4×Q8×C71C2211yescharacteristic, complemented
81#14556176—264no—
82#14556176—216no—
83#14556174—264no—
84#14556174—296no—
85C2×#11765866—264no—
86C2×#11765866D4116yescomplemented
87C2×#11765866C23112yes—
88C2×#11765866C23124yes—
89C2×#11765866C2318yes—
90C2×#11765866C2314yes—
91C2×#11765866C2314yes—
92C2×#11765865C23124yes—
93C2×#11765865C23112yes—
94C2×#11765865C23124yes—
95C2×#11765864C23112yes—
96C2×#11765864C2318yes—
97#41×D71—264no—
98#41×D71—296no—
99C2×Q8×D71C23112yes—
100C2×Q8×D71C2318yes—
101C22×D284C23124yes—
102C22×D284C2313yes—
103C2×D4×D71C23112yes—
104C2×D4×D71C23124yes—
105C2×D4×D71C23124yes—
106C2×D4×D71C23112yes—
107C2×D4×D71C23112yes—
108C22×C4×D71C23124yes—
109C22×C4×D71C2313yes—
110C22×C4×D71C2313yes—
111C22×C4×D71C2313yes—
112#14556128C2316yes—
113#14556127C23112yes—
114#14556127C2314yes—
115#14556126C23112yes—
116#14556125C2316yes—
117#14556124C23112yes—
118#14556124C23112yes—
119#14556124C2314yes—
120#14556117C23112yes—
121#14556116C23112yes—
122#14556115C23112yes—
123#14556114C23124yes—
124#14556114C2318yes—
125#14556113C23148yes—
126#14556110C23148yes—
127#14556108C23124yes—
128#14556107C23124yes—
129#14556104C23124yes—
130#14556103C23124yes—
131#14556103C23112yes—
132#14556103C23112yes—
133#14556102C23124yes—
134#14556102C23112yes—
135#14556102C2314yes—
136#14556101C23124yes—
137#14556101C23124yes—
138#14556100C23124yes—
139#14556100C2318yes—
140#14556099C23124yes—
141#14556099C23112yes—
142#14556099C23112yes—
143#14556098C23148yes—
144#14556096C23148yes—
145Q8×Dic71C2314yes—
146Q8×Dic71C2314yes—
147C4×D284C23112yes—
148C4×D284C23112yes—
149C4×D284C23112yes—
150C4×D284C23112yes—
151D4×Dic71C2314yes—
152D4×Dic71C23112yes—
153#14556090C23112yes—
154#14556090C23112yes—
155#14556090C2314yes—
156#14556090C23112yes—
157C4×C22⋊D71C23124yes—
158C4×C22⋊D71C23124yes—
159(C22⋊D71)⋊C4C2318yes—
160(C22⋊D71)⋊C4C23124yes—
161#14556086C23112yes—
162#14556086C23112yes—
163C2×C4⋊Dic71C2313yes—
164C4⋊C4×D71C23112yes—
165C4⋊C4×D71C23112yes—
166C2×(C2×D71)⋊C4C2316yes—
167C22⋊C4×D71C23124yes—
168C22⋊C4×D71C23124yes—
169C2×C4×Dic71C2311yescharacteristic
170C2×C4×Dic71C2313yes—
171C2×C4×Dic71C2313yes—
172C42×D71C2316yes—
173C42×D71C2316yes—
174C42×D71C2316yes—
175C42×D71C2316yes—
1762−1+4×C71—216no—
177C2×#41×C71C23112yes—
178C2×#41×C71C2318yes—
179C22×Q8×C71C2318yes—
180C22×Q8×C71C2311yescharacteristic
181C4⋊Q8×C71C2316yes—
182#127×C71C2316yes—
183#124×C71C23112yes—
184C22⋊Q8×C71C23124yes—
185#121×C71C23124yes—
186#121×C71C2314yes—
187#121×C71C23112yes—
188C4×Q8×C71C2314yes—
189C4×Q8×C71C2314yes—
190C4×D4×C71C23112yes—
191C4×D4×C71C23112yes—
192C2×C4⋊C4×C71C2313yes—
193C2×C42×C71C2313yes—
194C23×D71C24124yes—
195C23×D71C2413yes—
196#11765866—232no—
197#11765866—296no—
198#11765866—248no—
199#11765866C2×D4132yescomplemented
200#11765866C2×D4132yescomplemented
201#11765865—248no—
202#11765865—296no—
203#11765865—296no—
204#11765864—232no—
205#11765864—248no—
206C2×Dic142C24112yes—
207C2×Dic142C2418yes—
208Q8×D71—232no—
209Q8×D71—248no—
210C2×D284—296no—
211C2×D284C2×D4124yescomplemented
212C2×D284C2414yes—
213C2×D284C24124yes—
214C2×D284C24112yes—
215C2×D284C24112yes—
216C2×D284C24112yes—
217C2×C22⋊D71C24124yes—
218C2×C22⋊D71C2418yes—
219C2×C22⋊D71C2418yes—
220C2×C22⋊D71C2418yes—
221C2×C22⋊D71C24124yes—
222D4×D71—296no—
223D4×D71—296no—
224D4×D71—248no—
225D4×D71—424no—
226D4×D71—424no—
227C22×Dic71C2418yes—
228C22×Dic71C2411yescharacteristic
229C22×Dic71C2413yes—
230C22×Dic71C2411yescharacteristic
231C2×C4×D71—296no—
232C2×C4×D71—46no—
233C2×C4×D71—46no—
234C2×C4×D71C2×D4124yescomplemented
235C2×C4×D71C2418yes—
236C2×C4×D71C2416yes—
237C2×C4×D71C2416yes—
238C2×C4×D71C24124yes—
239C2×C4×D71C24124yes—
240C2×C4×D71C2416yes—
241C2×C4×D71C2416yes—
242C2×C4×D71C2416yes—
243C2×C4×D71C2416yes—
244C4⋊Dic71C2414yes—
245C4⋊Dic71C24112yes—
246C4⋊Dic71C24112yes—
247Dic71⋊C4C2418yes—
248Dic71⋊C4C24124yes—
249C22⋊Dic71C2418yes—
250C22⋊Dic71C24124yes—
251(C2×D71)⋊C4C2418yes—
252(C2×D71)⋊C4C2418yes—
253(C2×D71)⋊C4C24124yes—
254(C2×D71)⋊C4C24124yes—
255(C2×D71)⋊C4C24124yes—
256C4×Dic71C2411yescharacteristic
257C4×Dic71C2411yescharacteristic
258C4×Dic71C2411yescharacteristic
259C4×Dic71C2411yescharacteristic
260C4×Dic71C2416yes—
261C4×Dic71C2416yes—
262C4×Dic71C2416yes—
263C4×Dic71C2416yes—
264#41×C71—232no—
265#41×C71—248no—
266C2×Q8×C71—232no—
267C2×Q8×C71C2×D418yescomplemented
268C2×Q8×C71C24112yes—
269C2×Q8×C71C2414yes—
270C2×D4×C71C2418yes—
271C2×D4×C71C24112yes—
272C2×D4×C71C2414yes—
273C2×D4×C71C24112yes—
274C22×C4×C71C2411yescharacteristic
275C22×C4×C71C24124yes—
276C22×C4×C71C2413yes—
277C22×C4×C71C2413yes—
278C4⋊C4×C71C24112yes—
279C4⋊C4×C71C2414yes—
280C4⋊C4×C71C24112yes—
281C22⋊C4×C71C2418yes—
282C22⋊C4×C71C24124yes—
283C42×C71C2416yes—
284C42×C71C2416yes—
285C23×C71C2518yes—
286C23×C71C2511yescharacteristic
287C22×D71—248no—
288C22×D71—43no—
289C22×D71—43no—
290C22×D71—424no—
291C22×D71—424no—
292C22×D71C22×D4112yes—
293C22×D71C2518yes—
294C22×D71C2516yes—
295Q8×C71—224no—
296Q8×C71C22×D4116yes—
297D4×C71—216no—
298D4×C71—224no—
299D4×C71—28no—
300D4×C71—412no—
301C2×C4×C71—248no—
302C2×C4×C71—22no—
303C2×C4×C71—43no—
304C2×C4×C71C22×D4112yes—
305C2×C4×C71C2511yescharacteristic
306C2×C4×C71C2516yes—
307C2×C4×C71C2518yes—
308C2×C4×C71C2516yes—
309C2×C4×C71C2511yescharacteristic
310C22⋊D71—216no—
311C22⋊D71—248no—
312C22⋊D71—216no—
313C22⋊D71—216no—
314C22⋊D71—424no—
315C2×Dic71—216no—
316C2×Dic71—22no—
317C2×Dic71—43no—
318C2×Dic71C22×D414yes—
319C2×Dic71C2511yescharacteristic
320C2×Dic71C2516yes—
321C2×Dic71C2518yes—
322C2×Dic71C2511yescharacteristic
323C2×Dic71C2511yescharacteristic
324C2×Dic71C2511yescharacteristic
325D284—248no—
326D284—224no—
327D284—28no—
328D284—412no—
329D284C22×D4148yes—
330C4×D71—248no—
331C4×D71—248no—
332C4×D71—212no—
333C4×D71—216no—
334C4×D71—212no—
335C4×D71—46no—
336C4×D71—46no—
337C4×D71C22×D4124yes—
338C4×D71C22×D4124yes—
339Dic142—224no—
340Dic142—216no—
341C22×C71—21no—
342C22×C71—21no—
343C22×C71—28no—
344C22×C71—28no—
345C22×C71—28no—
346C22×C71C23×D412yes—
347C22×C71C2611yescharacteristic
348C2×D71—26no—
349C2×D71—26no—
350C2×D71—28no—
351C2×D71—28no—
352C2×D71—28no—
353C2×D71—412no—
354C2×D71—848no—
355C2×D71C23×D4112yes—
356C4×C71—28no—
357C4×C71—26no—
358C4×C71—21no—
359C4×C71C23×D4112yes—
360C4×C71#58512yescomplemented
361Dic71—28no—
362Dic71—26no—
363Dic71—21no—
364Dic71C23×D412yes—
365Dic71C23×D412yes—
366Dic71#58512yescomplemented
367#62812—711nomaximal, Sylow
368C2×C71—22no—
369C2×C71—48no—
370C2×C71C24×D411yescharacteristic
371C2×C71C2×#58511yescharacteristic
372C2×C71C2×#58511yescharacteristic
373D71—212no—
374D71—48no—
375C2×#585—712no—
376#3500—718no—
377#3499—714no—
378#3498—714no—
379#3497—712no—
380#3497—711no—
381#3497D7111yescharacteristic, complemented
382#3496—716no—
383#3496—716no—
384D4×#41—714no—
385D4×#41—714no—
386D4×#41—718no—
387#3449—716no—
388C2×#532—716no—
389C2×C4×#41—711no—
390C71#6281211yescharacteristic, complemented, Sylow
391#585—14232no—
392C2×2−1+4—712no—
393C2×2−1+4—718no—
394C2×2−1+4C2×D7112yescomplemented
395C2×H(5,𝔽2)—7112no—
396C2×H(5,𝔽2)—718no—
397C22×#41—7112no—
398C22×#41—718no—
399C22×#41—711no—
400C22×#41—718no—
401#550—718no—
402#550—714no—
403#550C2×D7114yescomplemented
404D4×Q8—718no—
405D4×Q8—714no—
406D4×Q8C2×D7114yescomplemented
407#548—718no—
408#548—718no—
409#548—718no—
410#548C2×D7118yescomplemented
411#547—7112no—
412#547—7124no—
413#547—7112no—
414#546—7124no—
415#546—7124no—
416#546—7124no—
417#546—7124no—
418D42—7112no—
419D42—7124no—
420D42—7112no—
421#537—7112no—
422#537—716no—
423#537C2×D7116yescomplemented
424#536—7124no—
425#535—7124no—
426#534—7124no—
427#532—7112no—
428#532—716no—
429#532—716no—
430#532—7112no—
431#532—714no—
432#532—7112no—
433#532—7112no—
434#532—7112no—
435#532—716no—
436#532C2×D7116yescomplemented
437C2×C4⋊Q8—716no—
438C2×#127—716no—
439C2×#124—7112no—
440#525—7124no—
441#525—7124no—
442C2×#121—7112no—
443C2×#121—7112no—
444C4×#41—714no—
445C4×#41—714no—
446C4×#41—714no—
447C4×#41—714no—
448C2×C4×Q8—711no—
449C2×C4×Q8C2×D7111yescharacteristic, complemented
450C2×C4×D4—7112no—
451C2×C4×D4—7112no—
452C2×C4×D4—713no—
453C2×C4×D4—713no—
454C2×#117—713no—
455C22×C42—713no—
4562−1+4—216no—
4572−1+4—14264no—
4582−1+4—14216no—
459H(5,𝔽2)—14296no—
460H(5,𝔽2)—14264no—
461C2×#41—7116no—
462C2×#41—714no—
463C2×#41—714no—
464C2×#41—7112no—
465C2×#41—7124no—
466C2×#41—718no—
467C2×#41—7112no—
468C2×#41—718no—
469C2×#41—7124no—
470C2×#41—7112no—
471C2×#41—7124no—
472C2×#41—14296no—
473C2×#41—14264no—
474C2×#41—14264no—
475C2×#41C22×D71112yes—
476C2×#41C22×D7118yes—
477C22×Q8—7112no—
478C22×Q8—718no—
479C22×Q8C22×D7118yes—
480C22×Q8C22×D7111yescharacteristic
481C22×D4—7112no—
482C22×D4—7112no—
483C22×D4—7124no—
484C22×D4—7112no—
485C22×D4—7124no—
486C22×D4—713no—
487C22×D4—7124no—
488C23×C4—713no—
489C23×C4—713no—
490C23×C4—713no—
491C23×C4—7124no—
492C4⋊Q8—7112no—
493C4⋊Q8—714no—
494C4⋊Q8—7112no—
495C4⋊Q8—716no—
496C4⋊Q8C22×D7116yes—
497#127—714no—
498#127—7112no—
499#127—7112no—
500#127—716no—
501#127C22×D7116yes—
502#124—7112no—
503#124—7112no—
504#124—718no—
505#124—7124no—
506#124—7112no—
507#124C22×D71112yes—
508#123—7148no—
509#123—7148no—
510C22⋊Q8—7124no—
511C22⋊Q8—7124no—
512C22⋊Q8—7124no—
513C22⋊Q8C22×D71124yes—
514#121—718no—
515#121—7124no—
516#121—7112no—
517#121—7112no—
518#121—7124no—
519#121—714no—
520#121—7112no—
521#121—7124no—
522#121—7112no—
523#121—7112no—
524#121—7124no—
525#121—7124no—
526#121—7124no—
527#121C22×D7114yes—
528#121C22×D71112yes—
529#121C22×D71124yes—
530#120—7148no—
531#120—7148no—
532C4×Q8—714no—
533C4×Q8—714no—
534C4×Q8C22×D7114yes—
535C4×Q8C22×D7114yes—
536C4×D4—714no—
537C4×D4—7112no—
538C4×D4—7124no—
539C4×D4—7124no—
540C4×D4—714no—
541C4×D4—7112no—
542C4×D4—7112no—
543C4×D4—7112no—
544C4×D4—718no—
545C4×D4—7124no—
546C4×D4—7112no—
547C4×D4—7112no—
548C4×D4—7112no—
549C4×D4—7112no—
550C4×D4C22×D71112yes—
551C4×D4C22×D71112yes—
552#117—7112no—
553#117—7112no—
554C2×C4⋊C4—713no—
555C2×C4⋊C4—7112no—
556C2×C4⋊C4—7112no—
557C2×C4⋊C4C22×D7113yes—
558C2×C22⋊C4—716no—
559C2×C22⋊C4—7124no—
560C2×C22⋊C4—7124no—
561C2×C42—713no—
562C2×C42—713no—
563C2×C42—711no—
564C2×C42—716no—
565C2×C42—716no—
566C2×C42—716no—
567C2×C42—716no—
568C2×C42C22×D7113yes—
569C24—713no—
570C24—7124no—
571#41—232no—
572#41—248no—
573#41—7132no—
574#41—7132no—
575#41—14296no—
576#41—14296no—
577#41—14232no—
578#41—14248no—
579#41—14248no—
580#41—14296no—
581#41—14232no—
582#41—14248no—
583C2×Q8—232no—
584C2×Q8—7112no—
585C2×Q8—718no—
586C2×Q8—14248no—
587C2×Q8—14232no—
588C2×Q8D4×D7118yescomplemented
589C2×Q8C23×D71112yes—
590C2×Q8C23×D7114yes—
591C2×D4—28424no—
592C2×D4—28424no—
593C2×D4—7124no—
594C2×D4—718no—
595C2×D4—7124no—
596C2×D4—718no—
597C2×D4—718no—
598C2×D4—7124no—
599C2×D4—7112no—
600C2×D4—7112no—
601C2×D4—714no—
602C2×D4—7124no—
603C2×D4—7112no—
604C2×D4—14296no—
605C2×D4—14248no—
606C2×D4—14296no—
607C2×D4—14296no—
608C2×D4C23×D7114yes—
609C2×D4C23×D7118yes—
610C2×D4C23×D71112yes—
611C2×D4C23×D71112yes—
612C22×C4—2846no—
613C22×C4—2846no—
614C22×C4—713no—
615C22×C4—716no—
616C22×C4—716no—
617C22×C4—711no—
618C22×C4—7124no—
619C22×C4—716no—
620C22×C4—716no—
621C22×C4—711no—
622C22×C4—718no—
623C22×C4—716no—
624C22×C4—716no—
625C22×C4—7124no—
626C22×C4—718no—
627C22×C4—7124no—
628C22×C4—14296no—
629C22×C4C23×D7111yescharacteristic
630C22×C4C23×D71124yes—
631C22×C4C23×D7113yes—
632C22×C4C23×D7113yes—
633C4⋊C4—718no—
634C4⋊C4—7124no—
635C4⋊C4—714no—
636C4⋊C4—7112no—
637C4⋊C4—7112no—
638C4⋊C4C23×D7114yes—
639C4⋊C4C23×D71112yes—
640C4⋊C4C23×D71112yes—
641C22⋊C4—718no—
642C22⋊C4—7124no—
643C22⋊C4—718no—
644C22⋊C4—718no—
645C22⋊C4—7124no—
646C22⋊C4—7124no—
647C22⋊C4—7124no—
648C22⋊C4C23×D7118yes—
649C22⋊C4C23×D71124yes—
650C42—711no—
651C42—711no—
652C42—711no—
653C42—711no—
654C42—716no—
655C42—716no—
656C42—716no—
657C42—716no—
658C42C23×D7116yes—
659C42C23×D7116yes—
660C23—2843no—
661C23—2843no—
662C23—28424no—
663C23—28424no—
664C23—7112no—
665C23—716no—
666C23—718no—
667C23—14248no—
668C23C24×D7118yes—
669C23C24×D7111yescharacteristic
670Q8—224no—
671Q8—14216no—
672Q8—14224no—
673Q8C2×D4×D71116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—28412no—
679D4—28424no—
680D4—7148no—
681D4—14248no—
682D4—14216no—
683D4—14216no—
684D4—14248no—
685D4—14216no—
686D4—14224no—
687D4—1428no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—2846no—
692C2×C4—2846no—
693C2×C4—2843no—
694C2×C4—714no—
695C2×C4—711no—
696C2×C4—711no—
697C2×C4—711no—
698C2×C4—7124no—
699C2×C4—7124no—
700C2×C4—711no—
701C2×C4—716no—
702C2×C4—718no—
703C2×C4—14212no—
704C2×C4—14216no—
705C2×C4—14248no—
706C2×C4—1422no—
707C2×C4—14216no—
708C2×C4—14248no—
709C2×C4—14212no—
710C2×C4C2×D4×D71112yes—
711C2×C4C24×D7111yescharacteristic
712C2×C4C24×D7116yes—
713C2×C4C24×D7118yes—
714C2×C4C24×D7116yes—
715C2×C4C24×D7111yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—28412no—
722C22—56848no—
723C22—7112no—
724C22—1428no—
725C22—1428no—
726C22—1428no—
727C22—1426no—
728C22—1426no—
729C22C22×D4×D7112yes—
730C22C25×D7111yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—712no—
735C4—712no—
736C4—712no—
737C4—1428no—
738C4—1421no—
739C4—1426no—
740C4C22×D4×D71112yes—
741C4#1798683612yescomplemented
742C2—22no—
743C2—48no—
744C2—2848no—
745C2—14212no—
746C2C23×D4×D7111yescharacteristic
747C2#585×D7111yescharacteristic
748C2C2×#1798683611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3497C2
hypercenter#3497D71
hypocenterC71#62812
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#17986836C2semidirect
2. #22602131C2semidirect
3. #22602124C2semidirect
4. #22602117C2semidirect
5. #22602111C2semidirect
6. #22602107C2semidirect
7. #22602103C2semidirect
8. #22602102C2semidirect
9. D4×#11765866C2semidirect
10. #22601830C2semidirect
11. #22601829C2semidirect
12. #22601668C2semidirect
13. #532×D71C2semidirect
14. C2×C4×#11765866C2semidirect
15. C71×#3497C2semidirect
17. C2×#14556176C22semidirect
18. C2×#14556176C22semidirect
19. C2×#14556174C22semidirect
20. C2×#14556174C22semidirect
22. C22×#11765866C22semidirect
23. C2×#41×D71C22semidirect
24. C2×#41×D71C22semidirect
25. #17986671C22semidirect
26. #17986668C22semidirect
27. Q8×D284C22semidirect
28. Q8×C22⋊D71C22semidirect
29. #17986661C22semidirect
30. #17986660C22semidirect
31. #17986656C22semidirect
32. #17986654C22semidirect
33. #17986652C22semidirect
34. #17986651C22semidirect
35. #17986646C22semidirect
36. #17986645C22semidirect
37. #17986642C22semidirect
38. #17986640C22semidirect
39. D4×D284C22semidirect
40. #17986634C22semidirect
41. #17986633C22semidirect
42. #17986580C22semidirect
43. #17986577C22semidirect
44. #17986572C22semidirect
45. #17986565C22semidirect
46. #17986557C22semidirect
47. #17986550C22semidirect
48. #17986549C22semidirect
49. #17986548C22semidirect
50. #17986547C22semidirect
51. #17986546C22semidirect
52. #17986546C22semidirect
53. #17986545C22semidirect
54. #17986544C22semidirect
55. #17986544C22semidirect
56. C4⋊Q8×D71C22semidirect
57. #127×D71C22semidirect
58. #124×D71C22semidirect
59. #17986512C22semidirect
60. #17986509C22semidirect
61. #121×D71C22semidirect
62. #121×D71C22semidirect
63. C4×#11765866C22semidirect
64. C4×#11765866C22semidirect
65. C4×#11765866C22semidirect
66. C4×#11765866C22semidirect
67. C2×Q8×Dic71C22semidirect
68. C2×C4×D284C22semidirect
69. C2×#14556090C22semidirect
70. C4×D4×D71C22semidirect
71. C4×D4×D71C22semidirect
72. C2×#14556086C22semidirect
73. C2×C42×D71C22semidirect
74. C2×2−1+4×C71C22semidirect
75. #550×C71C22semidirect
76. D4×Q8×C71C22semidirect
77. #548×C71C22semidirect
78. #537×C71C22semidirect
79. #532×C71C22semidirect
80. C2×C4×Q8×C71C22semidirect
86. C2×#11765866D4semidirect
199. #11765866C2×D4semidirect
200. #11765866C2×D4semidirect
211. C2×D284C2×D4semidirect
234. C2×C4×D71C2×D4semidirect
267. C2×Q8×C71C2×D4semidirect
360. C4×C71#585semidirect
366. Dic71#585semidirect
381. #3497D71semidirect
390. C71#62812semidirect
394. C2×2−1+4C2×D71semidirect
403. #550C2×D71semidirect
406. D4×Q8C2×D71semidirect
410. #548C2×D71semidirect
423. #537C2×D71semidirect
436. #532C2×D71semidirect
449. C2×C4×Q8C2×D71semidirect
588. C2×Q8D4×D71semidirect
741. C4#17986836semidirect

Maximal subgroups

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

subgroupindex
C2×#179868362
#226021312
#226021242
#226021172
#226021112
#226021072
#226021032
#226021022
D4×#117658662
#226018302
#226018292
#226016682
#532×D712
C2×C4×#117658662
C71×#34972
#6281271