Finite Group Databasebeta

← #35196816

Subgroups — #35196816

Order 20224.

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×#19099400C212yesmaximal, complemented
2#23777191C218yesmaximal, complemented
3#23777184C214yesmaximal, complemented
4#23777177C214yesmaximal, complemented
5#23777171C211yesmaximal, characteristic, complemented
6#23777167C212yesmaximal, complemented
7#23777163C216yesmaximal, complemented
8#23777162C216yesmaximal, complemented
9D4×#11929625C214yesmaximal, complemented
10#23776890C214yesmaximal, complemented
11#23776889C218yesmaximal, complemented
12#23776728C216yesmaximal, complemented
13#532×D79C216yesmaximal, complemented
14C2×C4×#11929625C211yesmaximal, characteristic, complemented
15C79×#3497C211yesmaximal, characteristic, complemented
16#19099400—232no—
17C2×#14579209C2212yescomplemented
18C2×#14579209C2218yescomplemented
19C2×#14579207C22112yescomplemented
20C2×#14579207C2218yescomplemented
21C22×#11929625C2211yescharacteristic
22C22×#11929625C2218yescomplemented
23C2×#41×D79C2218yescomplemented
24C2×#41×D79C22112yescomplemented
25#19099235C2214yescomplemented
26#19099232C2218yescomplemented
27Q8×D316C2214yescomplemented
28Q8×C22⋊D79C2218yescomplemented
29#19099225C2218yescomplemented
30#19099224C2218yescomplemented
31#19099220C2218yescomplemented
32#19099218C22112yescomplemented
33#19099216C22112yescomplemented
34#19099215C22124yescomplemented
35#19099210C22124yescomplemented
36#19099209C22124yescomplemented
37#19099206C22124yescomplemented
38#19099204C22124yescomplemented
39D4×D316C22112yescomplemented
40#19099198C22112yescomplemented
41#19099197C22124yescomplemented
42#19099144C2216yescomplemented
43#19099141C22112yescomplemented
44#19099136C22124yescomplemented
45#19099129C22124yescomplemented
46#19099121C22124yescomplemented
47#19099114C2216yescomplemented
48#19099113C2216yescomplemented
49#19099112C22112yescomplemented
50#19099111C2216yescomplemented
51#19099110C22112yescomplemented
52#19099110C22112yescomplemented
53#19099109C22112yescomplemented
54#19099108C2214yescomplemented
55#19099108C22112yescomplemented
56C4⋊Q8×D79C2216yescomplemented
57#127×D79C2216yescomplemented
58#124×D79C22112yescomplemented
59#19099076C22124yescomplemented
60#19099073C22124yescomplemented
61#121×D79C22112yescomplemented
62#121×D79C22112yescomplemented
63C4×#11929625C2214yescomplemented
64C4×#11929625C2214yescomplemented
65C4×#11929625C2214yescomplemented
66C4×#11929625C2214yescomplemented
67C2×Q8×Dic79C2211yescharacteristic, complemented
68C2×C4×D316C2213yescomplemented
69C2×#14579123C2213yescomplemented
70C4×D4×D79C22112yescomplemented
71C4×D4×D79C22112yescomplemented
72C2×#14579119C2213yescomplemented
73C2×C42×D79C2213yescomplemented
74C2×2−1+4×C79C2212yescomplemented
75#550×C79C2214yescomplemented
76D4×Q8×C79C2214yescomplemented
77#548×C79C2218yescomplemented
78#537×C79C2216yescomplemented
79#532×C79C2216yescomplemented
80C2×C4×Q8×C79C2211yescharacteristic, complemented
81#14579209—216no—
82#14579209—264no—
83#14579207—264no—
84#14579207—296no—
85C2×#11929625—264no—
86C2×#11929625D4116yescomplemented
87C2×#11929625C23124yes—
88C2×#11929625C2318yes—
89C2×#11929625C23112yes—
90C2×#11929625C2314yes—
91C2×#11929625C2314yes—
92C2×#11929624C23124yes—
93C2×#11929624C23112yes—
94C2×#11929624C23124yes—
95C2×#11929623C23112yes—
96C2×#11929623C2318yes—
97#41×D79—264no—
98#41×D79—296no—
99C2×Q8×D79C23112yes—
100C2×Q8×D79C2318yes—
101C22×D316C23124yes—
102C22×D316C2313yes—
103C2×D4×D79C23124yes—
104C2×D4×D79C23124yes—
105C2×D4×D79C23112yes—
106C2×D4×D79C23112yes—
107C2×D4×D79C23112yes—
108C22×C4×D79C23124yes—
109C22×C4×D79C2313yes—
110C22×C4×D79C2313yes—
111C22×C4×D79C2313yes—
112#14579161C2316yes—
113#14579160C23112yes—
114#14579160C2314yes—
115#14579159C23112yes—
116#14579158C2316yes—
117#14579157C23112yes—
118#14579157C2314yes—
119#14579157C23112yes—
120#14579150C23112yes—
121#14579149C23112yes—
122#14579148C23112yes—
123#14579147C23124yes—
124#14579147C2318yes—
125#14579146C23148yes—
126#14579143C23148yes—
127#14579141C23124yes—
128#14579140C23124yes—
129#14579137C23124yes—
130#14579136C23124yes—
131#14579136C23112yes—
132#14579136C23112yes—
133#14579135C23124yes—
134#14579135C23112yes—
135#14579135C2314yes—
136#14579134C23124yes—
137#14579134C23124yes—
138#14579133C23124yes—
139#14579133C2318yes—
140#14579132C23124yes—
141#14579132C23112yes—
142#14579132C23112yes—
143#14579131C23148yes—
144#14579129C23148yes—
145Q8×Dic79C2314yes—
146Q8×Dic79C2314yes—
147C4×D316C23112yes—
148C4×D316C23112yes—
149C4×D316C23112yes—
150C4×D316C23112yes—
151D4×Dic79C2314yes—
152D4×Dic79C23112yes—
153#14579123C23112yes—
154#14579123C23112yes—
155#14579123C2314yes—
156#14579123C23112yes—
157C4×C22⋊D79C23124yes—
158C4×C22⋊D79C23124yes—
159(C22⋊D79)⋊C4C2318yes—
160(C22⋊D79)⋊C4C23124yes—
161#14579119C23112yes—
162#14579119C23112yes—
163C2×C4⋊Dic79C2313yes—
164C4⋊C4×D79C23112yes—
165C4⋊C4×D79C23112yes—
166C2×(C2×D79)⋊C4C2316yes—
167C22⋊C4×D79C23124yes—
168C22⋊C4×D79C23124yes—
169C2×C4×Dic79C2311yescharacteristic
170C2×C4×Dic79C2313yes—
171C2×C4×Dic79C2313yes—
172C42×D79C2316yes—
173C42×D79C2316yes—
174C42×D79C2316yes—
175C42×D79C2316yes—
1762−1+4×C79—216no—
177C2×#41×C79C23112yes—
178C2×#41×C79C2318yes—
179C22×Q8×C79C2318yes—
180C22×Q8×C79C2311yescharacteristic
181C4⋊Q8×C79C2316yes—
182#127×C79C2316yes—
183#124×C79C23112yes—
184C22⋊Q8×C79C23124yes—
185#121×C79C23124yes—
186#121×C79C2314yes—
187#121×C79C23112yes—
188C4×Q8×C79C2314yes—
189C4×Q8×C79C2314yes—
190C4×D4×C79C23112yes—
191C4×D4×C79C23112yes—
192C2×C4⋊C4×C79C2313yes—
193C2×C42×C79C2313yes—
194C23×D79C24124yes—
195C23×D79C2413yes—
196#11929625—296no—
197#11929625—248no—
198#11929625—232no—
199#11929625C2×D4132yescomplemented
200#11929625C2×D4132yescomplemented
201#11929624—296no—
202#11929624—296no—
203#11929624—248no—
204#11929623—232no—
205#11929623—248no—
206C2×Dic158C24112yes—
207C2×Dic158C2418yes—
208Q8×D79—248no—
209Q8×D79—232no—
210C2×D316—296no—
211C2×D316C2×D4124yescomplemented
212C2×D316C24124yes—
213C2×D316C24112yes—
214C2×D316C2414yes—
215C2×D316C24112yes—
216C2×D316C24112yes—
217C2×C22⋊D79C24124yes—
218C2×C22⋊D79C2418yes—
219C2×C22⋊D79C2418yes—
220C2×C22⋊D79C2418yes—
221C2×C22⋊D79C24124yes—
222D4×D79—296no—
223D4×D79—248no—
224D4×D79—296no—
225D4×D79—424no—
226D4×D79—424no—
227C22×Dic79C2418yes—
228C22×Dic79C2411yescharacteristic
229C22×Dic79C2413yes—
230C22×Dic79C2411yescharacteristic
231C2×C4×D79—296no—
232C2×C4×D79—46no—
233C2×C4×D79—46no—
234C2×C4×D79C2×D4124yescomplemented
235C2×C4×D79C24124yes—
236C2×C4×D79C24124yes—
237C2×C4×D79C2418yes—
238C2×C4×D79C2416yes—
239C2×C4×D79C2416yes—
240C2×C4×D79C2416yes—
241C2×C4×D79C2416yes—
242C2×C4×D79C2416yes—
243C2×C4×D79C2416yes—
244C4⋊Dic79C2414yes—
245C4⋊Dic79C24112yes—
246C4⋊Dic79C24112yes—
247Dic79⋊C4C2418yes—
248Dic79⋊C4C24124yes—
249C22⋊Dic79C2418yes—
250C22⋊Dic79C24124yes—
251(C2×D79)⋊C4C2418yes—
252(C2×D79)⋊C4C2418yes—
253(C2×D79)⋊C4C24124yes—
254(C2×D79)⋊C4C24124yes—
255(C2×D79)⋊C4C24124yes—
256C4×Dic79C2411yescharacteristic
257C4×Dic79C2411yescharacteristic
258C4×Dic79C2411yescharacteristic
259C4×Dic79C2411yescharacteristic
260C4×Dic79C2416yes—
261C4×Dic79C2416yes—
262C4×Dic79C2416yes—
263C4×Dic79C2416yes—
264#41×C79—232no—
265#41×C79—248no—
266C2×Q8×C79—232no—
267C2×Q8×C79C2×D418yescomplemented
268C2×Q8×C79C24112yes—
269C2×Q8×C79C2414yes—
270C2×D4×C79C2418yes—
271C2×D4×C79C24112yes—
272C2×D4×C79C2414yes—
273C2×D4×C79C24112yes—
274C22×C4×C79C24124yes—
275C22×C4×C79C2411yescharacteristic
276C22×C4×C79C2413yes—
277C22×C4×C79C2413yes—
278C4⋊C4×C79C24112yes—
279C4⋊C4×C79C2414yes—
280C4⋊C4×C79C24112yes—
281C22⋊C4×C79C2418yes—
282C22⋊C4×C79C24124yes—
283C42×C79C2416yes—
284C42×C79C2416yes—
285C23×C79C2518yes—
286C23×C79C2511yescharacteristic
287C22×D79—248no—
288C22×D79—43no—
289C22×D79—43no—
290C22×D79—424no—
291C22×D79—424no—
292C22×D79C22×D4112yes—
293C22×D79C2518yes—
294C22×D79C2516yes—
295Q8×C79—224no—
296Q8×C79C22×D4116yes—
297D4×C79—216no—
298D4×C79—224no—
299D4×C79—28no—
300D4×C79—412no—
301C2×C4×C79—248no—
302C2×C4×C79—22no—
303C2×C4×C79—43no—
304C2×C4×C79C22×D4112yes—
305C2×C4×C79C2516yes—
306C2×C4×C79C2511yescharacteristic
307C2×C4×C79C2518yes—
308C2×C4×C79C2516yes—
309C2×C4×C79C2511yescharacteristic
310C22⋊D79—216no—
311C22⋊D79—248no—
312C22⋊D79—216no—
313C22⋊D79—216no—
314C22⋊D79—424no—
315C2×Dic79—216no—
316C2×Dic79—22no—
317C2×Dic79—43no—
318C2×Dic79C22×D414yes—
319C2×Dic79C2511yescharacteristic
320C2×Dic79C2516yes—
321C2×Dic79C2518yes—
322C2×Dic79C2511yescharacteristic
323C2×Dic79C2511yescharacteristic
324C2×Dic79C2511yescharacteristic
325D316—248no—
326D316—224no—
327D316—28no—
328D316—412no—
329D316C22×D4148yes—
330C4×D79—248no—
331C4×D79—248no—
332C4×D79—212no—
333C4×D79—216no—
334C4×D79—212no—
335C4×D79—46no—
336C4×D79—46no—
337C4×D79C22×D4124yes—
338C4×D79C22×D4124yes—
339Dic158—224no—
340Dic158—216no—
341C22×C79—21no—
342C22×C79—21no—
343C22×C79—28no—
344C22×C79—28no—
345C22×C79—28no—
346C22×C79C23×D412yes—
347C22×C79C2611yescharacteristic
348C2×D79—26no—
349C2×D79—26no—
350C2×D79—28no—
351C2×D79—28no—
352C2×D79—28no—
353C2×D79—412no—
354C2×D79—848no—
355C2×D79C23×D4112yes—
356C4×C79—28no—
357C4×C79—21no—
358C4×C79—26no—
359C4×C79C23×D4112yes—
360C4×C79#58512yescomplemented
361Dic79—28no—
362Dic79—26no—
363Dic79—21no—
364Dic79C23×D412yes—
365Dic79C23×D412yes—
366Dic79#58512yescomplemented
367#62812—791nomaximal, Sylow
368C2×C79—22no—
369C2×C79—48no—
370C2×C79C24×D411yescharacteristic
371C2×C79C2×#58511yescharacteristic
372C2×C79C2×#58511yescharacteristic
373D79—212no—
374D79—48no—
375C2×#585—792no—
376#3500—798no—
377#3499—794no—
378#3498—794no—
379#3497—792no—
380#3497—791no—
381#3497D7911yescharacteristic, complemented
382#3496—796no—
383#3496—796no—
384D4×#41—794no—
385D4×#41—794no—
386D4×#41—798no—
387#3449—796no—
388C2×#532—796no—
389C2×C4×#41—791no—
390C79#6281211yescharacteristic, complemented, Sylow
391#585—15832no—
392C2×2−1+4—792no—
393C2×2−1+4—798no—
394C2×2−1+4C2×D7912yescomplemented
395C2×H(5,𝔽2)—7912no—
396C2×H(5,𝔽2)—798no—
397C22×#41—7912no—
398C22×#41—798no—
399C22×#41—791no—
400C22×#41—798no—
401#550—798no—
402#550—794no—
403#550C2×D7914yescomplemented
404D4×Q8—798no—
405D4×Q8—794no—
406D4×Q8C2×D7914yescomplemented
407#548—798no—
408#548—798no—
409#548—798no—
410#548C2×D7918yescomplemented
411#547—7912no—
412#547—7924no—
413#547—7912no—
414#546—7924no—
415#546—7924no—
416#546—7924no—
417#546—7924no—
418D42—7912no—
419D42—7924no—
420D42—7912no—
421#537—7912no—
422#537—796no—
423#537C2×D7916yescomplemented
424#536—7924no—
425#535—7924no—
426#534—7924no—
427#532—7912no—
428#532—796no—
429#532—796no—
430#532—7912no—
431#532—794no—
432#532—7912no—
433#532—7912no—
434#532—7912no—
435#532—796no—
436#532C2×D7916yescomplemented
437C2×C4⋊Q8—796no—
438C2×#127—796no—
439C2×#124—7912no—
440#525—7924no—
441#525—7924no—
442C2×#121—7912no—
443C2×#121—7912no—
444C4×#41—794no—
445C4×#41—794no—
446C4×#41—794no—
447C4×#41—794no—
448C2×C4×Q8—791no—
449C2×C4×Q8C2×D7911yescharacteristic, complemented
450C2×C4×D4—7912no—
451C2×C4×D4—7912no—
452C2×C4×D4—793no—
453C2×C4×D4—793no—
454C2×#117—793no—
455C22×C42—793no—
4562−1+4—216no—
4572−1+4—15864no—
4582−1+4—15816no—
459H(5,𝔽2)—15896no—
460H(5,𝔽2)—15864no—
461C2×#41—7916no—
462C2×#41—794no—
463C2×#41—794no—
464C2×#41—7912no—
465C2×#41—7924no—
466C2×#41—798no—
467C2×#41—7912no—
468C2×#41—798no—
469C2×#41—7924no—
470C2×#41—7912no—
471C2×#41—7924no—
472C2×#41—15896no—
473C2×#41—15864no—
474C2×#41—15864no—
475C2×#41C22×D79112yes—
476C2×#41C22×D7918yes—
477C22×Q8—7912no—
478C22×Q8—798no—
479C22×Q8C22×D7918yes—
480C22×Q8C22×D7911yescharacteristic
481C22×D4—7912no—
482C22×D4—7912no—
483C22×D4—7924no—
484C22×D4—7912no—
485C22×D4—7924no—
486C22×D4—793no—
487C22×D4—7924no—
488C23×C4—793no—
489C23×C4—793no—
490C23×C4—793no—
491C23×C4—7924no—
492C4⋊Q8—7912no—
493C4⋊Q8—794no—
494C4⋊Q8—7912no—
495C4⋊Q8—796no—
496C4⋊Q8C22×D7916yes—
497#127—794no—
498#127—7912no—
499#127—7912no—
500#127—796no—
501#127C22×D7916yes—
502#124—7912no—
503#124—7912no—
504#124—798no—
505#124—7924no—
506#124—7912no—
507#124C22×D79112yes—
508#123—7948no—
509#123—7948no—
510C22⋊Q8—7924no—
511C22⋊Q8—7924no—
512C22⋊Q8—7924no—
513C22⋊Q8C22×D79124yes—
514#121—798no—
515#121—7924no—
516#121—7912no—
517#121—7912no—
518#121—7924no—
519#121—794no—
520#121—7912no—
521#121—7924no—
522#121—7912no—
523#121—7912no—
524#121—7924no—
525#121—7924no—
526#121—7924no—
527#121C22×D7914yes—
528#121C22×D79112yes—
529#121C22×D79124yes—
530#120—7948no—
531#120—7948no—
532C4×Q8—794no—
533C4×Q8—794no—
534C4×Q8C22×D7914yes—
535C4×Q8C22×D7914yes—
536C4×D4—794no—
537C4×D4—7912no—
538C4×D4—7924no—
539C4×D4—7924no—
540C4×D4—794no—
541C4×D4—7912no—
542C4×D4—7912no—
543C4×D4—7912no—
544C4×D4—798no—
545C4×D4—7924no—
546C4×D4—7912no—
547C4×D4—7912no—
548C4×D4—7912no—
549C4×D4—7912no—
550C4×D4C22×D79112yes—
551C4×D4C22×D79112yes—
552#117—7912no—
553#117—7912no—
554C2×C4⋊C4—793no—
555C2×C4⋊C4—7912no—
556C2×C4⋊C4—7912no—
557C2×C4⋊C4C22×D7913yes—
558C2×C22⋊C4—796no—
559C2×C22⋊C4—7924no—
560C2×C22⋊C4—7924no—
561C2×C42—793no—
562C2×C42—793no—
563C2×C42—791no—
564C2×C42—796no—
565C2×C42—796no—
566C2×C42—796no—
567C2×C42—796no—
568C2×C42C22×D7913yes—
569C24—793no—
570C24—7924no—
571#41—232no—
572#41—248no—
573#41—7932no—
574#41—7932no—
575#41—15896no—
576#41—15896no—
577#41—15832no—
578#41—15848no—
579#41—15848no—
580#41—15896no—
581#41—15832no—
582#41—15848no—
583C2×Q8—232no—
584C2×Q8—7912no—
585C2×Q8—798no—
586C2×Q8—15848no—
587C2×Q8—15832no—
588C2×Q8D4×D7918yescomplemented
589C2×Q8C23×D79112yes—
590C2×Q8C23×D7914yes—
591C2×D4—31624no—
592C2×D4—31624no—
593C2×D4—7924no—
594C2×D4—798no—
595C2×D4—7924no—
596C2×D4—798no—
597C2×D4—798no—
598C2×D4—7912no—
599C2×D4—7912no—
600C2×D4—794no—
601C2×D4—7924no—
602C2×D4—7912no—
603C2×D4—7924no—
604C2×D4—15896no—
605C2×D4—15848no—
606C2×D4—15896no—
607C2×D4—15896no—
608C2×D4C23×D7914yes—
609C2×D4C23×D7918yes—
610C2×D4C23×D79112yes—
611C2×D4C23×D79112yes—
612C22×C4—3166no—
613C22×C4—3166no—
614C22×C4—793no—
615C22×C4—796no—
616C22×C4—796no—
617C22×C4—791no—
618C22×C4—796no—
619C22×C4—796no—
620C22×C4—7924no—
621C22×C4—791no—
622C22×C4—798no—
623C22×C4—796no—
624C22×C4—796no—
625C22×C4—7924no—
626C22×C4—798no—
627C22×C4—7924no—
628C22×C4—15896no—
629C22×C4C23×D7911yescharacteristic
630C22×C4C23×D79124yes—
631C22×C4C23×D7913yes—
632C22×C4C23×D7913yes—
633C4⋊C4—798no—
634C4⋊C4—7924no—
635C4⋊C4—794no—
636C4⋊C4—7912no—
637C4⋊C4—7912no—
638C4⋊C4C23×D7914yes—
639C4⋊C4C23×D79112yes—
640C4⋊C4C23×D79112yes—
641C22⋊C4—798no—
642C22⋊C4—7924no—
643C22⋊C4—798no—
644C22⋊C4—798no—
645C22⋊C4—7924no—
646C22⋊C4—7924no—
647C22⋊C4—7924no—
648C22⋊C4C23×D7918yes—
649C22⋊C4C23×D79124yes—
650C42—791no—
651C42—791no—
652C42—791no—
653C42—791no—
654C42—796no—
655C42—796no—
656C42—796no—
657C42—796no—
658C42C23×D7916yes—
659C42C23×D7916yes—
660C23—3163no—
661C23—3163no—
662C23—31624no—
663C23—31624no—
664C23—7912no—
665C23—796no—
666C23—798no—
667C23—15848no—
668C23C24×D7918yes—
669C23C24×D7911yescharacteristic
670Q8—224no—
671Q8—15816no—
672Q8—15824no—
673Q8C2×D4×D79116yes—
674D4—216no—
675D4—28no—
676D4—224no—
677D4—412no—
678D4—31612no—
679D4—31624no—
680D4—7948no—
681D4—15848no—
682D4—15816no—
683D4—15816no—
684D4—15848no—
685D4—15816no—
686D4—1588no—
687D4—15824no—
688C2×C4—22no—
689C2×C4—248no—
690C2×C4—43no—
691C2×C4—3166no—
692C2×C4—3166no—
693C2×C4—3163no—
694C2×C4—791no—
695C2×C4—791no—
696C2×C4—791no—
697C2×C4—794no—
698C2×C4—7924no—
699C2×C4—7924no—
700C2×C4—791no—
701C2×C4—796no—
702C2×C4—798no—
703C2×C4—15812no—
704C2×C4—15816no—
705C2×C4—15848no—
706C2×C4—1582no—
707C2×C4—15816no—
708C2×C4—15812no—
709C2×C4—15848no—
710C2×C4C2×D4×D79112yes—
711C2×C4C24×D7911yescharacteristic
712C2×C4C24×D7916yes—
713C2×C4C24×D7918yes—
714C2×C4C24×D7911yescharacteristic
715C2×C4C24×D7916yes—
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—31612no—
722C22—7912no—
723C22—63248no—
724C22—1588no—
725C22—1588no—
726C22—1588no—
727C22—1586no—
728C22—1586no—
729C22C22×D4×D7912yes—
730C22C25×D7911yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—792no—
735C4—792no—
736C4—792no—
737C4—1588no—
738C4—1581no—
739C4—1586no—
740C4C22×D4×D79112yes—
741C4#1909940012yescomplemented
742C2—22no—
743C2—48no—
744C2—3168no—
745C2—15812no—
746C2C23×D4×D7911yescharacteristic
747C2#585×D7911yescharacteristic
748C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3497C2
hypercenter#3497D79
hypocenterC79#62812
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. #23777191C2semidirect
3. #23777184C2semidirect
4. #23777177C2semidirect
5. #23777171C2semidirect
6. #23777167C2semidirect
7. #23777163C2semidirect
8. #23777162C2semidirect
9. D4×#11929625C2semidirect
10. #23776890C2semidirect
11. #23776889C2semidirect
12. #23776728C2semidirect
13. #532×D79C2semidirect
14. C2×C4×#11929625C2semidirect
15. C79×#3497C2semidirect
17. C2×#14579209C22semidirect
18. C2×#14579209C22semidirect
19. C2×#14579207C22semidirect
20. C2×#14579207C22semidirect
22. C22×#11929625C22semidirect
23. C2×#41×D79C22semidirect
24. C2×#41×D79C22semidirect
25. #19099235C22semidirect
26. #19099232C22semidirect
27. Q8×D316C22semidirect
28. Q8×C22⋊D79C22semidirect
29. #19099225C22semidirect
30. #19099224C22semidirect
31. #19099220C22semidirect
32. #19099218C22semidirect
33. #19099216C22semidirect
34. #19099215C22semidirect
35. #19099210C22semidirect
36. #19099209C22semidirect
37. #19099206C22semidirect
38. #19099204C22semidirect
39. D4×D316C22semidirect
40. #19099198C22semidirect
41. #19099197C22semidirect
42. #19099144C22semidirect
43. #19099141C22semidirect
44. #19099136C22semidirect
45. #19099129C22semidirect
46. #19099121C22semidirect
47. #19099114C22semidirect
48. #19099113C22semidirect
49. #19099112C22semidirect
50. #19099111C22semidirect
51. #19099110C22semidirect
52. #19099110C22semidirect
53. #19099109C22semidirect
54. #19099108C22semidirect
55. #19099108C22semidirect
56. C4⋊Q8×D79C22semidirect
57. #127×D79C22semidirect
58. #124×D79C22semidirect
59. #19099076C22semidirect
60. #19099073C22semidirect
61. #121×D79C22semidirect
62. #121×D79C22semidirect
63. C4×#11929625C22semidirect
64. C4×#11929625C22semidirect
65. C4×#11929625C22semidirect
66. C4×#11929625C22semidirect
67. C2×Q8×Dic79C22semidirect
68. C2×C4×D316C22semidirect
69. C2×#14579123C22semidirect
70. C4×D4×D79C22semidirect
71. C4×D4×D79C22semidirect
72. C2×#14579119C22semidirect
73. C2×C42×D79C22semidirect
74. C2×2−1+4×C79C22semidirect
75. #550×C79C22semidirect
76. D4×Q8×C79C22semidirect
77. #548×C79C22semidirect
78. #537×C79C22semidirect
79. #532×C79C22semidirect
80. C2×C4×Q8×C79C22semidirect
86. C2×#11929625D4semidirect
199. #11929625C2×D4semidirect
200. #11929625C2×D4semidirect
211. C2×D316C2×D4semidirect
234. C2×C4×D79C2×D4semidirect
267. C2×Q8×C79C2×D4semidirect
360. C4×C79#585semidirect
366. Dic79#585semidirect
381. #3497D79semidirect
390. C79#62812semidirect
394. C2×2−1+4C2×D79semidirect
403. #550C2×D79semidirect
406. D4×Q8C2×D79semidirect
410. #548C2×D79semidirect
423. #537C2×D79semidirect
436. #532C2×D79semidirect
449. C2×C4×Q8C2×D79semidirect
588. C2×Q8D4×D79semidirect
741. C4#19099400semidirect

Maximal subgroups

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

subgroupindex
C2×#190994002
#237771912
#237771842
#237771772
#237771712
#237771672
#237771632
#237771622
D4×#119296252
#237768902
#237768892
#237767282
#532×D792
C2×C4×#119296252
C79×#34972
#6281279