Finite Group Databasebeta

← #35155217

Subgroups — #35155217

Order 20224.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099361C211yesmaximal, characteristic, complemented
2#23776729C211yesmaximal, characteristic, complemented
3#23776603C211yesmaximal, characteristic, complemented
4#23772948C214yesmaximal, complemented
5#23772937C214yesmaximal, complemented
6#23772927C212yesmaximal, complemented
7#23772918C212yesmaximal, complemented
8#23772909C212yesmaximal, complemented
9#23772900C212yesmaximal, complemented
10#23772851C218yesmaximal, complemented
11C2×#19098589C211yesmaximal, characteristic, complemented
12#23771919C211yesmaximal, characteristic, complemented
13C2×#19098560C211yesmaximal, characteristic, complemented
14C22×#135×C79C211yesmaximal, characteristic, complemented
15C22×#11929624C2211yescharacteristic
16#19099361—28no—
17C2×#14579192C2212yes—
18C2×#14579191C2212yescomplemented
19C2×#14579187C2212yes—
20C2×#14579186C2212yescomplemented
21C2×#14579181C2214yescomplemented
22C22×#11929608C2211yescharacteristic
23#19099141—22no—
24#19099137C2212yes—
25#19099134C2212yescomplemented
26#19099130C2212yes—
27#19099127C2212yescomplemented
28#19099122—22no—
29#19099109C2214yescomplemented
30#19099074—22no—
31#19099070—22no—
32#19099046—22no—
33#19099046C2214yescomplemented
34#19099041C2212yescomplemented
35#19099038—22no—
36#19099038C2212yescomplemented
37#41×Dic79—22no—
38#41×Dic79C2214yescomplemented
39C2×#14579120—22no—
40C2×#14579120C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42#19098787C2218yescomplemented
43#19098783C2218yescomplemented
44#19098780C2218yescomplemented
45#19098776C2218yescomplemented
46#19098771C2218yescomplemented
47#19098766C2218yescomplemented
48#19098761C2218yescomplemented
49#19098756C2218yescomplemented
50#19098589C2214yescomplemented
51#19098589C2212yescomplemented
52#19098589C2212yescomplemented
53C2×Dic79⋊C8C2214yescomplemented
54#19098572C2212yescomplemented
55#19098568C2212yescomplemented
56#19098564C2214yescomplemented
57#19098560C2212yes—
58#19098560C2212yes—
59#19098560C2214yescomplemented
60#19098559C2214yescomplemented
61C2×#14579086C2212yescomplemented
62C2×#14579083C2212yescomplemented
63C22×#41×C79C2211yescharacteristic
64C22×#41×C79C2211yescharacteristic
65C2×#135×C79—28no—
66C2×#135×C79C2214yes—
67C2×#135×C79C2214yescomplemented
68C22×Q16×C79C2211yescharacteristic, complemented
69C22×SD16×C79C2211yescharacteristic, complemented
70C22×SD16×C79C2211yescharacteristic, complemented
71C22×D8×C79C2211yescharacteristic, complemented
72C23×C8×C79C2211yescharacteristic
73C2×#11929624—21no—
74C2×#11929624—21no—
75C2×#11929624—24no—
76C2×#11929624—24no—
77C2×#11929624C2312yes—
78C2×#11929624C2312yes—
79C22×Dic158C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C22×C4×D79—21no—
83#14579192—28no—
84#14579191—28no—
85#14579187—28no—
86#14579186—28no—
87#14579181—216no—
88C2×#11929614C2314yes—
89C2×#11929612C2314yes—
90C2×#11929611C2314yes—
91C2×#11929609C2314yes—
92C2×#11929608—24no—
93C2×#11929608C2312yes—
94C2×#11929608C2312yes—
95C22×C79⋊C8C2312yes—
96#14579159C2314yes—
97#14579157C2314yes—
98#14579150C2314yes—
99#14579148C2314yes—
100#14579144—24no—
101#14579142—24no—
102#14579140—24no—
103#14579137—24no—
104#14579135—24no—
105#14579133—28no—
106#14579132—24no—
107#14579130—24no—
108#14579129—24no—
109Q8×Dic79—24no—
110Q8×Dic79C2318yes—
111D4×Dic79—28no—
112D4×Dic79—24no—
113D4×Dic79—28no—
114D4×Dic79C2318yes—
115C4×C22⋊D79—28no—
116#14579120—21no—
117#14579120—21no—
118#14579120—24no—
119#14579120—24no—
120#14579120—24no—
121#14579120D412yes—
122#14579120D412yes—
123#14579120C2312yes—
124#14579120C2312yes—
125#14579120C2312yes—
126#14579120C2312yes—
127C2×C4⋊Dic79—24no—
128C2×C4⋊Dic79D412yes—
129C2×C4⋊Dic79C2312yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—24no—
132C2×C22⋊Dic79D412yes—
133C2×C4×Dic79—21no—
134C2×C4×Dic79—24no—
135C2×C4×Dic79C2312yes—
136Dic79⋊C8C2318yes—
137Dic79⋊C8C2318yes—
138#14579086C2314yes—
139#14579086C2314yes—
140#14579085C2318yes—
141#14579083C2314yes—
142#14579083C2314yes—
143#14579082C2318yes—
144C2×#41×C79—21no—
145C2×#41×C79—21no—
146C2×#41×C79—21no—
147C2×#41×C79—21no—
148C2×#41×C79—24no—
149C2×#41×C79—24no—
150C2×#41×C79—24no—
151C2×#41×C79D418yescomplemented
152C2×#41×C79C2312yes—
153C2×#41×C79C2312yes—
154C2×#41×C79C2312yes—
155C2×#41×C79C2312yes—
156C22×Q8×C79C2311yescharacteristic
157C22×Q8×C79C2311yescharacteristic
158C22×D4×C79—21no—
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C22×D4×C79C2311yescharacteristic
162C23×C4×C79—21no—
163C23×C4×C79—21no—
164C23×C4×C79C2311yescharacteristic
165#135×C79—216no—
166#135×C79—216no—
167C2×Q16×C79—24no—
168C2×Q16×C79C2314yes—
169C2×SD16×C79—24no—
170C2×SD16×C79—24no—
171C2×SD16×C79C2314yes—
172C2×SD16×C79C2314yes—
173C2×D8×C79—24no—
174C2×D8×C79C2314yes—
175C22×C8×C79—24no—
176C22×C8×C79C2311yescharacteristic
177C22×C8×C79C2311yescharacteristic
178C22×C8×C79C2312yes—
179C22×C8×C79C2312yes—
180C23×D79—21no—
181#11929624—24no—
182#11929624—24no—
183#11929624—24no—
184#11929624—24no—
185#11929624—44no—
186#11929624—44no—
187C2×Dic158—22no—
188C2×Dic158—21no—
189C2×Dic158—22no—
190C2×Dic158C2412yes—
191C2×D316—21no—
192C2×D316—22no—
193C2×D316—22no—
194C2×D316C2412yes—
195C2×C22⋊D79—22no—
196C2×C22⋊D79—22no—
197C2×C22⋊D79—28no—
198C2×C22⋊D79—44no—
199C22×Dic79—28no—
200C22×Dic79—21no—
201C22×Dic79—22no—
202C22×Dic79C2×D414yes—
203C2×C4×D79—22no—
204C2×C4×D79—22no—
205C2×C4×D79—44no—
206#11929614—28no—
207#11929612—28no—
208#11929611—28no—
209#11929609—28no—
210#11929608—24no—
211#11929608—24no—
212C2×C79⋊C8—24no—
213C2×C79⋊C8C2414yes—
214C4⋊Dic79—28no—
215C4⋊Dic79—22no—
216C4⋊Dic79C2×D414yes—
217C4⋊Dic79C2×D414yes—
218C4⋊Dic79C2414yes—
219Dic79⋊C4—28no—
220C22⋊Dic79—28no—
221C22⋊Dic79—28no—
222C22⋊Dic79—22no—
223C22⋊Dic79—22no—
224C22⋊Dic79C2×D414yes—
225C22⋊Dic79C2×D414yes—
226(C2×D79)⋊C4—28no—
227C4×Dic79—28no—
228C4×Dic79—22no—
229C4×Dic79—22no—
230C4×Dic79C2×D414yes—
231C4×Dic79C2414yes—
232C24×C79—21no—
233C24×C79—21no—
234C24×C79C2×D411yescharacteristic
235#41×C79—28no—
236#41×C79—28no—
237#41×C79—24no—
238#41×C79—24no—
239#41×C79—24no—
240#41×C79—24no—
241#41×C79—24no—
242#41×C79—24no—
243#41×C79—44no—
244#41×C79—44no—
245#41×C79C2×D418yes—
246#41×C79C2×D418yes—
247C2×Q8×C79—21no—
248C2×Q8×C79—21no—
249C2×Q8×C79—22no—
250C2×Q8×C79—22no—
251C2×Q8×C79—22no—
252C2×Q8×C79C2×D414yes—
253C2×Q8×C79C2412yes—
254C2×Q8×C79C2412yes—
255C2×D4×C79—28no—
256C2×D4×C79—22no—
257C2×D4×C79—22no—
258C2×D4×C79—22no—
259C2×D4×C79—22no—
260C2×D4×C79—21no—
261C2×D4×C79—22no—
262C2×D4×C79—21no—
263C2×D4×C79—22no—
264C2×D4×C79—22no—
265C2×D4×C79—44no—
266C2×D4×C79C2×D414yes—
267C2×D4×C79C2412yes—
268C2×D4×C79C2412yes—
269C22×C4×C79—21no—
270C22×C4×C79—28no—
271C22×C4×C79—22no—
272C22×C4×C79—22no—
273C22×C4×C79—21no—
274C22×C4×C79—22no—
275C22×C4×C79—22no—
276C22×C4×C79—44no—
277C22×C4×C79C2×D411yescharacteristic
278C22×C4×C79C2×D411yescharacteristic
279C22×C4×C79C2×D411yescharacteristic
280C22×C4×C79C2×D414yes—
281C22×C4×C79#4114yes—
282C22×C4×C79C2411yescharacteristic
283C22×C4×C79C2411yescharacteristic
284C22×C4×C79C2411yescharacteristic
285Q16×C79—28no—
286SD16×C79—28no—
287SD16×C79—28no—
288D8×C79—28no—
289C2×C8×C79—22no—
290C2×C8×C79—22no—
291C2×C8×C79—24no—
292C2×C8×C79—24no—
293C2×C8×C79C2412yes—
294C2×C8×C79C2412yes—
295C23×C79—22no—
296C23×C79—24no—
297C23×C79—22no—
298C23×C79—42no—
299C23×C79—42no—
300C23×C79—82no—
301C23×C79—82no—
302C23×C79#12114yes—
303C23×C79C22×D411yescharacteristic
304C23×C79C22×D411yescharacteristic
305C23×C79C22×D411yescharacteristic
306C22×D79—22no—
307C22×D79—42no—
308C22×D79—82no—
309Q8×C79—24no—
310Q8×C79—22no—
311Q8×C79—22no—
312Q8×C79—22no—
313Q8×C79—42no—
314Q8×C79C22×D414yes—
315D4×C79—28no—
316D4×C79—28no—
317D4×C79—24no—
318D4×C79—22no—
319D4×C79—22no—
320D4×C79—22no—
321D4×C79—44no—
322D4×C79—44no—
323D4×C79—42no—
324D4×C79C22×D414yes—
325C2×C4×C79—24no—
326C2×C4×C79—22no—
327C2×C4×C79—28no—
328C2×C4×C79—28no—
329C2×C4×C79—22no—
330C2×C4×C79—42no—
331C2×C4×C79—44no—
332C2×C4×C79—44no—
333C2×C4×C79#12114yes—
334C2×C4×C79#12114yes—
335C2×C4×C79#12114yes—
336C2×C4×C79C22×D411yescharacteristic
337C2×C4×C79C22×D411yescharacteristic
338C2×C4×C79C22×D411yescharacteristic
339C2×C4×C79C22×D412yes—
340C2×C4×C79C22×D412yes—
341C2×C4×C79C22×D412yes—
342C2×C4×C79C2×#4112yes—
343C2×C4×C79C2×#4112yes—
344C2×C4×C79C2×#4112yes—
345C2×C4×C79C2511yescharacteristic
346C22⋊D79—44no—
347C22⋊D79—44no—
348C22⋊D79—88no—
349C2×Dic79—24no—
350C2×Dic79—22no—
351C2×Dic79—44no—
352C2×Dic79—42no—
353C2×Dic79—88no—
354C2×Dic79—82no—
355C2×Dic79C22×D418yes—
356D316—22no—
357D316—22no—
358D316—42no—
359C4×D79—44no—
360C4×D79—44no—
361Dic158—22no—
362Dic158—22no—
363Dic158—42no—
364C8×C79—22no—
365C8×C79—22no—
366C79⋊C8—24no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—22no—
370C22×C79—24no—
371C22×C79—44no—
372C22×C79—44no—
373C22×C79—44no—
374C22×C79—42no—
375C22×C79—84no—
376C22×C79—84no—
377C22×C79C2×#12112yes—
378C22×C79C2×#12112yes—
379C22×C79C2×#12112yes—
380C22×C79C23×D411yescharacteristic
381C2×D79—44no—
382C2×D79—42no—
383C2×D79—84no—
384C4×C79—24no—
385C4×C79—42no—
386C4×C79C2×#12112yes—
387C4×C79C2×#12112yes—
388C4×C79C2×#12112yes—
389C4×C79C23×D411yescharacteristic
390C4×C79C22×#4111yescharacteristic
391Dic79—28no—
392Dic79—44no—
393Dic79—42no—
394#60422—791nomaximal, Sylow
395C2×C79—22no—
396C2×C79—22no—
397C2×C79—22no—
398C2×C79—44no—
399C2×C79—82no—
400C2×C79C22×#12111yescharacteristic
401C2×C79#358412yes—
402D79—82no—
403C2×#575—791no—
404C22×#135D7911yescharacteristic, complemented
405#3449—791no—
406#3428—791no—
407#3046—794no—
408#3045—794no—
409#3044—792no—
410#3043—792no—
411#3042—792no—
412#3041—792no—
413#3035—798no—
414C2×#424—791no—
415#2896—791no—
416C2×#416—791no—
417C79#6042211yescharacteristic, complemented, Sylow
418C22×#41—791no—
419C22×#41C2×D7911yescharacteristic
420C22×#41C2×D7911yescharacteristic
421#575—1588no—
422C2×#137—792no—
423C2×#137—792no—
424C2×AGL(1,ℤ/8)—792no—
425C2×AGL(1,ℤ/8)—792no—
426C2×#135—28no—
427C2×#135—794no—
428C2×#135C2×D7914yes—
429C2×#135C2×D7914yescomplemented
430C22×Q16C2×D7911yescharacteristic, complemented
431C22×SD16C2×D7911yescharacteristic, complemented
432C22×SD16C2×D7911yescharacteristic, complemented
433C22×D8C2×D7911yescharacteristic, complemented
434C22×M16—791no—
435C23×C8C2×D7911yescharacteristic
436#537—1582no—
437#536—792no—
438#536—792no—
439#535—792no—
440#535—792no—
441#534—1582no—
442#532—794no—
443#525—1582no—
444#525—1582no—
445#520—794no—
446#520—1582no—
447#519—792no—
448#518—792no—
449#518—1582no—
450C4×#41—794no—
451C4×#41—1582no—
452C2×#117—791no—
453C2×#117—791no—
454C2×#117—1582no—
455#464—798no—
456#464—798no—
457#463—798no—
458#463—798no—
459#462—798no—
460#461—798no—
461#460—798no—
462#459—798no—
463#424—792no—
464#424—792no—
465#424—794no—
466C2×C4⋊C8—794no—
467#419—792no—
468#418—792no—
469#417—794no—
470#416—794no—
471#416—792no—
472#416—792no—
473#416—794no—
474C2×#103—792no—
475C2×#102—792no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41—24no—
483C2×#41—792no—
484C2×#41—792no—
485C2×#41—1584no—
486C2×#41—1584no—
487C2×#41—1581no—
488C2×#41—1581no—
489C2×#41C22⋊D7918yescomplemented
490C2×#41C22×D7912yes—
491C2×#41C22×D7912yes—
492C2×#41C22×D7912yes—
493C2×#41C22×D7912yes—
494C22×Q8—791no—
495C22×Q8C22×D7911yescharacteristic
496C22×Q8C22×D7911yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—791no—
500C22×D4—1581no—
501C22×D4C22×D7911yescharacteristic
502C22×D4C22×D7911yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—1581no—
506C23×C4C22×D7911yescharacteristic
507#137—1588no—
508#137—1588no—
509AGL(1,ℤ/8)—1588no—
510AGL(1,ℤ/8)—1588no—
511#135—216no—
512#135—216no—
513#135—15816no—
514C2×Q16—24no—
515C2×Q16—794no—
516C2×Q16C22×D7914yes—
517C2×SD16—24no—
518C2×SD16—24no—
519C2×SD16—794no—
520C2×SD16—794no—
521C2×SD16C22×D7914yes—
522C2×SD16C22×D7914yes—
523C2×D8—24no—
524C2×D8—794no—
525C2×D8C22×D7914yes—
526C2×M16—792no—
527C2×M16—792no—
528C2×M16—1584no—
529C22×C8—24no—
530C22×C8—792no—
531C22×C8C22×D7911yescharacteristic
532C22×C8C22×D7911yescharacteristic
533C22×C8C22×D7912yes—
534C22×C8C22×D7912yes—
535C4⋊Q8—794no—
536#127—794no—
537#124—794no—
538#124—794no—
539#123—1584no—
540#123—1584no—
541C22⋊Q8—1584no—
542C22⋊Q8—1584no—
543#121—1584no—
544#121—1584no—
545#121—1588no—
546#120—1584no—
547#120—1584no—
548C4×Q8—798no—
549C4×Q8—1584no—
550C4×D4—798no—
551C4×D4—1588no—
552C4×D4—1588no—
553C4×D4—1584no—
554C4×D4—1588no—
555#117—792no—
556#117—792no—
557#117—792no—
558#117—792no—
559#117—792no—
560#117—792no—
561#117—1584no—
562#117—1584no—
563#117—1584no—
564#117—1581no—
565#117—1581no—
566C2×C4⋊C4—792no—
567C2×C4⋊C4—792no—
568C2×C4⋊C4—1584no—
569C2×C22⋊C4—792no—
570C2×C22⋊C4—1584no—
571C2×C22⋊C4—1581no—
572C2×C42—792no—
573C2×C42—1584no—
574C2×C42—1581no—
575C4⋊C8—798no—
576C4⋊C8—798no—
577#103—798no—
578#103—794no—
579#103—794no—
580#102—798no—
581#102—794no—
582#102—794no—
583C24—21no—
584C24—21no—
585C24—1581no—
586C24D4×D7911yescharacteristic
587#41—24no—
588#41—24no—
589#41—28no—
590#41—28no—
591#41—24no—
592#41—24no—
593#41—24no—
594#41—24no—
595#41—44no—
596#41—44no—
597#41—3164no—
598#41—3164no—
599#41—1584no—
600#41—1584no—
601#41—1584no—
602#41—1584no—
603#41C2×C22⋊D7918yes—
604#41C2×C22⋊D7918yes—
605C2×Q8—22no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—792no—
611C2×Q8—1582no—
612C2×Q8—1582no—
613C2×Q8—1581no—
614C2×Q8C2×C22⋊D7914yes—
615C2×Q8C23×D7912yes—
616C2×Q8C23×D7912yes—
617C2×D4—28no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—3164no—
629C2×D4—792no—
630C2×D4—1588no—
631C2×D4—1582no—
632C2×D4—1582no—
633C2×D4—1582no—
634C2×D4—1581no—
635C2×D4—1582no—
636C2×D4C2×C22⋊D7914yes—
637C2×D4C23×D7912yes—
638C2×D4C23×D7912yes—
639C22×C4—21no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—44no—
647C22×C4—3164no—
648C22×C4—794no—
649C22×C4—1581no—
650C22×C4—1582no—
651C22×C4—1582no—
652C22×C4—1588no—
653C22×C4—1582no—
654C22×C4D4×D7911yescharacteristic
655C22×C4D4×D7911yescharacteristic
656C22×C4D4×D7911yescharacteristic
657C22×C4C2×C22⋊D7914yes—
658C22×C4#1192962314yes—
659C22×C4C23×D7911yescharacteristic
660C22×C4C23×D7911yescharacteristic
661C22×C4C23×D7911yescharacteristic
662Q16—28no—
663Q16—1588no—
664SD16—28no—
665SD16—28no—
666SD16—1588no—
667SD16—1588no—
668D8—28no—
669D8—1588no—
670M16—1584no—
671M16—1584no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—24no—
675C2×C8—24no—
676C2×C8—794no—
677C2×C8—1584no—
678C2×C8C23×D7912yes—
679C2×C8C23×D7912yes—
680C4⋊C4—794no—
681C4⋊C4—794no—
682C4⋊C4—794no—
683C4⋊C4—1588no—
684C4⋊C4—1588no—
685C4⋊C4—1582no—
686C22⋊C4—794no—
687C22⋊C4—794no—
688C22⋊C4—1588no—
689C22⋊C4—1588no—
690C22⋊C4—1588no—
691C22⋊C4—1582no—
692C22⋊C4—1582no—
693C42—794no—
694C42—794no—
695C42—1588no—
696C42—1582no—
697C42—1582no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—82no—
704C23—82no—
705C23—3162no—
706C23—6322no—
707C23—1582no—
708C23#1457913314yes—
709C23C2×D4×D7911yescharacteristic
710C23C2×D4×D7911yescharacteristic
711C23C2×D4×D7911yescharacteristic
712Q8—24no—
713Q8—22no—
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—3162no—
718Q8—1582no—
719Q8—1582no—
720Q8C22×C22⋊D7914yes—
721D4—28no—
722D4—28no—
723D4—24no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—44no—
728D4—44no—
729D4—42no—
730D4—3164no—
731D4—3164no—
732D4—3162no—
733D4—6328no—
734D4—1582no—
735D4—1582no—
736D4C22×C22⋊D7914yes—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—3162no—
746C2×C4—3164no—
747C2×C4—3164no—
748C2×C4—3164no—
749C2×C4—798no—
750C2×C4—6322no—
751C2×C4—6328no—
752C2×C4—1584no—
753C2×C4—1582no—
754C2×C4#1457913314yes—
755C2×C4#1457913314yes—
756C2×C4#1457913314yes—
757C2×C4C2×D4×D7911yescharacteristic
758C2×C4C2×D4×D7911yescharacteristic
759C2×C4C2×D4×D7911yescharacteristic
760C2×C4C22×C22⋊D7912yes—
761C2×C4C22×C22⋊D7912yes—
762C2×C4C22×C22⋊D7912yes—
763C2×C4C2×#1192962312yes—
764C2×C4C2×#1192962312yes—
765C2×C4C2×#1192962312yes—
766C2×C4C24×D7911yescharacteristic
767C8—22no—
768C8—22no—
769C8—1584no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—24no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—44no—
778C22—84no—
779C22—84no—
780C22—3162no—
781C22—3164no—
782C22—6324no—
783C22C2×#1457913312yes—
784C22C2×#1457913312yes—
785C22C2×#1457913312yes—
786C22C22×D4×D7911yescharacteristic
787C4—24no—
788C4—42no—
789C4—3162no—
790C4—3164no—
791C4—1588no—
792C4C2×#1457913312yes—
793C4C2×#1457913312yes—
794C4C2×#1457913312yes—
795C4C23×C22⋊D7911yescharacteristic
796C4C22×#1192962311yescharacteristic
797C2—22no—
798C2—22no—
799C2—22no—
800C2—44no—
801C2—82no—
802C2—6322no—
803C2C22×#1457913311yescharacteristic
804C2#2377816912yes—
subgroupG/H
centerC2×C4C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#135×C79C2
socleC22×C79C23×D4
hypercenterC22×#135D79
hypocenterC79#60422
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C2×#19099361C2semidirect
2. #23776729C2semidirect
3. #23776603C2semidirect
4. #23772948C2semidirect
5. #23772937C2semidirect
6. #23772927C2semidirect
7. #23772918C2semidirect
8. #23772909C2semidirect
9. #23772900C2semidirect
10. #23772851C2semidirect
11. C2×#19098589C2semidirect
12. #23771919C2semidirect
13. C2×#19098560C2semidirect
14. C22×#135×C79C2semidirect
18. C2×#14579191C22semidirect
20. C2×#14579186C22semidirect
21. C2×#14579181C22semidirect
25. #19099134C22semidirect
27. #19099127C22semidirect
29. #19099109C22semidirect
33. #19099046C22semidirect
34. #19099041C22semidirect
36. #19099038C22semidirect
38. #41×Dic79C22semidirect
42. #19098787C22semidirect
43. #19098783C22semidirect
44. #19098780C22semidirect
45. #19098776C22semidirect
46. #19098771C22semidirect
47. #19098766C22semidirect
48. #19098761C22semidirect
49. #19098756C22semidirect
50. #19098589C22semidirect
51. #19098589C22semidirect
52. #19098589C22semidirect
53. C2×Dic79⋊C8C22semidirect
54. #19098572C22semidirect
55. #19098568C22semidirect
56. #19098564C22semidirect
59. #19098560C22semidirect
60. #19098559C22semidirect
61. C2×#14579086C22semidirect
62. C2×#14579083C22semidirect
67. C2×#135×C79C22semidirect
68. C22×Q16×C79C22semidirect
69. C22×SD16×C79C22semidirect
70. C22×SD16×C79C22semidirect
71. C22×D8×C79C22semidirect
151. C2×#41×C79D4semidirect
404. C22×#135D79semidirect
417. C79#60422semidirect
429. C2×#135C2×D79semidirect
430. C22×Q16C2×D79semidirect
431. C22×SD16C2×D79semidirect
432. C22×SD16C2×D79semidirect
433. C22×D8C2×D79semidirect
489. C2×#41C22⋊D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993612
#237767292
#237766032
#237729482
#237729372
#237729272
#237729182
#237729092
#237729002
#237728512
C2×#190985892
#237719192
C2×#190985602
C22×#135×C792
#6042279