Finite Group Databasebeta

← #35155691

Subgroups — #35155691

Order 20224.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099361C211yesmaximal, characteristic, complemented
2C2×#19099361C211yesmaximal, characteristic, complemented
3C2×#19099330C211yesmaximal, characteristic, complemented
4#23773139C214yesmaximal, complemented
5#23773134C214yesmaximal, complemented
6#23773130C214yesmaximal, complemented
7#23773125C214yesmaximal, complemented
8#23773117C218yesmaximal, complemented
9C2×#19098611C211yesmaximal, characteristic, complemented
10C2×#19098547C211yesmaximal, characteristic, complemented
11C2×#19098545C211yesmaximal, characteristic, complemented
12C2×#575×C79C211yesmaximal, characteristic, complemented
13C22×#11929624C2211yescharacteristic
14#19099361—22no—
15#19099361—22no—
16#19099361—22no—
17#19099361—22no—
18#19099361—22no—
19#19099361—22no—
20#19099361C2214yes—
21#19099361C2214yescomplemented
22C2×#14579192—21no—
23C2×#14579192C2212yescomplemented
24C2×#14579191C2212yescomplemented
25C2×#14579191C2212yescomplemented
26C2×#14579187—21no—
27C2×#14579187C2212yescomplemented
28C2×#14579186C2212yescomplemented
29C2×#14579186C2212yescomplemented
30C2×#14579181—22no—
31C2×#14579181C2214yescomplemented
32#19099330—22no—
33#19099330—22no—
34#19099330C2214yescomplemented
35#19099330C2214yescomplemented
36C2×#14579168—22no—
37C2×#14579168C2214yescomplemented
38C22×#11929608—22no—
39C22×#11929608C2211yescharacteristic
40C22×#11929608C2211yescharacteristic
41C22×#11929608C2211yescharacteristic
42#19098836C22116yescomplemented
43#19098831C22116yescomplemented
44#19098828C22116yescomplemented
45#19098824C22116yescomplemented
46#19098611C2214yescomplemented
47#19098611C2214yescomplemented
48C2×#14579096C2214yescomplemented
49#19098547C2214yescomplemented
50#19098547C2214yescomplemented
51#19098545C2214yescomplemented
52#19098545C2214yescomplemented
53C2×#14579080C2212yescomplemented
54C2×#14579079C2212yescomplemented
55C2×#14579078C2212yescomplemented
56C2×#14579077C2212yescomplemented
57C22×#41×C79C2211yescharacteristic
58C22×#41×C79C2211yescharacteristic
59#575×C79—22no—
60#575×C79—22no—
61#575×C79C2214yes—
62#575×C79C2214yescomplemented
63C2×#137×C79—21no—
64C2×#137×C79C2212yescomplemented
65C2×AGL(1,ℤ/8)×C79—21no—
66C2×AGL(1,ℤ/8)×C79C2212yescomplemented
67C2×#135×C79—22no—
68C22×M16×C79C2211yescharacteristic
69C2×#11929624—21no—
70C2×#11929624—21no—
71C2×#11929624—21no—
72C2×#11929624—21no—
73C2×#11929624—21no—
74C2×#11929624—21no—
75C2×#11929624—21no—
76C2×#11929624—21no—
77C2×#11929624—21no—
78C2×#11929624—21no—
79C2×#11929624C2312yes—
80C2×#11929624C2312yes—
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C4×D79—21no—
85#14579192—24no—
86#14579192—24no—
87#14579192—24no—
88#14579192—24no—
89#14579191—24no—
90#14579191—24no—
91#14579191—24no—
92#14579191C2318yes—
93#14579187—24no—
94#14579187—24no—
95#14579187—24no—
96#14579187—24no—
97#14579186—24no—
98#14579186—24no—
99#14579186—24no—
100#14579186C2318yes—
101#14579181—28no—
102#14579181—28no—
103#14579181—28no—
104#14579181—28no—
105C2×#11929614—22no—
106C2×#11929614C2314yescomplemented
107C2×#11929612—22no—
108C2×#11929612C2314yescomplemented
109C2×#11929611—22no—
110C2×#11929611C2314yescomplemented
111C2×#11929609—22no—
112C2×#11929609C2314yescomplemented
113#14579168—28no—
114#14579168—28no—
115#14579168—28no—
116#14579168C23116yes—
117C2×#11929608—21no—
118C2×#11929608—21no—
119C2×#11929608—21no—
120C2×#11929608—21no—
121C2×#11929608—21no—
122C2×#11929608—21no—
123C2×#11929608—28no—
124C2×#11929608—28no—
125C2×#11929608—24no—
126C2×#11929608D412yes—
127C2×#11929608D412yes—
128C2×#11929608D412yes—
129C2×#11929608D412yes—
130C2×#11929608C2312yes—
131C2×#11929608C2312yes—
132C2×#11929608C2312yes—
133C2×#11929608C2312yes—
134C2×#11929608C2312yes—
135C2×#11929608C2312yes—
136C2×#11929608C2312yes—
137C2×#11929608C2312yes—
138C22×C79⋊C8—21no—
139C22×C79⋊C8—21no—
140C22×C79⋊C8—24no—
141C22×C79⋊C8C2312yes—
142#14579096C23116yescomplemented
143#14579080C2318yescomplemented
144#14579079C2318yescomplemented
145#14579078C2318yescomplemented
146#14579077C2318yescomplemented
147C2×#41×C79—21no—
148C2×#41×C79—21no—
149C2×#41×C79—21no—
150C2×#41×C79—21no—
151C2×#41×C79—21no—
152C2×#41×C79—21no—
153C2×#41×C79—21no—
154C2×#41×C79—21no—
155C2×#41×C79—21no—
156C2×#41×C79—21no—
157C2×#41×C79—21no—
158C2×#41×C79—21no—
159C2×#41×C79—21no—
160C2×#41×C79—21no—
161C2×#41×C79—21no—
162C2×#41×C79—21no—
163C2×#41×C79D412yes—
164C2×#41×C79D412yes—
165C2×#41×C79D412yes—
166C2×#41×C79C2312yes—
167C2×#41×C79C2312yes—
168C2×#41×C79C2312yes—
169C2×#41×C79C2312yes—
170C2×#41×C79C2312yes—
171C22×Q8×C79D411yescharacteristic
172C22×Q8×C79C2311yescharacteristic
173C22×D4×C79—21no—
174C22×D4×C79—21no—
175C22×D4×C79D411yescharacteristic
176C22×D4×C79C2311yescharacteristic
177C23×C4×C79—21no—
178C23×C4×C79—21no—
179C23×C4×C79C2311yescharacteristic
180#137×C79—24no—
181#137×C79—24no—
182#137×C79—24no—
183#137×C79C2318yes—
184AGL(1,ℤ/8)×C79—24no—
185AGL(1,ℤ/8)×C79—24no—
186AGL(1,ℤ/8)×C79—24no—
187AGL(1,ℤ/8)×C79C2318yes—
188#135×C79—28no—
189#135×C79—28no—
190C2×Q16×C79—22no—
191C2×SD16×C79—22no—
192C2×SD16×C79—22no—
193C2×D8×C79—22no—
194C2×M16×C79—21no—
195C2×M16×C79—21no—
196C2×M16×C79—21no—
197C2×M16×C79C2312yes—
198C2×M16×C79C2312yes—
199C2×M16×C79C2312yes—
200C22×C8×C79—21no—
201C23×D79—21no—
202#11929624—22no—
203#11929624—22no—
204#11929624—22no—
205#11929624—22no—
206#11929624—22no—
207#11929624—22no—
208#11929624—22no—
209#11929624—22no—
210#11929624—41no—
211#11929624—41no—
212#11929624—41no—
213#11929624—41no—
214#11929624—41no—
215#11929624—41no—
216#11929624—41no—
217#11929624—41no—
218C2×Dic158—21no—
219C2×Dic158—21no—
220C2×Dic158—21no—
221C2×Dic158—21no—
222C2×Dic158—21no—
223C2×Dic158C2412yes—
224C2×D316—21no—
225C2×D316—21no—
226C2×D316—21no—
227C2×D316—21no—
228C2×D316—21no—
229C2×D316C2412yes—
230C2×C22⋊D79—22no—
231C2×C22⋊D79—22no—
232C2×C22⋊D79—41no—
233C2×C22⋊D79—41no—
234C2×C22⋊D79—41no—
235C2×C22⋊D79—41no—
236C22×Dic79—21no—
237C2×C4×D79—22no—
238C2×C4×D79—22no—
239C2×C4×D79—41no—
240C2×C4×D79—41no—
241C2×C4×D79—41no—
242C2×C4×D79—41no—
243#11929614—28no—
244#11929614—28no—
245#11929612—28no—
246#11929612—28no—
247#11929611—28no—
248#11929611—28no—
249#11929609—28no—
250#11929609—28no—
251#11929608—216no—
252#11929608—22no—
253#11929608—22no—
254#11929608—22no—
255#11929608—22no—
256#11929608—22no—
257#11929608—22no—
258#11929608C2×D414yes—
259#11929608C2×D414yes—
260#11929608C2×D414yes—
261#11929608C2×D414yes—
262#11929608C2414yes—
263#11929608C2414yes—
264C2×C79⋊C8—216no—
265C2×C79⋊C8—22no—
266C2×C79⋊C8—22no—
267C2×C79⋊C8—22no—
268C2×C79⋊C8—22no—
269C2×C79⋊C8—22no—
270C2×C79⋊C8—22no—
271C2×C79⋊C8C2×D414yes—
272C2×C79⋊C8C2×D414yes—
273C2×C79⋊C8C2414yes—
274C24×C79—21no—
275C24×C79—21no—
276C24×C79#4111yescharacteristic
277#41×C79—22no—
278#41×C79—22no—
279#41×C79—22no—
280#41×C79—22no—
281#41×C79—22no—
282#41×C79—22no—
283#41×C79—22no—
284#41×C79—22no—
285#41×C79—22no—
286#41×C79—22no—
287#41×C79—22no—
288#41×C79—22no—
289#41×C79—22no—
290#41×C79—22no—
291#41×C79—22no—
292#41×C79—22no—
293#41×C79—22no—
294#41×C79—22no—
295#41×C79—22no—
296#41×C79—22no—
297#41×C79—41no—
298#41×C79—41no—
299#41×C79—41no—
300#41×C79—41no—
301#41×C79—41no—
302#41×C79—41no—
303#41×C79—41no—
304#41×C79—41no—
305#41×C79C2×D414yes—
306#41×C79C2×D414yes—
307#41×C79C2×D414yes—
308#41×C79C2414yes—
309C2×Q8×C79—21no—
310C2×Q8×C79—21no—
311C2×Q8×C79—21no—
312C2×Q8×C79—21no—
313C2×Q8×C79—21no—
314C2×Q8×C79—21no—
315C2×Q8×C79—21no—
316C2×Q8×C79—21no—
317C2×Q8×C79C2×D412yes—
318C2×Q8×C79C2×D412yes—
319C2×Q8×C79C2×D412yes—
320C2×Q8×C79C2412yes—
321C2×D4×C79—22no—
322C2×D4×C79—22no—
323C2×D4×C79—22no—
324C2×D4×C79—22no—
325C2×D4×C79—22no—
326C2×D4×C79—22no—
327C2×D4×C79—22no—
328C2×D4×C79—22no—
329C2×D4×C79—21no—
330C2×D4×C79—21no—
331C2×D4×C79—21no—
332C2×D4×C79—21no—
333C2×D4×C79—21no—
334C2×D4×C79—21no—
335C2×D4×C79—21no—
336C2×D4×C79—21no—
337C2×D4×C79—41no—
338C2×D4×C79—41no—
339C2×D4×C79—41no—
340C2×D4×C79—41no—
341C2×D4×C79C2×D412yes—
342C2×D4×C79C2×D412yes—
343C2×D4×C79C2×D412yes—
344C2×D4×C79C2412yes—
345C22×C4×C79—21no—
346C22×C4×C79—22no—
347C22×C4×C79—22no—
348C22×C4×C79—22no—
349C22×C4×C79—22no—
350C22×C4×C79—22no—
351C22×C4×C79—22no—
352C22×C4×C79—21no—
353C22×C4×C79—22no—
354C22×C4×C79—22no—
355C22×C4×C79—41no—
356C22×C4×C79—41no—
357C22×C4×C79—41no—
358C22×C4×C79—41no—
359C22×C4×C79C2×D411yescharacteristic
360C22×C4×C79C2×D411yescharacteristic
361C22×C4×C79C2×D411yescharacteristic
362C22×C4×C79C2×D411yescharacteristic
363C22×C4×C79C2×D411yescharacteristic
364C22×C4×C79C2×D411yescharacteristic
365C22×C4×C79C2×D411yescharacteristic
366C22×C4×C79C2×D411yescharacteristic
367C22×C4×C79#4111yescharacteristic
368C22×C4×C79#4111yescharacteristic
369C22×C4×C79#4111yescharacteristic
370C22×C4×C79C2411yescharacteristic
371C22×C4×C79C2411yescharacteristic
372C22×C4×C79C2411yescharacteristic
373Q16×C79—28no—
374SD16×C79—28no—
375SD16×C79—28no—
376D8×C79—28no—
377M16×C79—22no—
378M16×C79—22no—
379M16×C79—22no—
380M16×C79C2414yes—
381C2×C8×C79—22no—
382C2×C8×C79—22no—
383C2×C8×C79—22no—
384C23×C79—22no—
385C23×C79—22no—
386C23×C79—22no—
387C23×C79—22no—
388C23×C79—41no—
389C23×C79—41no—
390C23×C79—81no—
391C23×C79—82no—
392C23×C79—82no—
393C23×C79#12111yescharacteristic
394C23×C79#12111yescharacteristic
395C23×C79#12111yescharacteristic
396C23×C79#12111yescharacteristic
397C23×C79C2×#4111yescharacteristic
398C23×C79C2×#4111yescharacteristic
399C23×C79C2×#4111yescharacteristic
400C22×D79—22no—
401C22×D79—41no—
402C22×D79—41no—
403C22×D79—82no—
404Q8×C79—22no—
405Q8×C79—22no—
406Q8×C79—22no—
407Q8×C79—22no—
408Q8×C79—22no—
409Q8×C79—41no—
410Q8×C79—41no—
411Q8×C79C22×D414yes—
412D4×C79—24no—
413D4×C79—24no—
414D4×C79—24no—
415D4×C79—24no—
416D4×C79—22no—
417D4×C79—22no—
418D4×C79—22no—
419D4×C79—22no—
420D4×C79—22no—
421D4×C79—42no—
422D4×C79—42no—
423D4×C79—42no—
424D4×C79—42no—
425D4×C79—41no—
426D4×C79—41no—
427D4×C79C22×D414yes—
428C2×C4×C79—22no—
429C2×C4×C79—22no—
430C2×C4×C79—22no—
431C2×C4×C79—24no—
432C2×C4×C79—24no—
433C2×C4×C79—24no—
434C2×C4×C79—24no—
435C2×C4×C79—22no—
436C2×C4×C79—41no—
437C2×C4×C79—41no—
438C2×C4×C79—42no—
439C2×C4×C79—42no—
440C2×C4×C79—42no—
441C2×C4×C79—42no—
442C2×C4×C79#12111yescharacteristic
443C2×C4×C79#12111yescharacteristic
444C2×C4×C79#12111yescharacteristic
445C2×C4×C79#12111yescharacteristic
446C2×C4×C79#12111yescharacteristic
447C2×C4×C79#12111yescharacteristic
448C2×C4×C79#12111yescharacteristic
449C2×C4×C79#12111yescharacteristic
450C2×C4×C79#12111yescharacteristic
451C2×C4×C79#12111yescharacteristic
452C2×C4×C79#12111yescharacteristic
453C2×C4×C79#12111yescharacteristic
454C2×C4×C79C22×D411yescharacteristic
455C2×C4×C79C22×D411yescharacteristic
456C2×C4×C79C22×D411yescharacteristic
457C2×C4×C79C22×D411yescharacteristic
458C2×C4×C79C22×D411yescharacteristic
459C2×C4×C79C22×D411yescharacteristic
460C2×C4×C79C22×D411yescharacteristic
461C2×C4×C79C22×D411yescharacteristic
462C2×C4×C79C22×D411yescharacteristic
463C2×C4×C79C22×D411yescharacteristic
464C2×C4×C79C22×D411yescharacteristic
465C2×C4×C79C22×D411yescharacteristic
466C2×C4×C79C2×#4111yescharacteristic
467C2×C4×C79C2×#4111yescharacteristic
468C2×C4×C79C2×#4111yescharacteristic
469C2×C4×C79C2511yescharacteristic
470C22⋊D79—42no—
471C22⋊D79—42no—
472C22⋊D79—42no—
473C22⋊D79—42no—
474C2×Dic79—22no—
475C2×Dic79—41no—
476C2×Dic79—41no—
477D316—22no—
478D316—22no—
479D316—41no—
480D316—41no—
481C4×D79—42no—
482C4×D79—42no—
483C4×D79—42no—
484C4×D79—42no—
485Dic158—22no—
486Dic158—22no—
487Dic158—41no—
488Dic158—41no—
489C8×C79—24no—
490C79⋊C8—24no—
491C79⋊C8—24no—
492C79⋊C8C22×D418yes—
493C22×C79—24no—
494C22×C79—41no—
495C22×C79—41no—
496C22×C79—41no—
497C22×C79—41no—
498C22×C79—41no—
499C22×C79—41no—
500C22×C79—41no—
501C22×C79—44no—
502C22×C79—42no—
503C22×C79—82no—
504C22×C79—82no—
505C22×C79—82no—
506C22×C79—82no—
507C22×C79—82no—
508C22×C79C2×#12111yescharacteristic
509C22×C79C2×#12111yescharacteristic
510C22×C79C2×#12111yescharacteristic
511C22×C79C2×#12111yescharacteristic
512C22×C79C2×#12111yescharacteristic
513C22×C79C2×#12111yescharacteristic
514C22×C79C22×#4111yescharacteristic
515C2×D79—42no—
516C2×D79—82no—
517C2×D79—82no—
518C2×D79—82no—
519C4×C79—24no—
520C4×C79—42no—
521C4×C79C2×#12111yescharacteristic
522C4×C79C2×#12111yescharacteristic
523C4×C79C2×#12111yescharacteristic
524C4×C79C2×#12111yescharacteristic
525C4×C79C2×#12111yescharacteristic
526C4×C79C2×#12111yescharacteristic
527C4×C79C23×D411yescharacteristic
528C4×C79C23×D411yescharacteristic
529Dic79—42no—
530#60469—791nomaximal, Sylow
531C2×C79—21no—
532C2×C79—21no—
533C2×C79—21no—
534C2×C79—21no—
535C2×C79—21no—
536C2×C79—21no—
537C2×C79—21no—
538C2×C79—44no—
539C2×C79—82no—
540C2×C79C22×#12111yescharacteristic
541D79—82no—
542C2×#575—791no—
543C2×#575—791no—
544C2×#575D7911yescharacteristic, complemented
545C2×#568—791no—
546#3069—794no—
547#3069—794no—
548#3068—794no—
549#3068—794no—
550#3067—798no—
551C2×#430—791no—
552C2×#413—791no—
553C2×#413—791no—
554C79#6046911yescharacteristic, complemented, Sylow
555C22×#41—791no—
556C22×#41C2×D7911yescharacteristic
557C22×#41C2×D7911yescharacteristic
558#575—22no—
559#575—22no—
560#575—794no—
561#575—794no—
562#575—1582no—
563#575—1582no—
564#575—1582no—
565#575—1582no—
566#575—1582no—
567#575—1582no—
568#575C2×D7914yes—
569#575C2×D7914yescomplemented
570C2×#137—21no—
571C2×#137—792no—
572C2×#137—792no—
573C2×#137—792no—
574C2×#137—1581no—
575C2×#137C2×D7912yescomplemented
576C2×AGL(1,ℤ/8)—21no—
577C2×AGL(1,ℤ/8)—792no—
578C2×AGL(1,ℤ/8)—792no—
579C2×AGL(1,ℤ/8)—792no—
580C2×AGL(1,ℤ/8)—1581no—
581C2×AGL(1,ℤ/8)C2×D7912yescomplemented
582C2×#135—22no—
583C2×#135—794no—
584C2×#135—1582no—
585#568—794no—
586#568—794no—
587#568—1582no—
588#568—1582no—
589C2×#131—794no—
590C2×#131—1582no—
591C22×M16—791no—
592C22×M16—791no—
593C22×M16—791no—
594C22×M16—1582no—
595C22×M16C2×D7911yescharacteristic
596#473—7916no—
597#472—7916no—
598#471—7916no—
599#471—7916no—
600#430—794no—
601#430—794no—
602C2×#108—794no—
603#413—794no—
604#413—794no—
605#413—794no—
606#413—794no—
607C2×#101—792no—
608C2×#101—792no—
609C2×#100—792no—
610C2×#100—792no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—21no—
619C2×#41—21no—
620C2×#41—21no—
621C2×#41—21no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—21no—
627C2×#41—792no—
628C2×#41—792no—
629C2×#41—1581no—
630C2×#41—1581no—
631C2×#41—1581no—
632C2×#41—1581no—
633C2×#41—1581no—
634C2×#41—1581no—
635C2×#41—1581no—
636C2×#41—1581no—
637C2×#41—1581no—
638C2×#41—1581no—
639C2×#41C22⋊D7912yes—
640C2×#41C22⋊D7912yes—
641C2×#41C22⋊D7912yes—
642C2×#41C22×D7912yes—
643C2×#41C22×D7912yes—
644C2×#41C22×D7912yes—
645C2×#41C22×D7912yes—
646C2×#41C22×D7912yes—
647C22×Q8—791no—
648C22×Q8C22⋊D7911yescharacteristic
649C22×Q8C22×D7911yescharacteristic
650C22×D4—21no—
651C22×D4—21no—
652C22×D4—791no—
653C22×D4—1581no—
654C22×D4C22⋊D7911yescharacteristic
655C22×D4C22×D7911yescharacteristic
656C23×C4—21no—
657C23×C4—21no—
658C23×C4—1581no—
659C23×C4C22×D7911yescharacteristic
660#137—24no—
661#137—24no—
662#137—24no—
663#137—798no—
664#137—1584no—
665#137—1584no—
666#137—1584no—
667#137—1584no—
668#137—1584no—
669#137—1584no—
670#137—1584no—
671#137C22×D7918yes—
672AGL(1,ℤ/8)—24no—
673AGL(1,ℤ/8)—24no—
674AGL(1,ℤ/8)—24no—
675AGL(1,ℤ/8)—798no—
676AGL(1,ℤ/8)—1584no—
677AGL(1,ℤ/8)—1584no—
678AGL(1,ℤ/8)—1584no—
679AGL(1,ℤ/8)—1584no—
680AGL(1,ℤ/8)—1584no—
681AGL(1,ℤ/8)—1584no—
682AGL(1,ℤ/8)—1584no—
683AGL(1,ℤ/8)C22×D7918yes—
684#135—28no—
685#135—28no—
686#135—1588no—
687#135—1588no—
688#135—1588no—
689#135—1588no—
690C2×Q16—22no—
691C2×Q16—794no—
692C2×Q16—1582no—
693C2×SD16—22no—
694C2×SD16—22no—
695C2×SD16—794no—
696C2×SD16—794no—
697C2×SD16—1582no—
698C2×SD16—1582no—
699C2×D8—22no—
700C2×D8—794no—
701C2×D8—1582no—
702#131—7916no—
703#131—1588no—
704#131—1588no—
705#131—1588no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—792no—
710C2×M16—792no—
711C2×M16—792no—
712C2×M16—792no—
713C2×M16—792no—
714C2×M16—792no—
715C2×M16—792no—
716C2×M16—792no—
717C2×M16—792no—
718C2×M16—792no—
719C2×M16—792no—
720C2×M16—792no—
721C2×M16—1584no—
722C2×M16—1588no—
723C2×M16—1588no—
724C2×M16—1581no—
725C2×M16—1581no—
726C2×M16—1581no—
727C2×M16—1581no—
728C2×M16—1581no—
729C2×M16—1581no—
730C2×M16C22×D7912yes—
731C2×M16C22×D7912yes—
732C2×M16C22×D7912yes—
733C22×C8—21no—
734C22×C8—792no—
735C22×C8—1584no—
736C22×C8—1581no—
737C22×C8—1581no—
738#108—7916no—
739#101—798no—
740#101—798no—
741#100—798no—
742#100—798no—
743C24—21no—
744C24—21no—
745C24—1581no—
746C24#1192962311yescharacteristic
747#41—22no—
748#41—22no—
749#41—22no—
750#41—22no—
751#41—22no—
752#41—22no—
753#41—22no—
754#41—22no—
755#41—22no—
756#41—22no—
757#41—22no—
758#41—22no—
759#41—22no—
760#41—22no—
761#41—22no—
762#41—22no—
763#41—22no—
764#41—22no—
765#41—22no—
766#41—22no—
767#41—41no—
768#41—41no—
769#41—41no—
770#41—41no—
771#41—41no—
772#41—41no—
773#41—41no—
774#41—41no—
775#41—3161no—
776#41—3161no—
777#41—3161no—
778#41—3161no—
779#41—3161no—
780#41—3161no—
781#41—3161no—
782#41—3161no—
783#41—1582no—
784#41—1582no—
785#41—1582no—
786#41—1582no—
787#41—1582no—
788#41—1582no—
789#41—1582no—
790#41—1582no—
791#41C2×C22⋊D7914yes—
792#41C2×C22⋊D7914yes—
793#41C2×C22⋊D7914yes—
794#41C23×D7914yes—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—792no—
804C2×Q8—1581no—
805C2×Q8—1581no—
806C2×Q8—1581no—
807C2×Q8—1581no—
808C2×Q8—1581no—
809C2×Q8C2×C22⋊D7912yes—
810C2×Q8C2×C22⋊D7912yes—
811C2×Q8C2×C22⋊D7912yes—
812C2×Q8C23×D7912yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—3161no—
834C2×D4—3161no—
835C2×D4—3161no—
836C2×D4—3161no—
837C2×D4—792no—
838C2×D4—1582no—
839C2×D4—1582no—
840C2×D4—1581no—
841C2×D4—1581no—
842C2×D4—1581no—
843C2×D4—1581no—
844C2×D4—1581no—
845C2×D4C2×C22⋊D7912yes—
846C2×D4C2×C22⋊D7912yes—
847C2×D4C2×C22⋊D7912yes—
848C2×D4C23×D7912yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—3161no—
864C22×C4—3161no—
865C22×C4—3161no—
866C22×C4—3161no—
867C22×C4—1581no—
868C22×C4—1582no—
869C22×C4—1582no—
870C22×C4D4×D7911yescharacteristic
871C22×C4D4×D7911yescharacteristic
872C22×C4D4×D7911yescharacteristic
873C22×C4D4×D7911yescharacteristic
874C22×C4C2×C22⋊D7911yescharacteristic
875C22×C4C2×C22⋊D7911yescharacteristic
876C22×C4C2×C22⋊D7911yescharacteristic
877C22×C4C2×C22⋊D7911yescharacteristic
878C22×C4#1192962311yescharacteristic
879C22×C4#1192962311yescharacteristic
880C22×C4#1192962311yescharacteristic
881C22×C4C23×D7911yescharacteristic
882C22×C4C23×D7911yescharacteristic
883C22×C4C23×D7911yescharacteristic
884Q16—28no—
885Q16—1588no—
886Q16—1588no—
887SD16—28no—
888SD16—28no—
889SD16—1588no—
890SD16—1588no—
891SD16—1588no—
892SD16—1588no—
893D8—28no—
894D8—1588no—
895D8—1588no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—794no—
900M16—794no—
901M16—794no—
902M16—794no—
903M16—794no—
904M16—794no—
905M16—15816no—
906M16—1582no—
907M16—1582no—
908M16—1582no—
909M16—1582no—
910M16—1582no—
911M16—1582no—
912M16C23×D7914yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—794no—
917C2×C8—794no—
918C2×C8—794no—
919C2×C8—15816no—
920C2×C8—1582no—
921C2×C8—1582no—
922C2×C8—1582no—
923C2×C8—1582no—
924C2×C8—1582no—
925C2×C8—1582no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23—3161no—
936C23—3161no—
937C23—6322no—
938C23—1582no—
939C23#1457913311yescharacteristic
940C23#1457913311yescharacteristic
941C23#1457913311yescharacteristic
942C23#1457913311yescharacteristic
943C23C2×#1192962311yescharacteristic
944C23C2×#1192962311yescharacteristic
945C23C2×#1192962311yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—22no—
951Q8—41no—
952Q8—41no—
953Q8—3161no—
954Q8—3161no—
955Q8—1582no—
956Q8—1582no—
957Q8C22×C22⋊D7914yes—
958D4—24no—
959D4—24no—
960D4—24no—
961D4—24no—
962D4—22no—
963D4—22no—
964D4—22no—
965D4—22no—
966D4—22no—
967D4—42no—
968D4—42no—
969D4—42no—
970D4—42no—
971D4—41no—
972D4—41no—
973D4—3162no—
974D4—3162no—
975D4—3162no—
976D4—3162no—
977D4—3161no—
978D4—3161no—
979D4—1582no—
980D4—1582no—
981D4C22×C22⋊D7914yes—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—3161no—
997C2×C4—3161no—
998C2×C4—3162no—
999C2×C4—3162no—
1000C2×C4—3162no—
1001C2×C4—3162no—
1002C2×C4—1582no—
1003C2×C4#1457913311yescharacteristic
1004C2×C4#1457913311yescharacteristic
1005C2×C4#1457913311yescharacteristic
1006C2×C4#1457913311yescharacteristic
1007C2×C4#1457913311yescharacteristic
1008C2×C4#1457913311yescharacteristic
1009C2×C4#1457913311yescharacteristic
1010C2×C4#1457913311yescharacteristic
1011C2×C4#1457913311yescharacteristic
1012C2×C4#1457913311yescharacteristic
1013C2×C4#1457913311yescharacteristic
1014C2×C4#1457913311yescharacteristic
1015C2×C4C2×D4×D7911yescharacteristic
1016C2×C4C2×D4×D7911yescharacteristic
1017C2×C4C2×D4×D7911yescharacteristic
1018C2×C4C2×D4×D7911yescharacteristic
1019C2×C4C2×D4×D7911yescharacteristic
1020C2×C4C2×D4×D7911yescharacteristic
1021C2×C4C22×C22⋊D7911yescharacteristic
1022C2×C4C22×C22⋊D7911yescharacteristic
1023C2×C4C22×C22⋊D7911yescharacteristic
1024C2×C4C22×C22⋊D7911yescharacteristic
1025C2×C4C22×C22⋊D7911yescharacteristic
1026C2×C4C22×C22⋊D7911yescharacteristic
1027C2×C4C2×#1192962311yescharacteristic
1028C2×C4C2×#1192962311yescharacteristic
1029C2×C4C2×#1192962311yescharacteristic
1030C2×C4C24×D7911yescharacteristic
1031C8—24no—
1032C8—798no—
1033C8—1584no—
1034C8—1584no—
1035C22—24no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—44no—
1044C22—42no—
1045C22—82no—
1046C22—82no—
1047C22—82no—
1048C22—82no—
1049C22—82no—
1050C22—3162no—
1051C22—6322no—
1052C22—6322no—
1053C22—6322no—
1054C22C2×#1457913311yescharacteristic
1055C22C2×#1457913311yescharacteristic
1056C22C2×#1457913311yescharacteristic
1057C22C2×#1457913311yescharacteristic
1058C22C2×#1457913311yescharacteristic
1059C22C2×#1457913311yescharacteristic
1060C22C22×#1192962311yescharacteristic
1061C4—24no—
1062C4—42no—
1063C4—3162no—
1064C4C2×#1457913311yescharacteristic
1065C4C2×#1457913311yescharacteristic
1066C4C2×#1457913311yescharacteristic
1067C4C2×#1457913311yescharacteristic
1068C4C2×#1457913311yescharacteristic
1069C4C2×#1457913311yescharacteristic
1070C4C22×D4×D7911yescharacteristic
1071C4C23×C22⋊D7911yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—44no—
1080C2—82no—
1081C2—6322no—
1082C2C22×#1457913311yescharacteristic
subgroupG/H
centerC4C2×#14579133
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#575×C79C2
socleC2×C79C22×#121
hypercenterC2×#575D79
hypocenterC79#60469
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#19099361C2semidirect
2. C2×#19099361C2semidirect
3. C2×#19099330C2semidirect
4. #23773139C2semidirect
5. #23773134C2semidirect
6. #23773130C2semidirect
7. #23773125C2semidirect
8. #23773117C2semidirect
9. C2×#19098611C2semidirect
10. C2×#19098547C2semidirect
11. C2×#19098545C2semidirect
12. C2×#575×C79C2semidirect
21. #19099361C22semidirect
23. C2×#14579192C22semidirect
24. C2×#14579191C22semidirect
25. C2×#14579191C22semidirect
27. C2×#14579187C22semidirect
28. C2×#14579186C22semidirect
29. C2×#14579186C22semidirect
31. C2×#14579181C22semidirect
34. #19099330C22semidirect
35. #19099330C22semidirect
37. C2×#14579168C22semidirect
42. #19098836C22semidirect
43. #19098831C22semidirect
44. #19098828C22semidirect
45. #19098824C22semidirect
46. #19098611C22semidirect
47. #19098611C22semidirect
48. C2×#14579096C22semidirect
49. #19098547C22semidirect
50. #19098547C22semidirect
51. #19098545C22semidirect
52. #19098545C22semidirect
53. C2×#14579080C22semidirect
54. C2×#14579079C22semidirect
55. C2×#14579078C22semidirect
56. C2×#14579077C22semidirect
62. #575×C79C22semidirect
64. C2×#137×C79C22semidirect
66. C2×AGL(1,ℤ/8)×C79C22semidirect
106. C2×#11929614C23semidirect
108. C2×#11929612C23semidirect
110. C2×#11929611C23semidirect
112. C2×#11929609C23semidirect
142. #14579096C23semidirect
143. #14579080C23semidirect
144. #14579079C23semidirect
145. #14579078C23semidirect
146. #14579077C23semidirect
544. C2×#575D79semidirect
554. C79#60469semidirect
569. #575C2×D79semidirect
575. C2×#137C2×D79semidirect
581. C2×AGL(1,ℤ/8)C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993612
C2×#190993302
#237731392
#237731342
#237731302
#237731252
#237731172
C2×#190986112
C2×#190985472
C2×#190985452
C2×#575×C792
#6046979