Finite Group Databasebeta

← #3586×D71 #32911295

Subgroups — #3586×D71 #32911295

Order 18176.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#585×D71C211yesmaximal, characteristic, complemented
2C2×2−1+4×D71C211yesmaximal, characteristic, complemented
3#22603128C211yesmaximal, characteristic, complemented
4#22603127C211yesmaximal, characteristic, complemented
5#22603126C211yesmaximal, characteristic, complemented
6#22603125C218yesmaximal, complemented
7#22603124C216yesmaximal, complemented
8#22603123C216yesmaximal, complemented
9#22603122C218yesmaximal, complemented
10#578×D71C218yesmaximal, complemented
11#577×D71C218yesmaximal, complemented
12#575×D71C216yesmaximal, complemented
13C2×#137×D71C216yesmaximal, complemented
14#568×D71C211yesmaximal, characteristic, complemented
15C71×#3586C211yesmaximal, characteristic, complemented
16#17986836—21no—
17#17986836C2214yescomplemented
18#17986835—24no—
19#17986835C2211yescharacteristic, complemented
20#17986835C2216yescomplemented
21#17986834—23no—
22#17986834C2214yescomplemented
23C2×#14556176—21no—
24C2×#14556176C2213yescomplemented
25C2×#14556175—23no—
26C2×#14556175C2211yescharacteristic, complemented
27C2×#14556175C2213yescomplemented
282−1+4×D71—24no—
292−1+4×D71—24no—
302−1+4×D71—21no—
312−1+4×D71C2218yescomplemented
322−1+4×D71C2214yescomplemented
332−1+4×D71C2218yescomplemented
34H(5,𝔽2)×D71—23no—
35H(5,𝔽2)×D71C2214yescomplemented
36C2×#41×D71—24no—
37C2×#41×D71—23no—
38C2×#41×D71C2216yes—
39C2×#41×D71C2211yescharacteristic
40C2×#41×D71C2213yescomplemented
41C22×Q8×D71—21no—
42C22×Q8×D71C2213yescomplemented
43#17986816C2218yescomplemented
44#17986815C22124yescomplemented
45#17986815C22124yescomplemented
46#17986814C2218yescomplemented
47#17986814C2218yescomplemented
48#17986813C22124yescomplemented
49#17986812C22124yescomplemented
50#17986811C2218yescomplemented
51#17986810C2218yescomplemented
52#17986809C22124yescomplemented
53#17986808C22124yescomplemented
54#17986807C2218yescomplemented
55#17986806C22124yescomplemented
56#17986805C22124yescomplemented
57#17986799C2216yescomplemented
58#17986798C22112yescomplemented
59#17986798C22112yescomplemented
60#17986797C2216yescomplemented
61#17986797C2216yescomplemented
62#17986796C22124yescomplemented
63#17986795C22112yescomplemented
64#17986795C22112yescomplemented
65C2×#14556161C2216yescomplemented
66C2×#14556160C22112yescomplemented
67C2×#14556159C2216yescomplemented
68C2×#14556158C2216yescomplemented
69C2×#14556157C22112yescomplemented
70#137×D71C22112yescomplemented
71#137×D71C22124yescomplemented
72#137×D71C22112yescomplemented
73#137×D71C22124yescomplemented
74#137×D71C22124yescomplemented
75AGL(1,ℤ/8)×D71C2214yescomplemented
76AGL(1,ℤ/8)×D71C22112yescomplemented
77#135×D71C22124yescomplemented
78C2×Q16×D71C22112yescomplemented
79C2×SD16×D71C22112yescomplemented
80#17986766C2211yescharacteristic, complemented
81#17986765C2216yescomplemented
82#17986764C2218yescomplemented
83#131×D71C2218yescomplemented
84C2×M16×D71C2216yescomplemented
85#585×C71C2211yescharacteristic, complemented
86C2×2−1+4×C71C2211yescharacteristic, complemented
87#578×C71C2218yescomplemented
88#577×C71C2218yescomplemented
89#575×C71C2216yescomplemented
90C2×#137×C71C2216yescomplemented
91#568×C71C2211yescharacteristic, complemented
92#14556176—28no—
93#14556176—28no—
94#14556176—24no—
95#14556176—212no—
96#14556176—24no—
97#14556176—21no—
98#14556176C23124yescomplemented
99#14556176C23112yescomplemented
100#14556175—212no—
101#14556175—224no—
102#14556175—224no—
103#14556175—212no—
104#14556175—26no—
105#14556175—24no—
106#14556175—24no—
107#14556175C2314yescomplemented
108#14556175C2318yescomplemented
109#14556175C23124yescomplemented
110#14556175C23112yescomplemented
111#14556174—24no—
112#14556174—26no—
113#14556174—212no—
114#14556174C2314yescomplemented
115#14556174C23112yescomplemented
116#14556173—212no—
117#14556173—212no—
118#14556173—212no—
119#14556173—23no—
120#14556173C23112yescomplemented
121C2×#11765866—24no—
122C2×#11765866—23no—
123C2×#11765866D411yescharacteristic
124C2×#11765866C2316yes—
125C2×#11765866C2313yescomplemented
126C2×#11765865—212no—
127C2×#11765865—23no—
128C2×#11765865—26no—
129C2×#11765865—26no—
130C2×#11765865—23no—
131C2×#11765865C2316yes—
132C2×#11765865C2313yes—
133C2×#11765865C2313yescomplemented
134C2×#11765864—212no—
135C2×#11765864—26no—
136C2×#11765864—26no—
137C2×#11765864—23no—
138C2×#11765864—23no—
139C2×#11765864D413yes—
140C2×#11765864C2316yes—
141C2×#11765864C2313yescomplemented
142#41×D71—24no—
143#41×D71—212no—
144#41×D71—212no—
145#41×D71—24no—
146#41×D71—212no—
147#41×D71—224no—
148#41×D71—224no—
149#41×D71—26no—
150#41×D71—26no—
151#41×D71—26no—
152#41×D71—26no—
153#41×D71—26no—
154#41×D71—26no—
155#41×D71—24no—
156#41×D71D414yes—
157#41×D71D414yes—
158#41×D71C2314yes—
159#41×D71C23112yes—
160#41×D71C23112yes—
161#41×D71C23112yes—
162#41×D71C23112yes—
163#41×D71C2314yes—
164#41×D71C2314yes—
165#41×D71C23112yescomplemented
166C22×Dic142—23no—
167C22×Dic142—23no—
168C22×Dic142C2313yescomplemented
169C2×Q8×D71—23no—
170C2×Q8×D71—28no—
171C2×Q8×D71—28no—
172C2×Q8×D71—24no—
173C2×Q8×D71—23no—
174C2×Q8×D71—26no—
175C2×Q8×D71—26no—
176C2×Q8×D71—23no—
177C2×Q8×D71—21no—
178C2×Q8×D71D411yescharacteristic
179C2×Q8×D71C2313yes—
180C2×Q8×D71C23112yes—
181C2×Q8×D71C2316yes—
182C2×Q8×D71C23112yescomplemented
183C2×Q8×D71C2316yescomplemented
184C2×D4×D71—23no—
185C2×D4×D71—26no—
186C2×D4×D71—212no—
187C2×D4×D71D413yes—
188C2×D4×D71C2316yes—
189C2×D4×D71C2311yescharacteristic
190C22×C4×D71—23no—
191C22×C4×D71—23no—
192C22×C4×D71—26no—
193C22×C4×D71C2313yes—
194#14556161C23112yescomplemented
195#14556161C23124yescomplemented
196#14556161C23112yescomplemented
197#14556160C23124yescomplemented
198#14556160C23148yescomplemented
199#14556160C23124yescomplemented
200#14556159C23112yescomplemented
201#14556159C23124yescomplemented
202#14556159C23112yescomplemented
203#14556158C23112yescomplemented
204#14556158C23124yescomplemented
205#14556158C23112yescomplemented
206#14556157C23124yescomplemented
207#14556157C23148yescomplemented
208#14556157C23124yescomplemented
209#14556156C2314yescomplemented
210#14556156C23112yescomplemented
211#14556155C2318yescomplemented
212#14556155C23124yescomplemented
213#14556154C2314yescomplemented
214#14556154C23112yescomplemented
215#14556153C2314yescomplemented
216#14556153C23112yescomplemented
217#14556152C2318yescomplemented
218#14556152C23124yescomplemented
219#14556151C23124yescomplemented
220#14556150C23124yescomplemented
221#14556149C23124yescomplemented
222#14556149C23124yescomplemented
223#14556148C23124yescomplemented
224#14556148C23124yescomplemented
225#14556147C23124yescomplemented
226C2×Dic284C23112yescomplemented
227C2×#11765855C23112yescomplemented
228C2×#11765855C23112yescomplemented
229Q16×D71C23124yes—
230Q16×D71C23148yescomplemented
231C2×#11765854C23112yescomplemented
232C2×#11765853C23112yescomplemented
233C2×#11765852C23112yescomplemented
234SD16×D71C23124yes—
235SD16×D71C2318yes—
236SD16×D71C23148yescomplemented
237D8×D71C2318yes—
238#14556136C23124yescomplemented
239#14556135C2318yescomplemented
240#14556134C23124yescomplemented
241C2×#11765849C2316yescomplemented
242C2×#11765848C23112yescomplemented
243M16×D71C2314yes—
244M16×D71C23112yes—
245M16×D71C23112yescomplemented
246M16×D71C23112yescomplemented
247C2×C8×D71C23112yes—
2482−1+4×C71—24no—
2492−1+4×C71—21no—
2502−1+4×C71C2318yescomplemented
2512−1+4×C71C2314yescomplemented
252H(5,𝔽2)×C71—23no—
253H(5,𝔽2)×C71C2314yescomplemented
254C2×#41×C71—24no—
255C2×#41×C71—23no—
256C2×#41×C71C2316yes—
257C2×#41×C71C2311yescharacteristic
258C2×#41×C71C2313yescomplemented
259C22×Q8×C71—21no—
260C22×Q8×C71C2313yescomplemented
261#137×C71C23112yescomplemented
262#137×C71C23124yescomplemented
263#137×C71C23112yescomplemented
264AGL(1,ℤ/8)×C71C2314yescomplemented
265AGL(1,ℤ/8)×C71C23112yescomplemented
266#135×C71C23124yescomplemented
267C2×Q16×C71C23112yescomplemented
268C2×SD16×C71C23112yescomplemented
269#131×C71C2318yescomplemented
270C2×M16×C71C2316yescomplemented
271C23×D71—21no—
272C23×D71—26no—
273C23×D71C2×D413yes—
274#11765866—24no—
275#11765866—212no—
276#11765866—224no—
277#11765866—26no—
278#11765866—26no—
279#11765866—26no—
280#11765866C2×D414yes—
281#11765866C2×D414yes—
282#11765866C2414yes—
283#11765866C24112yes—
284#11765866C24112yes—
285#11765865—26no—
286#11765865—26no—
287#11765865—26no—
288#11765865—224no—
289#11765865—248no—
290#11765865—212no—
291#11765865—224no—
292#11765865—212no—
293#11765865—24no—
294#11765865—212no—
295#11765865—212no—
296#11765865—212no—
297#11765865—212no—
298#11765865—212no—
299#11765865C2×D4112yes—
300#11765865C24112yes—
301#11765865C2414yes—
302#11765865C24112yes—
303#11765865C24112yes—
304#11765864—212no—
305#11765864—224no—
306#11765864—224no—
307#11765864—248no—
308#11765864—212no—
309#11765864—24no—
310#11765864—212no—
311#11765864—212no—
312#11765864—212no—
313#11765864—212no—
314#11765864—26no—
315#11765864—26no—
316#11765864—26no—
317#11765864—212no—
318#11765864C2×D4112yes—
319#11765864C2×D4112yes—
320#11765864C2414yes—
321#11765864C24112yes—
322#11765864C24112yes—
323C2×Dic142—23no—
324C2×Dic142—26no—
325C2×Dic142—23no—
326C2×Dic142—26no—
327C2×Dic142—212no—
328C2×Dic142—212no—
329C2×Dic142—26no—
330C2×Dic142—224no—
331C2×Dic142—212no—
332C2×Dic142C2×D413yes—
333C2×Dic142C2413yes—
334C2×Dic142C24112yes—
335C2×Dic142C2416yes—
336Q8×D71—28no—
337Q8×D71—24no—
338Q8×D71—23no—
339Q8×D71—212no—
340Q8×D71—23no—
341Q8×D71—212no—
342Q8×D71—26no—
343Q8×D71—212no—
344Q8×D71—212no—
345Q8×D71—212no—
346Q8×D71—26no—
347Q8×D71—224no—
348Q8×D71—212no—
349Q8×D71C2×D414yes—
350Q8×D71C2×D414yes—
351Q8×D71C2416yes—
352Q8×D71C24124yes—
353Q8×D71C24112yes—
354Q8×D71C2416yes—
355Q8×D71C2414yes—
356C2×D284—23no—
357C2×D284—26no—
358C2×D284—212no—
359C2×D284C2×D413yes—
360C2×D284C2416yes—
361C2×D284C2411yescharacteristic
362C2×C22⋊D71—23no—
363C2×C22⋊D71—26no—
364C2×C22⋊D71—23no—
365C2×C22⋊D71—26no—
366C2×C22⋊D71—224no—
367C2×C22⋊D71—21no—
368C2×C22⋊D71—26no—
369C2×C22⋊D71C2×D416yes—
370D4×D71—24no—
371D4×D71—212no—
372D4×D71—212no—
373D4×D71—212no—
374D4×D71—212no—
375D4×D71—212no—
376D4×D71—212no—
377D4×D71—224no—
378D4×D71—212no—
379D4×D71—26no—
380D4×D71—21no—
381D4×D71—21no—
382D4×D71—26no—
383D4×D71C2×D4112yes—
384D4×D71C2×D4112yes—
385D4×D71C2414yes—
386D4×D71C2412yes—
387D4×D71C24112yes—
388D4×D71C2412yes—
389C22×Dic71—23no—
390C22×Dic71—23no—
391C22×Dic71—26no—
392C22×Dic71C2×D413yes—
393C2×C4×D71—23no—
394C2×C4×D71—26no—
395C2×C4×D71—212no—
396C2×C4×D71—212no—
397C2×C4×D71—26no—
398C2×C4×D71—23no—
399C2×C4×D71—26no—
400C2×C4×D71—23no—
401C2×C4×D71—26no—
402C2×C4×D71—24no—
403C2×C4×D71—212no—
404C2×C4×D71—212no—
405C2×C4×D71—212no—
406C2×C4×D71—212no—
407C2×C4×D71—212no—
408C2×C4×D71C2×D413yes—
409C2×C4×D71C2×D416yes—
410C2×C4×D71C2×D416yes—
411C2×C4×D71C2×D413yes—
412C2×C4×D71C2411yescharacteristic
413C2×C4×D71C2416yes—
414C2×C4×D71C2416yes—
415C2×C4×D71C2413yes—
416Dic284C24124yes—
417#11765855C24124yes—
418#11765855C24124yes—
419#11765854C24124yes—
420#11765854C2418yes—
421#11765853C24124yes—
422#11765853C2418yes—
423#11765852C24124yes—
424#11765852C2418yes—
425D568C2418yes—
426#11765850C2418yes—
427#11765850C2418yes—
428#11765849C2414yes—
429#11765849C24112yes—
430#11765848C2418yes—
431#11765848C24124yes—
432C2×C71⋊C8C24112yes—
433C8×D71C2418yes—
434C8×D71C24124yes—
435#41×C71—24no—
436#41×C71—212no—
437#41×C71—224no—
438#41×C71—26no—
439#41×C71—26no—
440#41×C71—26no—
441#41×C71C2×D414yes—
442#41×C71C2414yes—
443#41×C71C24112yes—
444#41×C71C24112yes—
445#41×C71C2414yes—
446C2×Q8×C71—28no—
447C2×Q8×C71—24no—
448C2×Q8×C71—23no—
449C2×Q8×C71—26no—
450C2×Q8×C71C2×D411yescharacteristic
451C2×Q8×C71C2413yes—
452C2×Q8×C71C24112yes—
453C2×Q8×C71C2416yes—
454C2×D4×C71—23no—
455C2×D4×C71—26no—
456C2×D4×C71—212no—
457C2×D4×C71C2×D413yes—
458C2×D4×C71C2416yes—
459C2×D4×C71C2411yescharacteristic
460C22×C4×C71—23no—
461C22×C4×C71—23no—
462C22×C4×C71—26no—
463C22×C4×C71C2413yes—
464Q16×C71C24124yes—
465SD16×C71C24124yes—
466SD16×C71C2418yes—
467D8×C71C2418yes—
468M16×C71C2414yes—
469M16×C71C24112yes—
470C2×C8×C71C24112yes—
471C23×C71—21no—
472C23×C71—26no—
473C23×C71C22×D413yes—
474C22×D71—21no—
475C22×D71—26no—
476C22×D71—22no—
477C22×D71—22no—
478C22×D71—24no—
479C22×D71—212no—
480C22×D71—46no—
481C22×D71—44no—
482C22×D71—812no—
483C22×D71C22×D411yescharacteristic
484C22×D71C22×D416yes—
485C22×D71C22×D416yes—
486C22×D71C22×D413yes—
487Q8×C71—212no—
488Q8×C71—23no—
489Q8×C71—26no—
490Q8×C71C22×D414yes—
491Q8×C71C2516yes—
492Q8×C71C2514yes—
493D4×C71—24no—
494D4×C71—212no—
495D4×C71—212no—
496D4×C71—26no—
497D4×C71—21no—
498D4×C71C22×D4112yes—
499D4×C71C2512yes—
500D4×C71C2514yes—
501C2×C4×C71—23no—
502C2×C4×C71—26no—
503C2×C4×C71—212no—
504C2×C4×C71—24no—
505C2×C4×C71—212no—
506C2×C4×C71—212no—
507C2×C4×C71C22×D413yes—
508C2×C4×C71C22×D416yes—
509C2×C4×C71C2516yes—
510C2×C4×C71C2511yescharacteristic
511C22⋊D71—24no—
512C22⋊D71—212no—
513C22⋊D71—212no—
514C22⋊D71—24no—
515C22⋊D71—212no—
516C22⋊D71—212no—
517C22⋊D71—24no—
518C22⋊D71—212no—
519C22⋊D71—22no—
520C22⋊D71—22no—
521C22⋊D71C22×D4124yes—
522C2×Dic71—23no—
523C2×Dic71—26no—
524C2×Dic71—212no—
525C2×Dic71—24no—
526C2×Dic71—212no—
527C2×Dic71—212no—
528C2×Dic71C22×D413yes—
529C2×Dic71C22×D416yes—
530C2×Dic71C22×D411yescharacteristic
531C2×Dic71C22×D416yes—
532D284—24no—
533D284—212no—
534D284—212no—
535D284—26no—
536D284—21no—
537D284C22×D4112yes—
538D284C2512yes—
539D284C2514yes—
540C4×D71—24no—
541C4×D71—26no—
542C4×D71—26no—
543C4×D71—212no—
544C4×D71—224no—
545C4×D71—24no—
546C4×D71—212no—
547C4×D71—212no—
548C4×D71—24no—
549C4×D71—212no—
550C4×D71—212no—
551C4×D71C22×D411yescharacteristic
552C4×D71C22×D416yes—
553C4×D71C22×D416yes—
554C4×D71C22×D416yes—
555C4×D71C22×D416yes—
556C4×D71C22×D411yescharacteristic
557C4×D71C22×D416yes—
558C4×D71C2511yescharacteristic
559C4×D71C2516yes—
560C4×D71C2511yescharacteristic
561Dic142—212no—
562Dic142—23no—
563Dic142—26no—
564Dic142—26no—
565Dic142—224no—
566Dic142—26no—
567Dic142—24no—
568Dic142—212no—
569Dic142C22×D4112yes—
570Dic142C2516yes—
571Dic142C2514yes—
572C8×C71C2518yes—
573C71⋊C8C2518yes—
574C22×C71—22no—
575C22×C71—24no—
576C22×C71—43no—
577C22×C71—42no—
578C22×C71—86no—
579C22×C71C23×D411yescharacteristic
580C22×C71C23×D416yes—
581C2×D71—22no—
582C2×D71—212no—
583C2×D71—22no—
584C2×D71—24no—
585C2×D71—46no—
586C2×D71—43no—
587C2×D71—44no—
588C2×D71—42no—
589C2×D71—44no—
590C2×D71—48no—
591C2×D71—812no—
592C2×D71—86no—
593C2×D71C23×D411yescharacteristic
594C2×D71C23×D416yes—
595C2×D71C23×D411yescharacteristic
596C4×C71—26no—
597C4×C71—24no—
598C4×C71C23×D416yes—
599C4×C71C23×D411yescharacteristic
600C4×C71C2611yescharacteristic
601Dic71—26no—
602Dic71—24no—
603Dic71C23×D411yescharacteristic
604Dic71C23×D416yes—
605Dic71C23×D411yescharacteristic
606C2×#3586—711nomaximal, Sylow
607C2×C71—21no—
608C2×C71—26no—
609C2×C71—42no—
610C2×C71—44no—
611C2×C71C24×D411yescharacteristic
612D71—21no—
613D71—26no—
614D71—42no—
615D71—44no—
616D71#358612yesdirect product factor
617C2×#585—711no—
618C22×2−1+4—711no—
619#3586—711no—
620#3586—711no—
621#3586—718no—
622#3586—718no—
623#3586—716no—
624#3586—716no—
625#3586—711no—
626#3586D7111yescharacteristic, direct product factor
627C2×#578—718no—
628C2×#577—718no—
629C2×#575—716no—
630C22×#137—716no—
631C2×#568—711no—
632C71C2×#358611yescharacteristic, complemented, Sylow
633#585—714no—
634#585—714no—
635#585—716no—
636#585—711no—
637#585—1424no—
638#585—1423no—
639#585—1421no—
640#585C2×D7111yescharacteristic, complemented
641C2×2−1+4—718no—
642C2×2−1+4—718no—
643C2×2−1+4—714no—
644C2×2−1+4—711no—
645C2×2−1+4—713no—
646C2×2−1+4—713no—
647C2×2−1+4—1421no—
648C2×2−1+4—1421no—
649C2×2−1+4—1423no—
650C2×2−1+4—1424no—
651C2×2−1+4—1424no—
652C2×2−1+4C2×D7111yescharacteristic, complemented
653C2×H(5,𝔽2)—714no—
654C2×H(5,𝔽2)—1423no—
655C22×#41—711no—
656C22×#41—716no—
657C22×#41—713no—
658C22×#41—1423no—
659C22×#41—1424no—
660C23×Q8—713no—
661C23×Q8—1421no—
662#578—718no—
663#578—718no—
664#578—7124no—
665#578—7124no—
666#578—7124no—
667#578—7124no—
668#578—718no—
669#578C2×D7118yescomplemented
670#577—718no—
671#577—718no—
672#577—7124no—
673#577—7124no—
674#577—7124no—
675#577—7124no—
676#577—718no—
677#577C2×D7118yescomplemented
678#575—716no—
679#575—716no—
680#575—7112no—
681#575—7112no—
682#575—7112no—
683#575—7112no—
684#575—7124no—
685#575—716no—
686#575C2×D7116yescomplemented
687C2×#137—716no—
688C2×#137—716no—
689C2×#137—7124no—
690C2×#137—7124no—
691C2×#137—7112no—
692C2×#137—7124no—
693C2×#137—7112no—
694C2×#137—7112no—
695C2×#137—7112no—
696C2×#137—716no—
697C2×#137C2×D7116yescomplemented
698C2×AGL(1,ℤ/8)—714no—
699C2×AGL(1,ℤ/8)—7112no—
700C2×#135—7124no—
701C22×Q16—7112no—
702C22×SD16—7112no—
703#568—711no—
704#568—718no—
705#568—716no—
706#568C2×D7111yescharacteristic, complemented
707C2×#131—718no—
708C22×M16—716no—
7092−1+4—24no—
7102−1+4—21no—
7112−1+4—7124no—
7122−1+4—718no—
7132−1+4—7112no—
7142−1+4—714no—
7152−1+4—7124no—
7162−1+4—7112no—
7172−1+4—1424no—
7182−1+4—1428no—
7192−1+4—1428no—
7202−1+4—14212no—
7212−1+4—1424no—
7222−1+4—1424no—
7232−1+4—1426no—
7242−1+4—14224no—
7252−1+4—14224no—
7262−1+4—14212no—
7272−1+4—14212no—
7282−1+4—1424no—
7292−1+4—1421no—
7302−1+4C22×D7118yescomplemented
7312−1+4C22×D7114yescomplemented
732H(5,𝔽2)—23no—
733H(5,𝔽2)—7112no—
734H(5,𝔽2)—714no—
735H(5,𝔽2)—7112no—
736H(5,𝔽2)—14212no—
737H(5,𝔽2)—14212no—
738H(5,𝔽2)—14212no—
739H(5,𝔽2)—14212no—
740H(5,𝔽2)—1426no—
741H(5,𝔽2)—1424no—
742H(5,𝔽2)—1423no—
743H(5,𝔽2)C22×D7114yescomplemented
744C2×#41—24no—
745C2×#41—23no—
746C2×#41—714no—
747C2×#41—714no—
748C2×#41—714no—
749C2×#41—714no—
750C2×#41—711no—
751C2×#41—713no—
752C2×#41—713no—
753C2×#41—7112no—
754C2×#41—7112no—
755C2×#41—714no—
756C2×#41—7112no—
757C2×#41—7112no—
758C2×#41—7112no—
759C2×#41—716no—
760C2×#41—713no—
761C2×#41—716no—
762C2×#41—713no—
763C2×#41—716no—
764C2×#41—713no—
765C2×#41—1423no—
766C2×#41—1426no—
767C2×#41—1426no—
768C2×#41—1423no—
769C2×#41—14212no—
770C2×#41—1423no—
771C2×#41—1426no—
772C2×#41—1426no—
773C2×#41—1426no—
774C2×#41—1426no—
775C2×#41—1426no—
776C2×#41—1426no—
777C2×#41—1426no—
778C2×#41—1426no—
779C2×#41—14212no—
780C2×#41—1423no—
781C2×#41—14212no—
782C2×#41—14224no—
783C2×#41—14224no—
784C2×#41—1424no—
785C2×#41—1424no—
786C2×#41—1424no—
787C2×#41—14212no—
788C2×#41—14212no—
789C2×#41—1424no—
790C2×#41—1423no—
791C2×#41C22×D7116yes—
792C2×#41C22×D7111yescharacteristic
793C2×#41C22×D7113yescomplemented
794C22×Q8—21no—
795C22×Q8—711no—
796C22×Q8—7112no—
797C22×Q8—716no—
798C22×Q8—713no—
799C22×Q8—716no—
800C22×Q8—7112no—
801C22×Q8—713no—
802C22×Q8—1423no—
803C22×Q8—1423no—
804C22×Q8—1423no—
805C22×Q8—1426no—
806C22×Q8—1423no—
807C22×Q8—1426no—
808C22×Q8—1428no—
809C22×Q8—1428no—
810C22×Q8—1423no—
811C22×Q8—1424no—
812C22×Q8—1421no—
813C22×Q8C22×D7113yescomplemented
814C22×D4—713no—
815C22×D4—716no—
816C22×D4—711no—
817C22×D4—14212no—
818C22×D4—1423no—
819C22×D4—1426no—
820C23×C4—713no—
821C23×C4—1423no—
822C23×C4—1426no—
823C23×C4—1423no—
824#137—7112no—
825#137—7124no—
826#137—7112no—
827#137—7112no—
828#137—7124no—
829#137—7112no—
830#137—7124no—
831#137—7148no—
832#137—7124no—
833#137—7124no—
834#137—7148no—
835#137—7124no—
836#137—7112no—
837#137—7124no—
838#137—7112no—
839#137C22×D71112yescomplemented
840#137C22×D71124yescomplemented
841#137C22×D71112yescomplemented
842AGL(1,ℤ/8)—714no—
843AGL(1,ℤ/8)—7112no—
844AGL(1,ℤ/8)—714no—
845AGL(1,ℤ/8)—7112no—
846AGL(1,ℤ/8)—718no—
847AGL(1,ℤ/8)—7124no—
848AGL(1,ℤ/8)—718no—
849AGL(1,ℤ/8)—7124no—
850AGL(1,ℤ/8)—714no—
851AGL(1,ℤ/8)—7112no—
852AGL(1,ℤ/8)C22×D7114yescomplemented
853AGL(1,ℤ/8)C22×D71112yescomplemented
854#135—7124no—
855#135—7124no—
856#135—7124no—
857#135—7124no—
858#135—7124no—
859#135—7124no—
860#135—7124no—
861#135C22×D71124yescomplemented
862C2×Q16—7112no—
863C2×Q16—7112no—
864C2×Q16—7124no—
865C2×Q16—7148no—
866C2×Q16—7112no—
867C2×Q16C22×D71112yescomplemented
868C2×SD16—7112no—
869C2×SD16—7112no—
870C2×SD16—7124no—
871C2×SD16—7148no—
872C2×SD16—718no—
873C2×SD16—7112no—
874C2×SD16C22×D71112yescomplemented
875C2×D8—718no—
876#131—718no—
877#131—7124no—
878#131—7124no—
879#131C22×D7118yescomplemented
880C2×M16—716no—
881C2×M16—714no—
882C2×M16—7112no—
883C2×M16—7112no—
884C2×M16—7112no—
885C2×M16—7112no—
886C2×M16C22×D7116yescomplemented
887C22×C8—7112no—
888C24—713no—
889C24—1421no—
890C24—1426no—
891#41—24no—
892#41—212no—
893#41—224no—
894#41—26no—
895#41—26no—
896#41—26no—
897#41—714no—
898#41—714no—
899#41—7112no—
900#41—7112no—
901#41—7112no—
902#41—7112no—
903#41—7112no—
904#41—7112no—
905#41—714no—
906#41—7112no—
907#41—7112no—
908#41—714no—
909#41—7112no—
910#41—7112no—
911#41—714no—
912#41—1424no—
913#41—14212no—
914#41—14212no—
915#41—14212no—
916#41—14212no—
917#41—14212no—
918#41—14224no—
919#41—14212no—
920#41—14248no—
921#41—14224no—
922#41—14212no—
923#41—1424no—
924#41—14212no—
925#41—1426no—
926#41—14212no—
927#41—14212no—
928#41—1426no—
929#41—14212no—
930#41—14212no—
931#41—1426no—
932#41—1426no—
933#41—1426no—
934#41—1426no—
935#41—14224no—
936#41—14248no—
937#41—14212no—
938#41—14212no—
939#41—14224no—
940#41—1424no—
941#41—14212no—
942#41—14224no—
943#41—1426no—
944#41—1426no—
945#41—1426no—
946#41D4×D7114yes—
947#41C23×D71112yes—
948#41C23×D71112yes—
949#41C23×D7114yes—
950#41C23×D7114yes—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—23no—
954C2×Q8—26no—
955C2×Q8—714no—
956C2×Q8—714no—
957C2×Q8—713no—
958C2×Q8—716no—
959C2×Q8—714no—
960C2×Q8—7124no—
961C2×Q8—7112no—
962C2×Q8—716no—
963C2×Q8—7112no—
964C2×Q8—716no—
965C2×Q8—713no—
966C2×Q8—1423no—
967C2×Q8—1426no—
968C2×Q8—14212no—
969C2×Q8—14212no—
970C2×Q8—1426no—
971C2×Q8—14224no—
972C2×Q8—14212no—
973C2×Q8—1423no—
974C2×Q8—1423no—
975C2×Q8—14212no—
976C2×Q8—14212no—
977C2×Q8—1426no—
978C2×Q8—14212no—
979C2×Q8—14212no—
980C2×Q8—14212no—
981C2×Q8—1426no—
982C2×Q8—14224no—
983C2×Q8—14212no—
984C2×Q8—1428no—
985C2×Q8—1424no—
986C2×Q8—1423no—
987C2×Q8—1426no—
988C2×Q8D4×D7111yescharacteristic
989C2×Q8C23×D71112yes—
990C2×Q8C23×D7116yes—
991C2×Q8C23×D7113yes—
992C2×D4—23no—
993C2×D4—26no—
994C2×D4—212no—
995C2×D4—716no—
996C2×D4—7112no—
997C2×D4—7112no—
998C2×D4—712no—
999C2×D4—714no—
1000C2×D4—7112no—
1001C2×D4—712no—
1002C2×D4—713no—
1003C2×D4—716no—
1004C2×D4—711no—
1005C2×D4—14212no—
1006C2×D4—1423no—
1007C2×D4—1426no—
1008C2×D4—1426no—
1009C2×D4—1421no—
1010C2×D4—1421no—
1011C2×D4—1426no—
1012C2×D4—1421no—
1013C2×D4—1426no—
1014C2×D4—14224no—
1015C2×D4—14212no—
1016C2×D4—1424no—
1017C2×D4—14212no—
1018C2×D4—14212no—
1019C2×D4—14212no—
1020C2×D4—14212no—
1021C2×D4—14212no—
1022C2×D4—14224no—
1023C2×D4—1423no—
1024C2×D4—1426no—
1025C2×D4—1423no—
1026C2×D4—1426no—
1027C2×D4—14212no—
1028C2×D4D4×D7113yes—
1029C2×D4C23×D7116yes—
1030C2×D4C23×D7111yescharacteristic
1031C22×C4—23no—
1032C22×C4—23no—
1033C22×C4—26no—
1034C22×C4—713no—
1035C22×C4—713no—
1036C22×C4—716no—
1037C22×C4—713no—
1038C22×C4—716no—
1039C22×C4—716no—
1040C22×C4—711no—
1041C22×C4—713no—
1042C22×C4—716no—
1043C22×C4—1424no—
1044C22×C4—14212no—
1045C22×C4—1423no—
1046C22×C4—14212no—
1047C22×C4—14212no—
1048C22×C4—1426no—
1049C22×C4—14212no—
1050C22×C4—14212no—
1051C22×C4—1423no—
1052C22×C4—1426no—
1053C22×C4—1426no—
1054C22×C4—14212no—
1055C22×C4—14212no—
1056C22×C4—1423no—
1057C22×C4—1426no—
1058C22×C4—1423no—
1059C22×C4—1423no—
1060C22×C4—1426no—
1061C22×C4C23×D7113yes—
1062Q16—7124no—
1063Q16—7124no—
1064Q16—7124no—
1065Q16C23×D71124yes—
1066SD16—7124no—
1067SD16—718no—
1068SD16—7124no—
1069SD16—718no—
1070SD16—7124no—
1071SD16—718no—
1072SD16C23×D71124yes—
1073SD16C23×D7118yes—
1074D8—718no—
1075D8—718no—
1076D8—718no—
1077D8C23×D7118yes—
1078M16—714no—
1079M16—7112no—
1080M16—718no—
1081M16—7124no—
1082M16C23×D7114yes—
1083M16C23×D71112yes—
1084C2×C8—7112no—
1085C2×C8—718no—
1086C2×C8—7124no—
1087C2×C8C23×D71112yes—
1088C23—21no—
1089C23—26no—
1090C23—2844no—
1091C23—2846no—
1092C23—56812no—
1093C23—716no—
1094C23—713no—
1095C23—711no—
1096C23—716no—
1097C23—1422no—
1098C23—1422no—
1099C23—1424no—
1100C23—14212no—
1101C23—1421no—
1102C23—1426no—
1103C23C2×D4×D7113yes—
1104Q8—23no—
1105Q8—212no—
1106Q8—26no—
1107Q8—7112no—
1108Q8—716no—
1109Q8—714no—
1110Q8—1426no—
1111Q8—1426no—
1112Q8—14224no—
1113Q8—1424no—
1114Q8—14212no—
1115Q8—1423no—
1116Q8—14212no—
1117Q8—1426no—
1118Q8C2×D4×D7114yes—
1119Q8C24×D7116yes—
1120Q8C24×D7114yes—
1121D4—24no—
1122D4—212no—
1123D4—212no—
1124D4—26no—
1125D4—21no—
1126D4—7124no—
1127D4—7112no—
1128D4—712no—
1129D4—714no—
1130D4—1424no—
1131D4—14212no—
1132D4—14212no—
1133D4—1424no—
1134D4—14212no—
1135D4—1422no—
1136D4—1422no—
1137D4—1424no—
1138D4—14212no—
1139D4—14212no—
1140D4—1424no—
1141D4—14212no—
1142D4—14212no—
1143D4—1426no—
1144D4—1421no—
1145D4C2×D4×D71112yes—
1146D4C24×D7112yes—
1147D4C24×D7114yes—
1148C2×C4—23no—
1149C2×C4—26no—
1150C2×C4—212no—
1151C2×C4—24no—
1152C2×C4—212no—
1153C2×C4—212no—
1154C2×C4—711no—
1155C2×C4—713no—
1156C2×C4—716no—
1157C2×C4—716no—
1158C2×C4—711no—
1159C2×C4—711no—
1160C2×C4—716no—
1161C2×C4—716no—
1162C2×C4—716no—
1163C2×C4—716no—
1164C2×C4—716no—
1165C2×C4—711no—
1166C2×C4—716no—
1167C2×C4—711no—
1168C2×C4—1424no—
1169C2×C4—14212no—
1170C2×C4—14212no—
1171C2×C4—1424no—
1172C2×C4—1426no—
1173C2×C4—1426no—
1174C2×C4—14212no—
1175C2×C4—14224no—
1176C2×C4—1424no—
1177C2×C4—14212no—
1178C2×C4—14212no—
1179C2×C4—1423no—
1180C2×C4—1426no—
1181C2×C4—14212no—
1182C2×C4—1424no—
1183C2×C4—14212no—
1184C2×C4—14212no—
1185C2×C4C2×D4×D7113yes—
1186C2×C4C2×D4×D7116yes—
1187C2×C4C24×D7116yes—
1188C2×C4C24×D7111yescharacteristic
1189C8—718no—
1190C8C24×D7118yes—
1191C22—22no—
1192C22—24no—
1193C22—43no—
1194C22—42no—
1195C22—86no—
1196C22—2842no—
1197C22—2843no—
1198C22—2846no—
1199C22—2844no—
1200C22—2848no—
1201C22—2844no—
1202C22—5686no—
1203C22—56812no—
1204C22—711no—
1205C22—711no—
1206C22—716no—
1207C22—1422no—
1208C22—14212no—
1209C22—1422no—
1210C22—1424no—
1211C22C22×D4×D7111yescharacteristic
1212C22C22×D4×D7116yes—
1213C4—24no—
1214C4—26no—
1215C4—711no—
1216C4—711no—
1217C4—716no—
1218C4—1424no—
1219C4—1426no—
1220C4C22×D4×D7111yescharacteristic
1221C4C22×D4×D7116yes—
1222C4C25×D7111yescharacteristic
1223C2—21no—
1224C2—26no—
1225C2—42no—
1226C2—44no—
1227C2—2842no—
1228C2—2844no—
1229C2—712no—
1230C2—1421no—
1231C2—1426no—
1232C2C23×D4×D7111yescharacteristic
subgroupG/H
centerC2C23×D4×D71
commutator, cosocleC4×C71C26
FrattiniC4C25×D71
FittingC71×#3586C2
socleC2×C71C24×D4
hypercenter#3586D71
hypocenterC71C2×#3586
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. #585×D71C2semidirect
2. C2×2−1+4×D71C2semidirect
3. #22603128C2semidirect
4. #22603127C2semidirect
5. #22603126C2semidirect
6. #22603125C2semidirect
7. #22603124C2semidirect
8. #22603123C2semidirect
9. #22603122C2semidirect
10. #578×D71C2semidirect
11. #577×D71C2semidirect
12. #575×D71C2semidirect
13. C2×#137×D71C2semidirect
14. #568×D71C2semidirect
15. C71×#3586C2semidirect
17. #17986836C22semidirect
19. #17986835C22semidirect
20. #17986835C22semidirect
22. #17986834C22semidirect
24. C2×#14556176C22semidirect
26. C2×#14556175C22semidirect
27. C2×#14556175C22semidirect
31. 2−1+4×D71C22semidirect
32. 2−1+4×D71C22semidirect
33. 2−1+4×D71C22semidirect
35. H(5,𝔽2)×D71C22semidirect
40. C2×#41×D71C22semidirect
42. C22×Q8×D71C22semidirect
43. #17986816C22semidirect
44. #17986815C22semidirect
45. #17986815C22semidirect
46. #17986814C22semidirect
47. #17986814C22semidirect
48. #17986813C22semidirect
49. #17986812C22semidirect
50. #17986811C22semidirect
51. #17986810C22semidirect
52. #17986809C22semidirect
53. #17986808C22semidirect
54. #17986807C22semidirect
55. #17986806C22semidirect
56. #17986805C22semidirect
57. #17986799C22semidirect
58. #17986798C22semidirect
59. #17986798C22semidirect
60. #17986797C22semidirect
61. #17986797C22semidirect
62. #17986796C22semidirect
63. #17986795C22semidirect
64. #17986795C22semidirect
65. C2×#14556161C22semidirect
66. C2×#14556160C22semidirect
67. C2×#14556159C22semidirect
68. C2×#14556158C22semidirect
69. C2×#14556157C22semidirect
70. #137×D71C22semidirect
71. #137×D71C22semidirect
72. #137×D71C22semidirect
73. #137×D71C22semidirect
74. #137×D71C22semidirect
75. AGL(1,ℤ/8)×D71C22semidirect
76. AGL(1,ℤ/8)×D71C22semidirect
77. #135×D71C22semidirect
78. C2×Q16×D71C22semidirect
79. C2×SD16×D71C22semidirect
80. #17986766C22semidirect
81. #17986765C22semidirect
82. #17986764C22semidirect
83. #131×D71C22semidirect
84. C2×M16×D71C22semidirect
85. #585×C71C22semidirect
86. C2×2−1+4×C71C22semidirect
87. #578×C71C22semidirect
88. #577×C71C22semidirect
89. #575×C71C22semidirect
90. C2×#137×C71C22semidirect
91. #568×C71C22semidirect
98. #14556176C23semidirect
99. #14556176C23semidirect
107. #14556175C23semidirect
108. #14556175C23semidirect
109. #14556175C23semidirect
110. #14556175C23semidirect
114. #14556174C23semidirect
115. #14556174C23semidirect
120. #14556173C23semidirect
125. C2×#11765866C23semidirect
133. C2×#11765865C23semidirect
141. C2×#11765864C23semidirect
165. #41×D71C23semidirect
168. C22×Dic142C23semidirect
182. C2×Q8×D71C23semidirect
183. C2×Q8×D71C23semidirect
194. #14556161C23semidirect
195. #14556161C23semidirect
196. #14556161C23semidirect
197. #14556160C23semidirect
198. #14556160C23semidirect
199. #14556160C23semidirect
200. #14556159C23semidirect
201. #14556159C23semidirect
202. #14556159C23semidirect
203. #14556158C23semidirect
204. #14556158C23semidirect
205. #14556158C23semidirect
206. #14556157C23semidirect
207. #14556157C23semidirect
208. #14556157C23semidirect
209. #14556156C23semidirect
210. #14556156C23semidirect
211. #14556155C23semidirect
212. #14556155C23semidirect
213. #14556154C23semidirect
214. #14556154C23semidirect
215. #14556153C23semidirect
216. #14556153C23semidirect
217. #14556152C23semidirect
218. #14556152C23semidirect
219. #14556151C23semidirect
220. #14556150C23semidirect
221. #14556149C23semidirect
222. #14556149C23semidirect
223. #14556148C23semidirect
224. #14556148C23semidirect
225. #14556147C23semidirect
226. C2×Dic284C23semidirect
227. C2×#11765855C23semidirect
228. C2×#11765855C23semidirect
230. Q16×D71C23semidirect
231. C2×#11765854C23semidirect
232. C2×#11765853C23semidirect
233. C2×#11765852C23semidirect
236. SD16×D71C23semidirect
238. #14556136C23semidirect
239. #14556135C23semidirect
240. #14556134C23semidirect
241. C2×#11765849C23semidirect
242. C2×#11765848C23semidirect
245. M16×D71C23semidirect
246. M16×D71C23semidirect
250. 2−1+4×C71C23semidirect
251. 2−1+4×C71C23semidirect
253. H(5,𝔽2)×C71C23semidirect
258. C2×#41×C71C23semidirect
260. C22×Q8×C71C23semidirect
261. #137×C71C23semidirect
262. #137×C71C23semidirect
263. #137×C71C23semidirect
264. AGL(1,ℤ/8)×C71C23semidirect
265. AGL(1,ℤ/8)×C71C23semidirect
266. #135×C71C23semidirect
267. C2×Q16×C71C23semidirect
268. C2×SD16×C71C23semidirect
269. #131×C71C23semidirect
270. C2×M16×C71C23semidirect
616. D71#3586direct (N × H)
626. #3586D71direct (N × H)
632. C71C2×#3586semidirect
640. #585C2×D71semidirect
652. C2×2−1+4C2×D71semidirect
669. #578C2×D71semidirect
677. #577C2×D71semidirect
686. #575C2×D71semidirect
697. C2×#137C2×D71semidirect
706. #568C2×D71semidirect
730. 2−1+4C22×D71semidirect
731. 2−1+4C22×D71semidirect
743. H(5,𝔽2)C22×D71semidirect
793. C2×#41C22×D71semidirect
813. C22×Q8C22×D71semidirect
839. #137C22×D71semidirect
840. #137C22×D71semidirect
841. #137C22×D71semidirect
852. AGL(1,ℤ/8)C22×D71semidirect
853. AGL(1,ℤ/8)C22×D71semidirect
861. #135C22×D71semidirect
867. C2×Q16C22×D71semidirect
874. C2×SD16C22×D71semidirect
879. #131C22×D71semidirect
886. C2×M16C22×D71semidirect

Maximal subgroups

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

subgroupindex
#585×D712
C2×2−1+4×D712
#226031282
#226031272
#226031262
#226031252
#226031242
#226031232
#226031222
#578×D712
#577×D712
#575×D712
C2×#137×D712
#568×D712
C71×#35862
C2×#358671