Finite Group Databasebeta

← #3517×D71 #32905700

Subgroups — #3517×D71 #32905700

Order 18176.

7854 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602347C211yesmaximal, characteristic, complemented
2#22602346C211yesmaximal, characteristic, complemented
3#22602345C213yesmaximal, complemented
4#22602344C213yesmaximal, complemented
5#22602343C213yesmaximal, complemented
6#22602342C216yesmaximal, complemented
7#22602341C211yesmaximal, characteristic, complemented
8#22602340C212yesmaximal, complemented
9#22602339C216yesmaximal, complemented
10#22602338C213yesmaximal, complemented
11#22602337C212yesmaximal, complemented
12#557×D71C211yesmaximal, characteristic, complemented
13#553×D71C216yesmaximal, complemented
14#550×D71C212yesmaximal, complemented
15#550×D71C211yesmaximal, characteristic, complemented
16#550×D71C213yesmaximal, complemented
17#547×D71C213yesmaximal, complemented
18#540×D71C216yesmaximal, complemented
19#532×D71C213yesmaximal, complemented
20#529×D71C213yesmaximal, complemented
21#520×D71C212yesmaximal, complemented
22C4×#41×D71C211yesmaximal, characteristic, complemented
23C71×#3517C211yesmaximal, characteristic, complemented
24C2×#41×D71C2211yescharacteristic
25C2×#41×D71C2212yes—
26C2×#41×D71C2216yes—
27#17986728C2211yescharacteristic, complemented
28#17986727C2213yescomplemented
29#17986726C2216yescomplemented
30#17986725C2212yescomplemented
31#17986724C2213yescomplemented
32#17986702C2216yescomplemented
33#17986701C2216yescomplemented
34#17986700C22112yescomplemented
35#17986699C2216yescomplemented
36#17986698C22112yescomplemented
37#17986697C2216yescomplemented
38#17986696C2216yescomplemented
39#17986695C2216yescomplemented
40#17986694C22112yescomplemented
41#17986693C2216yescomplemented
42#17986692C22112yescomplemented
43#17986671C2212yescomplemented
44#17986671C2213yescomplemented
45#17986671C2211yescharacteristic, complemented
46#17986670C2216yescomplemented
47#17986670C2216yescomplemented
48#17986670C2213yescomplemented
49#17986670C2213yescomplemented
50#17986669C2216yescomplemented
51#17986669C2213yescomplemented
52#17986669C2213yescomplemented
53#17986669C2216yescomplemented
54#17986668C2212yescomplemented
55#17986668C2212yescomplemented
56#17986668C2216yescomplemented
57#17986668C2212yescomplemented
58#17986667C2216yescomplemented
59#17986667C2216yescomplemented
60#17986667C22112yescomplemented
61#17986667C2216yescomplemented
62#17986667C2216yescomplemented
63#17986654C2213yescomplemented
64#17986653C2213yescomplemented
65#17986652C2213yescomplemented
66#17986651C2216yescomplemented
67#17986650C2216yescomplemented
68#17986649C2216yescomplemented
69#17986648C2216yescomplemented
70#17986647C22112yescomplemented
71#17986605C2216yescomplemented
72#17986604C2216yescomplemented
73#17986603C2216yescomplemented
74#17986602C2216yescomplemented
75#17986602C2216yescomplemented
76#17986601C22112yescomplemented
77#17986601C22112yescomplemented
78#17986600C2216yescomplemented
79#17986600C2216yescomplemented
80#17986599C22112yescomplemented
81#17986599C22112yescomplemented
82#17986550C2213yescomplemented
83#17986549C2213yescomplemented
84#17986548C2216yescomplemented
85#17986547C2213yescomplemented
86#17986546C2216yescomplemented
87#17986546C2216yescomplemented
88#17986545C2216yescomplemented
89#17986544C2216yescomplemented
90#17986544C2216yescomplemented
91C4⋊Q8×D71C2213yes—
92#127×D71C2213yes—
93#127×D71C2216yes—
94#17986536C2213yescomplemented
95#17986535C2213yescomplemented
96#17986534C2213yescomplemented
97#17986533C2213yescomplemented
98#17986532C2216yescomplemented
99#17986531C2213yescomplemented
100#17986530C2213yescomplemented
101#17986529C2216yescomplemented
102#17986528C2213yescomplemented
103#17986527C2216yescomplemented
104#17986526C2216yescomplemented
105#126×D71C2216yes—
106#125×D71C2211yescharacteristic
107#125×D71C2216yes—
108#124×D71C2213yes—
109#123×D71C22112yes—
110#123×D71C2216yes—
111C22⋊Q8×D71C2213yes—
112#121×D71C2216yes—
113#121×D71C2213yes—
114#121×D71C2216yes—
115#121×D71C2216yes—
116#121×D71C22112yes—
117#121×D71C2216yes—
118#17986482C2212yescomplemented
119#17986481C2212yescomplemented
120#17986481C2212yescomplemented
121#17986480C2216yescomplemented
122#17986479C2216yescomplemented
123#17986478C2216yescomplemented
124#17986478C2216yescomplemented
125#41×Dic71C2211yescharacteristic, complemented
126C4×#11765866C2211yescharacteristic, complemented
127C4×#11765866C2211yescharacteristic, complemented
128C4×#11765865C2213yescomplemented
129#17986467C2213yescomplemented
130C4×#11765864C2213yescomplemented
131C4×#11765864C2213yescomplemented
132C4×Q8×D71C2211yescharacteristic
133C4×Q8×D71C2211yescharacteristic
134C4×Q8×D71C2212yes—
135C4×Q8×D71C2213yes—
136C4×D4×D71C2213yes—
137C4×D4×D71C2213yes—
138C4×D4×D71C2216yes—
139C4×D4×D71C2216yes—
140C4×D4×D71C2213yes—
141C4×D4×D71C2216yes—
142C4×D4×D71C2216yes—
143#117×D71C2213yes—
144#117×D71C2216yes—
145C2×C4⋊C4×D71C2216yes—
146C2×C42×D71C2213yes—
147#557×C71C2211yescharacteristic, complemented
148#553×C71C2216yescomplemented
149#550×C71C2212yescomplemented
150#550×C71C2211yescharacteristic, complemented
151#550×C71C2213yescomplemented
152#547×C71C2213yescomplemented
153#540×C71C2216yescomplemented
154#532×C71C2213yescomplemented
155#529×C71C2213yescomplemented
156#520×C71C2212yescomplemented
157C4×#41×C71C2211yescharacteristic, complemented
158C2×#11765866C2311yescharacteristic
159C2×#11765866C2312yes—
160C2×#11765866C2316yes—
161C2×#11765865C2313yes—
162C2×#11765865C2316yes—
163C2×#11765865C23112yes—
164C2×#11765865C2316yes—
165C2×#11765864C2313yes—
166C2×#11765864C2316yes—
167C2×#11765864C23112yes—
168C2×#11765864C2316yes—
169#41×D71—28no—
170#41×D71—216no—
171#41×D71—424no—
172C2×Q8×D71C2313yes—
173C2×Q8×D71C2311yescharacteristic
174C2×D4×D71C2313yes—
175C2×D4×D71C2313yes—
176C2×D4×D71C2316yes—
177C2×D4×D71C23112yes—
178C2×D4×D71C2316yes—
179C2×D4×D71C2316yes—
180C22×C4×D71C2313yes—
181C22×C4×D71C2313yes—
182C22×C4×D71C2316yes—
183C22×C4×D71C23112yes—
184C22×C4×D71C2313yes—
185#14556128C2313yes—
186#14556127C2316yes—
187#14556127C2316yes—
188#14556126C2316yes—
189#14556125C2316yes—
190#14556125C2313yes—
191#14556124C23112yes—
192#14556124C23112yes—
193#14556124C2316yes—
194#14556124C2316yes—
195#14556124C2316yes—
196#14556124C2316yes—
197#14556124C2316yes—
198#14556123C2316yes—
199#14556123C2316yes—
200#14556123C2316yes—
201#14556122C2316yes—
202#14556121C2316yes—
203#14556121C2316yes—
204#14556121C2316yes—
205#14556120C2316yes—
206#14556120C2311yescharacteristic
207#14556119C2316yes—
208#14556119C2316yes—
209#14556119C2311yescharacteristic
210#14556119C2311yescharacteristic
211#14556118C23112yes—
212#14556118C23112yes—
213#14556118C2312yes—
214#14556118C2312yes—
215#14556117C2313yes—
216#14556116C2313yes—
217#14556115C2313yes—
218#14556114C2316yes—
219#14556114C2316yes—
220#14556113C2316yes—
221#14556113C23112yes—
222#14556113C2316yes—
223#14556113C23112yes—
224#14556112C2316yes—
225#14556112C23112yes—
226#14556111C2316yes—
227#14556111C23112yes—
228#14556110C2316yes—
229#14556110C23112yes—
230#14556110C2316yes—
231#14556110C23112yes—
232#14556109C2316yes—
233#14556109C23112yes—
234#14556108C2313yes—
235#14556107C2313yes—
236#14556106C2316yes—
237#14556105C2316yes—
238#14556104C2313yes—
239#14556103C2316yes—
240#14556103C2316yes—
241#14556103C2316yes—
242#14556103C23112yes—
243#14556103C2313yes—
244#14556103C2316yes—
245#14556102C2316yes—
246#14556102C23112yes—
247#14556102C2316yes—
248#14556102C2316yes—
249#14556102C2313yes—
250#14556102C2316yes—
251#14556101C23112yes—
252#14556101C23112yes—
253#14556101C23112yes—
254#14556101C23112yes—
255#14556101C23112yes—
256#14556101C2316yes—
257#14556101C23112yes—
258#14556100C23112yes—
259#14556100C23112yes—
260#14556100C23112yes—
261#14556100C23112yes—
262#14556100C23112yes—
263#14556100C2316yes—
264#14556100C23112yes—
265#14556099C2316yes—
266#14556099C23112yes—
267#14556099C2316yes—
268#14556099C2316yes—
269#14556099C2313yes—
270#14556099C2316yes—
271Q8×Dic71C2313yes—
272Q8×Dic71C2311yescharacteristic
273Q8×Dic71C2312yes—
274Q8×Dic71C2311yescharacteristic
275C4×Dic142C2313yes—
276C4×Dic142C2313yes—
277C4×Dic142C2316yes—
278C4×Dic142C2316yes—
279C4×Dic142C2313yes—
280#14556093C2313yes—
281#14556093C2316yes—
282#14556093C2316yes—
283#14556093C2313yes—
284#14556093C2313yes—
285C4×D284C2313yes—
286C4×D284C2316yes—
287C4×D284C2313yes—
288C4×D284C2313yes—
289C4×D284C2316yes—
290C4×D284C2316yes—
291C4×D284C2316yes—
292D4×Dic71C2313yes—
293D4×Dic71C2316yes—
294D4×Dic71C2313yes—
295D4×Dic71C2313yes—
296D4×Dic71C2316yes—
297D4×Dic71C2316yes—
298D4×Dic71C2316yes—
299#14556090C2313yes—
300#14556090C2316yes—
301#14556090C2313yes—
302#14556090C2313yes—
303#14556090C2316yes—
304#14556090C2316yes—
305#14556090C2316yes—
306C4×C22⋊D71C2316yes—
307C4×C22⋊D71C23112yes—
308C4×C22⋊D71C2316yes—
309C4×C22⋊D71C2316yes—
310C4×C22⋊D71C2316yes—
311C4×C22⋊D71C23112yes—
312C4×C22⋊D71C2316yes—
313C4×C22⋊D71C23112yes—
314(C22⋊D71)⋊C4C2316yes—
315(C22⋊D71)⋊C4C23112yes—
316(C22⋊D71)⋊C4C2316yes—
317(C22⋊D71)⋊C4C2316yes—
318(C22⋊D71)⋊C4C23112yes—
319(C22⋊D71)⋊C4C2316yes—
320(C22⋊D71)⋊C4C2316yes—
321(C22⋊D71)⋊C4C23112yes—
322#14556087C2316yes—
323#14556087C2313yes—
324#14556086C2316yes—
325#14556086C2316yes—
326#14556086C2313yes—
327#14556086C2313yes—
328#14556085C2316yes—
329#14556085C2316yes—
330#14556085C2316yes—
331#14556084C2316yes—
332#14556084C2316yes—
333#14556084C2316yes—
334C2×C4⋊Dic71C2316yes—
335C2×Dic71⋊C4C23112yes—
336C4⋊C4×D71C23112yes—
337C4⋊C4×D71C2316yes—
338C4⋊C4×D71C2316yes—
339C4⋊C4×D71C2313yes—
340C4⋊C4×D71C2316yes—
341C4⋊C4×D71C2316yes—
342C4⋊C4×D71C2312yes—
343C4⋊C4×D71C2313yes—
344C4⋊C4×D71C2311yescharacteristic
345C4⋊C4×D71C2312yes—
346C4⋊C4×D71C2316yes—
347C4⋊C4×D71C2311yescharacteristic
348C4⋊C4×D71C2316yes—
349C22⋊C4×D71C2316yes—
350C22⋊C4×D71C2316yes—
351C22⋊C4×D71C2316yes—
352C22⋊C4×D71C2316yes—
353C22⋊C4×D71C2316yes—
354C22⋊C4×D71C2316yes—
355C2×C4×Dic71C2313yes—
356C2×C4×Dic71C2313yes—
357C2×C4×Dic71C2313yes—
358C42×D71C2311yescharacteristic
359C42×D71C2313yes—
360C42×D71C2313yes—
361C42×D71C2313yes—
362C42×D71C2313yes—
363C42×D71C2313yes—
364C42×D71C2313yes—
365C42×D71C2313yes—
366C42×D71C2316yes—
367C2×#41×C71C2311yescharacteristic
368C2×#41×C71C2312yes—
369C2×#41×C71C2316yes—
370C4⋊Q8×C71C2313yes—
371#127×C71C2316yes—
372#127×C71C2313yes—
373#126×C71C2316yes—
374#125×C71C2316yes—
375#125×C71C2311yescharacteristic
376#124×C71C2313yes—
377#123×C71C2316yes—
378#123×C71C23112yes—
379C22⋊Q8×C71C2313yes—
380#121×C71C2316yes—
381#121×C71C23112yes—
382#121×C71C2316yes—
383#121×C71C2316yes—
384#121×C71C2313yes—
385#121×C71C2316yes—
386C4×Q8×C71C2311yescharacteristic
387C4×Q8×C71C2312yes—
388C4×Q8×C71C2313yes—
389C4×Q8×C71C2311yescharacteristic
390C4×D4×C71C2313yes—
391C4×D4×C71C2316yes—
392C4×D4×C71C2313yes—
393C4×D4×C71C2313yes—
394C4×D4×C71C2316yes—
395C4×D4×C71C2316yes—
396C4×D4×C71C2316yes—
397#117×C71C2316yes—
398#117×C71C2313yes—
399C2×C4⋊C4×C71C2316yes—
400C2×C42×C71C2313yes—
401C23×D71C2413yes—
402C23×D71C2416yes—
403#11765866—24no—
404#11765866—28no—
405#11765866—412no—
406#11765865—212no—
407#11765865—224no—
408#11765865—424no—
409#11765865—412no—
410#11765864—212no—
411#11765864—224no—
412#11765864—412no—
413#11765864—424no—
414C2×Dic142C2416yes—
415C2×Dic142C2413yes—
416C2×Dic142C2413yes—
417Q8×D71—212no—
418Q8×D71#4118yescomplemented
419C2×D284C2413yes—
420C2×D284C2413yes—
421C2×D284C2416yes—
422C2×D284C24112yes—
423C2×D284C2416yes—
424C2×D284C2416yes—
425C2×C22⋊D71C2416yes—
426C2×C22⋊D71C2416yes—
427C2×C22⋊D71C24112yes—
428C2×C22⋊D71C24112yes—
429C2×C22⋊D71C24112yes—
430C2×C22⋊D71C24112yes—
431C2×C22⋊D71C2416yes—
432C2×C22⋊D71C2416yes—
433D4×D71—212no—
434D4×D71—224no—
435D4×D71—212no—
436D4×D71—412no—
437D4×D71—412no—
438D4×D71—424no—
439C22×Dic71C2413yes—
440C22×Dic71C2413yes—
441C22×Dic71C2416yes—
442C22×Dic71C24112yes—
443C22×Dic71C2413yes—
444C2×C4×D71—212no—
445C2×C4×D71—224no—
446C2×C4×D71—212no—
447C2×C4×D71—46no—
448C2×C4×D71—424no—
449C2×C4×D71C2413yes—
450C2×C4×D71C2411yescharacteristic
451C2×C4×D71C2411yescharacteristic
452C2×C4×D71C2412yes—
453C2×C4×D71C2416yes—
454C2×C4×D71C2413yes—
455C2×C4×D71C2413yes—
456C2×C4×D71C2413yes—
457C2×C4×D71C2416yes—
458C2×C4×D71C2413yes—
459C2×C4×D71C2413yes—
460C2×C4×D71C2416yes—
461C2×C4×D71C2412yes—
462C2×C4×D71C24112yes—
463C2×C4×D71C24112yes—
464C2×C4×D71C2413yes—
465C2×C4×D71C2413yes—
466C2×C4×D71C2413yes—
467C2×C4×D71C2411yescharacteristic
468C4⋊Dic71C2413yes—
469C4⋊Dic71C2416yes—
470C4⋊Dic71C2416yes—
471C4⋊Dic71C2412yes—
472C4⋊Dic71C2413yes—
473C4⋊Dic71C2411yescharacteristic
474C4⋊Dic71C2412yes—
475C4⋊Dic71C2416yes—
476C4⋊Dic71C2411yescharacteristic
477C4⋊Dic71C2416yes—
478Dic71⋊C4C2416yes—
479Dic71⋊C4C2416yes—
480Dic71⋊C4C2416yes—
481Dic71⋊C4C24112yes—
482Dic71⋊C4C2412yes—
483Dic71⋊C4C2412yes—
484Dic71⋊C4C2416yes—
485Dic71⋊C4C2412yes—
486Dic71⋊C4C2412yes—
487Dic71⋊C4C2412yes—
488Dic71⋊C4C24112yes—
489Dic71⋊C4C2412yes—
490Dic71⋊C4C2416yes—
491Dic71⋊C4C2416yes—
492C22⋊Dic71C2416yes—
493C22⋊Dic71C2416yes—
494C22⋊Dic71C2416yes—
495C22⋊Dic71C2416yes—
496C22⋊Dic71C2416yes—
497C22⋊Dic71C2416yes—
498(C2×D71)⋊C4C2416yes—
499(C2×D71)⋊C4C2416yes—
500(C2×D71)⋊C4C2416yes—
501(C2×D71)⋊C4C2416yes—
502(C2×D71)⋊C4C2416yes—
503(C2×D71)⋊C4C2416yes—
504(C2×D71)⋊C4C2416yes—
505(C2×D71)⋊C4C2416yes—
506(C2×D71)⋊C4C2416yes—
507(C2×D71)⋊C4C2416yes—
508(C2×D71)⋊C4C2416yes—
509(C2×D71)⋊C4C2416yes—
510C4×Dic71C2411yescharacteristic
511C4×Dic71C2411yescharacteristic
512C4×Dic71C2411yescharacteristic
513C4×Dic71C2413yes—
514C4×Dic71C2413yes—
515C4×Dic71C2413yes—
516C4×Dic71C2413yes—
517C4×Dic71C2413yes—
518C4×Dic71C2413yes—
519C4×Dic71C2413yes—
520C4×Dic71C2413yes—
521C4×Dic71C2413yes—
522C4×Dic71C2416yes—
523C4×Dic71C2416yes—
524C4×Dic71C2416yes—
525#41×C71—24no—
526#41×C71—28no—
527#41×C71—412no—
528C2×Q8×C71C2413yes—
529C2×Q8×C71C2411yescharacteristic
530C2×D4×C71C2413yes—
531C2×D4×C71C2413yes—
532C2×D4×C71C2416yes—
533C2×D4×C71C24112yes—
534C2×D4×C71C2416yes—
535C2×D4×C71C2416yes—
536C22×C4×C71C2413yes—
537C22×C4×C71C2413yes—
538C22×C4×C71C2416yes—
539C22×C4×C71C24112yes—
540C22×C4×C71C2413yes—
541C4⋊C4×C71C2413yes—
542C4⋊C4×C71C2416yes—
543C4⋊C4×C71C2416yes—
544C4⋊C4×C71C2412yes—
545C4⋊C4×C71C2413yes—
546C4⋊C4×C71C2411yescharacteristic
547C4⋊C4×C71C2412yes—
548C4⋊C4×C71C2416yes—
549C4⋊C4×C71C2411yescharacteristic
550C4⋊C4×C71C2416yes—
551C22⋊C4×C71C2416yes—
552C22⋊C4×C71C2416yes—
553C22⋊C4×C71C2416yes—
554C22⋊C4×C71C2416yes—
555C22⋊C4×C71C2416yes—
556C22⋊C4×C71C2416yes—
557C42×C71C2411yescharacteristic
558C42×C71C2413yes—
559C42×C71C2413yes—
560C42×C71C2413yes—
561C42×C71C2416yes—
562C23×C71C2513yes—
563C23×C71C2516yes—
564C22×D71—26no—
565C22×D71—212no—
566C22×D71—26no—
567C22×D71—212no—
568C22×D71—26no—
569C22×D71—212no—
570C22×D71C2513yes—
571C22×D71C2516yes—
572C22×D71C2511yescharacteristic
573Q8×C71—26no—
574Q8×C71C2×#4114yescomplemented
575D4×C71—26no—
576D4×C71—212no—
577D4×C71—26no—
578D4×C71—412no—
579D4×C71—46no—
580D4×C71—46no—
581C2×C4×C71—26no—
582C2×C4×C71—212no—
583C2×C4×C71—26no—
584C2×C4×C71—412no—
585C2×C4×C71—43no—
586C2×C4×C71C2511yescharacteristic
587C2×C4×C71C2511yescharacteristic
588C2×C4×C71C2512yes—
589C2×C4×C71C2513yes—
590C2×C4×C71C2513yes—
591C2×C4×C71C2516yes—
592C2×C4×C71C2512yes—
593C2×C4×C71C2513yes—
594C2×C4×C71C2511yescharacteristic
595C22⋊D71—212no—
596C22⋊D71—224no—
597C22⋊D71—212no—
598C22⋊D71—412no—
599C22⋊D71—46no—
600C22⋊D71—46no—
601C22⋊D71—412no—
602C22⋊D71—412no—
603C2×Dic71—26no—
604C2×Dic71—212no—
605C2×Dic71—26no—
606C2×Dic71—43no—
607C2×Dic71—412no—
608C2×Dic71C2511yescharacteristic
609C2×Dic71C2511yescharacteristic
610C2×Dic71C2512yes—
611C2×Dic71C2513yes—
612C2×Dic71C2513yes—
613C2×Dic71C2516yes—
614C2×Dic71C2512yes—
615C2×Dic71C2513yes—
616C2×Dic71C2511yescharacteristic
617D284—26no—
618D284—212no—
619D284—26no—
620D284—46no—
621D284—46no—
622D284—412no—
623C4×D71—22no—
624C4×D71—24no—
625C4×D71—26no—
626C4×D71—212no—
627C4×D71—22no—
628C4×D71—26no—
629C4×D71—24no—
630C4×D71—26no—
631C4×D71—212no—
632C4×D71—26no—
633C4×D71—26no—
634C4×D71—212no—
635C4×D71—26no—
636C4×D71—43no—
637C4×D71—43no—
638C4×D71—412no—
639C4×D71—412no—
640C4×D71C2×#41112yes—
641C4×D71H(5,𝔽2)14yes—
642Dic142—26no—
643Dic142—212no—
644Dic142C2×#41112yescomplemented
645C22×C71—23no—
646C22×C71—26no—
647C22×C71—23no—
648C22×C71—26no—
649C22×C71—23no—
650C22×C71—26no—
651C22×C71C2611yescharacteristic
652C2×D71—23no—
653C2×D71—26no—
654C2×D71—23no—
655C2×D71—26no—
656C2×D71—23no—
657C2×D71—26no—
658C2×D71—412no—
659C2×D71—424no—
660C2×D71C22×#4112yes—
661C2×D71C2×H(5,𝔽2)12yes—
662C2×D71#58512yes—
663C4×C71—21no—
664C4×C71—22no—
665C4×C71—26no—
666C4×C71—23no—
667C4×C71—21no—
668C4×C71—23no—
669C4×C71—22no—
670C4×C71C22×#4116yes—
671C4×C71C2×H(5,𝔽2)12yes—
672Dic71—21no—
673Dic71—22no—
674Dic71—26no—
675Dic71—23no—
676Dic71—21no—
677Dic71—23no—
678Dic71—22no—
679Dic71C22×#4116yes—
680Dic71C2×H(5,𝔽2)12yes—
681C2×#3517—711nomaximal, Sylow
682C2×C71—43no—
683C2×C71—46no—
684C2×C71C23×#4111yescharacteristic
685C2×C71C22×H(5,𝔽2)11yescharacteristic
686C2×C71C2×#58511yescharacteristic
687D71—43no—
688D71—46no—
689D71#351714yesdirect product factor
690#3517—711no—
691#3517—716no—
692#3517—712no—
693#3517—711no—
694#3517—713no—
695#3517—713no—
696#3517—716no—
697#3517—713no—
698#3517—713no—
699#3517—712no—
700#3517—711no—
701#3517D7111yescharacteristic, direct product factor
702C2×#557—711no—
703C2×#553—716no—
704C2×#550—713no—
705C2×#550—711no—
706C2×#550—712no—
707C2×#547—713no—
708C2×#540—716no—
709C2×#532—713no—
710C2×#529—713no—
711C2×#520—712no—
712C2×C4×#41—711no—
713C71C2×#351711yescharacteristic, complemented, Sylow
714C22×#41—716no—
715C22×#41—711no—
716C22×#41—712no—
717#557—713no—
718#557—716no—
719#557—712no—
720#557—713no—
721#557—711no—
722#557C2×D7111yescharacteristic, complemented
723#553—7112no—
724#553—716no—
725#553—7112no—
726#553—7112no—
727#553—716no—
728#553—716no—
729#553—716no—
730#553—7112no—
731#553—716no—
732#553—716no—
733#553—716no—
734#553C2×D7116yescomplemented
735#550—716no—
736#550—712no—
737#550—712no—
738#550—712no—
739#550—716no—
740#550—713no—
741#550—713no—
742#550—716no—
743#550—716no—
744#550—7112no—
745#550—716no—
746#550—716no—
747#550—716no—
748#550—713no—
749#550—711no—
750#550—712no—
751#550—716no—
752#550—713no—
753#550—713no—
754#550—716no—
755#550C2×D7113yescomplemented
756#550C2×D7111yescharacteristic, complemented
757#550C2×D7112yescomplemented
758#547—716no—
759#547—713no—
760#547—7112no—
761#547—716no—
762#547—716no—
763#547—713no—
764#547—713no—
765#547—716no—
766#547C2×D7113yescomplemented
767#540—716no—
768#540—716no—
769#540—7112no—
770#540—7112no—
771#540—7112no—
772#540—7112no—
773#540—716no—
774#540—716no—
775#540—716no—
776#540—716no—
777#540—716no—
778#540C2×D7116yescomplemented
779#532—716no—
780#532—713no—
781#532—713no—
782#532—716no—
783#532—716no—
784#532—716no—
785#532—716no—
786#532—716no—
787#532—713no—
788#532C2×D7113yescomplemented
789C2×C4⋊Q8—713no—
790C2×#127—713no—
791C2×#127—716no—
792#529—716no—
793#529—713no—
794#529—713no—
795#529—716no—
796#529—713no—
797#529—713no—
798#529—713no—
799#529—716no—
800#529—713no—
801#529—716no—
802#529—713no—
803#529C2×D7113yescomplemented
804C2×#126—716no—
805C2×#125—711no—
806C2×#125—716no—
807C2×#124—713no—
808C2×#123—716no—
809C2×#123—7112no—
810C2×C22⋊Q8—713no—
811C2×#121—713no—
812C2×#121—716no—
813C2×#121—716no—
814C2×#121—716no—
815C2×#121—7112no—
816C2×#121—716no—
817#520—712no—
818#520—712no—
819#520—712no—
820#520—716no—
821#520—716no—
822#520—716no—
823#520—716no—
824#520C2×D7112yescomplemented
825C4×#41—711no—
826C4×#41—711no—
827C4×#41—711no—
828C4×#41—713no—
829C4×#41—713no—
830C4×#41—713no—
831C4×#41—713no—
832C4×#41C2×D7111yescharacteristic, complemented
833C2×C4×Q8—711no—
834C2×C4×Q8—711no—
835C2×C4×Q8—712no—
836C2×C4×Q8—713no—
837C2×C4×D4—713no—
838C2×C4×D4—713no—
839C2×C4×D4—716no—
840C2×C4×D4—716no—
841C2×C4×D4—713no—
842C2×C4×D4—716no—
843C2×C4×D4—716no—
844C2×#117—713no—
845C2×#117—716no—
846C22×C4⋊C4—716no—
847C22×C42—713no—
848C2×#41—28424no—
849C2×#41—716no—
850C2×#41—711no—
851C2×#41—712no—
852C2×#41—716no—
853C2×#41—7112no—
854C2×#41—713no—
855C2×#41—716no—
856C2×#41—716no—
857C2×#41—7112no—
858C2×#41—713no—
859C2×#41—716no—
860C2×#41—1428no—
861C2×#41—14216no—
862C2×#41C22×D7111yescharacteristic
863C2×#41C22×D7112yes—
864C2×#41C22×D7116yes—
865C22×Q8—711no—
866C22×Q8—713no—
867C22×D4—716no—
868C22×D4—716no—
869C22×D4—7112no—
870C22×D4—713no—
871C22×D4—716no—
872C22×D4—713no—
873C23×C4—7112no—
874C23×C4—713no—
875C23×C4—716no—
876C23×C4—713no—
877C23×C4—713no—
878C4⋊Q8—716no—
879C4⋊Q8—716no—
880C4⋊Q8—716no—
881C4⋊Q8—713no—
882C4⋊Q8C22×D7113yes—
883#127—716no—
884#127—716no—
885#127—716no—
886#127—716no—
887#127—716no—
888#127—7112no—
889#127—7112no—
890#127—713no—
891#127—716no—
892#127C22×D7113yes—
893#127C22×D7116yes—
894#126—716no—
895#126—716no—
896#126—716no—
897#126—716no—
898#126—716no—
899#126—716no—
900#126—716no—
901#126C22×D7116yes—
902#125—712no—
903#125—712no—
904#125—711no—
905#125—711no—
906#125—7112no—
907#125—7112no—
908#125—716no—
909#125—716no—
910#125—711no—
911#125—716no—
912#125C22×D7111yescharacteristic
913#125C22×D7116yes—
914#124—713no—
915#124—713no—
916#124—716no—
917#124—716no—
918#124—713no—
919#124C22×D7113yes—
920#123—716no—
921#123—7112no—
922#123—716no—
923#123—7112no—
924#123—716no—
925#123—716no—
926#123—7112no—
927#123—7112no—
928#123—716no—
929#123—716no—
930#123—716no—
931#123—7112no—
932#123—7112no—
933#123—7112no—
934#123C22×D7116yes—
935#123C22×D71112yes—
936C22⋊Q8—713no—
937C22⋊Q8—713no—
938C22⋊Q8—716no—
939C22⋊Q8—713no—
940C22⋊Q8—716no—
941C22⋊Q8C22×D7113yes—
942#121—713no—
943#121—716no—
944#121—716no—
945#121—7112no—
946#121—716no—
947#121—7112no—
948#121—716no—
949#121—7112no—
950#121—7112no—
951#121—716no—
952#121—7112no—
953#121—7112no—
954#121—7112no—
955#121—713no—
956#121—716no—
957#121—716no—
958#121—716no—
959#121—7112no—
960#121—716no—
961#121—713no—
962#121—716no—
963#121—716no—
964#121—716no—
965#121—7112no—
966#121—716no—
967#121—716no—
968#121—7112no—
969#121—7112no—
970#121—7112no—
971#121—7112no—
972#121—7112no—
973#121—7112no—
974#121C22×D7113yes—
975#121C22×D7116yes—
976#121C22×D7116yes—
977#121C22×D7116yes—
978#121C22×D71112yes—
979#121C22×D7116yes—
980C4×Q8—711no—
981C4×Q8—711no—
982C4×Q8—712no—
983C4×Q8—713no—
984C4×Q8—713no—
985C4×Q8—713no—
986C4×Q8—716no—
987C4×Q8—716no—
988C4×Q8—713no—
989C4×Q8—713no—
990C4×Q8—713no—
991C4×Q8—716no—
992C4×Q8—716no—
993C4×Q8—713no—
994C4×Q8C22×D7111yescharacteristic
995C4×Q8C22×D7111yescharacteristic
996C4×Q8C22×D7112yes—
997C4×Q8C22×D7113yes—
998C4×D4—713no—
999C4×D4—713no—
1000C4×D4—716no—
1001C4×D4—716no—
1002C4×D4—713no—
1003C4×D4—716no—
1004C4×D4—716no—
1005C4×D4—716no—
1006C4×D4—716no—
1007C4×D4—7112no—
1008C4×D4—7112no—
1009C4×D4—716no—
1010C4×D4—716no—
1011C4×D4—716no—
1012C4×D4—7112no—
1013C4×D4—713no—
1014C4×D4—713no—
1015C4×D4—716no—
1016C4×D4—716no—
1017C4×D4—713no—
1018C4×D4—716no—
1019C4×D4—716no—
1020C4×D4—716no—
1021C4×D4—716no—
1022C4×D4—7112no—
1023C4×D4—7112no—
1024C4×D4—716no—
1025C4×D4—716no—
1026C4×D4—716no—
1027C4×D4—7112no—
1028C4×D4—713no—
1029C4×D4—713no—
1030C4×D4—716no—
1031C4×D4—716no—
1032C4×D4—713no—
1033C4×D4—716no—
1034C4×D4—716no—
1035C4×D4C22×D7113yes—
1036C4×D4C22×D7113yes—
1037C4×D4C22×D7116yes—
1038C4×D4C22×D7116yes—
1039C4×D4C22×D7113yes—
1040C4×D4C22×D7116yes—
1041C4×D4C22×D7116yes—
1042#117—713no—
1043#117—716no—
1044#117—713no—
1045#117—713no—
1046#117—716no—
1047#117—716no—
1048#117—716no—
1049#117—716no—
1050#117—716no—
1051#117—716no—
1052#117—716no—
1053#117—716no—
1054#117C22×D7113yes—
1055#117C22×D7116yes—
1056C2×C4⋊C4—7112no—
1057C2×C4⋊C4—716no—
1058C2×C4⋊C4—713no—
1059C2×C4⋊C4—716no—
1060C2×C4⋊C4—716no—
1061C2×C4⋊C4—7112no—
1062C2×C4⋊C4—716no—
1063C2×C4⋊C4—716no—
1064C2×C4⋊C4—712no—
1065C2×C4⋊C4—713no—
1066C2×C4⋊C4—711no—
1067C2×C4⋊C4—712no—
1068C2×C4⋊C4—716no—
1069C2×C4⋊C4—711no—
1070C2×C4⋊C4—716no—
1071C2×C4⋊C4C22×D7116yes—
1072C2×C22⋊C4—716no—
1073C2×C22⋊C4—716no—
1074C2×C22⋊C4—716no—
1075C2×C22⋊C4—716no—
1076C2×C22⋊C4—716no—
1077C2×C22⋊C4—716no—
1078C2×C42—713no—
1079C2×C42—713no—
1080C2×C42—713no—
1081C2×C42—713no—
1082C2×C42—713no—
1083C2×C42—716no—
1084C2×C42—713no—
1085C2×C42—713no—
1086C2×C42—713no—
1087C2×C42—713no—
1088C2×C42—713no—
1089C2×C42—711no—
1090C2×C42C22×D7113yes—
1091C24—716no—
1092C24—713no—
1093#41—24no—
1094#41—28no—
1095#41—412no—
1096#41—28412no—
1097#41—28424no—
1098#41—28412no—
1099#41—28424no—
1100#41—28412no—
1101#41—14212no—
1102#41—14224no—
1103#41—14212no—
1104#41—14224no—
1105#41—1424no—
1106#41—1428no—
1107C2×Q8—718no—
1108C2×Q8—713no—
1109C2×Q8—716no—
1110C2×Q8—713no—
1111C2×Q8—14212no—
1112C2×Q8C23×D7113yes—
1113C2×Q8C23×D7111yescharacteristic
1114C2×D4—28412no—
1115C2×D4—28412no—
1116C2×D4—28424no—
1117C2×D4—7112no—
1118C2×D4—716no—
1119C2×D4—716no—
1120C2×D4—7112no—
1121C2×D4—7112no—
1122C2×D4—716no—
1123C2×D4—7112no—
1124C2×D4—716no—
1125C2×D4—716no—
1126C2×D4—716no—
1127C2×D4—7112no—
1128C2×D4—713no—
1129C2×D4—716no—
1130C2×D4—713no—
1131C2×D4—14212no—
1132C2×D4—14212no—
1133C2×D4—14224no—
1134C2×D4C23×D7113yes—
1135C2×D4C23×D7116yes—
1136C2×D4C23×D7113yes—
1137C2×D4C23×D7116yes—
1138C2×D4C23×D7116yes—
1139C2×D4C23×D71112yes—
1140C22×C4—2846no—
1141C22×C4—28424no—
1142C22×C4—713no—
1143C22×C4—7112no—
1144C22×C4—713no—
1145C22×C4—713no—
1146C22×C4—7112no—
1147C22×C4—7112no—
1148C22×C4—713no—
1149C22×C4—711no—
1150C22×C4—713no—
1151C22×C4—713no—
1152C22×C4—716no—
1153C22×C4—711no—
1154C22×C4—711no—
1155C22×C4—712no—
1156C22×C4—713no—
1157C22×C4—713no—
1158C22×C4—713no—
1159C22×C4—713no—
1160C22×C4—713no—
1161C22×C4—713no—
1162C22×C4—716no—
1163C22×C4—712no—
1164C22×C4—716no—
1165C22×C4—716no—
1166C22×C4—14212no—
1167C22×C4—14224no—
1168C22×C4—14212no—
1169C22×C4C23×D7113yes—
1170C22×C4C23×D7113yes—
1171C22×C4C23×D7116yes—
1172C22×C4C23×D7113yes—
1173C22×C4C23×D71112yes—
1174C4⋊C4—716no—
1175C4⋊C4—716no—
1176C4⋊C4—716no—
1177C4⋊C4—7112no—
1178C4⋊C4—712no—
1179C4⋊C4—712no—
1180C4⋊C4—716no—
1181C4⋊C4—712no—
1182C4⋊C4—712no—
1183C4⋊C4—712no—
1184C4⋊C4—7112no—
1185C4⋊C4—712no—
1186C4⋊C4—716no—
1187C4⋊C4—716no—
1188C4⋊C4—713no—
1189C4⋊C4—716no—
1190C4⋊C4—716no—
1191C4⋊C4—712no—
1192C4⋊C4—713no—
1193C4⋊C4—711no—
1194C4⋊C4—712no—
1195C4⋊C4—716no—
1196C4⋊C4—711no—
1197C4⋊C4—716no—
1198C4⋊C4C23×D7113yes—
1199C4⋊C4C23×D7116yes—
1200C4⋊C4C23×D7116yes—
1201C4⋊C4C23×D7112yes—
1202C4⋊C4C23×D7113yes—
1203C4⋊C4C23×D7111yescharacteristic
1204C4⋊C4C23×D7112yes—
1205C4⋊C4C23×D7116yes—
1206C4⋊C4C23×D7111yescharacteristic
1207C4⋊C4C23×D7116yes—
1208C22⋊C4—716no—
1209C22⋊C4—716no—
1210C22⋊C4—716no—
1211C22⋊C4—716no—
1212C22⋊C4—716no—
1213C22⋊C4—716no—
1214C22⋊C4—716no—
1215C22⋊C4—716no—
1216C22⋊C4—716no—
1217C22⋊C4—716no—
1218C22⋊C4—716no—
1219C22⋊C4—716no—
1220C22⋊C4—716no—
1221C22⋊C4—716no—
1222C22⋊C4—716no—
1223C22⋊C4—716no—
1224C22⋊C4—716no—
1225C22⋊C4—716no—
1226C22⋊C4C23×D7116yes—
1227C22⋊C4C23×D7116yes—
1228C22⋊C4C23×D7116yes—
1229C22⋊C4C23×D7116yes—
1230C22⋊C4C23×D7116yes—
1231C22⋊C4C23×D7116yes—
1232C42—711no—
1233C42—711no—
1234C42—711no—
1235C42—713no—
1236C42—713no—
1237C42—713no—
1238C42—713no—
1239C42—713no—
1240C42—713no—
1241C42—713no—
1242C42—713no—
1243C42—713no—
1244C42—716no—
1245C42—716no—
1246C42—716no—
1247C42C23×D7111yescharacteristic
1248C42C23×D7113yes—
1249C42C23×D7113yes—
1250C42C23×D7113yes—
1251C42C23×D7116yes—
1252C23—711no—
1253C23—716no—
1254C23—713no—
1255C23—14212no—
1256C23—1426no—
1257C23—1426no—
1258C23—14212no—
1259C23—1426no—
1260C23—14212no—
1261C23C24×D7113yes—
1262C23C24×D7116yes—
1263Q8—26no—
1264Q8—7112no—
1265Q8—14212no—
1266Q8—1426no—
1267Q8#41×D7114yescomplemented
1268D4—26no—
1269D4—212no—
1270D4—26no—
1271D4—412no—
1272D4—46no—
1273D4—46no—
1274D4—28412no—
1275D4—2846no—
1276D4—2846no—
1277D4—28412no—
1278D4—28412no—
1279D4—28412no—
1280D4—2846no—
1281D4—2846no—
1282D4—14212no—
1283D4—14212no—
1284D4—14224no—
1285D4—1426no—
1286D4—14212no—
1287D4—1426no—
1288C2×C4—26no—
1289C2×C4—212no—
1290C2×C4—26no—
1291C2×C4—412no—
1292C2×C4—43no—
1293C2×C4—28412no—
1294C2×C4—28412no—
1295C2×C4—2843no—
1296C2×C4—2843no—
1297C2×C4—28412no—
1298C2×C4—2843no—
1299C2×C4—713no—
1300C2×C4—711no—
1301C2×C4—7112no—
1302C2×C4—714no—
1303C2×C4—711no—
1304C2×C4—711no—
1305C2×C4—712no—
1306C2×C4—713no—
1307C2×C4—713no—
1308C2×C4—716no—
1309C2×C4—712no—
1310C2×C4—1426no—
1311C2×C4—1426no—
1312C2×C4—14212no—
1313C2×C4—1426no—
1314C2×C4—1422no—
1315C2×C4—14212no—
1316C2×C4—1426no—
1317C2×C4—1422no—
1318C2×C4—1424no—
1319C2×C4—1424no—
1320C2×C4—1426no—
1321C2×C4—1426no—
1322C2×C4—14212no—
1323C2×C4—1426no—
1324C2×C4—14212no—
1325C2×C4—1426no—
1326C2×C4C24×D7111yescharacteristic
1327C2×C4C24×D7111yescharacteristic
1328C2×C4C24×D7112yes—
1329C2×C4C24×D7113yes—
1330C2×C4C24×D7113yes—
1331C2×C4C24×D7116yes—
1332C2×C4C24×D7112yes—
1333C2×C4C24×D7113yes—
1334C2×C4C24×D7111yescharacteristic
1335C22—23no—
1336C22—26no—
1337C22—23no—
1338C22—26no—
1339C22—23no—
1340C22—26no—
1341C22—28424no—
1342C22—28412no—
1343C22—712no—
1344C22—712no—
1345C22—712no—
1346C22—1426no—
1347C22—1423no—
1348C22—1426no—
1349C22—1423no—
1350C22—1423no—
1351C22—1426no—
1352C22C25×D7111yescharacteristic
1353C4—21no—
1354C4—22no—
1355C4—23no—
1356C4—26no—
1357C4—21no—
1358C4—23no—
1359C4—22no—
1360C4—716no—
1361C4—712no—
1362C4—1421no—
1363C4—1422no—
1364C4—1423no—
1365C4—1426no—
1366C4—1421no—
1367C4—1423no—
1368C4—1422no—
1369C4C2×#41×D7116yes—
1370C4H(5,𝔽2)×D7112yes—
1371C2—43no—
1372C2—46no—
1373C2—2846no—
1374C2—2843no—
1375C2—714no—
1376C2C22×#41×D7111yescharacteristic
1377C2C2×H(5,𝔽2)×D7111yescharacteristic
1378C2#585×D7111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3517C2
hypercenter#3517D71
hypocenterC71C2×#3517
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #22602347C2semidirect
2. #22602346C2semidirect
3. #22602345C2semidirect
4. #22602344C2semidirect
5. #22602343C2semidirect
6. #22602342C2semidirect
7. #22602341C2semidirect
8. #22602340C2semidirect
9. #22602339C2semidirect
10. #22602338C2semidirect
11. #22602337C2semidirect
12. #557×D71C2semidirect
13. #553×D71C2semidirect
14. #550×D71C2semidirect
15. #550×D71C2semidirect
16. #550×D71C2semidirect
17. #547×D71C2semidirect
18. #540×D71C2semidirect
19. #532×D71C2semidirect
20. #529×D71C2semidirect
21. #520×D71C2semidirect
22. C4×#41×D71C2semidirect
23. C71×#3517C2semidirect
27. #17986728C22semidirect
28. #17986727C22semidirect
29. #17986726C22semidirect
30. #17986725C22semidirect
31. #17986724C22semidirect
32. #17986702C22semidirect
33. #17986701C22semidirect
34. #17986700C22semidirect
35. #17986699C22semidirect
36. #17986698C22semidirect
37. #17986697C22semidirect
38. #17986696C22semidirect
39. #17986695C22semidirect
40. #17986694C22semidirect
41. #17986693C22semidirect
42. #17986692C22semidirect
43. #17986671C22semidirect
44. #17986671C22semidirect
45. #17986671C22semidirect
46. #17986670C22semidirect
47. #17986670C22semidirect
48. #17986670C22semidirect
49. #17986670C22semidirect
50. #17986669C22semidirect
51. #17986669C22semidirect
52. #17986669C22semidirect
53. #17986669C22semidirect
54. #17986668C22semidirect
55. #17986668C22semidirect
56. #17986668C22semidirect
57. #17986668C22semidirect
58. #17986667C22semidirect
59. #17986667C22semidirect
60. #17986667C22semidirect
61. #17986667C22semidirect
62. #17986667C22semidirect
63. #17986654C22semidirect
64. #17986653C22semidirect
65. #17986652C22semidirect
66. #17986651C22semidirect
67. #17986650C22semidirect
68. #17986649C22semidirect
69. #17986648C22semidirect
70. #17986647C22semidirect
71. #17986605C22semidirect
72. #17986604C22semidirect
73. #17986603C22semidirect
74. #17986602C22semidirect
75. #17986602C22semidirect
76. #17986601C22semidirect
77. #17986601C22semidirect
78. #17986600C22semidirect
79. #17986600C22semidirect
80. #17986599C22semidirect
81. #17986599C22semidirect
82. #17986550C22semidirect
83. #17986549C22semidirect
84. #17986548C22semidirect
85. #17986547C22semidirect
86. #17986546C22semidirect
87. #17986546C22semidirect
88. #17986545C22semidirect
89. #17986544C22semidirect
90. #17986544C22semidirect
94. #17986536C22semidirect
95. #17986535C22semidirect
96. #17986534C22semidirect
97. #17986533C22semidirect
98. #17986532C22semidirect
99. #17986531C22semidirect
100. #17986530C22semidirect
101. #17986529C22semidirect
102. #17986528C22semidirect
103. #17986527C22semidirect
104. #17986526C22semidirect
118. #17986482C22semidirect
119. #17986481C22semidirect
120. #17986481C22semidirect
121. #17986480C22semidirect
122. #17986479C22semidirect
123. #17986478C22semidirect
124. #17986478C22semidirect
125. #41×Dic71C22semidirect
126. C4×#11765866C22semidirect
127. C4×#11765866C22semidirect
128. C4×#11765865C22semidirect
129. #17986467C22semidirect
130. C4×#11765864C22semidirect
131. C4×#11765864C22semidirect
147. #557×C71C22semidirect
148. #553×C71C22semidirect
149. #550×C71C22semidirect
150. #550×C71C22semidirect
151. #550×C71C22semidirect
152. #547×C71C22semidirect
153. #540×C71C22semidirect
154. #532×C71C22semidirect
155. #529×C71C22semidirect
156. #520×C71C22semidirect
157. C4×#41×C71C22semidirect
418. Q8×D71#41semidirect
574. Q8×C71C2×#41semidirect
644. Dic142C2×#41semidirect
689. D71#3517direct (N × H)
701. #3517D71direct (N × H)
713. C71C2×#3517semidirect
722. #557C2×D71semidirect
734. #553C2×D71semidirect
755. #550C2×D71semidirect
756. #550C2×D71semidirect
757. #550C2×D71semidirect
766. #547C2×D71semidirect
778. #540C2×D71semidirect
788. #532C2×D71semidirect
803. #529C2×D71semidirect
824. #520C2×D71semidirect
832. C4×#41C2×D71semidirect
1267. Q8#41×D71semidirect

Maximal subgroups

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

subgroupindex
#226023472
#226023462
#226023452
#226023442
#226023432
#226023422
#226023412
#226023402
#226023392
#226023382
#226023372
#557×D712
#553×D712
#550×D712
#547×D712
#540×D712
#532×D712
#529×D712
#520×D712
C4×#41×D712
C71×#35172
C2×#351771