Finite Group Databasebeta

← C4×#17986661 #32157281

Subgroups — C4×#17986661 #32157281

Order 18176.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986661C211yesmaximal, characteristic
2C2×C4×#11765866C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
4#22591411C213yesmaximal, complemented
5#22591369C213yesmaximal, complemented
6#22591358C213yesmaximal, complemented
7#22591272C213yesmaximal, complemented
8#22591261C211yesmaximal, characteristic, complemented
9#22591178C211yesmaximal, characteristic, complemented
10Q8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
11C4×#14556116C213yesmaximal, complemented
12C4×#14556108C213yesmaximal, complemented
13C4×#14556103C213yesmaximal, complemented
14C42×D284C213yesmaximal, complemented
15C42×Q8×C71C211yesmaximal, characteristic, complemented
16C22×#11765866C2211yescharacteristic
17C22×Q8×D71C2211yescharacteristic
18#17986661C4116yesdirect product factor
19C2×#14556116C2213yes—
20C2×#14556108C2213yes—
21C2×#14556103C2213yes—
22C4×#11765866—28no—
23C2×Q8×Dic71C2211yescharacteristic
24C2×Q8×Dic71C2211yescharacteristic
25C2×C4×Dic142C2213yes—
26C2×#14556093C2213yes—
27C4×Q8×D71—28no—
28C2×C4×D284C2213yes—
29C2×C4×D284C2213yes—
30C2×C4×D284C2213yes—
31C2×C4×D284C2213yes—
32C2×#14556090C2213yes—
33C2×#14556086C2213yes—
34C2×C4⋊C4×D71C2213yes—
35C2×C42×D71C2213yes—
36C2×C42×D71C2213yes—
37#17985905C2213yes—
38#17985904C2213yes—
39#17985901C2213yes—
40#17985900C2213yes—
41#17985898C2213yes—
42#17985898C2213yes—
43#17985891C2216yes—
44#17985890C2216yes—
45#17985890C2216yes—
46#17985884C2216yes—
47#17985877C2216yes—
48#17985873C2216yes—
49#17985865C2213yes—
50#17985856C2213yes—
51#17985856C2213yes—
52C4×C4⋊Dic71C2213yes—
53C4×C4⋊Dic71C2213yes—
54C4×C4⋊Dic71C2213yes—
55C4×(C2×D71)⋊C4C2213yes—
56C4×(C2×D71)⋊C4C2213yes—
57C4×(C2×D71)⋊C4C2216yes—
58C4×(C2×D71)⋊C4C2213yes—
59C4×(C2×D71)⋊C4C2213yes—
60C4×(C2×D71)⋊C4C2213yes—
61C4×(C2×D71)⋊C4C2211yescharacteristic
62C2×C4×Q8×C71C2211yescharacteristic
63C2×C4×Q8×C71C2211yescharacteristic
64C2×C4×Q8×C71C2211yescharacteristic
65C4×C4⋊C4×C71C2213yes—
66C4×C4⋊C4×C71C2213yes—
67C4×C4⋊C4×C71C2213yes—
68C43×C71C2213yes—
69C2×#11765866—24no—
70C2×#11765866—24no—
71C2×#11765866C2×C418yescomplemented
72C22×Dic142C2313yes—
73C2×Q8×D71—24no—
74C2×Q8×D71—24no—
75C2×Q8×D71C2×C418yescomplemented
76C22×D284C2313yes—
77C22×D284C2313yes—
78C22×C4×D71C2313yes—
79C22×C4×D71C2313yes—
80C22×C4×D71C2313yes—
81C22×C4×D71C2313yes—
82C22×C4×D71C2313yes—
83C22×C4×D71C2311yescharacteristic
84#14556116C2×C4124yescomplemented
85#14556108C2×C4124yescomplemented
86#14556103C2×C4124yescomplemented
87Q8×Dic71—24no—
88Q8×Dic71—24no—
89C4×Dic142—212no—
90#14556093—212no—
91C4×D284—212no—
92C4×D284—212no—
93C4×D284—212no—
94C4×D284C2×C4124yescomplemented
95#14556090—212no—
96#14556086—212no—
97C2×C4⋊Dic71C2313yes—
98C2×C4⋊Dic71C2313yes—
99C2×C4⋊Dic71C2313yes—
100C2×C4⋊Dic71C2313yes—
101C2×C4⋊Dic71C2313yes—
102C2×Dic71⋊C4C2316yes—
103C4⋊C4×D71—212no—
104C2×(C2×D71)⋊C4C2313yes—
105C2×(C2×D71)⋊C4C2313yes—
106C2×(C2×D71)⋊C4C2313yes—
107C2×(C2×D71)⋊C4C2316yes—
108C2×(C2×D71)⋊C4C2316yes—
109C2×(C2×D71)⋊C4C2311yescharacteristic
110C2×(C2×D71)⋊C4C2313yes—
111C2×(C2×D71)⋊C4C2316yes—
112C2×(C2×D71)⋊C4C2311yescharacteristic
113C2×C4×Dic71C2313yes—
114C2×C4×Dic71C2311yescharacteristic
115C2×C4×Dic71C2313yes—
116C2×C4×Dic71C2313yes—
117C2×C4×Dic71C2313yes—
118C2×C4×Dic71C2313yes—
119C42×D71—212no—
120C42×D71—212no—
121C71⋊#95C2311yescharacteristic
122C71⋊#95C2311yescharacteristic
123C71⋊#95C2313yes—
124C71⋊#95C2313yes—
125C71⋊#95C2313yes—
126C71⋊#95C2313yes—
127C71⋊#95C2316yes—
128C71⋊#95C2316yes—
129C22×Q8×C71C2311yescharacteristic
130C4×Q8×C71—24no—
131C4×Q8×C71C2×C418yescomplemented
132C4×Q8×C71D418yescomplemented
133C2×C4⋊C4×C71C2313yes—
134C2×C4⋊C4×C71C2313yes—
135C2×C4⋊C4×C71C2313yes—
136C2×C42×C71C2311yescharacteristic
137C2×C42×C71C2313yes—
138C2×C42×C71C2313yes—
139C2×C42×C71C2313yes—
140C2×C42×C71C2313yes—
141C2×C42×C71C2313yes—
142C2×C42×C71C2313yes—
143#95×C71C2316yes—
144C23×D71C2413yes—
145C23×D71C2411yescharacteristic
146#11765866—232no—
147C2×Dic142—26no—
148C2×Dic142—26no—
149C2×Dic142C22×C4112yes—
150Q8×D71—232no—
151C2×D284—26no—
152C2×D284—26no—
153C2×D284—26no—
154C2×D284—26no—
155C2×D284C22×C4112yes—
156C2×D284C22×C4112yes—
157C22×Dic71C2413yes—
158C22×Dic71C2413yes—
159C22×Dic71C2411yescharacteristic
160C22×Dic71C2413yes—
161C22×Dic71C2411yescharacteristic
162C22×Dic71C2411yescharacteristic
163C2×C4×D71—26no—
164C2×C4×D71—26no—
165C2×C4×D71—22no—
166C2×C4×D71—26no—
167C2×C4×D71—26no—
168C2×C4×D71—22no—
169C2×C4×D71—26no—
170C2×C4×D71—26no—
171C2×C4×D71—26no—
172C2×C4×D71—26no—
173C2×C4×D71—26no—
174C2×C4×D71—26no—
175C2×C4×D71—26no—
176C2×C4×D71—43no—
177C2×C4×D71—43no—
178C2×C4×D71C22×C4112yes—
179C2×C4×D71C22×C4112yes—
180C2×C4×D71#4114yescomplemented
181C4⋊Dic71—26no—
182C4⋊Dic71—26no—
183C4⋊Dic71—26no—
184C4⋊Dic71—26no—
185C4⋊Dic71C22×C4112yes—
186Dic71⋊C4—212no—
187(C2×D71)⋊C4—26no—
188(C2×D71)⋊C4—212no—
189(C2×D71)⋊C4—26no—
190(C2×D71)⋊C4—26no—
191(C2×D71)⋊C4—46no—
192(C2×D71)⋊C4C22×C414yes—
193(C2×D71)⋊C4C22×C4112yes—
194(C2×D71)⋊C4C22×C4124yes—
195(C2×D71)⋊C4#4114yescomplemented
196C4×Dic71—22no—
197C4×Dic71—26no—
198C4×Dic71—26no—
199C4×Dic71—26no—
200C4×Dic71—26no—
201C4×Dic71—26no—
202C2×Q8×C71C22×C414yes—
203C2×Q8×C71C2×D414yes—
204C2×Q8×C71#4114yes—
205C22×C4×C71C2413yes—
206C22×C4×C71C2413yes—
207C22×C4×C71C2411yescharacteristic
208C22×C4×C71C2413yes—
209C22×C4×C71C2411yescharacteristic
210C22×C4×C71C2413yes—
211C22×C4×C71C2411yescharacteristic
212C4⋊C4×C71—26no—
213C4⋊C4×C71C22×C4112yes—
214C4⋊C4×C71C2×D4112yes—
215C42×C71—26no—
216C42×C71—26no—
217C42×C71—26no—
218C42×C71—22no—
219C42×C71—43no—
220C42×C71C22×C4112yes—
221C42×C71C2×D4112yes—
222C23×C71C2511yescharacteristic
223C22×D71—21no—
224C22×D71—21no—
225C22×D71—21no—
226C22×D71—21no—
227C22×D71—23no—
228C22×D71—23no—
229C22×D71—23no—
230C22×D71—23no—
231C22×D71—23no—
232C22×D71—23no—
233C22×D71C23×C416yes—
234C22×D71C23×C412yes—
235C22×D71C2×#4112yes—
236C22×D71C2×#4112yes—
237Q8×C71C4×D4116yescomplemented
238C2×C4×C71—21no—
239C2×C4×C71—23no—
240C2×C4×C71—23no—
241C2×C4×C71—23no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—23no—
246C2×C4×C71—23no—
247C2×C4×C71—23no—
248C2×C4×C71—23no—
249C2×C4×C71C23×C412yes—
250C2×C4×C71C23×C416yes—
251C2×C4×C71C23×C416yes—
252C2×C4×C71C22×D416yes—
253C2×C4×C71C22×D416yes—
254C2×C4×C71C22×D412yes—
255C2×C4×C71C2×#4112yes—
256C2×C4×C71C2×#4112yes—
257C2×C4×C71C2×#4116yes—
258C2×C4×C712−1+412yes—
259C2×Dic71—21no—
260C2×Dic71—21no—
261C2×Dic71—21no—
262C2×Dic71—23no—
263C2×Dic71—21no—
264C2×Dic71—23no—
265C2×Dic71—21no—
266C2×Dic71—21no—
267C2×Dic71—23no—
268C2×Dic71—23no—
269C2×Dic71—23no—
270C2×Dic71—23no—
271C2×Dic71—23no—
272C2×Dic71—23no—
273C2×Dic71C23×C416yes—
274C2×Dic71C23×C412yes—
275C2×Dic71C2×#4112yes—
276C2×Dic71C2×#4112yes—
277D284—224no—
278D284—224no—
279C4×D71—224no—
280C4×D71—224no—
281C4×D71—28no—
282C4×D71—412no—
283C4×D71—412no—
284C4×D71—412no—
285Dic142—224no—
286C22×C71C24×C411yescharacteristic
287C22×C71C23×D411yescharacteristic
288C22×C71C22×#4111yescharacteristic
289C22×C71C22×#4111yescharacteristic
290C22×C71C22×#4111yescharacteristic
291C22×C71C2×2−1+411yescharacteristic
292C22×C71#58511yescharacteristic
293C2×D71—22no—
294C2×D71—22no—
295C2×D71—22no—
296C2×D71—22no—
297C2×D71—22no—
298C2×D71—22no—
299C2×D71—26no—
300C2×D71—26no—
301C2×D71—26no—
302C2×D71—43no—
303C2×D71—43no—
304C2×D71—43no—
305C2×D71—43no—
306C2×D71C4×#4114yescomplemented
307C4×C71—26no—
308C4×C71—22no—
309C4×C71—26no—
310C4×C71—22no—
311C4×C71—43no—
312C4×C71C2×C4×D4112yes—
313C4×C71#54814yescomplemented
314Dic71—26no—
315Dic71—22no—
316Dic71—22no—
317Dic71—22no—
318Dic71—43no—
319Dic71—43no—
320C4×#548—711nomaximal, Sylow
321C2×C71C22×C4×D411yescharacteristic
322C2×C71C2×C4×#4111yescharacteristic
323C2×C71C4×2−1+411yescharacteristic
324C2×C71C2×#54811yescharacteristic
325C2×C71D4×#4111yescharacteristic
326C2×C71#348011yescharacteristic
327C2×C71#348211yescharacteristic
328D71—24no—
329D71—46no—
330C2×#548—711no—
331C2×C4×#41—711no—
332C22×C4×Q8—711no—
333#2367—713no—
334#2362—713no—
335#2361—713no—
336#2352—713no—
337#2351—711no—
338#2341—711no—
339Q8×C22⋊C4—711no—
340C4×#124—713no—
341C4×C22⋊Q8—713no—
342C4×#121—713no—
343C42×Q8D7111yescharacteristic, complemented
344C42×D4—713no—
345C71C4×#54811yescharacteristic, complemented, Sylow
346C22×#41—711no—
347C23×Q8—711no—
348#548—7116no—
349C2×#124—713no—
350C2×C22⋊Q8—713no—
351C2×#121—713no—
352C4×#41—1428no—
353C2×C4×Q8—711no—
354C2×C4×Q8—711no—
355C2×C4×Q8—713no—
356C2×C4×Q8—713no—
357C2×C4×Q8—1428no—
358C2×C4×Q8C2×D7111yescharacteristic
359C2×C4×Q8C2×D7111yescharacteristic
360C2×C4×Q8C2×D7111yescharacteristic
361C2×C4×D4—713no—
362C2×C4×D4—713no—
363C2×C4×D4—713no—
364C2×C4×D4—713no—
365C2×C4×D4—713no—
366C2×#117—713no—
367C22×C4⋊C4—713no—
368C22×C42—713no—
369C22×C42—713no—
370#391—713no—
371#391—713no—
372#390—713no—
373#390—713no—
374#389—713no—
375#389—713no—
376#388—716no—
377#388—716no—
378#388—716no—
379#387—716no—
380#386—716no—
381#385—716no—
382#382—713no—
383#380—713no—
384#380—713no—
385C4×C4⋊C4—713no—
386C4×C4⋊C4—713no—
387C4×C4⋊C4—713no—
388C4×C4⋊C4C2×D7113yes—
389C4×C4⋊C4C2×D7113yes—
390C4×C4⋊C4C2×D7113yes—
391C4×C22⋊C4—713no—
392C4×C22⋊C4—713no—
393C4×C22⋊C4—713no—
394C4×C22⋊C4—713no—
395C4×C22⋊C4—711no—
396C4×C22⋊C4—713no—
397C4×C22⋊C4—716no—
398C43C2×D7113yes—
399C2×#41—718no—
400C2×#41—1424no—
401C2×#41—1424no—
402C22×Q8—718no—
403C22×Q8—713no—
404C22×Q8—1424no—
405C22×Q8—1424no—
406C22×Q8C22×D7111yescharacteristic
407C22×D4—713no—
408C22×D4—713no—
409C23×C4—713no—
410C23×C4—713no—
411C23×C4—713no—
412C23×C4—713no—
413C23×C4—711no—
414C23×C4—713no—
415#124—7124no—
416C22⋊Q8—7124no—
417#121—7124no—
418C4×Q8—24no—
419C4×Q8—1424no—
420C4×Q8—1424no—
421C4×Q8—14212no—
422C4×Q8—14212no—
423C4×Q8C4×D7118yescomplemented
424C4×Q8D28418yescomplemented
425C4×D4—7124no—
426C4×D4—14212no—
427C4×D4—14212no—
428C4×D4—14212no—
429C4×D4—14212no—
430#117—14212no—
431C2×C4⋊C4—713no—
432C2×C4⋊C4—713no—
433C2×C4⋊C4—716no—
434C2×C4⋊C4—713no—
435C2×C4⋊C4—713no—
436C2×C4⋊C4—713no—
437C2×C4⋊C4—14212no—
438C2×C4⋊C4C22×D7113yes—
439C2×C4⋊C4C22×D7113yes—
440C2×C4⋊C4C22×D7113yes—
441C2×C22⋊C4—716no—
442C2×C22⋊C4—711no—
443C2×C22⋊C4—711no—
444C2×C22⋊C4—713no—
445C2×C22⋊C4—716no—
446C2×C22⋊C4—716no—
447C2×C22⋊C4—713no—
448C2×C22⋊C4—713no—
449C2×C22⋊C4—713no—
450C2×C42—713no—
451C2×C42—713no—
452C2×C42—713no—
453C2×C42—713no—
454C2×C42—713no—
455C2×C42—711no—
456C2×C42—14212no—
457C2×C42—14212no—
458C2×C42C22×D7113yes—
459C2×C42C22×D7113yes—
460C2×C42C22×D7113yes—
461C2×C42C22×D7111yescharacteristic
462C2×C42C22×D7113yes—
463C2×C42C22×D7113yes—
464C2×C42C22×D7113yes—
465#95—711no—
466#95—711no—
467#95—713no—
468#95—713no—
469#95—713no—
470#95—713no—
471#95—716no—
472#95—716no—
473#95C22×D7116yes—
474C24—711no—
475C24—713no—
476#41—14232no—
477C2×Q8—7112no—
478C2×Q8—14232no—
479C2×Q8—1426no—
480C2×Q8—1426no—
481C2×Q8C2×C4×D7114yes—
482C2×Q8C2×D28414yes—
483C2×Q8#1176586514yes—
484C2×D4—7112no—
485C2×D4—7112no—
486C2×D4—1426no—
487C2×D4—1426no—
488C2×D4—1426no—
489C2×D4—1426no—
490C22×C4—2843no—
491C22×C4—2843no—
492C22×C4—711no—
493C22×C4—711no—
494C22×C4—713no—
495C22×C4—711no—
496C22×C4—7112no—
497C22×C4—7112no—
498C22×C4—714no—
499C22×C4—713no—
500C22×C4—713no—
501C22×C4—1426no—
502C22×C4—1426no—
503C22×C4—1426no—
504C22×C4—1426no—
505C22×C4—1426no—
506C22×C4—1426no—
507C22×C4—1426no—
508C22×C4—1422no—
509C22×C4—1426no—
510C22×C4—1426no—
511C22×C4—1426no—
512C22×C4—1426no—
513C22×C4—1422no—
514C22×C4C23×D7113yes—
515C22×C4C23×D7111yescharacteristic
516C22×C4C23×D7113yes—
517C22×C4C23×D7113yes—
518C22×C4C23×D7111yescharacteristic
519C22×C4C23×D7113yes—
520C22×C4C23×D7111yescharacteristic
521C4⋊C4—26no—
522C4⋊C4—7112no—
523C4⋊C4—1426no—
524C4⋊C4—1426no—
525C4⋊C4—14212no—
526C4⋊C4—1426no—
527C4⋊C4—1426no—
528C4⋊C4C2×C4×D71112yes—
529C4⋊C4C2×D284112yes—
530C22⋊C4—2846no—
531C22⋊C4—714no—
532C22⋊C4—7112no—
533C22⋊C4—7124no—
534C22⋊C4—714no—
535C22⋊C4—1426no—
536C22⋊C4—1426no—
537C22⋊C4—14212no—
538C22⋊C4—1426no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—22no—
543C42—43no—
544C42—1422no—
545C42—1426no—
546C42—1426no—
547C42—1426no—
548C42—1426no—
549C42—1426no—
550C42C2×C4×D71112yes—
551C42C2×D284112yes—
552C23—712no—
553C23—712no—
554C23—712no—
555C23—716no—
556C23—1423no—
557C23—1423no—
558C23—1423no—
559C23—1423no—
560C23—1423no—
561C23—1423no—
562C23—1421no—
563C23—1421no—
564C23—1421no—
565C23—1421no—
566C23C24×D7111yescharacteristic
567Q8—14224no—
568Q8C4×D284116yescomplemented
569D4—14224no—
570D4—14224no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—28412no—
583C2×C4—28412no—
584C2×C4—28412no—
585C2×C4—716no—
586C2×C4—712no—
587C2×C4—712no—
588C2×C4—712no—
589C2×C4—1423no—
590C2×C4—1423no—
591C2×C4—1423no—
592C2×C4—1423no—
593C2×C4—1423no—
594C2×C4—1423no—
595C2×C4—1421no—
596C2×C4—1421no—
597C2×C4—1421no—
598C2×C4—1423no—
599C2×C4—1421no—
600C2×C4—1423no—
601C2×C4—1421no—
602C2×C4—1421no—
603C2×C4—1428no—
604C2×C4—14224no—
605C2×C4—14224no—
606C2×C4C22×C4×D7112yes—
607C2×C4C22×C4×D7116yes—
608C2×C4C22×C4×D7116yes—
609C2×C4C22×D28416yes—
610C2×C4C22×D28412yes—
611C2×C4C22×D28416yes—
612C2×C4#41×D7112yes—
613C2×C4#41×D7112yes—
614C2×C4C2×#1176586516yes—
615C2×C4#1455617612yes—
616C22—2843no—
617C22—2843no—
618C22—2843no—
619C22—2843no—
620C22—714no—
621C22—1426no—
622C22—1426no—
623C22—1426no—
624C22—1422no—
625C22—1422no—
626C22—1422no—
627C22—1422no—
628C22—1422no—
629C22—1422no—
630C22C23×C4×D7111yescharacteristic
631C22C23×D28411yescharacteristic
632C22C2×#41×D7111yescharacteristic
633C22C2×#41×D7111yescharacteristic
634C22C22×#1176586511yescharacteristic
635C22C2×#1455617611yescharacteristic
636C22#1798683511yescharacteristic
637C4—26no—
638C4—22no—
639C4—26no—
640C4—22no—
641C4—43no—
642C4—2843no—
643C4—2843no—
644C4—1422no—
645C4—1426no—
646C4—1422no—
647C4—1422no—
648C4C2×C4×D284112yes—
649C4#1798666114yesdirect product factor
650C2—2846no—
651C2—1424no—
652C2C22×C4×D28411yescharacteristic
653C2C4×#41×D7111yescharacteristic
654C2C4×#1455617611yescharacteristic
655C2C2×#1798666111yescharacteristic
656C2#41×D28411yescharacteristic
657C2#2260193811yescharacteristic
658C2#2260195711yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC42×Q8×C71C2
socle, cosocleC23×C71C25
prime radicalC2×#17986661C2
hypercenterC42×Q8D71
hypocenterC71C4×#548
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11765866C2semidirect
3. C2×C4×Q8×D71C2semidirect
4. #22591411C2semidirect
5. #22591369C2semidirect
6. #22591358C2semidirect
7. #22591272C2semidirect
8. #22591261C2semidirect
9. #22591178C2semidirect
10. Q8×(C2×D71)⋊C4C2semidirect
11. C4×#14556116C2semidirect
12. C4×#14556108C2semidirect
13. C4×#14556103C2semidirect
14. C42×D284C2semidirect
15. C42×Q8×C71C2semidirect
18. #17986661C4direct (N × H)
71. C2×#11765866C2×C4semidirect
75. C2×Q8×D71C2×C4semidirect
84. #14556116C2×C4semidirect
85. #14556108C2×C4semidirect
86. #14556103C2×C4semidirect
94. C4×D284C2×C4semidirect
131. C4×Q8×C71C2×C4semidirect
132. C4×Q8×C71D4semidirect
180. C2×C4×D71#41semidirect
195. (C2×D71)⋊C4#41semidirect
237. Q8×C71C4×D4semidirect
306. C2×D71C4×#41semidirect
313. C4×C71#548semidirect
343. C42×Q8D71semidirect
345. C71C4×#548semidirect
423. C4×Q8C4×D71semidirect
424. C4×Q8D284semidirect
568. Q8C4×D284semidirect
649. C4#17986661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866612
C2×C4×#117658662
C2×C4×Q8×D712
#225914112
#225913692
#225913582
#225912722
#225912612
#225911782
Q8×(C2×D71)⋊C42
C4×#145561162
C4×#145561082
C4×#145561032
C42×D2842
C42×Q8×C712
C4×#54871