Finite Group Databasebeta

← #32158410

Subgroups — #32158410

Order 18176.

2834 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986474C211yesmaximal, characteristic
2#22591278C214yesmaximal, complemented
3#22591267C214yesmaximal, complemented
4#22591202C214yesmaximal, complemented
5#22591191C214yesmaximal, complemented
6#22590966C214yesmaximal, complemented
7#22590952C211yesmaximal, characteristic, complemented
8#22590780C214yesmaximal, complemented
9C2×#17985879C211yesmaximal, characteristic
10C2×#17985871C211yesmaximal, characteristic, complemented
11#22590693C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
13C71×#2308C211yesmaximal, characteristic
14C24×Dic71C2211yescharacteristic
15#17986474C4116yescomplemented
16C2×D4×Dic71C2214yes—
17C2×D4×Dic71C2214yes—
18C2×#14556087C2212yes—
19C2×#14556084C2214yescomplemented
20C22×Dic71⋊C4C2212yescomplemented
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C22⋊Dic71C2212yes—
23C22×C22⋊Dic71C2211yescharacteristic
24C22×C22⋊Dic71C2211yescharacteristic
25C22×C22⋊Dic71C2212yes—
26C22×C4×Dic71C2212yescomplemented
27#17985893C2214yescomplemented
28#17985893C2214yescomplemented
29#17985887C2214yescomplemented
30#17985887C2214yescomplemented
31#17985884C2214yescomplemented
32#17985884C2214yescomplemented
33#17985882C2214yescomplemented
34#17985882C2214yescomplemented
35#17985879C2214yes—
36#17985879C2212yes—
37#17985879C2212yes—
38#17985872C2214yescomplemented
39#17985871C2214yes—
40#17985871C2214yes—
41#17985871C2212yescomplemented
42#17985871C2212yescomplemented
43#17985866C2214yescomplemented
44#17985863C2214yescomplemented
45#17985860C2214yescomplemented
46#17985857C2214yescomplemented
47#17985857C2214yescomplemented
48#17985850C2214yescomplemented
49C22⋊C4×Dic71C2214yes—
50C22⋊C4×Dic71C2214yes—
51C22⋊C4×Dic71C2214yescomplemented
52C22⋊C4×Dic71C2214yescomplemented
53C22⋊C4×Dic71C2214yescomplemented
54C4×C22⋊Dic71C2212yescomplemented
55C4×C22⋊Dic71C2212yescomplemented
56#17985844C2214yescomplemented
57C2×C71⋊#95C2212yes—
58C2×C71⋊#95C2212yescomplemented
59C2×C71⋊#95C2212yescomplemented
60C23×D4×C71C2211yescharacteristic
61C22×C22⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63#386×C71C2212yes—
64#386×C71C2212yes—
65#386×C71C2214yes—
66#381×C71C2212yes—
67#379×C71C2212yes—
68C23×Dic71—24no—
69C23×Dic71—44no—
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2312yes—
72C23×Dic71C2312yes—
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2312yes—
75C23×Dic71C2312yes—
76C23×Dic71C2312yes—
77C23×Dic71C2314yes—
78D4×Dic71C2×C4132yescomplemented
79D4×Dic71C2×C4132yescomplemented
80#14556087C2×C4116yescomplemented
81#14556084—48no—
82C2×C4⋊Dic71C2314yes—
83C2×Dic71⋊C4—44no—
84C2×Dic71⋊C4C2314yes—
85C2×Dic71⋊C4C2314yes—
86C2×Dic71⋊C4C2314yes—
87C2×Dic71⋊C4C2314yes—
88C2×C22⋊Dic71—24no—
89C2×C22⋊Dic71—44no—
90C2×C22⋊Dic71C2×C418yes—
91C2×C22⋊Dic71C2×C418yes—
92C2×C22⋊Dic71C2×C4116yescomplemented
93C2×C22⋊Dic71C2312yes—
94C2×C22⋊Dic71C2312yes—
95C2×C22⋊Dic71C2314yes—
96C2×C22⋊Dic71C2314yes—
97C2×C22⋊Dic71C2312yes—
98C2×C22⋊Dic71C2312yes—
99C2×C22⋊Dic71C2312yes—
100C2×C22⋊Dic71C2312yes—
101C2×C22⋊Dic71C2314yes—
102C2×C4×Dic71—44no—
103C2×C4×Dic71C2314yes—
104C2×C4×Dic71C2314yes—
105C2×C4×Dic71C2314yes—
106C2×C4×Dic71C2314yes—
107C2×C4×Dic71C2314yes—
108C71⋊#95C2314yes—
109C71⋊#95C2314yes—
110C71⋊#95C2314yes—
111C71⋊#95C2314yes—
112C71⋊#95C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C25×C71C2311yescharacteristic
119C25×C71C2311yescharacteristic
120C22×D4×C71—24no—
121C22×D4×C71—24no—
122C22×D4×C71C2×C418yes—
123C22×D4×C71C2312yes—
124C22×D4×C71C2312yes—
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2311yescharacteristic
127C23×C4×C71C2312yes—
128C23×C4×C71C2311yescharacteristic
129C2×C22⋊C4×C71—24no—
130C2×C22⋊C4×C71—24no—
131C2×C22⋊C4×C71C2312yes—
132C2×C22⋊C4×C71C2312yes—
133C2×C22⋊C4×C71C2312yes—
134C2×C22⋊C4×C71C2312yes—
135C2×C22⋊C4×C71C2314yes—
136C2×C22⋊C4×C71C2314yes—
137#95×C71C2314yes—
138#95×C71C2314yes—
139C22×Dic71—22no—
140C22×Dic71—24no—
141C22×Dic71—24no—
142C22×Dic71—24no—
143C22×Dic71—22no—
144C22×Dic71—24no—
145C22×Dic71—24no—
146C22×Dic71—24no—
147C22×Dic71—42no—
148C22×Dic71—42no—
149C22×Dic71—42no—
150C22×Dic71—42no—
151C22×Dic71—44no—
152C22×Dic71—42no—
153C22×Dic71—42no—
154C22×Dic71—42no—
155C22×Dic71—44no—
156C22×Dic71—42no—
157C22×Dic71—42no—
158C22×Dic71—416no—
159C22×Dic71C22×C418yes—
160C22×Dic71C22×C418yes—
161C22×Dic71C22×C4116yescomplemented
162C22×Dic71C2412yes—
163C22×Dic71C2414yes—
164C22×Dic71C2414yes—
165C22×Dic71C2414yes—
166C22×Dic71C2412yes—
167C4⋊Dic71C22×C4116yescomplemented
168Dic71⋊C4—28no—
169Dic71⋊C4—44no—
170Dic71⋊C4—44no—
171Dic71⋊C4—44no—
172C22⋊Dic71—24no—
173C22⋊Dic71—24no—
174C22⋊Dic71—28no—
175C22⋊Dic71—44no—
176C22⋊Dic71C22×C418yes—
177C22⋊Dic71C22×C418yes—
178C22⋊Dic71C22×C418yes—
179C22⋊Dic71C22×C418yes—
180C22⋊Dic71C22×C4116yescomplemented
181C4×Dic71—28no—
182C4×Dic71—44no—
183C4×Dic71—44no—
184C4×Dic71—44no—
185C4×Dic71C22×C4116yescomplemented
186C24×C71—22no—
187C24×C71—22no—
188C24×C71—42no—
189C24×C71—42no—
190C24×C71—42no—
191C24×C71—42no—
192C24×C71C22×C414yes—
193C24×C71C22×C414yes—
194C24×C71#4114yes—
195C24×C71#4114yes—
196C24×C71C2412yes—
197C24×C71C2411yescharacteristic
198C24×C71C2411yescharacteristic
199C24×C71C2411yescharacteristic
200C2×D4×C71—232no—
201C2×D4×C71—24no—
202C2×D4×C71—24no—
203C2×D4×C71—24no—
204C2×D4×C71—24no—
205C2×D4×C71C22×C418yes—
206C2×D4×C71C22×C418yes—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—24no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—42no—
213C22×C4×C71—42no—
214C22×C4×C71—42no—
215C22×C4×C71—42no—
216C22×C4×C71C22×C414yes—
217C22×C4×C71C2412yes—
218C22×C4×C71C2414yes—
219C22×C4×C71C2412yes—
220C22×C4×C71C2412yes—
221C22⋊C4×C71—24no—
222C22⋊C4×C71—24no—
223C22⋊C4×C71—24no—
224C22⋊C4×C71—24no—
225C22⋊C4×C71—44no—
226C22⋊C4×C71—44no—
227C23×C71—22no—
228C23×C71—22no—
229C23×C71—22no—
230C23×C71—22no—
231C23×C71—22no—
232C23×C71—22no—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—24no—
236C23×C71—24no—
237C23×C71—28no—
238C23×C71—48no—
239C23×C71—44no—
240C23×C71—48no—
241C23×C71—44no—
242C23×C71—48no—
243C23×C71—82no—
244C23×C71—82no—
245C23×C71—84no—
246C23×C71#117116yescomplemented
247C23×C71C23×C414yes—
248C23×C71C23×C412yes—
249C23×C71C23×C412yes—
250C23×C71C23×C412yes—
251C23×C71C2×#4112yes—
252C23×C71C2×#4112yes—
253C23×C71C2×#4112yes—
254C23×C71C2×#4112yes—
255C23×C71C2×#4112yes—
256C23×C71C2×#4112yes—
257C23×C71C2511yescharacteristic
258D4×C71—216no—
259D4×C71—216no—
260C2×C4×C71—28no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—24no—
266C2×C4×C71—24no—
267C2×C4×C71—24no—
268C2×C4×C71—24no—
269C2×C4×C71—24no—
270C2×C4×C71—48no—
271C2×C4×C71—82no—
272C2×C4×C71—82no—
273C2×C4×C71C23×C414yes—
274C2×Dic71—28no—
275C2×Dic71—22no—
276C2×Dic71—24no—
277C2×Dic71—22no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—24no—
281C2×Dic71—24no—
282C2×Dic71—22no—
283C2×Dic71—24no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—24no—
287C2×Dic71—48no—
288C2×Dic71—48no—
289C2×Dic71—416no—
290C2×Dic71—48no—
291C2×Dic71—48no—
292C2×Dic71—44no—
293C2×Dic71—84no—
294C2×Dic71C23×C418yes—
295C2×Dic71C23×C418yes—
296C2×Dic71H(5,𝔽2)14yes—
297C22×C71—24no—
298C22×C71—24no—
299C22×C71—24no—
300C22×C71—22no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—24no—
307C22×C71—24no—
308C22×C71—24no—
309C22×C71—24no—
310C22×C71—28no—
311C22×C71—416no—
312C22×C71—42no—
313C22×C71—42no—
314C22×C71—44no—
315C22×C71—88no—
316C22×C71C2×#11714yes—
317C22×C71C2×#11714yes—
318C22×C71C2×#11714yes—
319C22×C71C24×C411yescharacteristic
320C22×C71C22×#4111yescharacteristic
321C22×C71C22×#4111yescharacteristic
322C22×C71C2×H(5,𝔽2)12yes—
323C22×C71#58512yes—
324C4×C71—24no—
325C4×C71—42no—
326C4×C71—42no—
327C4×C71—44no—
328Dic71—28no—
329Dic71—28no—
330Dic71—24no—
331Dic71—42no—
332Dic71—44no—
333#34251—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71—24no—
336C2×C71—24no—
337C2×C71—44no—
338C2×C71C22×#11711yescharacteristic
339C2×C71C4×H(5,𝔽2)12yes—
340C2×C71#349011yescharacteristic
341C2×C71#349111yescharacteristic
342C2×C71#350512yes—
343C2×#518—711no—
344#2353—714no—
345#2352—714no—
346#2343—714no—
347#2342—714no—
348#2318—714no—
349#2315—711no—
350#2308D7111yescharacteristic
351#2290—714no—
352C2×#386—711no—
353C2×#385—711no—
354#2273—711no—
355C2×C4×C22⋊C4—711no—
356C71#3425111yescharacteristic, complemented, Sylow
357C23×D4C2×D7111yescharacteristic
358C24×C4—711no—
359#518—7116no—
360C2×C4×D4—714no—
361C2×C4×D4—714no—
362C2×#117—712no—
363C2×#117—714no—
364C22×C4⋊C4—712no—
365C22×C22⋊C4—712no—
366C22×C22⋊C4—711no—
367C22×C22⋊C4—712no—
368C22×C22⋊C4—711no—
369C22×C22⋊C4—711no—
370C22×C22⋊C4C2×D7111yescharacteristic
371C22×C22⋊C4C2×D7111yescharacteristic
372C22×C42—712no—
373#388—714no—
374#388—714no—
375#388—714no—
376#388—714no—
377#387—714no—
378#387—714no—
379#387—714no—
380#387—714no—
381#386—712no—
382#386—714no—
383#386—712no—
384#386C2×D7114yes—
385#386C2×D7112yes—
386#386C2×D7112yes—
387#385—714no—
388#385—714no—
389#385—712no—
390#385—714no—
391#385—712no—
392#383—714no—
393#382—714no—
394#381—714no—
395#381C2×D7112yes—
396#380—714no—
397#380—714no—
398#379C2×D7112yes—
399C4×C4⋊C4—714no—
400C4×C22⋊C4—712no—
401C4×C22⋊C4—712no—
402C4×C22⋊C4—714no—
403C4×C22⋊C4—714no—
404C4×C22⋊C4—714no—
405C4×C22⋊C4—714no—
406C4×C22⋊C4—714no—
407#376—714no—
408C2×#95—712no—
409C2×#95—712no—
410C2×#95—712no—
411C25C22×D7111yescharacteristic
412C25C22×D7111yescharacteristic
413C22×D4—24no—
414C22×D4—24no—
415C22×D4C4×D7118yes—
416C22×D4C22×D7112yes—
417C22×D4C22×D7112yes—
418C23×C4—2844no—
419C23×C4—712no—
420C23×C4—714no—
421C23×C4—712no—
422C23×C4—712no—
423C23×C4—711no—
424C23×C4—712no—
425C23×C4—712no—
426C23×C4—711no—
427C23×C4—1424no—
428C23×C4C22×D7111yescharacteristic
429C23×C4C22×D7111yescharacteristic
430C23×C4C22×D7111yescharacteristic
431C23×C4C22×D7112yes—
432C4×D4—7132no—
433C4×D4—7132no—
434#117—2848no—
435#117—7116no—
436C2×C4⋊C4—2844no—
437C2×C4⋊C4—714no—
438C2×C4⋊C4—714no—
439C2×C4⋊C4—714no—
440C2×C4⋊C4—714no—
441C2×C4⋊C4—714no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—2844no—
445C2×C22⋊C4—714no—
446C2×C22⋊C4—718no—
447C2×C22⋊C4—718no—
448C2×C22⋊C4—7116no—
449C2×C22⋊C4—712no—
450C2×C22⋊C4—712no—
451C2×C22⋊C4—712no—
452C2×C22⋊C4—712no—
453C2×C22⋊C4—714no—
454C2×C22⋊C4—714no—
455C2×C22⋊C4—712no—
456C2×C22⋊C4—712no—
457C2×C22⋊C4—1424no—
458C2×C22⋊C4C22×D7112yes—
459C2×C22⋊C4C22×D7112yes—
460C2×C22⋊C4C22×D7112yes—
461C2×C22⋊C4C22×D7112yes—
462C2×C22⋊C4C22×D7114yes—
463C2×C22⋊C4C22×D7114yes—
464C2×C42—2844no—
465C2×C42—714no—
466C2×C42—714no—
467C2×C42—714no—
468C2×C42—714no—
469C2×C42—714no—
470#95—714no—
471#95—714no—
472#95—714no—
473#95—714no—
474#95—714no—
475#95—714no—
476#95—714no—
477#95—714no—
478#95—714no—
479#95—714no—
480#95C22×D7114yes—
481#95C22×D7114yes—
482C24—22no—
483C24—22no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24C2×C4×D7114yes—
489C24C2×C4×D7114yes—
490C24#1176586414yes—
491C24#1176586414yes—
492C24C23×D7112yes—
493C24C23×D7111yescharacteristic
494C24C23×D7111yescharacteristic
495C24C23×D7111yescharacteristic
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—232no—
501C2×D4C2×C4×D7118yes—
502C2×D4C2×C4×D7118yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—28416no—
513C22×C4—2842no—
514C22×C4—2842no—
515C22×C4—2844no—
516C22×C4—2842no—
517C22×C4—2842no—
518C22×C4—2842no—
519C22×C4—2842no—
520C22×C4—2844no—
521C22×C4—2842no—
522C22×C4—2842no—
523C22×C4—2842no—
524C22×C4—718no—
525C22×C4—718no—
526C22×C4—7116no—
527C22×C4—714no—
528C22×C4—712no—
529C22×C4—714no—
530C22×C4—712no—
531C22×C4—714no—
532C22×C4—1424no—
533C22×C4—1424no—
534C22×C4—1422no—
535C22×C4—1424no—
536C22×C4—1424no—
537C22×C4—1424no—
538C22×C4—1424no—
539C22×C4—1422no—
540C22×C4C2×C4×D7114yes—
541C22×C4C23×D7112yes—
542C22×C4C23×D7114yes—
543C22×C4C23×D7112yes—
544C22×C4C23×D7112yes—
545C4⋊C4—2844no—
546C4⋊C4—2844no—
547C4⋊C4—2844no—
548C4⋊C4—7116no—
549C4⋊C4—1428no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—2844no—
557C22⋊C4—718no—
558C22⋊C4—718no—
559C22⋊C4—718no—
560C22⋊C4—718no—
561C22⋊C4—7116no—
562C22⋊C4—1428no—
563C22⋊C4—1424no—
564C22⋊C4—1424no—
565C42—2844no—
566C42—2844no—
567C42—2844no—
568C42—7116no—
569C42—1428no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—28no—
581C23—44no—
582C23—48no—
583C23—44no—
584C23—48no—
585C23—48no—
586C23—82no—
587C23—82no—
588C23—84no—
589C23#14556084116yescomplemented
590C23C22×C4×D7114yes—
591C23C22×C4×D7112yes—
592C23C22×C4×D7112yes—
593C23C22×C4×D7112yes—
594C23C2×#1176586412yes—
595C23C2×#1176586412yes—
596C23C2×#1176586412yes—
597C23C2×#1176586412yes—
598C23C2×#1176586412yes—
599C23C2×#1176586412yes—
600C23C24×D7111yescharacteristic
601D4—216no—
602D4—216no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—28no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—48no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—2844no—
617C2×C4—2848no—
618C2×C4—2848no—
619C2×C4—2848no—
620C2×C4—2848no—
621C2×C4—28416no—
622C2×C4—5684no—
623C2×C4—718no—
624C2×C4—718no—
625C2×C4—714no—
626C2×C4—1424no—
627C2×C4—1422no—
628C2×C4—1424no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1424no—
632C2×C4—1428no—
633C2×C4—1422no—
634C2×C4—1424no—
635C2×C4—1422no—
636C2×C4—1424no—
637C2×C4—1424no—
638C2×C4—1424no—
639C2×C4C22×C4×D7114yes—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—24no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—28no—
654C22—416no—
655C22—42no—
656C22—42no—
657C22—44no—
658C22—88no—
659C22C2×#1455608414yes—
660C22C2×#1455608414yes—
661C22C2×#1455608414yes—
662C22C23×C4×D7111yescharacteristic
663C22C22×#1176586411yescharacteristic
664C22C22×#1176586411yescharacteristic
665C22H(5,𝔽2)×D7112yes—
666C22#1798683412yes—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—44no—
671C4—2842no—
672C4—2844no—
673C4—1424no—
674C4—1428no—
675C4—1428no—
676C2—24no—
677C2—24no—
678C2—24no—
679C2—44no—
680C2C22×#1455608411yescharacteristic
681C2#2260154412yes—
682C2#2260202811yescharacteristic
683C2#2260203711yescharacteristic
684C2#2260217712yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2308C2
socle, cosocleC23×C71C25
prime radicalC23×D4×C71C22
hypercenter#2308D71
hypocenterC71#34251
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. #22591278C2semidirect
3. #22591267C2semidirect
4. #22591202C2semidirect
5. #22591191C2semidirect
6. #22590966C2semidirect
7. #22590952C2semidirect
8. #22590780C2semidirect
10. C2×#17985871C2semidirect
11. #22590693C2semidirect
12. C2×C22⋊C4×Dic71C2semidirect
15. #17986474C4semidirect
19. C2×#14556084C22semidirect
20. C22×Dic71⋊C4C22semidirect
26. C22×C4×Dic71C22semidirect
27. #17985893C22semidirect
28. #17985893C22semidirect
29. #17985887C22semidirect
30. #17985887C22semidirect
31. #17985884C22semidirect
32. #17985884C22semidirect
33. #17985882C22semidirect
34. #17985882C22semidirect
38. #17985872C22semidirect
41. #17985871C22semidirect
42. #17985871C22semidirect
43. #17985866C22semidirect
44. #17985863C22semidirect
45. #17985860C22semidirect
46. #17985857C22semidirect
47. #17985857C22semidirect
48. #17985850C22semidirect
51. C22⋊C4×Dic71C22semidirect
52. C22⋊C4×Dic71C22semidirect
53. C22⋊C4×Dic71C22semidirect
54. C4×C22⋊Dic71C22semidirect
55. C4×C22⋊Dic71C22semidirect
56. #17985844C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
78. D4×Dic71C2×C4semidirect
79. D4×Dic71C2×C4semidirect
80. #14556087C2×C4semidirect
92. C2×C22⋊Dic71C2×C4semidirect
161. C22×Dic71C22×C4semidirect
167. C4⋊Dic71C22×C4semidirect
180. C22⋊Dic71C22×C4semidirect
185. C4×Dic71C22×C4semidirect
246. C23×C71#117semidirect
356. C71#34251semidirect
589. C23#14556084semidirect

Maximal subgroups

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

subgroupindex
C2×#179864742
#225912782
#225912672
#225912022
#225911912
#225909662
#225909522
#225907802
C2×#179858792
C2×#179858712
#225906932
C2×C22⋊C4×Dic712
C71×#23082
#3425171