Finite Group Databasebeta

← #31920687

Subgroups — #31920687

Order 18176.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985898C211yesmaximal, characteristic
2C2×#17985898C211yesmaximal, characteristic
3C2×#17985865C211yesmaximal, characteristic
4C2×C4⋊C4×Dic71C211yesmaximal, characteristic
5#22586597C212yesmaximal
6#22586593C212yesmaximal
7#22586574C212yesmaximal
8#22586569C212yesmaximal
9#22586569C211yesmaximal, characteristic
10C4×C71⋊#95C211yesmaximal, characteristic
11C2×#389×C71C211yesmaximal, characteristic
12C22×C4⋊Dic71C2211yescharacteristic
13C22×C4⋊Dic71C2212yes—
14C22×C4⋊Dic71C2212yes—
15C22×C4⋊Dic71C2211yescharacteristic
16C22×C4×Dic71C2211yescharacteristic
17C22×C4×Dic71C2212yes—
18C22×C4×Dic71C2211yescharacteristic
19#17985898—24no—
20#17985898—24no—
21#17985865—24no—
22C4⋊C4×Dic71—24no—
23C2×C71⋊#95C2212yes—
24C2×C71⋊#95C2212yes—
25C2×C71⋊#95C2212yes—
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2211yescharacteristic
28C2×C71⋊#95C2211yescharacteristic
29C2×C71⋊#95C2211yescharacteristic
30C2×C71⋊#95C2211yescharacteristic
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C22×C4⋊C4×C71C2211yescharacteristic
35C22×C4⋊C4×C71C2212yes—
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C42×C71C2211yescharacteristic
38#389×C71C418yescomplemented
39C2×#95×C71C2212yes—
40C23×Dic71C2312yes—
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C2×C4⋊Dic71—24no—
47C2×C4⋊Dic71—24no—
48C2×C4⋊Dic71—24no—
49C2×C4⋊Dic71—22no—
50C2×C4⋊Dic71—22no—
51C2×C4⋊Dic71—24no—
52C2×C4⋊Dic71—22no—
53C2×C4⋊Dic71—22no—
54C2×C4⋊Dic71—22no—
55C2×C4⋊Dic71—42no—
56C2×C4⋊Dic71—42no—
57C2×C4⋊Dic71D414yes—
58C2×C4×Dic71—24no—
59C2×C4×Dic71—22no—
60C2×C4×Dic71—24no—
61C2×C4×Dic71—22no—
62C2×C4×Dic71—22no—
63C2×C4×Dic71—22no—
64C2×C4×Dic71—22no—
65C2×C4×Dic71—42no—
66C2×C4×Dic71Q814yes—
67C71⋊#95—24no—
68C71⋊#95—24no—
69C71⋊#95—24no—
70C71⋊#95—22no—
71C71⋊#95—22no—
72C71⋊#95—22no—
73C71⋊#95—22no—
74C71⋊#95—24no—
75C71⋊#95—24no—
76C71⋊#95—24no—
77C71⋊#95—42no—
78C23×C4×C71C2311yescharacteristic
79C23×C4×C71C2311yescharacteristic
80C23×C4×C71C2312yes—
81C23×C4×C71C2312yes—
82C23×C4×C71C2311yescharacteristic
83C2×C4⋊C4×C71—22no—
84C2×C4⋊C4×C71—22no—
85C2×C4⋊C4×C71—42no—
86C2×C4⋊C4×C71—42no—
87C2×C4⋊C4×C71C2×C414yes—
88C2×C4⋊C4×C71C2×C418yes—
89C2×C4⋊C4×C71C2×C414yes—
90C2×C4⋊C4×C71D414yes—
91C2×C4⋊C4×C71Q814yes—
92C2×C42×C71—22no—
93C2×C42×C71—22no—
94C2×C42×C71C2×C414yes—
95#95×C71C2×C418yes—
96C22×Dic71—21no—
97C22×Dic71—21no—
98C22×Dic71—21no—
99C22×Dic71—21no—
100C22×Dic71—21no—
101C22×Dic71—21no—
102C22×Dic71—21no—
103C22×Dic71—22no—
104C22×Dic71—21no—
105C22×Dic71—21no—
106C22×Dic71—21no—
107C22×Dic71—21no—
108C22×Dic71—21no—
109C22×Dic71—21no—
110C22×Dic71—22no—
111C22×Dic71—21no—
112C22×Dic71—21no—
113C22×Dic71—21no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—21no—
117C22×Dic71—22no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—22no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71C2×D414yes—
132C22×Dic71C2×Q812yes—
133C22×Dic71C2×Q812yes—
134C22×Dic71#4112yes—
135C22×Dic71#4112yes—
136C22×Dic71#4112yes—
137C22×Dic71#4112yes—
138C4⋊Dic71—28no—
139C4⋊Dic71—48no—
140C4⋊Dic71—48no—
141C4⋊Dic71—44no—
142C4×Dic71—28no—
143C4×Dic71—48no—
144C4×Dic71—44no—
145C24×C71C2411yescharacteristic
146C22×C4×C71—22no—
147C22×C4×C71—22no—
148C22×C4×C71—22no—
149C22×C4×C71—22no—
150C22×C4×C71—21no—
151C22×C4×C71—21no—
152C22×C4×C71—22no—
153C22×C4×C71—21no—
154C22×C4×C71—21no—
155C22×C4×C71—22no—
156C22×C4×C71—21no—
157C22×C4×C71—21no—
158C22×C4×C71—21no—
159C22×C4×C71—21no—
160C22×C4×C71—22no—
161C22×C4×C71—22no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—22no—
165C22×C4×C71—22no—
166C22×C4×C71—21no—
167C22×C4×C71—21no—
168C22×C4×C71C22×C412yes—
169C22×C4×C71C22×C414yes—
170C22×C4×C71C22×C412yes—
171C22×C4×C71C22×C414yes—
172C22×C4×C71C22×C412yes—
173C22×C4×C71C2×D412yes—
174C22×C4×C71C2×D414yes—
175C22×C4×C71C2×D412yes—
176C22×C4×C71C2×Q812yes—
177C22×C4×C71C2×Q814yes—
178C22×C4×C71C2×Q812yes—
179C22×C4×C71#4112yes—
180C22×C4×C71#4112yes—
181C4⋊C4×C71—28no—
182C4⋊C4×C71—48no—
183C4⋊C4×C71C4⋊C4116yescomplemented
184C42×C71—28no—
185C23×C71C23×C411yescharacteristic
186C23×C71C22×D411yescharacteristic
187C23×C71C22×D411yescharacteristic
188C23×C71C22×Q811yescharacteristic
189C23×C71C22×Q811yescharacteristic
190C23×C71C2×#4111yescharacteristic
191C23×C71C2×#4111yescharacteristic
192C23×C71C2×#4111yescharacteristic
193C23×C71C2×#4111yescharacteristic
194C23×C71C2×#4111yescharacteristic
195C23×C71C2×#4111yescharacteristic
196C23×C71H(5,𝔽2)11yescharacteristic
197C23×C71H(5,𝔽2)11yescharacteristic
198C23×C712−1+411yescharacteristic
199C23×C712−1+411yescharacteristic
200C2×C4×C71—24no—
201C2×C4×C71—24no—
202C2×C4×C71—24no—
203C2×C4×C71—24no—
204C2×C4×C71—24no—
205C2×C4×C71—24no—
206C2×C4×C71—22no—
207C2×C4×C71—22no—
208C2×C4×C71—24no—
209C2×C4×C71—22no—
210C2×C4×C71—22no—
211C2×C4×C71—24no—
212C2×C4×C71—22no—
213C2×C4×C71—24no—
214C2×C4×C71—22no—
215C2×C4×C71—41no—
216C2×C4×C71—42no—
217C2×C4×C71—41no—
218C2×C4×C71—41no—
219C2×C4×C71—41no—
220C2×C4×C71—42no—
221C2×C4×C71—41no—
222C2×C4×C71—41no—
223C2×C4×C71—42no—
224C2×C4×C71—41no—
225C2×C4×C71—42no—
226C2×C4×C71—41no—
227C2×C4×C71C2×C4⋊C418yes—
228C2×C4×C71C2×C4⋊C414yes—
229C2×C4×C71C4×D414yes—
230C2×C4×C71C4×Q814yes—
231C2×C4×C71#12114yes—
232C2×C4×C71C22⋊Q814yes—
233C2×C4×C71#12514yes—
234C2×C4×C71C4⋊Q814yes—
235C2×Dic71—22no—
236C2×Dic71—22no—
237C2×Dic71—22no—
238C2×Dic71—22no—
239C2×Dic71—22no—
240C2×Dic71—22no—
241C2×Dic71—24no—
242C2×Dic71—22no—
243C2×Dic71—22no—
244C2×Dic71—22no—
245C2×Dic71—22no—
246C2×Dic71—22no—
247C2×Dic71—22no—
248C2×Dic71—22no—
249C2×Dic71—24no—
250C2×Dic71—24no—
251C2×Dic71—22no—
252C2×Dic71—22no—
253C2×Dic71—41no—
254C2×Dic71—41no—
255C2×Dic71—42no—
256C2×Dic71—41no—
257C2×Dic71—41no—
258C2×Dic71—42no—
259C2×Dic71—42no—
260C2×Dic71—41no—
261C2×Dic71—41no—
262C2×Dic71—41no—
263C2×Dic71—41no—
264C2×Dic71—42no—
265C2×Dic71—41no—
266C2×Dic71—41no—
267C2×Dic71—41no—
268C2×Dic71—41no—
269C2×Dic71—42no—
270C2×Dic71—42no—
271C2×Dic71—42no—
272C2×Dic71—42no—
273C2×Dic71—42no—
274C2×Dic71—42no—
275C2×Dic71—42no—
276C2×Dic71#12514yes—
277C22×C71C22×C4⋊C411yescharacteristic
278C22×C71C2×C4×D411yescharacteristic
279C22×C71C2×C4×Q811yescharacteristic
280C22×C71C4×#4111yescharacteristic
281C22×C71C4×#4111yescharacteristic
282C22×C71#51811yescharacteristic
283C22×C71#51911yescharacteristic
284C22×C71C2×#12111yescharacteristic
285C22×C71C2×C22⋊Q811yescharacteristic
286C22×C71C2×#12511yescharacteristic
287C22×C71C2×#12511yescharacteristic
288C22×C71#52911yescharacteristic
289C22×C71#52911yescharacteristic
290C22×C71C2×C4⋊Q811yescharacteristic
291C22×C71#53311yescharacteristic
292C22×C71#54211yescharacteristic
293C22×C71#54211yescharacteristic
294C22×C71#54411yescharacteristic
295C22×C71#54411yescharacteristic
296C22×C71#54611yescharacteristic
297C22×C71#54611yescharacteristic
298C22×C71#54611yescharacteristic
299C22×C71#54711yescharacteristic
300C22×C71#54811yescharacteristic
301C22×C71#54811yescharacteristic
302C22×C71#54811yescharacteristic
303C22×C71#55011yescharacteristic
304C22×C71#55211yescharacteristic
305C22×C71#55311yescharacteristic
306C22×C71#55411yescharacteristic
307C22×C71#55411yescharacteristic
308C22×C71#55511yescharacteristic
309C22×C71#55611yescharacteristic
310C22×C71#55711yescharacteristic
311C22×C71#55711yescharacteristic
312C4×C71—28no—
313C4×C71—42no—
314C4×C71—42no—
315C4×C71—44no—
316C4×C71#38918yes—
317Dic71—24no—
318Dic71—42no—
319Dic71—44no—
320Dic71—42no—
321Dic71—42no—
322Dic71—82no—
323#14006—711nomaximal, Sylow
324C2×C71C2×#38911yescharacteristic
325C2×C71C4×#12511yescharacteristic
326C2×C71#233111yescharacteristic
327C2×C71#234911yescharacteristic
328C2×C71#235111yescharacteristic
329C2×C71#236211yescharacteristic
330C2×C71#236311yescharacteristic
331C2×C71#242611yescharacteristic
332C2×C71#242711yescharacteristic
333C2×C71#243911yescharacteristic
334C2×C71#244211yescharacteristic
335C2×C71#250811yescharacteristic
336C2×C71#250911yescharacteristic
337C2×C71#255011yescharacteristic
338C2×C71#255211yescharacteristic
339C2×#389—711no—
340C2×#389—711no—
341C2×#389D7111yescharacteristic
342C2×#382—711no—
343C2×C4×C4⋊C4—711no—
344#1442—712no—
345#1441—712no—
346#1436—712no—
347C4⋊#95—712no—
348C4⋊#95—711no—
349C4×#95—711no—
350C71#1400611yescharacteristic, complemented, Sylow
351C22×C4⋊C4—712no—
352C22×C4⋊C4—712no—
353C22×C4⋊C4—711no—
354C22×C4⋊C4—711no—
355C22×C4⋊C4C2×D7111yescharacteristic
356C22×C4⋊C4C2×D7112yes—
357C22×C4⋊C4C2×D7111yescharacteristic
358C22×C42—712no—
359C22×C42—711no—
360C22×C42—711no—
361C22×C42C2×D7111yescharacteristic
362#389—1424no—
363#389—1424no—
364#389Dic7118yescomplemented
365#382—1424no—
366C4×C4⋊C4—1424no—
367C2×#95—712no—
368C2×#95—711no—
369C2×#95—711no—
370C2×#95—711no—
371C2×#95—711no—
372C2×#95—712no—
373C2×#95—712no—
374C2×#95—712no—
375C2×#95—712no—
376C2×#95—712no—
377C2×#95—712no—
378C2×#95C2×D7112yes—
379C23×C4—711no—
380C23×C4—712no—
381C23×C4—711no—
382C23×C4—711no—
383C23×C4—711no—
384C23×C4—712no—
385C23×C4C22×D7112yes—
386C23×C4C22×D7111yescharacteristic
387C23×C4C22×D7111yescharacteristic
388C23×C4C22×D7112yes—
389C23×C4C22×D7111yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—2842no—
395C2×C4⋊C4—2842no—
396C2×C4⋊C4—714no—
397C2×C4⋊C4—1424no—
398C2×C4⋊C4—1424no—
399C2×C4⋊C4—1424no—
400C2×C4⋊C4—1422no—
401C2×C4⋊C4—1424no—
402C2×C4⋊C4—1422no—
403C2×C4⋊C4—1422no—
404C2×C4⋊C4—1422no—
405C2×C4⋊C4—1422no—
406C2×C4⋊C4Dic14214yes—
407C2×C4⋊C4D28414yes—
408C2×C4⋊C4C2×Dic7114yes—
409C2×C4⋊C4C2×Dic7118yes—
410C2×C4⋊C4C2×Dic7114yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—2842no—
414C2×C42—714no—
415C2×C42—1424no—
416C2×C42—1422no—
417C2×C42—1424no—
418C2×C42—1422no—
419C2×C42—1422no—
420C2×C42—1422no—
421C2×C42—1422no—
422C2×C42C2×Dic7114yes—
423#95—2842no—
424#95—1424no—
425#95—1424no—
426#95—1424no—
427#95—1422no—
428#95—1422no—
429#95—1422no—
430#95—1422no—
431#95—1424no—
432#95—1424no—
433#95—1424no—
434#95C2×Dic7118yes—
435C24C23×D7111yescharacteristic
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—712no—
459C22×C4—712no—
460C22×C4—712no—
461C22×C4—714no—
462C22×C4—712no—
463C22×C4—712no—
464C22×C4—712no—
465C22×C4—1422no—
466C22×C4—1422no—
467C22×C4—1422no—
468C22×C4—1422no—
469C22×C4—1422no—
470C22×C4—1422no—
471C22×C4—1422no—
472C22×C4—1421no—
473C22×C4—1421no—
474C22×C4—1421no—
475C22×C4—1421no—
476C22×C4—1422no—
477C22×C4—1421no—
478C22×C4—1421no—
479C22×C4—1421no—
480C22×C4—1421no—
481C22×C4—1421no—
482C22×C4—1422no—
483C22×C4—1422no—
484C22×C4—1421no—
485C22×C4—1421no—
486C22×C4—1421no—
487C22×C4—1422no—
488C22×C4—1421no—
489C22×C4—1422no—
490C22×C4—1421no—
491C22×C4—1421no—
492C22×C4—1421no—
493C22×C4—1422no—
494C22×C4—1421no—
495C22×C4—1421no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4C22×Dic7112yes—
501C22×C4C22×Dic7114yes—
502C22×C4C22×Dic7112yes—
503C22×C4C22×Dic7114yes—
504C22×C4C22×Dic7112yes—
505C22×C4D4×D7112yes—
506C22×C4C2×D28414yes—
507C22×C4C2×D28412yes—
508C22×C4Q8×D7112yes—
509C22×C4C2×Dic14214yes—
510C22×C4C2×Dic14212yes—
511C22×C4#1176586412yes—
512C22×C4#1176586612yes—
513C4⋊C4—28no—
514C4⋊C4—48no—
515C4⋊C4—2848no—
516C4⋊C4—2848no—
517C4⋊C4—2844no—
518C4⋊C4—1428no—
519C4⋊C4C4⋊Dic71116yescomplemented
520C42—28no—
521C42—2848no—
522C42—2844no—
523C42—1428no—
524C23C23×Dic7111yescharacteristic
525C23C2×D4×D7111yescharacteristic
526C23C22×D28411yescharacteristic
527C23C2×Q8×D7111yescharacteristic
528C23C22×Dic14211yescharacteristic
529C23#41×D7111yescharacteristic
530C23#41×D7111yescharacteristic
531C23#41×D7111yescharacteristic
532C23#41×D7111yescharacteristic
533C23C2×#1176586411yescharacteristic
534C23C2×#1176586611yescharacteristic
535C23#1455617311yescharacteristic
536C23#1455617311yescharacteristic
537C23#1455617611yescharacteristic
538C23#1455617611yescharacteristic
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—2841no—
567C2×C4—2841no—
568C2×C4—2842no—
569C2×C4—2842no—
570C2×C4—2841no—
571C2×C4—2841no—
572C2×C4—2841no—
573C2×C4—2841no—
574C2×C4—2841no—
575C2×C4—2842no—
576C2×C4—2841no—
577C2×C4—2841no—
578C2×C4—2841no—
579C2×C4—2841no—
580C2×C4—2841no—
581C2×C4—2842no—
582C2×C4—2842no—
583C2×C4—2842no—
584C2×C4—2842no—
585C2×C4—2842no—
586C2×C4—2842no—
587C2×C4—2842no—
588C2×C4—2842no—
589C2×C4—714no—
590C2×C4—1422no—
591C2×C4—1422no—
592C2×C4—1422no—
593C2×C4—1424no—
594C2×C4—1424no—
595C2×C4—1422no—
596C2×C4—1422no—
597C2×C4—1424no—
598C2×C4—1422no—
599C2×C4—1422no—
600C2×C4—1422no—
601C2×C4—1422no—
602C2×C4—1422no—
603C2×C4—1422no—
604C2×C4—1422no—
605C2×C4—1422no—
606C2×C4—1422no—
607C2×C4—1422no—
608C2×C4C2×C4⋊Dic7118yes—
609C2×C4C2×C4⋊Dic7114yes—
610C2×C4D4×Dic7114yes—
611C2×C4Q8×Dic7114yes—
612C2×C4#1455610314yes—
613C2×C4#1455610814yes—
614C2×C4#1455611914yes—
615C2×C4#1455612714yes—
616C22C22×C4⋊Dic7111yescharacteristic
617C22C2×D4×Dic7111yescharacteristic
618C22C2×Q8×Dic7111yescharacteristic
619C22#41×Dic7111yescharacteristic
620C22#41×Dic7111yescharacteristic
621C22#1798647411yescharacteristic
622C22#1798647711yescharacteristic
623C22C2×#1455610311yescharacteristic
624C22C2×#1455610811yescharacteristic
625C22#125×D7111yescharacteristic
626C22C2×#1455611911yescharacteristic
627C22#1798653411yescharacteristic
628C22#1798653411yescharacteristic
629C22C2×#1455612711yescharacteristic
630C22#1798655511yescharacteristic
631C22#1798662311yescharacteristic
632C22#1798662311yescharacteristic
633C22#1798662611yescharacteristic
634C22#1798662611yescharacteristic
635C22#1798664411yescharacteristic
636C22#1798664411yescharacteristic
637C22#1798664611yescharacteristic
638C22#1798665111yescharacteristic
639C22#1798665911yescharacteristic
640C22#1798666111yescharacteristic
641C22#1798666111yescharacteristic
642C22#1798666711yescharacteristic
643C22#1798668311yescharacteristic
644C22#1798669611yescharacteristic
645C22#1798670811yescharacteristic
646C22#1798670811yescharacteristic
647C22#1798671311yescharacteristic
648C22#1798672011yescharacteristic
649C22#1798672511yescharacteristic
650C22#1798672511yescharacteristic
651C4—28no—
652C4—42no—
653C4—42no—
654C4—44no—
655C4—2842no—
656C4—2842no—
657C4—2844no—
658C4—2842no—
659C4—5682no—
660C4—1424no—
661C4#1798589818yes—
662C2C2×#1798589811yescharacteristic
663C2#125×Dic7111yescharacteristic
664C2#2259108911yescharacteristic
665C2#2259125011yescharacteristic
666C2#2259126111yescharacteristic
667C2#2259137111yescharacteristic
668C2#2259138211yescharacteristic
669C2#2259190411yescharacteristic
670C2#2259191511yescharacteristic
671C2#2259202911yescharacteristic
672C2#2259206211yescharacteristic
673C2#2259288011yescharacteristic
674C2#2259289111yescharacteristic
675C2#2259336411yescharacteristic
676C2#2259337711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#389×C71C2
socle, prime radical, cosocleC24×C71C24
hypercenterC2×#389D71
hypocenterC71#14006
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. #389×C71C4semidirect
183. C4⋊C4×C71C4⋊C4semidirect
350. C71#14006semidirect
364. #389Dic71semidirect
519. C4⋊C4C4⋊Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179858982
C2×#179858652
C2×C4⋊C4×Dic712
#225865972
#225865932
#225865742
#225865692
C4×C71⋊#952
C2×#389×C712
#1400671