Finite Group Databasebeta

← #31920208

Subgroups — #31920208

Order 18176.

2150 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985874C211yesmaximal, characteristic
2C2×#17985872C211yesmaximal, characteristic
3C2×#17985871C211yesmaximal, characteristic
4C2×#17985857C211yesmaximal, characteristic
5C2×C22⋊C4×Dic71C211yesmaximal, characteristic
6C22×C71⋊#95C211yesmaximal, characteristic
7#22586604C212yesmaximal, complemented
8#22586603C212yesmaximal, complemented
9#22586569C212yesmaximal, complemented
10Dic71⋊#95C212yesmaximal, complemented
11C2×#385×C71C211yesmaximal, characteristic
12C24×Dic71C2211yescharacteristic
13C24×Dic71C2211yescharacteristic
14C22×C4⋊Dic71C2212yes—
15C22×Dic71⋊C4C2212yes—
16C22×Dic71⋊C4C2212yes—
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2211yescharacteristic
19C22×C22⋊Dic71C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C4×Dic71C2212yes—
22#17985874—24no—
23#17985872—24no—
24#17985871—24no—
25#17985857—24no—
26C22⋊C4×Dic71C418yescomplemented
27C2×C71⋊#95—24no—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2211yescharacteristic
35C2×C71⋊#95C2212yes—
36C24×C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2212yes—
38C22×C22⋊C4×C71C2211yescharacteristic
39C22×C22⋊C4×C71C2211yescharacteristic
40#385×C71—24no—
41C2×#95×C71C2212yes—
42C23×Dic71—24no—
43C23×Dic71—22no—
44C23×Dic71—22no—
45C23×Dic71—22no—
46C23×Dic71—42no—
47C23×Dic71—42no—
48C23×Dic71—42no—
49C23×Dic71C2×C414yes—
50C23×Dic71D414yes—
51C23×Dic71Q814yes—
52C23×Dic71C2311yescharacteristic
53C23×Dic71C2311yescharacteristic
54C23×Dic71C2312yes—
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2311yescharacteristic
57C23×Dic71C2312yes—
58C2×C4⋊Dic71—24no—
59C2×C4⋊Dic71—24no—
60C2×C4⋊Dic71—42no—
61C2×Dic71⋊C4—22no—
62C2×Dic71⋊C4—22no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4—24no—
66C2×Dic71⋊C4—24no—
67C2×Dic71⋊C4—42no—
68C2×Dic71⋊C4—42no—
69C2×Dic71⋊C4—42no—
70C2×Dic71⋊C4—42no—
71C2×C22⋊Dic71—22no—
72C2×C22⋊Dic71—22no—
73C2×C22⋊Dic71—22no—
74C2×C22⋊Dic71C2×C414yes—
75C2×C22⋊Dic71D414yes—
76C2×C22⋊Dic71Q814yes—
77C2×C4×Dic71—42no—
78C2×C4×Dic71—42no—
79C2×C4×Dic71C2×C418yescomplemented
80C71⋊#95—24no—
81C71⋊#95—24no—
82C71⋊#95—22no—
83C71⋊#95—22no—
84C71⋊#95—24no—
85C71⋊#95—24no—
86C71⋊#95—24no—
87C71⋊#95C2×C418yescomplemented
88C25×C71C2311yescharacteristic
89C23×C4×C71—22no—
90C23×C4×C71—24no—
91C23×C4×C71—22no—
92C23×C4×C71—22no—
93C23×C4×C71—42no—
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C23×C4×C71C2312yes—
97C23×C4×C71C2312yes—
98C2×C4⋊C4×C71—24no—
99C2×C4⋊C4×C71—24no—
100C2×C4⋊C4×C71—42no—
101C2×C22⋊C4×C71—22no—
102C2×C22⋊C4×C71—22no—
103C2×C22⋊C4×C71—22no—
104C2×C22⋊C4×C71C2×C414yes—
105C2×C22⋊C4×C71D414yes—
106C2×C22⋊C4×C71Q814yes—
107#95×C71—24no—
108C22×Dic71—22no—
109C22×Dic71—22no—
110C22×Dic71—22no—
111C22×Dic71—22no—
112C22×Dic71—22no—
113C22×Dic71—22no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—28no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—22no—
122C22×Dic71—22no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—48no—
134C22×Dic71—44no—
135C22×Dic71—44no—
136C22×Dic71—48no—
137C22×Dic71—48no—
138C22×Dic71—48no—
139C22×Dic71—44no—
140C22×Dic71—44no—
141C22×Dic71C4⋊C4116yescomplemented
142C22×Dic71C22×C412yes—
143C22×Dic71C22×C412yes—
144C22×Dic71C22×C414yes—
145C22×Dic71C2×D412yes—
146C22×Dic71C2×D412yes—
147C22×Dic71C2×D414yes—
148C22×Dic71C2×Q812yes—
149C22×Dic71C2×Q812yes—
150C22×Dic71C2×Q814yes—
151C22×Dic71#4114yes—
152C4⋊Dic71—48no—
153Dic71⋊C4—48no—
154Dic71⋊C4—48no—
155Dic71⋊C4—44no—
156Dic71⋊C4—44no—
157C22⋊Dic71—44no—
158C22⋊Dic71C4⋊C4116yescomplemented
159C4×Dic71—48no—
160C24×C71—22no—
161C24×C71—22no—
162C24×C71—22no—
163C24×C71—22no—
164C24×C71C22×C412yes—
165C24×C71C2×D412yes—
166C24×C71C2×D412yes—
167C24×C71C2×D412yes—
168C24×C71C2×Q812yes—
169C24×C71C2×Q812yes—
170C24×C71C2×Q812yes—
171C24×C71C2411yescharacteristic
172C22×C4×C71—22no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—28no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—48no—
194C22×C4×C71—48no—
195C22×C4×C71—44no—
196C22×C4×C71—44no—
197C22×C4×C71C22×C414yes—
198C22×C4×C71C2×D414yes—
199C22×C4×C71C2×Q814yes—
200C22×C4×C71#4114yes—
201C4⋊C4×C71—48no—
202C22⋊C4×C71—44no—
203C22⋊C4×C71C4⋊C4116yescomplemented
204C23×C71—24no—
205C23×C71—24no—
206C23×C71—22no—
207C23×C71—22no—
208C23×C71—24no—
209C23×C71—22no—
210C23×C71—22no—
211C23×C71—24no—
212C23×C71—24no—
213C23×C71—24no—
214C23×C71—24no—
215C23×C71—24no—
216C23×C71—24no—
217C23×C71—24no—
218C23×C71—24no—
219C23×C71—24no—
220C23×C71C2×C4⋊C414yes—
221C23×C71C2×C4⋊C414yes—
222C23×C71C2×C4⋊C414yes—
223C23×C71#12714yes—
224C23×C71C4⋊Q814yes—
225C23×C71C4⋊Q814yes—
226C23×C71C4⋊Q814yes—
227C23×C71C23×C411yescharacteristic
228C23×C71C22×D411yescharacteristic
229C23×C71C22×D411yescharacteristic
230C23×C71C22×D411yescharacteristic
231C23×C71C22×Q811yescharacteristic
232C23×C71C22×Q811yescharacteristic
233C23×C71C22×Q811yescharacteristic
234C23×C71C2×#4112yes—
235C23×C71C2×#4112yes—
236C23×C71H(5,𝔽2)12yes—
237C23×C71H(5,𝔽2)12yes—
238C2×C4×C71—24no—
239C2×C4×C71—24no—
240C2×C4×C71—24no—
241C2×C4×C71—24no—
242C2×C4×C71—24no—
243C2×C4×C71—24no—
244C2×C4×C71—24no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—416no—
248C2×C4×C71—42no—
249C2×C4×C71—42no—
250C2×C4×C71—42no—
251C2×C4×C71—42no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—42no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—42no—
262C2×C4×C71C2×C4⋊C418yes—
263C2×Dic71—24no—
264C2×Dic71—24no—
265C2×Dic71—24no—
266C2×Dic71—24no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—22no—
271C2×Dic71—24no—
272C2×Dic71—24no—
273C2×Dic71—24no—
274C2×Dic71—24no—
275C2×Dic71—24no—
276C2×Dic71—24no—
277C2×Dic71—24no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—416no—
281C2×Dic71—416no—
282C2×Dic71—42no—
283C2×Dic71—42no—
284C2×Dic71—42no—
285C2×Dic71—42no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—42no—
293C2×Dic71—42no—
294C2×Dic71—42no—
295C2×Dic71—42no—
296C2×Dic71C2×C4⋊C418yes—
297C2×Dic71C2×C4⋊C414yes—
298C2×Dic71C2×C4⋊C414yes—
299C22×C71—24no—
300C22×C71—24no—
301C22×C71—24no—
302C22×C71—28no—
303C22×C71—28no—
304C22×C71—24no—
305C22×C71—24no—
306C22×C71—28no—
307C22×C71—28no—
308C22×C71—24no—
309C22×C71#38418yes—
310C22×C71C22×C4⋊C411yescharacteristic
311C22×C71C22×C4⋊C411yescharacteristic
312C22×C71C22×C4⋊C411yescharacteristic
313C22×C71C4×#4112yes—
314C22×C71#51812yes—
315C22×C71#52511yescharacteristic
316C22×C71#52511yescharacteristic
317C22×C71C2×#12711yescharacteristic
318C22×C71C2×C4⋊Q811yescharacteristic
319C22×C71C2×C4⋊Q811yescharacteristic
320C22×C71C2×C4⋊Q811yescharacteristic
321C22×C71#53312yes—
322C22×C71#53411yescharacteristic
323C22×C71#53411yescharacteristic
324C22×C71#54312yes—
325C22×C71#54612yes—
326C22×C71#54612yes—
327C22×C71#54612yes—
328C22×C71#54612yes—
329C22×C71#55412yes—
330C22×C71#55412yes—
331C22×C71#55412yes—
332C22×C71#55412yes—
333C4×C71—28no—
334C4×C71—44no—
335C4×C71—81no—
336C4×C71—81no—
337Dic71—24no—
338Dic71—24no—
339Dic71—28no—
340Dic71—44no—
341Dic71—81no—
342Dic71—81no—
343#13965—711nomaximal, Sylow
344C2×C71—28no—
345C2×C71C2×#38411yescharacteristic
346C2×C71#229611yescharacteristic
347C2×C71#231511yescharacteristic
348C2×C71#234912yes—
349C2×C71#234912yes—
350C2×C71#253911yescharacteristic
351C2×C71#253911yescharacteristic
352C2×C71#254912yes—
353C2×C71#254912yes—
354C2×C71#258311yescharacteristic
355C2×C71#258311yescharacteristic
356C2×#385—711no—
357C2×#385—711no—
358C2×#385—711no—
359C2×#385D7111yescharacteristic
360C2×#380—711no—
361C2×C4×C22⋊C4—711no—
362C22×#95—711no—
363#1444—712no—
364#1444—712no—
365C4⋊#95—712no—
366C4⋊#95—712no—
367C71#1396511yescharacteristic, complemented, Sylow
368C24×C4—711no—
369C24×C4—711no—
370C24×C4C2×D7111yescharacteristic
371C22×C4⋊C4—711no—
372C22×C4⋊C4—711no—
373C22×C4⋊C4—712no—
374C22×C4⋊C4—712no—
375C22×C4⋊C4—712no—
376C22×C4⋊C4C2×D7112yes—
377C22×C22⋊C4—711no—
378C22×C22⋊C4—711no—
379C22×C22⋊C4C2×D7111yescharacteristic
380C22×C22⋊C4C2×D7111yescharacteristic
381C22×C42—712no—
382#385—24no—
383#385—1424no—
384#385—1424no—
385#385—1424no—
386#380—1424no—
387C4×C22⋊C4—718no—
388C2×#95—712no—
389C2×#95—712no—
390C2×#95—711no—
391C2×#95—711no—
392C2×#95—712no—
393C2×#95—712no—
394C2×#95—712no—
395C2×#95—712no—
396C2×#95—1424no—
397C2×#95C2×D7112yes—
398C25C22×D7111yescharacteristic
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—2842no—
405C23×C4—2842no—
406C23×C4—2842no—
407C23×C4—714no—
408C23×C4—714no—
409C23×C4—714no—
410C23×C4—712no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4—712no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—1422no—
417C23×C4—1422no—
418C23×C4—1424no—
419C23×C4—1422no—
420C23×C4C22×D7111yescharacteristic
421C23×C4C22×D7111yescharacteristic
422C23×C4C22×D7112yes—
423C23×C4C22×D7112yes—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—2842no—
428C2×C4⋊C4—2842no—
429C2×C4⋊C4—2842no—
430C2×C4⋊C4—2842no—
431C2×C4⋊C4—2842no—
432C2×C4⋊C4—1422no—
433C2×C4⋊C4—1422no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1424no—
437C2×C4⋊C4—1424no—
438C2×C4⋊C4—1424no—
439C2×C4⋊C4—1424no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—714no—
444C2×C22⋊C4—714no—
445C2×C22⋊C4—714no—
446C2×C22⋊C4—1422no—
447C2×C22⋊C4—1422no—
448C2×C22⋊C4—1422no—
449C2×C22⋊C4Dic14214yes—
450C2×C22⋊C4C4×D7114yes—
451C2×C22⋊C4C22⋊D7114yes—
452C2×C42—2842no—
453C2×C42—2842no—
454C2×C42—718no—
455#95—24no—
456#95—718no—
457#95—1424no—
458#95—1424no—
459#95—1422no—
460#95—1422no—
461#95—1424no—
462#95—1424no—
463#95—1424no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24C2×C4×D7112yes—
469C24D4×D7112yes—
470C24D4×D7112yes—
471C24C2×C22⋊D7112yes—
472C24Q8×D7112yes—
473C24Q8×D7112yes—
474C24C2×Dic14212yes—
475C24C23×D7111yescharacteristic
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—2844no—
502C22×C4—2844no—
503C22×C4—2848no—
504C22×C4—2848no—
505C22×C4—2844no—
506C22×C4—2848no—
507C22×C4—2848no—
508C22×C4—2844no—
509C22×C4—7116no—
510C22×C4—712no—
511C22×C4—714no—
512C22×C4—712no—
513C22×C4—712no—
514C22×C4—714no—
515C22×C4—712no—
516C22×C4—714no—
517C22×C4—712no—
518C22×C4—712no—
519C22×C4—714no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4—1421no—
525C22×C4—1421no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1428no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4—1422no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1422no—
545C22×C4C2×C4×D7114yes—
546C22×C4C2×C22⋊D7114yes—
547C22×C4C2×Dic14214yes—
548C22×C4#1176586414yes—
549C4⋊C4—48no—
550C4⋊C4—2848no—
551C4⋊C4—2848no—
552C4⋊C4—2844no—
553C4⋊C4—2844no—
554C4⋊C4—2848no—
555C22⋊C4—44no—
556C22⋊C4—2844no—
557C22⋊C4—7116no—
558C22⋊C4Dic71⋊C4116yescomplemented
559C42—2848no—
560C23—22no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23C4⋊C4×D7114yes—
577C23C4⋊C4×D7114yes—
578C23C2×Dic71⋊C414yes—
579C23#1455612414yes—
580C23#1455612614yes—
581C23#1455612714yes—
582C23#1455612714yes—
583C23C22×C4×D7111yescharacteristic
584C23C2×D4×D7111yescharacteristic
585C23C2×D4×D7111yescharacteristic
586C23C22×C22⋊D7111yescharacteristic
587C23C2×Q8×D7111yescharacteristic
588C23C2×Q8×D7111yescharacteristic
589C23C22×Dic14211yescharacteristic
590C23#41×D7112yes—
591C23C2×#1176586412yes—
592C23#1455617312yes—
593C23#1455617412yes—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—416no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—28416no—
619C2×C4—2842no—
620C2×C4—2842no—
621C2×C4—2842no—
622C2×C4—2842no—
623C2×C4—2841no—
624C2×C4—2842no—
625C2×C4—2842no—
626C2×C4—2842no—
627C2×C4—2842no—
628C2×C4—2841no—
629C2×C4—2841no—
630C2×C4—2841no—
631C2×C4—2841no—
632C2×C4—2841no—
633C2×C4—28416no—
634C2×C4—718no—
635C2×C4—714no—
636C2×C4—714no—
637C2×C4—1424no—
638C2×C4—1424no—
639C2×C4—1424no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—1424no—
644C2×C4—1424no—
645C2×C4—1424no—
646C2×C4—1424no—
647C2×C4—1424no—
648C2×C4—1424no—
649C2×C4—1424no—
650C2×C4—1424no—
651C2×C4—1424no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4C2×Dic71⋊C418yes—
655C22—28no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22#1798586818yes—
666C22C2×C4⋊C4×D7111yescharacteristic
667C22C2×C4⋊C4×D7111yescharacteristic
668C22C22×Dic71⋊C411yescharacteristic
669C22C4×#1176586412yes—
670C22#1798647112yes—
671C22#1798650511yescharacteristic
672C22#1798650711yescharacteristic
673C22C2×#1455612411yescharacteristic
674C22C2×#1455612611yescharacteristic
675C22C2×#1455612711yescharacteristic
676C22C2×#1455612711yescharacteristic
677C22#1798655112yes—
678C22#1798655911yescharacteristic
679C22#1798656011yescharacteristic
680C22#1798662412yes—
681C22#1798663612yes—
682C22#1798663712yes—
683C22#1798664112yes—
684C22#1798664312yes—
685C22#1798670312yes—
686C22#1798670612yes—
687C22#1798670712yes—
688C22#1798670812yes—
689C4—28no—
690C4—44no—
691C4—81no—
692C4—81no—
693C4—2844no—
694C4—5681no—
695C4—5681no—
696C4—1428no—
697C4—1424no—
698C4—1424no—
699C2—28no—
700C2C2×#1798586811yescharacteristic
701C2#2259081911yescharacteristic
702C2#2259095111yescharacteristic
703C2#2259124512yes—
704C2#2259124612yes—
705C2#2259326811yescharacteristic
706C2#2259327011yescharacteristic
707C2#2259334812yes—
708C2#2259335312yes—
709C2#2259371711yescharacteristic
710C2#2259371911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#385×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71#13965
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
7. #22586604C2semidirect
8. #22586603C2semidirect
9. #22586569C2semidirect
10. Dic71⋊#95C2semidirect
26. C22⋊C4×Dic71C4semidirect
79. C2×C4×Dic71C2×C4semidirect
87. C71⋊#95C2×C4semidirect
141. C22×Dic71C4⋊C4semidirect
158. C22⋊Dic71C4⋊C4semidirect
203. C22⋊C4×C71C4⋊C4semidirect
367. C71#13965semidirect
558. C22⋊C4Dic71⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#179858742
C2×#179858722
C2×#179858712
C2×#179858572
C2×C22⋊C4×Dic712
C22×C71⋊#952
#225866042
#225866032
#225865692
Dic71⋊#952
C2×#385×C712
#1396571