Finite Group Databasebeta

← C2×#22592723 #32166420

Subgroups — C2×#22592723 #32166420

Order 18176.

2398 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22592723C2116yesmaximal, direct product factor
2C2×C71⋊#401C211yesmaximal, characteristic, complemented
3C2×#17985941C211yesmaximal, characteristic, complemented
4C2×#17985938C211yesmaximal, characteristic, complemented
5C2×#17985937C211yesmaximal, characteristic, complemented
6C2×#17985885C211yesmaximal, characteristic, complemented
7C2×#17985882C211yesmaximal, characteristic, complemented
8C2×#17985880C211yesmaximal, characteristic, complemented
9C2×#17985871C211yesmaximal, characteristic
10C2×#17985866C211yesmaximal, characteristic, complemented
11C2×#17985860C211yesmaximal, characteristic
12C2×#17985860C211yesmaximal, characteristic
13C2×#17985859C211yesmaximal, characteristic
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic
15C22×C71⋊#95C211yesmaximal, characteristic
16C2×#385×C71C211yesmaximal, characteristic
17C24×Dic71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×C22⋊Dic71C2211yescharacteristic
24C22×C22⋊Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26C22×C4×Dic71C2211yescharacteristic
27C71⋊#401C2218yescomplemented
28#17985941C2218yescomplemented
29#17985938C2218yescomplemented
30#17985937C2218yescomplemented
31#17985885C2218yescomplemented
32#17985882C2218yescomplemented
33#17985880C2218yescomplemented
34#17985871C2218yes—
35#17985866C2218yescomplemented
36#17985860C2218yes—
37#17985860C2218yes—
38#17985859C2218yes—
39C22⋊C4×Dic71C2218yes—
40C2×C71⋊#95C2211yescharacteristic
41C2×C71⋊#95C2211yescharacteristic
42C2×C71⋊#95C2211yescharacteristic
43C2×C71⋊#95C2211yescharacteristic
44C2×C71⋊#95C2211yescharacteristic
45C2×C71⋊#95C2211yescharacteristic
46C2×C71⋊#95C2211yescharacteristic
47C2×C71⋊#95C2211yescharacteristic
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2218yes—
59C24×C4×C71C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64#385×C71C2218yes—
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C23×Dic71—24no—
68C23×Dic71—24no—
69C23×Dic71—24no—
70C23×Dic71—24no—
71C23×Dic71—24no—
72C23×Dic71—42no—
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2314yes—
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2314yes—
82C23×Dic71C2311yescharacteristic
83C2×C4⋊Dic71—24no—
84C2×C4⋊Dic71—42no—
85C2×C4⋊Dic71C2314yes—
86C2×C4⋊Dic71C2314yes—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4—42no—
89C2×Dic71⋊C4C2314yes—
90C2×Dic71⋊C4C2314yes—
91C2×C22⋊Dic71—24no—
92C2×C22⋊Dic71—24no—
93C2×C22⋊Dic71C2314yes—
94C2×C22⋊Dic71C2314yes—
95C2×C4×Dic71—24no—
96C2×C4×Dic71—42no—
97C2×C4×Dic71C2314yes—
98C2×C4×Dic71C2314yes—
99C71⋊#95C2314yes—
100C71⋊#95C2314yes—
101C71⋊#95C2314yes—
102C71⋊#95C2314yes—
103C71⋊#95C2314yes—
104C71⋊#95C2314yes—
105C71⋊#95C2314yes—
106C71⋊#95C2314yes—
107C71⋊#95C2314yes—
108C71⋊#95C2314yes—
109C71⋊#95C2314yes—
110C71⋊#95C2314yes—
111C71⋊#95C2314yes—
112C71⋊#95C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C25×C71C2311yescharacteristic
118C23×C4×C71—24no—
119C23×C4×C71—24no—
120C23×C4×C71—42no—
121C23×C4×C71C2311yescharacteristic
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2314yes—
127C23×C4×C71C2311yescharacteristic
128C2×C4⋊C4×C71—24no—
129C2×C4⋊C4×C71—42no—
130C2×C4⋊C4×C71C2314yes—
131C2×C4⋊C4×C71C2314yes—
132C2×C22⋊C4×C71—24no—
133C2×C22⋊C4×C71—24no—
134C2×C22⋊C4×C71C2314yes—
135C2×C22⋊C4×C71C2314yes—
136#95×C71C2314yes—
137#95×C71C2314yes—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—28no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—28no—
145C22×Dic71—28no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—28no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—28no—
166C22×Dic71—44no—
167C22×Dic71—416no—
168C22×Dic71—416no—
169C22×Dic71#4114yes—
170C22×Dic71C2412yes—
171C22×Dic71C2412yes—
172C22×Dic71C2412yes—
173C22×Dic71C2412yes—
174C22×Dic71C2412yes—
175C22×Dic71C2412yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C4⋊Dic71—28no—
179C4⋊Dic71—44no—
180Dic71⋊C4—28no—
181Dic71⋊C4—44no—
182C22⋊Dic71—28no—
183C22⋊Dic71—28no—
184C4×Dic71—28no—
185C4×Dic71—44no—
186C24×C71—22no—
187C24×C71—22no—
188C24×C71—22no—
189C24×C71—22no—
190C24×C71#4114yes—
191C24×C71#4114yes—
192C24×C71#4114yes—
193C24×C71C2412yes—
194C24×C71C2411yescharacteristic
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—22no—
203C22×C4×C71—28no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—28no—
214C22×C4×C71—44no—
215C22×C4×C71—416no—
216C22×C4×C71#4114yes—
217C22×C4×C71C2412yes—
218C22×C4×C71C2412yes—
219C22×C4×C71C2412yes—
220C22×C4×C71C2412yes—
221C22×C4×C71C2412yes—
222C22×C4×C71C2412yes—
223C4⋊C4×C71—28no—
224C4⋊C4×C71—44no—
225C22⋊C4×C71—28no—
226C22⋊C4×C71—28no—
227C23×C71—28no—
228C23×C71—28no—
229C23×C71—28no—
230C23×C71—28no—
231C23×C71—28no—
232C23×C71—28no—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—22no—
236C23×C71—22no—
237C23×C71#126116yes—
238C23×C71C2×#4112yes—
239C23×C71C2×#4114yes—
240C23×C71C2×#4112yes—
241C23×C71C2×#4112yes—
242C23×C71C2×#4114yes—
243C23×C71C2×#4112yes—
244C23×C71C2×#4114yes—
245C23×C71C2×#4112yes—
246C23×C71H(5,𝔽2)12yes—
247C23×C712−1+412yes—
248C23×C71C2511yescharacteristic
249C2×C4×C71—28no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—416no—
268C2×C4×C71—44no—
269C2×C4×C71—44no—
270C2×C4×C71—44no—
271C2×C4×C71—44no—
272C2×C4×C71—44no—
273C2×C4×C71C2×#4114yes—
274C2×Dic71—28no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—22no—
278C2×Dic71—22no—
279C2×Dic71—22no—
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—416no—
299C2×Dic71—416no—
300C2×Dic71—44no—
301C2×Dic71—44no—
302C2×Dic71—44no—
303C2×Dic71—44no—
304C2×Dic71—44no—
305C2×Dic71—44no—
306C2×Dic71—44no—
307C2×Dic71C2×#4114yes—
308C22×C71—24no—
309C22×C71—24no—
310C22×C71—24no—
311C22×C71—24no—
312C22×C71—24no—
313C22×C71—24no—
314C22×C71—232no—
315C22×C71C2×#12618yes—
316C22×C71C2×#12614yes—
317C22×C71#52914yes—
318C22×C71#53914yes—
319C22×C71#55114yes—
320C22×C71#55114yes—
321C22×C71#55214yes—
322C22×C71#55214yes—
323C22×C71C22×#4111yescharacteristic
324C22×C71C22×#4111yescharacteristic
325C22×C71C22×#4111yescharacteristic
326C22×C71C22×#4111yescharacteristic
327C22×C71C22×#4111yescharacteristic
328C22×C71C2×H(5,𝔽2)11yescharacteristic
329C22×C71C2×2−1+411yescharacteristic
330C4×C71—24no—
331C4×C71—42no—
332C4×C71—42no—
333C4×C71—42no—
334C4×C71—42no—
335C4×C71—42no—
336Dic71—24no—
337Dic71—42no—
338Dic71—42no—
339Dic71—42no—
340Dic71—42no—
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344C2×#2493—711nomaximal, Sylow
345C2×C71—28no—
346C2×C71#249318yescomplemented
347C2×C71C22×#12611yescharacteristic
348C2×C71C2×#52911yescharacteristic
349C2×C71C2×#53911yescharacteristic
350C2×C71C2×#55111yescharacteristic
351C2×C71C2×#55111yescharacteristic
352C2×C71C2×#55211yescharacteristic
353C2×C71C2×#55211yescharacteristic
354#2493—7116no—
355C2×#401—711no—
356C2×#400—711no—
357C2×#400—711no—
358C2×#400—711no—
359C2×#387—711no—
360C2×#387—711no—
361C2×#387—711no—
362C2×#385—711no—
363C2×#385D7111yescharacteristic
364C2×#383—711no—
365C2×#381—711no—
366C2×#381—711no—
367C2×#380—711no—
368C2×C4×C22⋊C4—711no—
369C22×#95—711no—
370C71C2×#249311yescharacteristic, complemented, Sylow
371C24×C4—711no—
372C24×C4—711no—
373C24×C4C2×D7111yescharacteristic
374C22×C4⋊C4—711no—
375C22×C4⋊C4—711no—
376C22×C4⋊C4—711no—
377C22×C4⋊C4—711no—
378C22×C4⋊C4C2×D7111yescharacteristic
379C22×C4⋊C4C2×D7111yescharacteristic
380C22×C22⋊C4—711no—
381C22×C22⋊C4—711no—
382C22×C22⋊C4C2×D7111yescharacteristic
383C22×C22⋊C4C2×D7111yescharacteristic
384C22×C42—711no—
385C22×C42—711no—
386#401—718no—
387#400—718no—
388#400—718no—
389#400—718no—
390#387—718no—
391#387—718no—
392#387—718no—
393#385—718no—
394#385C2×D7118yes—
395#383—718no—
396#381—718no—
397#381—718no—
398#380—718no—
399C4×C22⋊C4—718no—
400C2×#95—711no—
401C2×#95—711no—
402C2×#95—711no—
403C2×#95—711no—
404C2×#95—711no—
405C2×#95—711no—
406C2×#95—711no—
407C2×#95—711no—
408C2×#95—711no—
409C2×#95—711no—
410C2×#95—711no—
411C2×#95—711no—
412C2×#95—711no—
413C2×#95—711no—
414C2×#95—711no—
415C2×#95—718no—
416C2×#95—711no—
417C2×#95—711no—
418C2×#95—711no—
419C2×#95C2×D7111yescharacteristic
420C2×#95C2×D7111yescharacteristic
421C25C22×D7111yescharacteristic
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—2842no—
426C23×C4—714no—
427C23×C4—711no—
428C23×C4—714no—
429C23×C4—711no—
430C23×C4—711no—
431C23×C4—711no—
432C23×C4—711no—
433C23×C4—711no—
434C23×C4—711no—
435C23×C4—711no—
436C23×C4—1424no—
437C23×C4—1424no—
438C23×C4—1424no—
439C23×C4—1424no—
440C23×C4—1424no—
441C23×C4C22×D7111yescharacteristic
442C23×C4C22×D7111yescharacteristic
443C23×C4C22×D7111yescharacteristic
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7114yes—
447C23×C4C22×D7111yescharacteristic
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—2842no—
451C2×C4⋊C4—2842no—
452C2×C4⋊C4—714no—
453C2×C4⋊C4—714no—
454C2×C4⋊C4—714no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—1424no—
457C2×C4⋊C4—1424no—
458C2×C4⋊C4C22×D7114yes—
459C2×C4⋊C4C22×D7114yes—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—714no—
463C2×C22⋊C4—714no—
464C2×C22⋊C4—1424no—
465C2×C22⋊C4—1424no—
466C2×C22⋊C4C22×D7114yes—
467C2×C22⋊C4C22×D7114yes—
468C2×C42—2842no—
469C2×C42—714no—
470C2×C42—714no—
471C2×C42—1424no—
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#95—714no—
481#95—714no—
482#95—714no—
483#95—714no—
484#95—714no—
485#95—714no—
486#95—714no—
487#95—714no—
488#95—714no—
489#95—714no—
490#95C22×D7114yes—
491#95C22×D7114yes—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24#1176586414yes—
497C24#1176586514yes—
498C24#1176586614yes—
499C24C23×D7112yes—
500C24C23×D7111yescharacteristic
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—44no—
521C22×C4—416no—
522C22×C4—28416no—
523C22×C4—28416no—
524C22×C4—2844no—
525C22×C4—714no—
526C22×C4—712no—
527C22×C4—712no—
528C22×C4—712no—
529C22×C4—712no—
530C22×C4—712no—
531C22×C4—712no—
532C22×C4—712no—
533C22×C4—712no—
534C22×C4—1428no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1428no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1428no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1428no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1428no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1422no—
562C22×C4#1176586414yes—
563C22×C4C23×D7112yes—
564C22×C4C23×D7112yes—
565C22×C4C23×D7112yes—
566C22×C4C23×D7112yes—
567C22×C4C23×D7112yes—
568C22×C4C23×D7112yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—2844no—
572C4⋊C4—2844no—
573C4⋊C4—1428no—
574C4⋊C4—1428no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—1428no—
578C22⋊C4—1428no—
579C42—2844no—
580C42—1428no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—28no—
586C23—28no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—28no—
591C23#14556123116yes—
592C23#41×D7112yes—
593C23C2×#1176586414yes—
594C23C2×#1176586412yes—
595C23C2×#1176586412yes—
596C23C2×#1176586514yes—
597C23C2×#1176586512yes—
598C23C2×#1176586614yes—
599C23C2×#1176586612yes—
600C23#1455617312yes—
601C23#1455617512yes—
602C23C24×D7111yescharacteristic
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—28no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—416no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—2844no—
628C2×C4—2844no—
629C2×C4—2844no—
630C2×C4—28416no—
631C2×C4—2844no—
632C2×C4—2844no—
633C2×C4—2844no—
634C2×C4—2844no—
635C2×C4—28416no—
636C2×C4—714no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1428no—
661C2×C4C2×#1176586414yes—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—232no—
668C22—24no—
669C22C2×#1455612318yes—
670C22C2×#1455612314yes—
671C22#1798653514yes—
672C22#1798659814yes—
673C22#1798667814yes—
674C22#1798668014yes—
675C22#1798668614yes—
676C22#1798668914yes—
677C22C2×#41×D7111yescharacteristic
678C22C22×#1176586411yescharacteristic
679C22C22×#1176586411yescharacteristic
680C22C22×#1176586511yescharacteristic
681C22C22×#1176586611yescharacteristic
682C22C2×#1455617311yescharacteristic
683C22C2×#1455617511yescharacteristic
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—2842no—
691C4—2842no—
692C4—2842no—
693C4—2842no—
694C4—2842no—
695C4—2842no—
696C4—2842no—
697C4—1424no—
698C2—28no—
699C2#2259272318yesdirect product factor
700C2C22×#1455612311yescharacteristic
701C2C2×#1798653511yescharacteristic
702C2C2×#1798659811yescharacteristic
703C2C2×#1798667811yescharacteristic
704C2C2×#1798668011yescharacteristic
705C2C2×#1798668611yescharacteristic
706C2C2×#1798668911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71C2×#2493
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #22592723C2direct (N × H)
2. C2×C71⋊#401C2semidirect
3. C2×#17985941C2semidirect
4. C2×#17985938C2semidirect
5. C2×#17985937C2semidirect
6. C2×#17985885C2semidirect
7. C2×#17985882C2semidirect
8. C2×#17985880C2semidirect
10. C2×#17985866C2semidirect
27. C71⋊#401C22semidirect
28. #17985941C22semidirect
29. #17985938C22semidirect
30. #17985937C22semidirect
31. #17985885C22semidirect
32. #17985882C22semidirect
33. #17985880C22semidirect
35. #17985866C22semidirect
346. C2×C71#2493semidirect
370. C71C2×#2493semidirect
699. C2#22592723direct (N × H)

Maximal subgroups

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

subgroupindex
#225927232
C2×C71⋊#4012
C2×#179859412
C2×#179859382
C2×#179859372
C2×#179858852
C2×#179858822
C2×#179858802
C2×#179858712
C2×#179858662
C2×#179858602
C2×#179858592
C2×C22⋊C4×Dic712
C22×C71⋊#952
C2×#385×C712
C2×#249371