Finite Group Databasebeta

← #31921157

Subgroups — #31921157

Order 18176.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic71⋊C4C211yesmaximal, characteristic
2C2×#17985894C212yesmaximal, complemented
3C2×#17985871C211yesmaximal, characteristic
4C2×#17985871C211yesmaximal, characteristic
5C2×C4×C22⋊Dic71C211yesmaximal, characteristic
6#22586603C212yesmaximal, complemented
7#22586591C212yesmaximal, complemented
8#22586575C212yesmaximal, complemented
9#22586562C211yesmaximal, characteristic
10#22586562C211yesmaximal, characteristic
11C2×#385×C71C211yesmaximal, characteristic
12C24×Dic71C2211yescharacteristic
13C24×Dic71C2211yescharacteristic
14C22×Dic71⋊C4—28no—
15C22×Dic71⋊C4—24no—
16C22×Dic71⋊C4C2212yes—
17C22×Dic71⋊C4C2212yes—
18C22×Dic71⋊C4C2212yes—
19C22×Dic71⋊C4C2212yes—
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C4×Dic71C2212yes—
23#17985894—28no—
24#17985871—24no—
25#17985871C418yescomplemented
26C4×C22⋊Dic71—24no—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C24×C4×C71C2211yescharacteristic
35C22×C4⋊C4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C22⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2211yescharacteristic
39#385×C71—24no—
40C2×#95×C71C2211yescharacteristic
41C2×#95×C71C2211yescharacteristic
42C23×Dic71—24no—
43C23×Dic71—24no—
44C23×Dic71—24no—
45C23×Dic71—22no—
46C23×Dic71—22no—
47C23×Dic71—22no—
48C23×Dic71—22no—
49C23×Dic71—22no—
50C23×Dic71—42no—
51C23×Dic71C2×C414yes—
52C23×Dic71C2312yes—
53C23×Dic71C2312yes—
54C23×Dic71C2312yes—
55C23×Dic71C2312yes—
56C2×Dic71⋊C4—232no—
57C2×Dic71⋊C4—24no—
58C2×Dic71⋊C4—24no—
59C2×Dic71⋊C4—24no—
60C2×Dic71⋊C4—24no—
61C2×Dic71⋊C4—24no—
62C2×Dic71⋊C4—24no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4—24no—
66C2×Dic71⋊C4—42no—
67C2×Dic71⋊C4C2×C418yescomplemented
68C2×Dic71⋊C4D418yes—
69C2×C22⋊Dic71—22no—
70C2×C22⋊Dic71—22no—
71C2×C22⋊Dic71C2×C414yes—
72C2×C22⋊Dic71D414yes—
73C2×C22⋊Dic71Q814yes—
74C2×C22⋊Dic71Q814yes—
75C2×C4×Dic71—24no—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—42no—
78C71⋊#95—24no—
79C71⋊#95—24no—
80C71⋊#95—24no—
81C71⋊#95—24no—
82C71⋊#95—24no—
83C71⋊#95—42no—
84C71⋊#95C2×C418yescomplemented
85C25×C71C2311yescharacteristic
86C23×C4×C71—22no—
87C23×C4×C71—22no—
88C23×C4×C71—24no—
89C23×C4×C71—42no—
90C23×C4×C71D414yes—
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C23×C4×C71C2311yescharacteristic
97C2×C4⋊C4×C71—24no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71—22no—
100C2×C4⋊C4×C71—42no—
101C2×C22⋊C4×C71—22no—
102C2×C22⋊C4×C71—22no—
103C2×C22⋊C4×C71—22no—
104C2×C22⋊C4×C71—22no—
105C2×C22⋊C4×C71—22no—
106C2×C22⋊C4×C71C2×C414yes—
107#95×C71—22no—
108#95×C71—22no—
109C22×Dic71—216no—
110C22×Dic71—28no—
111C22×Dic71—28no—
112C22×Dic71—28no—
113C22×Dic71—22no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—22no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—216no—
122C22×Dic71—28no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—48no—
136C22×Dic71—48no—
137C22×Dic71—44no—
138C22×Dic71—44no—
139C22×Dic71C22×C414yes—
140C22×Dic71C22×C414yes—
141C22×Dic71C2×D414yes—
142C22×Dic71C2×D414yes—
143C22×Dic71C2×D414yes—
144C22×Dic71C2×Q814yes—
145C22×Dic71C2×Q814yes—
146C22×Dic71#4114yes—
147Dic71⋊C4—216no—
148Dic71⋊C4—216no—
149Dic71⋊C4—216no—
150Dic71⋊C4—48no—
151C22⋊Dic71—28no—
152C22⋊Dic71C4⋊C4116yescomplemented
153C4×Dic71—48no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71—22no—
157C24×C71—22no—
158C24×C71C22×C412yes—
159C24×C71C2×D412yes—
160C24×C71C2×D412yes—
161C24×C71C2×Q812yes—
162C24×C71C2×Q812yes—
163C24×C71#4112yes—
164C24×C71#4112yes—
165C24×C71C2411yescharacteristic
166C22×C4×C71—21no—
167C22×C4×C71—21no—
168C22×C4×C71—22no—
169C22×C4×C71—28no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—22no—
173C22×C4×C71—21no—
174C22×C4×C71—22no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—28no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—22no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—44no—
194C22×C4×C71—48no—
195C22×C4×C71—48no—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C22×C412yes—
198C22×C4×C71C2×D414yes—
199C22×C4×C71C2×D412yes—
200C22×C4×C71C2×D412yes—
201C4⋊C4×C71—44no—
202C4⋊C4×C71—44no—
203C22⋊C4×C71—28no—
204C22⋊C4×C71—44no—
205C23×C71—24no—
206C23×C71—24no—
207C23×C71—22no—
208C23×C71—22no—
209C23×C71—24no—
210C23×C71—22no—
211C23×C71—22no—
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×C71—24no—
221C23×C71C2×C4⋊C414yes—
222C23×C71C4×D414yes—
223C23×C71C4×Q814yes—
224C23×C71#12114yes—
225C23×C71C22⋊Q814yes—
226C23×C71#12514yes—
227C23×C71C4⋊Q814yes—
228C23×C71C23×C411yescharacteristic
229C23×C71C22×D411yescharacteristic
230C23×C71C22×D412yes—
231C23×C71C22×D411yescharacteristic
232C23×C71C22×Q811yescharacteristic
233C23×C71C22×Q811yescharacteristic
234C23×C71C2×#4112yes—
235C23×C71C2×#4111yescharacteristic
236C23×C71C2×#4111yescharacteristic
237C23×C71H(5,𝔽2)12yes—
238C23×C712−1+412yes—
239C2×C4×C71—22no—
240C2×C4×C71—22no—
241C2×C4×C71—24no—
242C2×C4×C71—24no—
243C2×C4×C71—22no—
244C2×C4×C71—22no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—416no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—42no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—42no—
257C2×C4×C71—42no—
258C2×C4×C71—42no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—41no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—42no—
268C2×C4×C71—42no—
269C2×C4×C71#12014yes—
270C2×Dic71—232no—
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—24no—
281C2×Dic71—24no—
282C2×Dic71—24no—
283C2×Dic71—24no—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—24no—
287C2×Dic71—24no—
288C2×Dic71—24no—
289C2×Dic71—416no—
290C2×Dic71—42no—
291C2×Dic71—42no—
292C2×Dic71—42no—
293C2×Dic71—42no—
294C2×Dic71—42no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71C2×C4⋊C418yescomplemented
299C2×Dic71C4×D418yes—
300C22×C71—24no—
301C22×C71—24no—
302C22×C71—28no—
303C22×C71—28no—
304C22×C71—24no—
305C22×C71—24no—
306C22×C71—24no—
307C22×C71—28no—
308C22×C71—28no—
309C22×C71—24no—
310C22×C71#38918yescomplemented
311C22×C71C22×C4⋊C411yescharacteristic
312C22×C71C2×C4×D412yes—
313C22×C71C2×C4×D411yescharacteristic
314C22×C71C2×C4×Q811yescharacteristic
315C22×C71#52012yes—
316C22×C71C2×#12011yescharacteristic
317C22×C71C2×#12111yescharacteristic
318C22×C71C2×C22⋊Q811yescharacteristic
319C22×C71#52511yescharacteristic
320C22×C71#52512yes—
321C22×C71C2×#12511yescharacteristic
322C22×C71C2×C4⋊Q811yescharacteristic
323C22×C71#53411yescharacteristic
324C22×C71#53611yescharacteristic
325C22×C71#53912yes—
326C22×C71D4212yes—
327C22×C71#54612yes—
328C22×C71#54712yes—
329C22×C71D4×Q812yes—
330C22×C71D4×Q812yes—
331C22×C71#55212yes—
332C22×C71#55412yes—
333C22×C71#55412yes—
334C4×C71—24no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71—81no—
339C4×C71—81no—
340Dic71—28no—
341Dic71—28no—
342Dic71—44no—
343Dic71—44no—
344#14043—711nomaximal, Sylow
345C2×C71—28no—
346C2×C71C2×#38911yescharacteristic
347C2×C71C4×#12011yescharacteristic
348C2×C71#232211yescharacteristic
349C2×C71D4×C4⋊C412yes—
350C2×C71#236012yes—
351C2×C71#241011yescharacteristic
352C2×C71#241311yescharacteristic
353C2×C71#243411yescharacteristic
354C2×C71#244912yes—
355C2×C71#247312yes—
356C2×C71#258311yescharacteristic
357C23×C4⋊C4—711no—
358C2×#389—712no—
359C2×#385—711no—
360C2×#385—711no—
361C2×#385D7111yescharacteristic
362C2×C4×C22⋊C4—711no—
363#1444—712no—
364#1441—712no—
365#1436—712no—
366C22⋊#95—711no—
367C22⋊#95—711no—
368C71#1404311yescharacteristic, complemented, Sylow
369C24×C4—711no—
370C24×C4—711no—
371C24×C4C2×D7111yescharacteristic
372C22×C4⋊C4—712no—
373C22×C4⋊C4—712no—
374C22×C4⋊C4—712no—
375C22×C4⋊C4—712no—
376C22×C4⋊C4—1428no—
377C22×C4⋊C4—1424no—
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—712no—
385#389—1428no—
386#385—24no—
387#385—718no—
388#385—1424no—
389C4×C22⋊C4—1424no—
390C2×#95—712no—
391C2×#95—712no—
392C2×#95—712no—
393C2×#95—712no—
394C2×#95—712no—
395C2×#95—712no—
396C2×#95—712no—
397C2×#95C2×D7111yescharacteristic
398C2×#95C2×D7111yescharacteristic
399C25C22×D7111yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—2842no—
405C23×C4—712no—
406C23×C4—712no—
407C23×C4—714no—
408C23×C4—712no—
409C23×C4—712no—
410C23×C4—1422no—
411C23×C4—1422no—
412C23×C4—1424no—
413C23×C4—1422no—
414C23×C4—1424no—
415C23×C4—1424no—
416C23×C4—1422no—
417C23×C4—1422no—
418C23×C4C22⋊D7114yes—
419C23×C4C22×D7111yescharacteristic
420C23×C4C22×D7111yescharacteristic
421C23×C4C22×D7111yescharacteristic
422C23×C4C22×D7111yescharacteristic
423C23×C4C22×D7111yescharacteristic
424C23×C4C22×D7111yescharacteristic
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—2842no—
430C2×C4⋊C4—718no—
431C2×C4⋊C4—718no—
432C2×C4⋊C4—1424no—
433C2×C4⋊C4—1424no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1424no—
437C2×C4⋊C4—1424no—
438C2×C4⋊C4—14232no—
439C2×C4⋊C4—1424no—
440C2×C4⋊C4—1424no—
441C2×C4⋊C4—1424no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—714no—
448C2×C22⋊C4—714no—
449C2×C22⋊C4—714no—
450C2×C22⋊C4—714no—
451C2×C22⋊C4—1422no—
452C2×C22⋊C4—1422no—
453C2×C22⋊C4C4×D7114yes—
454C2×C42—2842no—
455C2×C42—1424no—
456C2×C42—1424no—
457#95—22no—
458#95—22no—
459#95—2842no—
460#95—718no—
461#95—1424no—
462#95—1424no—
463#95—1424no—
464#95—1424no—
465#95—1424no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C4×D7112yes—
471C24D4×D7112yes—
472C24C2×C22⋊D7112yes—
473C24Q8×D7112yes—
474C24Q8×D7112yes—
475C24#1176586412yes—
476C24#1176586512yes—
477C24C23×D7111yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—2844no—
509C22×C4—2844no—
510C22×C4—2848no—
511C22×C4—2848no—
512C22×C4—714no—
513C22×C4—714no—
514C22×C4—714no—
515C22×C4—714no—
516C22×C4—714no—
517C22×C4—714no—
518C22×C4—714no—
519C22×C4—714no—
520C22×C4—1428no—
521C22×C4—1422no—
522C22×C4—1422no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—14216no—
534C22×C4—1428no—
535C22×C4—1428no—
536C22×C4—14216no—
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×C4—1428no—
546C22×C4C2×C4×D7112yes—
547C22×C4C2×C4×D7112yes—
548C22×C4D4×D7114yes—
549C22×C4C2×C22⋊D7112yes—
550C22×C4C2×C22⋊D7112yes—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—2848no—
554C4⋊C4—14216no—
555C4⋊C4—14216no—
556C4⋊C4—14216no—
557C22⋊C4—28no—
558C22⋊C4—44no—
559C22⋊C4—7116no—
560C22⋊C4—1428no—
561C42—2848no—
562C23—22no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23C4⋊C4×D7114yes—
579C23C4×C22⋊D7114yes—
580C23#1455609314yes—
581C23#1455610014yes—
582C23#1455610614yes—
583C23#1455611814yes—
584C23#1455612614yes—
585C23C22×C4×D7111yescharacteristic
586C23C2×D4×D7111yescharacteristic
587C23C2×D4×D7112yes—
588C23C22×C22⋊D7111yescharacteristic
589C23C2×Q8×D7111yescharacteristic
590C23C2×Q8×D7111yescharacteristic
591C23#41×D7112yes—
592C23C2×#1176586411yescharacteristic
593C23C2×#1176586511yescharacteristic
594C23#1455617312yes—
595C23#1455617512yes—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—416no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—28416no—
627C2×C4—2842no—
628C2×C4—2842no—
629C2×C4—2842no—
630C2×C4—2842no—
631C2×C4—2842no—
632C2×C4—2842no—
633C2×C4—2842no—
634C2×C4—2842no—
635C2×C4—718no—
636C2×C4—718no—
637C2×C4—1424no—
638C2×C4—1424no—
639C2×C4—1424no—
640C2×C4—1424no—
641C2×C4—1424no—
642C2×C4—1424no—
643C2×C4—14232no—
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—1424no—
653C2×C4—1424no—
654C2×C4—1424no—
655C2×C4—1424no—
656C2×C4#1455609614yes—
657C22—24no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—28no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—24no—
667C22#1798589418yescomplemented
668C22C2×C4⋊C4×D7111yescharacteristic
669C22C4×D4×D7112yes—
670C22C2×C4×C22⋊D7111yescharacteristic
671C22C2×#1455609311yescharacteristic
672C22#1798647812yes—
673C22C2×#1455609611yescharacteristic
674C22C2×#1455610011yescharacteristic
675C22C2×#1455610611yescharacteristic
676C22#1798650611yescharacteristic
677C22#1798650812yes—
678C22C2×#1455611811yescharacteristic
679C22C2×#1455612611yescharacteristic
680C22#1798655811yescharacteristic
681C22#1798657011yescharacteristic
682C22#1798659112yes—
683C22#1798663112yes—
684C22#1798663612yes—
685C22#1798664712yes—
686C22#1798666212yes—
687C22#1798666212yes—
688C22#1798668612yes—
689C22#1798670312yes—
690C22#1798670312yes—
691C4—24no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—2844no—
698C4—2844no—
699C4—1428no—
700C4—1428no—
701C2—28no—
702C2C2×#1798589411yescharacteristic
703C2C4×#1455609611yescharacteristic
704C2#2259100511yescharacteristic
705C2#2259123812yes—
706C2#2259134012yes—
707C2#2259171511yescharacteristic
708C2#2259174811yescharacteristic
709C2#2259198511yescharacteristic
710C2#2259215112yes—
711C2#2259248312yes—
712C2#2259372111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#385×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71#14043
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#17985894C2semidirect
6. #22586603C2semidirect
7. #22586591C2semidirect
8. #22586575C2semidirect
25. #17985871C4semidirect
67. C2×Dic71⋊C4C2×C4semidirect
84. C71⋊#95C2×C4semidirect
152. C22⋊Dic71C4⋊C4semidirect
298. C2×Dic71C2×C4⋊C4semidirect
310. C22×C71#389semidirect
368. C71#14043semidirect
667. C22#17985894semidirect

Maximal subgroups

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

subgroupindex
C23×Dic71⋊C42
C2×#179858942
C2×#179858712
C2×C4×C22⋊Dic712
#225866032
#225865912
#225865752
#225865622
C2×#385×C712
#1404371