Finite Group Databasebeta

← #31921156

Subgroups — #31921156

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
1C2×#17985894C212yesmaximal, complemented
2C2×#17985872C211yesmaximal, characteristic
3C2×#17985872C211yesmaximal, characteristic
4C2×#17985872C211yesmaximal, characteristic
5C2×C4×C22⋊Dic71C211yesmaximal, characteristic
6#22586603C212yesmaximal, complemented
7#22586590C212yesmaximal, complemented
8#22586572C212yesmaximal, complemented
9#22586563C211yesmaximal, characteristic
10#22586563C211yesmaximal, characteristic
11C23×C4⋊C4×C71C211yesmaximal, characteristic
12C22×Dic71⋊C4C2211yescharacteristic
13C22×Dic71⋊C4C2212yes—
14C22×Dic71⋊C4C2212yes—
15C22×Dic71⋊C4C2211yescharacteristic
16C22×C22⋊Dic71C2211yescharacteristic
17C22×C22⋊Dic71C2211yescharacteristic
18C22×C22⋊Dic71C2211yescharacteristic
19C22×C22⋊Dic71C2211yescharacteristic
20C22×C4×Dic71C2212yes—
21#17985894—28no—
22#17985872—24no—
23#17985872—24no—
24#17985872C418yescomplemented
25C4×C22⋊Dic71—24no—
26C2×C71⋊#95C2211yescharacteristic
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2211yescharacteristic
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C24×C4×C71C2211yescharacteristic
36C24×C4×C71C2211yescharacteristic
37C24×C4×C71C2211yescharacteristic
38C22×C4⋊C4×C71—24no—
39C22×C4⋊C4×C71—28no—
40C22×C4⋊C4×C71C2212yes—
41C22×C4⋊C4×C71C2212yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2312yes—
47C23×Dic71C2312yes—
48C2×Dic71⋊C4—24no—
49C2×Dic71⋊C4—24no—
50C2×Dic71⋊C4—22no—
51C2×Dic71⋊C4—22no—
52C2×Dic71⋊C4—24no—
53C2×Dic71⋊C4—24no—
54C2×Dic71⋊C4—24no—
55C2×Dic71⋊C4—42no—
56C2×Dic71⋊C4—42no—
57C2×Dic71⋊C4C2×C418yescomplemented
58C2×C22⋊Dic71—22no—
59C2×C22⋊Dic71—22no—
60C2×C22⋊Dic71—22no—
61C2×C22⋊Dic71—22no—
62C2×C22⋊Dic71—22no—
63C2×C22⋊Dic71—22no—
64C2×C22⋊Dic71—22no—
65C2×C22⋊Dic71C2×C414yes—
66C2×C22⋊Dic71C2×C414yes—
67C2×C22⋊Dic71D414yes—
68C2×C22⋊Dic71Q814yes—
69C2×C22⋊Dic71Q814yes—
70C2×C4×Dic71—24no—
71C2×C4×Dic71—24no—
72C2×C4×Dic71—42no—
73C71⋊#95—24no—
74C71⋊#95—24no—
75C71⋊#95—22no—
76C71⋊#95—22no—
77C71⋊#95—24no—
78C71⋊#95—24no—
79C71⋊#95—24no—
80C71⋊#95—42no—
81C71⋊#95C2×C418yescomplemented
82C25×C71C2311yescharacteristic
83C23×C4×C71—22no—
84C23×C4×C71—22no—
85C23×C4×C71—24no—
86C23×C4×C71—24no—
87C23×C4×C71—22no—
88C23×C4×C71—22no—
89C23×C4×C71—22no—
90C23×C4×C71—24no—
91C23×C4×C71—24no—
92C23×C4×C71—22no—
93C23×C4×C71—22no—
94C23×C4×C71—42no—
95C23×C4×C71—42no—
96C23×C4×C71C2×C414yes—
97C23×C4×C71D414yes—
98C23×C4×C71C2311yescharacteristic
99C23×C4×C71C2312yes—
100C23×C4×C71C2312yes—
101C23×C4×C71C2311yescharacteristic
102C2×C4⋊C4×C71—232no—
103C2×C4⋊C4×C71—24no—
104C2×C4⋊C4×C71—24no—
105C2×C4⋊C4×C71—24no—
106C2×C4⋊C4×C71—24no—
107C2×C4⋊C4×C71—24no—
108C2×C4⋊C4×C71D418yes—
109C22×Dic71—22no—
110C22×Dic71—22no—
111C22×Dic71—22no—
112C22×Dic71—22no—
113C22×Dic71—22no—
114C22×Dic71—22no—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—22no—
122C22×Dic71—22no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—22no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—22no—
133C22×Dic71—21no—
134C22×Dic71—21no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71C22×C412yes—
138C22×Dic71C22×C412yes—
139C22×Dic71C22×C414yes—
140C22×Dic71C2×D414yes—
141C22×Dic71C2×Q814yes—
142C22×Dic71C2×Q814yes—
143Dic71⋊C4—216no—
144Dic71⋊C4—48no—
145Dic71⋊C4—44no—
146Dic71⋊C4—44no—
147C22⋊Dic71—28no—
148C22⋊Dic71—28no—
149C22⋊Dic71—44no—
150C22⋊Dic71C4⋊C4116yescomplemented
151C4×Dic71—48no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71C22×C412yes—
157C24×C71C2×D412yes—
158C24×C71C2×D412yes—
159C24×C71C2×Q812yes—
160C24×C71C2×Q812yes—
161C24×C71#4112yes—
162C24×C71#4112yes—
163C24×C71C2411yescharacteristic
164C22×C4×C71—28no—
165C22×C4×C71—216no—
166C22×C4×C71—28no—
167C22×C4×C71—28no—
168C22×C4×C71—22no—
169C22×C4×C71—22no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—22no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—216no—
176C22×C4×C71—28no—
177C22×C4×C71—28no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—21no—
182C22×C4×C71—22no—
183C22×C4×C71—21no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—28no—
189C22×C4×C71—44no—
190C22×C4×C71—48no—
191C22×C4×C71—48no—
192C22×C4×C71—48no—
193C22×C4×C71—48no—
194C22×C4×C71—44no—
195C22×C4×C71—44no—
196C22×C4×C71C22×C414yes—
197C22×C4×C71C2×D412yes—
198C22×C4×C71C2×D414yes—
199C22×C4×C71C2×D414yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D414yes—
202C22×C4×C71#4114yes—
203C4⋊C4×C71—216no—
204C4⋊C4×C71—216no—
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×D411yescharacteristic
231C23×C71C22×D412yes—
232C23×C71C22×Q811yescharacteristic
233C23×C71C22×Q811yescharacteristic
234C23×C71C2×#4111yescharacteristic
235C23×C71C2×#4111yescharacteristic
236C23×C71C2×#4112yes—
237C23×C71H(5,𝔽2)12yes—
238C23×C712−1+412yes—
239C2×C4×C71—232no—
240C2×C4×C71—24no—
241C2×C4×C71—24no—
242C2×C4×C71—24no—
243C2×C4×C71—22no—
244C2×C4×C71—24no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—22no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—22no—
251C2×C4×C71—24no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—24no—
255C2×C4×C71—24no—
256C2×C4×C71—416no—
257C2×C4×C71—416no—
258C2×C4×C71—42no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—42no—
262C2×C4×C71—42no—
263C2×C4×C71—42no—
264C2×C4×C71C4×D418yes—
265C2×C4×C71#12014yes—
266C2×Dic71—24no—
267C2×Dic71—24no—
268C2×Dic71—24no—
269C2×Dic71—24no—
270C2×Dic71—24no—
271C2×Dic71—24no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—24no—
275C2×Dic71—24no—
276C2×Dic71—24no—
277C2×Dic71—24no—
278C2×Dic71—24no—
279C2×Dic71—41no—
280C2×Dic71—42no—
281C2×Dic71—41no—
282C2×Dic71—42no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—42no—
286C2×Dic71—42no—
287C2×Dic71—42no—
288C2×Dic71—42no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71C2×C4⋊C418yescomplemented
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×D411yescharacteristic
313C22×C71C2×C4×D412yes—
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—28no—
336C4×C71—42no—
337C4×C71—44no—
338Dic71—28no—
339Dic71—42no—
340Dic71—44no—
341Dic71—42no—
342Dic71—81no—
343Dic71—81no—
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⋊C4D7111yescharacteristic
358C2×#389—712no—
359C2×#385—711no—
360C2×#385—711no—
361C2×#385—711no—
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×C4C2×D7111yescharacteristic
370C24×C4C2×D7111yescharacteristic
371C24×C4C2×D7111yescharacteristic
372C22×C4⋊C4—24no—
373C22×C4⋊C4—28no—
374C22×C4⋊C4—711no—
375C22×C4⋊C4—712no—
376C22×C4⋊C4—712no—
377C22×C4⋊C4—711no—
378C22×C4⋊C4C2×D7112yes—
379C22×C4⋊C4C2×D7112yes—
380C22×C22⋊C4—711no—
381C22×C22⋊C4—711no—
382C22×C22⋊C4—711no—
383C22×C22⋊C4—711no—
384C22×C42—712no—
385#389—1428no—
386#385—718no—
387#385—1424no—
388#385—1424no—
389C4×C22⋊C4—1424no—
390C2×#95—712no—
391C2×#95—712no—
392C2×#95—712no—
393C2×#95—712no—
394C2×#95—712no—
395C2×#95—711no—
396C2×#95—712no—
397C2×#95—711no—
398C2×#95—712no—
399C25C22×D7111yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—712no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—712no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4C4×D7114yes—
420C23×C4C22⋊D7114yes—
421C23×C4C22×D7111yescharacteristic
422C23×C4C22×D7112yes—
423C23×C4C22×D7112yes—
424C23×C4C22×D7111yescharacteristic
425C2×C4⋊C4—232no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—2842no—
432C2×C4⋊C4—2842no—
433C2×C4⋊C4—718no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1422no—
436C2×C4⋊C4—1422no—
437C2×C4⋊C4—1424no—
438C2×C4⋊C4—1424no—
439C2×C4⋊C4—1424no—
440C2×C4⋊C4—1424no—
441C2×C4⋊C4C22⋊D7118yes—
442C2×C22⋊C4—714no—
443C2×C22⋊C4—714no—
444C2×C22⋊C4—714no—
445C2×C22⋊C4—714no—
446C2×C22⋊C4—714no—
447C2×C22⋊C4—1422no—
448C2×C22⋊C4—1422no—
449C2×C22⋊C4—1422no—
450C2×C22⋊C4—1422no—
451C2×C22⋊C4—1422no—
452C2×C22⋊C4—1422no—
453C2×C22⋊C4—1422no—
454C2×C42—2842no—
455C2×C42—1424no—
456C2×C42—1424no—
457#95—2842no—
458#95—718no—
459#95—1424no—
460#95—1424no—
461#95—1422no—
462#95—1422no—
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—28no—
479C22×C4—216no—
480C22×C4—28no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—714no—
511C22×C4—714no—
512C22×C4—714no—
513C22×C4—712no—
514C22×C4—712no—
515C22×C4—714no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1422no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4—1421no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1421no—
533C22×C4—1422no—
534C22×C4—1421no—
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×C4C2×C4×D7114yes—
545C22×C4C2×C22⋊D7112yes—
546C22×C4C2×C22⋊D7114yes—
547C22×C4C2×C22⋊D7114yes—
548C22×C4C2×C22⋊D7112yes—
549C22×C4C2×C22⋊D7114yes—
550C22×C4#1176586514yes—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—2844no—
554C4⋊C4—2848no—
555C4⋊C4—2844no—
556C4⋊C4—14216no—
557C22⋊C4—2844no—
558C22⋊C4—7116no—
559C22⋊C4—1428no—
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
587C23C22×C22⋊D7111yescharacteristic
588C23C22×C22⋊D7112yes—
589C23C2×Q8×D7111yescharacteristic
590C23C2×Q8×D7111yescharacteristic
591C23C2×#1176586411yescharacteristic
592C23C2×#1176586511yescharacteristic
593C23C2×#1176586512yes—
594C23#1455617312yes—
595C23#1455617612yes—
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—416no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—2841no—
622C2×C4—2842no—
623C2×C4—2842no—
624C2×C4—2842no—
625C2×C4—2842no—
626C2×C4—2841no—
627C2×C4—2841no—
628C2×C4—2842no—
629C2×C4—2842no—
630C2×C4—2841no—
631C2×C4—2841no—
632C2×C4—2842no—
633C2×C4—2842no—
634C2×C4—2842no—
635C2×C4—2842no—
636C2×C4—2841no—
637C2×C4—2841no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—718no—
642C2×C4—1424no—
643C2×C4—1424no—
644C2×C4—1422no—
645C2×C4—1422no—
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×C4C4×C22⋊D7118yes—
656C2×C4#1455609714yes—
657C22—24no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—28no—
663C22—24no—
664C22—28no—
665C22—24no—
666C22—24no—
667C22#1798589418yescomplemented
668C22C2×C4⋊C4×D7111yescharacteristic
669C22C2×C4×C22⋊D7112yes—
670C22C2×C4×C22⋊D7111yescharacteristic
671C22C2×#1455609311yescharacteristic
672C22#1798648012yes—
673C22C2×#1455609711yescharacteristic
674C22C2×#1455610011yescharacteristic
675C22C2×#1455610611yescharacteristic
676C22#1798651011yescharacteristic
677C22#1798651012yes—
678C22C2×#1455611811yescharacteristic
679C22C2×#1455612611yescharacteristic
680C22#1798655811yescharacteristic
681C22#1798657311yescharacteristic
682C22#1798659612yes—
683C22D4×C22⋊D7112yes—
684C22#1798664312yes—
685C22#1798665012yes—
686C22Q8×C22⋊D7112yes—
687C22Q8×C22⋊D7112yes—
688C22#1798668412yes—
689C22#1798670412yes—
690C22#1798670412yes—
691C4—28no—
692C4—24no—
693C4—44no—
694C4—42no—
695C4—2842no—
696C4—2842no—
697C4—2844no—
698C4—5681no—
699C4—5681no—
700C4—1428no—
701C2—28no—
702C2C2×#1798589411yescharacteristic
703C2C4×#1455609711yescharacteristic
704C2#2259100911yescharacteristic
705C2C4⋊C4×C22⋊D7112yes—
706C2#2259134512yes—
707C2#2259171411yescharacteristic
708C2#2259174711yescharacteristic
709C2#2259198011yescharacteristic
710C2#2259214912yes—
711C2#2259247512yes—
712C2#2259372011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC23×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC23×C4⋊C4D71
hypocenterC71#14043
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#17985894C2semidirect
6. #22586603C2semidirect
7. #22586590C2semidirect
8. #22586572C2semidirect
24. #17985872C4semidirect
57. C2×Dic71⋊C4C2×C4semidirect
81. C71⋊#95C2×C4semidirect
150. C22⋊Dic71C4⋊C4semidirect
299. 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
C2×#179858942
C2×#179858722
C2×C4×C22⋊Dic712
#225866032
#225865902
#225865722
#225865632
C23×C4⋊C4×C712
#1404371