Finite Group Databasebeta

← #31919355

Subgroups — #31919355

Order 18176.

2950 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D71C211yesmaximal, characteristic
2C2×#17985878C212yesmaximal
3C2×#17985859C211yesmaximal, characteristic, complemented
4C2×#17985856C212yesmaximal, complemented
5#22586590C212yesmaximal, complemented
6#22586582C212yesmaximal, complemented
7#22586569C212yesmaximal, complemented
8#22586563C212yesmaximal, complemented
9C23×C4⋊C4×C71C211yesmaximal, characteristic, complemented
10C23×C22⋊D71C2211yescharacteristic
11C23×C4×D71C2211yescharacteristic
12C2×C4×C22⋊D71—24no—
13C2×C4×C22⋊D71—24no—
14C2×C4×C22⋊D71C418yescomplemented
15C22×C4⋊Dic71C2212yes—
16C22×Dic71⋊C4C2211yescharacteristic
17C22×C22⋊Dic71C2212yes—
18C22×C22⋊Dic71C2211yescharacteristic
19C22×(C2×D71)⋊C4C2214yes—
20C22×(C2×D71)⋊C4C2211yescharacteristic
21C22×C4×Dic71C2211yescharacteristic
22#17985878—28no—
23#17985859—24no—
24#17985856—28no—
25C2×C71⋊#95C2214yes—
26C2×C71⋊#95C2214yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2214yes—
29C24×C4×C71C2212yes—
30C24×C4×C71C2211yescharacteristic
31C22×C4⋊C4×C71—24no—
32C22×C4⋊C4×C71—28no—
33C22×C4⋊C4×C71C2212yes—
34C22×C4⋊C4×C71C2212yes—
35C24×D71C2311yescharacteristic
36C22×C22⋊D71—22no—
37C22×C22⋊D71—22no—
38C22×C22⋊D71—22no—
39C22×C22⋊D71—22no—
40C22×C22⋊D71C2×C414yes—
41C22×C22⋊D71D414yes—
42C22×C22⋊D71Q814yes—
43C23×Dic71C2314yes—
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2311yescharacteristic
47C22×C4×D71—24no—
48C22×C4×D71—22no—
49C22×C4×D71—22no—
50C22×C4×D71—24no—
51C22×C4×D71C2×C414yescomplemented
52C4×C22⋊D71—232no—
53C2×C4⋊Dic71—24no—
54C2×C4⋊Dic71—24no—
55C2×C4⋊Dic71—24no—
56C2×Dic71⋊C4—22no—
57C2×Dic71⋊C4—22no—
58C2×Dic71⋊C4C2×C414yescomplemented
59C2×C22⋊Dic71—22no—
60C2×C22⋊Dic71—22no—
61C2×C22⋊Dic71—24no—
62C2×C22⋊Dic71—24no—
63C2×C22⋊Dic71—24no—
64C2×C22⋊Dic71C2×C414yes—
65C2×(C2×D71)⋊C4—28no—
66C2×(C2×D71)⋊C4—22no—
67C2×(C2×D71)⋊C4—22no—
68C2×(C2×D71)⋊C4—28no—
69C2×(C2×D71)⋊C4—44no—
70C2×(C2×D71)⋊C4C2×C414yescomplemented
71C2×C4×Dic71—22no—
72C2×C4×Dic71—22no—
73C2×C4×Dic71C2×C414yescomplemented
74C71⋊#95—28no—
75C71⋊#95—28no—
76C71⋊#95—24no—
77C71⋊#95—44no—
78C25×C71C2311yescharacteristic
79C23×C4×C71—24no—
80C23×C4×C71—24no—
81C23×C4×C71—24no—
82C23×C4×C71—28no—
83C23×C4×C71—24no—
84C23×C4×C71—24no—
85C23×C4×C71—44no—
86C23×C4×C71C2×C414yes—
87C23×C4×C71D414yes—
88C23×C4×C71D414yes—
89C23×C4×C71C2314yes—
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C2×C4⋊C4×C71—232no—
93C2×C4⋊C4×C71—28no—
94C2×C4⋊C4×C71—24no—
95C2×C4⋊C4×C71—24no—
96C2×C4⋊C4×C71—24no—
97C2×C4⋊C4×C71D418yescomplemented
98C23×D71—21no—
99C23×D71—21no—
100C23×D71—22no—
101C23×D71—22no—
102C23×D71—21no—
103C23×D71—21no—
104C23×D71—22no—
105C23×D71—22no—
106C23×D71C22×C412yes—
107C23×D71C2×D412yes—
108C23×D71C2×Q812yes—
109C2×C22⋊D71—28no—
110C2×C22⋊D71—28no—
111C2×C22⋊D71—28no—
112C2×C22⋊D71—28no—
113C2×C22⋊D71—28no—
114C2×C22⋊D71—28no—
115C2×C22⋊D71C4⋊C4116yescomplemented
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—22no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—24no—
129C22×Dic71—24no—
130C22×Dic71—24no—
131C22×Dic71—24no—
132C22×Dic71—24no—
133C22×Dic71—24no—
134C22×Dic71—24no—
135C22×Dic71C22×C412yes—
136C22×Dic71C22×C412yes—
137C22×Dic71C22×C412yes—
138C22×Dic71C2×D412yes—
139C22×Dic71C2×Q812yes—
140C2×C4×D71—28no—
141C2×C4×D71—216no—
142C2×C4×D71—44no—
143C2×C4×D71—48no—
144C2×C4×D71—44no—
145C4⋊Dic71—48no—
146Dic71⋊C4—28no—
147C22⋊Dic71—28no—
148C22⋊Dic71—48no—
149(C2×D71)⋊C4—28no—
150(C2×D71)⋊C4—416no—
151C4×Dic71—28no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71C22×C412yes—
157C24×C71C2×D412yes—
158C24×C71C2×D412yes—
159C24×C71C2×D412yes—
160C24×C71C2×Q812yes—
161C24×C71#4112yes—
162C24×C71#4112yes—
163C24×C71C2411yescharacteristic
164C22×C4×C71—22no—
165C22×C4×C71—22no—
166C22×C4×C71—216no—
167C22×C4×C71—28no—
168C22×C4×C71—216no—
169C22×C4×C71—28no—
170C22×C4×C71—216no—
171C22×C4×C71—24no—
172C22×C4×C71—24no—
173C22×C4×C71—24no—
174C22×C4×C71—24no—
175C22×C4×C71—24no—
176C22×C4×C71—24no—
177C22×C4×C71—416no—
178C22×C4×C71—416no—
179C22×C4×C71—48no—
180C22×C4×C71—48no—
181C22×C4×C71C22⋊C4116yescomplemented
182C22×C4×C71C22×C412yes—
183C22×C4×C71C22×C412yes—
184C22×C4×C71C2×D418yes—
185C22×C4×C71C2×D412yes—
186C22×C4×C71C2×D412yes—
187C22×C4×C71C2×D414yes—
188C22×C4×C71C2×D412yes—
189C22×C4×C71C2×D412yes—
190C22×C4×C71#4114yes—
191C4⋊C4×C71—216no—
192C4⋊C4×C71—216no—
193C23×C71—24no—
194C23×C71—24no—
195C23×C71—22no—
196C23×C71—24no—
197C23×C71—22no—
198C23×C71—22no—
199C23×C71—22no—
200C23×C71—24no—
201C23×C71—24no—
202C23×C71—24no—
203C23×C71—24no—
204C23×C71—24no—
205C23×C71—24no—
206C23×C71—24no—
207C23×C71—24no—
208C23×C71—24no—
209C23×C71C2×C22⋊C414yes—
210C23×C71C2×C4⋊C414yes—
211C23×C71#11714yes—
212C23×C71#12114yes—
213C23×C71#12114yes—
214C23×C71C22⋊Q814yes—
215C23×C71C22⋊Q814yes—
216C23×C71C23×C411yescharacteristic
217C23×C71C22×D411yescharacteristic
218C23×C71C22×D411yescharacteristic
219C23×C71C22×D412yes—
220C23×C71C22×D411yescharacteristic
221C23×C71C22×Q811yescharacteristic
222C23×C71C2×#4111yescharacteristic
223C23×C71C2×#4112yes—
224C23×C71C2×#4111yescharacteristic
225C23×C71H(5,𝔽2)12yes—
226C23×C712−1+412yes—
227C22×D71—22no—
228C22×D71—22no—
229C22×D71—24no—
230C22×D71—24no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—24no—
236C22×D71—24no—
237C22×D71—24no—
238C22×D71—24no—
239C22×D71—41no—
240C22×D71—42no—
241C22×D71—41no—
242C22×D71—41no—
243C22×D71—41no—
244C22×D71—42no—
245C22×D71—42no—
246C22×D71—42no—
247C22×D71—42no—
248C22×D71—42no—
249C22×D71C2×C4⋊C414yescomplemented
250C2×C4×C71—24no—
251C2×C4×C71—22no—
252C2×C4×C71—24no—
253C2×C4×C71—22no—
254C2×C4×C71—232no—
255C2×C4×C71—28no—
256C2×C4×C71—28no—
257C2×C4×C71—28no—
258C2×C4×C71—432no—
259C2×C4×C71—44no—
260C2×C4×C71—44no—
261C2×C4×C71—44no—
262C2×C4×C71—44no—
263C2×C4×C71C2×C22⋊C414yes—
264C2×C4×C71C2×C22⋊C414yes—
265C2×C4×C71C4×D418yes—
266C2×C4×C71#12014yes—
267C2×C4×C71#12118yes—
268C2×C4×C71#12314yes—
269C22⋊D71—232no—
270C2×Dic71—22no—
271C2×Dic71—22no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—22no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—22no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—41no—
281C2×Dic71—42no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—42no—
286C2×Dic71—44no—
287C2×Dic71—44no—
288C2×Dic71—44no—
289C2×Dic71—44no—
290C2×Dic71—44no—
291C2×Dic71—44no—
292C2×Dic71—44no—
293C2×Dic71C2×C4⋊C414yescomplemented
294C4×D71—416no—
295C22×C71—24no—
296C22×C71—28no—
297C22×C71—28no—
298C22×C71—24no—
299C22×C71—24no—
300C22×C71—28no—
301C22×C71—28no—
302C22×C71—24no—
303C22×C71—24no—
304C22×C71—24no—
305C22×C71#38018yescomplemented
306C22×C71C22×C22⋊C411yescharacteristic
307C22×C71C22×C4⋊C411yescharacteristic
308C22×C71C2×#11711yescharacteristic
309C22×C71C2×C4×D412yes—
310C22×C71#52012yes—
311C22×C71C2×#12011yescharacteristic
312C22×C71C2×#12111yescharacteristic
313C22×C71C2×#12112yes—
314C22×C71C2×#12111yescharacteristic
315C22×C71C2×C22⋊Q811yescharacteristic
316C22×C71C2×C22⋊Q811yescharacteristic
317C22×C71C2×#12311yescharacteristic
318C22×C71#53511yescharacteristic
319C22×C71#53611yescharacteristic
320C22×C71#53712yes—
321C22×C71D4212yes—
322C22×C71#54612yes—
323C22×C71#54712yes—
324C22×C71#54812yes—
325C22×C71D4×Q812yes—
326C22×C71#55212yes—
327C22×C71#55312yes—
328C22×C71#55412yes—
329C2×D71—28no—
330C2×D71—24no—
331C2×D71—42no—
332C2×D71—44no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—44no—
336C2×D71—44no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71—42no—
340C4×C71—24no—
341C4×C71—48no—
342C4×C71#38618yescomplemented
343Dic71—24no—
344Dic71—42no—
345Dic71—42no—
346Dic71—84no—
347#13872—711nomaximal, Sylow
348C2×C71—28no—
349C2×C71C2×#38011yescharacteristic
350C2×C71C2×#38611yescharacteristic
351C2×C71#231111yescharacteristic
352C2×C71D4×C4⋊C412yes—
353C2×C71#235212yes—
354C2×C71#240811yescharacteristic
355C2×C71#240911yescharacteristic
356C2×C71#241612yes—
357C2×C71#241712yes—
358C2×C71#248611yescharacteristic
359C2×C71#248711yescharacteristic
360D71—44no—
361C22×C4×D4—711no—
362C23×C4⋊C4D7111yescharacteristic, complemented
363C2×#386—712no—
364C2×#380—711no—
365C2×#380—712no—
366#1441—712no—
367#1439—712no—
368C4⋊#95—712no—
369C22⋊#95—712no—
370C71#1387211yescharacteristic, complemented, Sylow
371C23×D4—711no—
372C24×C4—711no—
373C24×C4C2×D7112yes—
374C24×C4C2×D7111yescharacteristic
375C2×C4×D4—718no—
376C2×C4×D4—1424no—
377C2×C4×D4—1424no—
378C22×C4⋊C4—24no—
379C22×C4⋊C4—28no—
380C22×C4⋊C4—711no—
381C22×C4⋊C4—712no—
382C22×C4⋊C4C2×D7112yes—
383C22×C4⋊C4C2×D7112yes—
384C22×C22⋊C4—714no—
385C22×C22⋊C4—711no—
386C22×C22⋊C4—711no—
387C22×C22⋊C4—712no—
388C22×C42—711no—
389#386—1428no—
390#380—1424no—
391#380—1428no—
392C2×#95—714no—
393C2×#95—714no—
394C2×#95—714no—
395C2×#95—712no—
396C25—711no—
397C25C22×D7111yescharacteristic
398C22×D4—714no—
399C22×D4—714no—
400C22×D4—714no—
401C22×D4—1422no—
402C22×D4—1422no—
403C22×D4—1422no—
404C22×D4—1422no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—28no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—44no—
412C23×C4—711no—
413C23×C4—711no—
414C23×C4—711no—
415C23×C4—714no—
416C23×C4—714no—
417C23×C4—1422no—
418C23×C4—1424no—
419C23×C4—1422no—
420C23×C4—1424no—
421C23×C4C4×D7114yes—
422C23×C4D28414yes—
423C23×C4C22⋊D7114yes—
424C23×C4C22×D7114yes—
425C23×C4C22×D7111yescharacteristic
426C23×C4C22×D7111yescharacteristic
427C4×D4—14232no—
428C2×C4⋊C4—232no—
429C2×C4⋊C4—28no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—714no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1424no—
437C2×C4⋊C4—1422no—
438C2×C4⋊C4—1422no—
439C2×C4⋊C4C22⋊D7118yescomplemented
440C2×C22⋊C4—2844no—
441C2×C22⋊C4—714no—
442C2×C22⋊C4—714no—
443C2×C22⋊C4—1428no—
444C2×C22⋊C4—1424no—
445C2×C22⋊C4—1424no—
446C2×C22⋊C4—1424no—
447C2×C22⋊C4—1428no—
448C2×C22⋊C4—1422no—
449C2×C22⋊C4—1422no—
450C2×C22⋊C4—1422no—
451C2×C22⋊C4—1422no—
452C2×C42—714no—
453C2×C42—1422no—
454C2×C42—1422no—
455#95—2844no—
456#95—1428no—
457#95—1428no—
458#95—1424no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—712no—
464C24—712no—
465C24—712no—
466C24—1422no—
467C24—1421no—
468C24—1421no—
469C24—1421no—
470C24—1422no—
471C24—1421no—
472C24—1422no—
473C24—1422no—
474C24C2×C4×D7112yes—
475C24D4×D7112yes—
476C24C2×C22⋊D7112yes—
477C24C2×D28412yes—
478C24Q8×D7112yes—
479C24#1176586412yes—
480C24#1176586612yes—
481C24C23×D7111yescharacteristic
482C2×D4—7116no—
483C2×D4—1428no—
484C2×D4—1428no—
485C2×D4—1428no—
486C2×D4—1428no—
487C2×D4—1428no—
488C2×D4—1428no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—216no—
492C22×C4—28no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—216no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—416no—
503C22×C4—416no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—2844no—
507C22×C4—2848no—
508C22×C4—2844no—
509C22×C4—712no—
510C22×C4—712no—
511C22×C4—712no—
512C22×C4—712no—
513C22×C4—712no—
514C22×C4—1424no—
515C22×C4—1424no—
516C22×C4—1424no—
517C22×C4—1424no—
518C22×C4—1424no—
519C22×C4—1424no—
520C22×C4—1424no—
521C22×C4—1422no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4—1421no—
525C22×C4—1421no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1428no—
530C22×C4—14216no—
531C22×C4—1421no—
532C22×C4—1421no—
533C22×C4—1421no—
534C22×C4—1421no—
535C22×C4(C2×D71)⋊C4116yescomplemented
536C22×C4C2×C4×D7112yes—
537C22×C4C2×C4×D7112yes—
538C22×C4C2×C22⋊D7118yes—
539C22×C4C2×C22⋊D7112yes—
540C22×C4C2×C22⋊D7112yes—
541C22×C4C2×C22⋊D7114yes—
542C22×C4C2×D28412yes—
543C22×C4C2×D28412yes—
544C22×C4#1176586514yes—
545C4⋊C4—216no—
546C4⋊C4—216no—
547C4⋊C4—2848no—
548C4⋊C4—1428no—
549C22⋊C4—28416no—
550C22⋊C4—2848no—
551C22⋊C4—1428no—
552C22⋊C4—1428no—
553C42—1428no—
554C23—22no—
555C23—22no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—22no—
568C23—24no—
569C23—22no—
570C23—2841no—
571C23—2841no—
572C23—2842no—
573C23—2842no—
574C23—2842no—
575C23—2842no—
576C23—2842no—
577C23—2841no—
578C23—2842no—
579C23—2841no—
580C23—714no—
581C23—1424no—
582C23—1424no—
583C23—1424no—
584C23—1422no—
585C23—1424no—
586C23—1422no—
587C23—1424no—
588C23—1424no—
589C23—1422no—
590C23—1422no—
591C23—1422no—
592C23—1422no—
593C23C2×(C2×D71)⋊C414yes—
594C23C4⋊C4×D7114yes—
595C23#1455608614yes—
596C23#1455609914yes—
597C23#1455610314yes—
598C23#1455610414yes—
599C23#1455610814yes—
600C23C22×C4×D7111yescharacteristic
601C23C2×D4×D7111yescharacteristic
602C23C22×C22⋊D7111yescharacteristic
603C23C22×C22⋊D7112yes—
604C23C22×D28411yescharacteristic
605C23C2×Q8×D7111yescharacteristic
606C23C2×#1176586411yescharacteristic
607C23C2×#1176586512yes—
608C23C2×#1176586611yescharacteristic
609C23#1455617312yes—
610C23#1455617612yes—
611D4—14232no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—232no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—432no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—2841no—
626C2×C4—2841no—
627C2×C4—2842no—
628C2×C4—2841no—
629C2×C4—2842no—
630C2×C4—2841no—
631C2×C4—28416no—
632C2×C4—2844no—
633C2×C4—2844no—
634C2×C4—2844no—
635C2×C4—2844no—
636C2×C4—2844no—
637C2×C4—2844no—
638C2×C4—2844no—
639C2×C4—714no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—1424no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4C2×(C2×D71)⋊C414yes—
651C2×C4C2×(C2×D71)⋊C414yes—
652C2×C4C4×C22⋊D7118yes—
653C2×C4#1455609714yes—
654C2×C4#1455610218yes—
655C2×C4#1455611114yes—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—2844no—
667C22—2844no—
668C22—2842no—
669C22—2844no—
670C22—2842no—
671C22—2842no—
672C22—2842no—
673C22—2842no—
674C22—2842no—
675C22—1428no—
676C22—1424no—
677C22#1798585618yescomplemented
678C22C22×(C2×D71)⋊C411yescharacteristic
679C22C2×C4⋊C4×D7111yescharacteristic
680C22C2×#1455608611yescharacteristic
681C22C2×C4×C22⋊D7112yes—
682C22#1798648012yes—
683C22C2×#1455609711yescharacteristic
684C22C2×#1455609911yescharacteristic
685C22C2×#1455610212yes—
686C22C2×#1455610311yescharacteristic
687C22C2×#1455610411yescharacteristic
688C22C2×#1455610811yescharacteristic
689C22C2×#1455611111yescharacteristic
690C22#1798656611yescharacteristic
691C22#1798657311yescharacteristic
692C22#1798658012yes—
693C22D4×C22⋊D7112yes—
694C22#1798664312yes—
695C22#1798665012yes—
696C22#1798666012yes—
697C22Q8×C22⋊D7112yes—
698C22#1798668412yes—
699C22#1798669712yes—
700C22#1798670412yes—
701C4—24no—
702C4—48no—
703C4—2842no—
704C4—2842no—
705C4—5684no—
706C4—1424no—
707C4#1798587818yescomplemented
708C2—28no—
709C2—2844no—
710C2C2×#1798585611yescharacteristic
711C2C2×#1798587811yescharacteristic
712C2#2259093311yescharacteristic
713C2C4⋊C4×C22⋊D7112yes—
714C2#2259126512yes—
715C2#2259169011yescharacteristic
716C2#2259169911yescharacteristic
717C2#2259177412yes—
718C2#2259178512yes—
719C2#2259264211yescharacteristic
720C2#2259265111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC23×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC23×C4⋊C4D71
hypocenterC71#13872
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#17985859C2semidirect
4. C2×#17985856C2semidirect
5. #22586590C2semidirect
6. #22586582C2semidirect
7. #22586569C2semidirect
8. #22586563C2semidirect
9. C23×C4⋊C4×C71C2semidirect
14. C2×C4×C22⋊D71C4semidirect
51. C22×C4×D71C2×C4semidirect
58. C2×Dic71⋊C4C2×C4semidirect
70. C2×(C2×D71)⋊C4C2×C4semidirect
73. C2×C4×Dic71C2×C4semidirect
97. C2×C4⋊C4×C71D4semidirect
115. C2×C22⋊D71C4⋊C4semidirect
181. C22×C4×C71C22⋊C4semidirect
249. C22×D71C2×C4⋊C4semidirect
293. C2×Dic71C2×C4⋊C4semidirect
305. C22×C71#380semidirect
342. C4×C71#386semidirect
362. C23×C4⋊C4D71semidirect
370. C71#13872semidirect
439. C2×C4⋊C4C22⋊D71semidirect
535. C22×C4(C2×D71)⋊C4semidirect
677. C22#17985856semidirect
707. C4#17985878semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D712
C2×#179858782
C2×#179858592
C2×#179858562
#225865902
#225865822
#225865692
#225865632
C23×C4⋊C4×C712
#1387271