Finite Group Databasebeta

← #1802×D71 #31996895

Subgroups — #1802×D71 #31996895

Order 18176.

2030 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
1C2×C4×D4×D71C211yesmaximal, characteristic
2C2×C4⋊C8×D71C211yesmaximal, characteristic, complemented
3C2×#102×D71C212yesmaximal
4#384×D71C211yesmaximal, characteristic, complemented
5#22588341C211yesmaximal, characteristic, complemented
6#22588340C211yesmaximal, characteristic, complemented
7#22588339C212yesmaximal, complemented
8#22588338C212yesmaximal, complemented
9#22588337C211yesmaximal, characteristic, complemented
10#340×D71C212yesmaximal, complemented
11C71×#1802C211yesmaximal, characteristic, complemented
12C22×D4×D71C2211yescharacteristic
13C23×C4×D71—21no—
14C22×C8×D71C2212yes—
15C2×C4×D284C2211yescharacteristic
16C2×D4×Dic71C2211yescharacteristic
17C2×#14556090C2211yescharacteristic
18C2×C4×C22⋊D71—21no—
19C2×(C22⋊D71)⋊C4—21no—
20C4×D4×D71—24no—
21C4×D4×D71C418yescomplemented
22C2×C4⋊C4×D71—21no—
23C2×C4⋊C4×D71—21no—
24C2×C4⋊C4×D71C2212yes—
25C2×C4⋊C4×D71C2211yescharacteristic
26C2×C22⋊C4×D71—21no—
27C2×C42×D71C2211yescharacteristic
28C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
29C2×Dic71⋊C8C2212yescomplemented
30C4⋊C8×D71—24no—
31C2×#14556050C2212yes—
32C2×#14556049C2212yes—
33C2×#14556048C2212yes—
34#102×D71—28no—
35#17985869C2211yescharacteristic, complemented
36#17985868—21no—
37#17985868—21no—
38#17985868C2212yescomplemented
39#17985762C2212yescomplemented
40#17985761C2212yescomplemented
41#17985761C2212yescomplemented
42C2×C4×D4×C71C2211yescharacteristic
43C2×C4⋊C8×C71C2211yescharacteristic, complemented
44C2×#102×C71C2212yes—
45#384×C71C2211yescharacteristic, complemented
46#340×C71C2212yescomplemented
47C24×D71—21no—
48C22×D284C2311yescharacteristic
49C22×C22⋊D71—21no—
50C2×D4×D71—22no—
51C2×D4×D71—22no—
52C2×D4×D71—22no—
53C2×D4×D71C2×C414yes—
54C2×D4×D71D414yes—
55C2×D4×D71Q814yes—
56C23×Dic71—21no—
57C22×C4×D71—21no—
58C22×C4×D71—21no—
59C22×C4×D71—28no—
60C22×C4×D71—22no—
61C22×C4×D71—21no—
62C22×C4×D71—44no—
63C22×C4×D71—44no—
64C22×C4×D71D411yescharacteristic
65C22×C4×D71D411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C71⋊C8C2312yes—
68C2×C8×D71—24no—
69C2×C8×D71—24no—
70C2×C8×D71—24no—
71C4×D284—22no—
72C4×D284C2×C414yescomplemented
73D4×Dic71—22no—
74D4×Dic71C2×C414yescomplemented
75#14556090—22no—
76#14556090C2×C414yescomplemented
77C4×C22⋊D71—28no—
78(C22⋊D71)⋊C4—28no—
79C2×C4⋊Dic71—21no—
80C2×C4⋊Dic71—21no—
81C2×C4⋊Dic71C2312yes—
82C2×C4⋊Dic71C2311yescharacteristic
83C2×Dic71⋊C4—21no—
84C2×Dic71⋊C4—22no—
85C2×Dic71⋊C4—22no—
86C2×Dic71⋊C4—22no—
87C4⋊C4×D71—22no—
88C4⋊C4×D71—24no—
89C4⋊C4×D71—24no—
90C4⋊C4×D71—44no—
91C4⋊C4×D71—44no—
92C4⋊C4×D71C2×C414yes—
93C2×C22⋊Dic71—21no—
94C2×(C2×D71)⋊C4—21no—
95C2×(C2×D71)⋊C4—21no—
96C22⋊C4×D71—28no—
97C2×C4×Dic71D411yescharacteristic
98C2×C4×Dic71D411yescharacteristic
99C2×C4×Dic71C2311yescharacteristic
100C42×D71C2×C414yes—
101C42×D71D414yes—
102C4⋊(C71⋊C8)—22no—
103Dic71⋊C8—24no—
104#14556050—24no—
105#14556049—24no—
106#14556048—24no—
107C22×D4×C71C2311yescharacteristic
108C23×C4×C71—21no—
109C22×C8×C71C2312yes—
110C4×D4×C71—22no—
111C4×D4×C71C2×C414yescomplemented
112C2×C4⋊C4×C71—21no—
113C2×C4⋊C4×C71—21no—
114C2×C4⋊C4×C71C2312yes—
115C2×C4⋊C4×C71C2311yescharacteristic
116C2×C22⋊C4×C71—21no—
117C2×C42×C71C2311yescharacteristic
118C4⋊C8×C71—22no—
119#102×C71—24no—
120C23×D71—21no—
121C23×D71—24no—
122C23×D71—24no—
123C23×D71—24no—
124C23×D71—42no—
125C23×D71—42no—
126C23×D71—42no—
127C23×D71—42no—
128C23×D71C2×D411yescharacteristic
129C2×D284—21no—
130C2×D284—21no—
131C2×D284—21no—
132C2×D284C22×C412yes—
133C2×D284C2×D412yes—
134C2×D284C2×Q812yes—
135C2×C22⋊D71—24no—
136C2×C22⋊D71—24no—
137C2×C22⋊D71—24no—
138D4×D71—28no—
139D4×D71—28no—
140D4×D71—28no—
141D4×D71C4⋊C4116yescomplemented
142C22×Dic71—21no—
143C22×Dic71—24no—
144C22×Dic71—22no—
145C22×Dic71—42no—
146C22×Dic71—42no—
147C22×Dic71C2×D411yescharacteristic
148C22×Dic71C2×D411yescharacteristic
149C22×Dic71C2×D411yescharacteristic
150C2×C4×D71—22no—
151C2×C4×D71—22no—
152C2×C4×D71—24no—
153C2×C4×D71—24no—
154C2×C4×D71—24no—
155C2×C4×D71—42no—
156C2×C4×D71—42no—
157C2×C4×D71—42no—
158C2×C4×D71—42no—
159C2×C4×D71—42no—
160C2×C4×D71—42no—
161C2×C4×D71—432no—
162C2×C4×D71—44no—
163C2×C4×D71—44no—
164C2×C4×D71—44no—
165C2×C4×D71C22⋊C414yes—
166C2×C4×D71C22⋊C414yes—
167C2×C4×D71D814yes—
168C2×C4×D71SD1614yes—
169C2×C4×D71C22×C412yes—
170C2×C4×D71C2×D412yes—
171C2×C4×D71C2×D412yes—
172C2×C4×D71C2×Q812yes—
173C2×C4×D71#4112yes—
174C2×C4×D71#4112yes—
175C2×C71⋊C8—22no—
176C2×C71⋊C8—22no—
177C2×C71⋊C8—22no—
178C8×D71—48no—
179C4⋊Dic71—21no—
180C4⋊Dic71—22no—
181C4⋊Dic71—22no—
182C4⋊Dic71—42no—
183C4⋊Dic71—42no—
184C4⋊Dic71C22×C412yes—
185Dic71⋊C4—24no—
186Dic71⋊C4—44no—
187Dic71⋊C4—44no—
188Dic71⋊C4—44no—
189C22⋊Dic71—24no—
190(C2×D71)⋊C4—24no—
191(C2×D71)⋊C4—24no—
192C4×Dic71C22⋊C414yes—
193C4×Dic71C22⋊C414yes—
194C4×Dic71C22×C412yes—
195C4×Dic71C2×D412yes—
196C24×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71C22×C412yes—
201C2×D4×C71C2×D412yes—
202C2×D4×C71C2×Q812yes—
203C22×C4×C71—21no—
204C22×C4×C71—24no—
205C22×C4×C71—22no—
206C22×C4×C71—42no—
207C22×C4×C71—42no—
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2411yescharacteristic
211C2×C8×C71—22no—
212C2×C8×C71—22no—
213C2×C8×C71—22no—
214C4⋊C4×C71—21no—
215C4⋊C4×C71—22no—
216C4⋊C4×C71—22no—
217C4⋊C4×C71—42no—
218C4⋊C4×C71—42no—
219C4⋊C4×C71C22×C412yes—
220C22⋊C4×C71—24no—
221C42×C71C22×C412yes—
222C42×C71C2×D412yes—
223C23×C71—22no—
224C23×C71—22no—
225C23×C71—22no—
226C23×C71—41no—
227C23×C71—41no—
228C23×C71—41no—
229C23×C71—41no—
230C23×C71C22×D411yescharacteristic
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—216no—
235C22×D71—41no—
236C22×D71—41no—
237C22×D71—41no—
238C22×D71—41no—
239C22×D71—48no—
240C22×D71—48no—
241C22×D71—48no—
242C22×D71—48no—
243C22×D71—48no—
244C22×D71—48no—
245C22×D71C2×C22⋊C412yes—
246C22×D71#12112yes—
247C22×D71C22⋊Q812yes—
248C22×D71C2×D812yes—
249C22×D71C2×SD1612yes—
250C22×D71AGL(1,ℤ/8)12yes—
251C22×D71#13712yes—
252D4×C71—22no—
253D4×C71—22no—
254D4×C71—22no—
255D4×C71C2×C4⋊C414yescomplemented
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—22no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—48no—
262C2×C4×C71—42no—
263C2×C4×C71—42no—
264C2×C4×C71—42no—
265C2×C4×C71C2×C22⋊C412yes—
266C2×C4×C71C2×C22⋊C412yes—
267C2×C4×C71C2×D812yes—
268C2×C4×C71C2×SD1612yes—
269C2×C4×C71C23×C411yescharacteristic
270C2×C4×C71C22×D411yescharacteristic
271C2×C4×C71C22×D411yescharacteristic
272C2×C4×C71C22×Q811yescharacteristic
273C2×C4×C71C2×#4111yescharacteristic
274C2×C4×C71C2×#4111yescharacteristic
275C22⋊D71—216no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—22no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—48no—
282C2×Dic71—42no—
283C2×Dic71—42no—
284C2×Dic71—42no—
285C2×Dic71C2×C22⋊C412yes—
286C2×Dic71C2×C22⋊C412yes—
287C2×Dic71C2×C22⋊C412yes—
288C2×Dic71#12112yes—
289C2×Dic71C22⋊Q812yes—
290C2×Dic71C2×D812yes—
291C2×Dic71C2×SD1612yes—
292D284—22no—
293D284—22no—
294D284—22no—
295D284C2×C4⋊C414yescomplemented
296C4×D71—28no—
297C4×D71—48no—
298C4×D71—48no—
299C4×D71—48no—
300C4×D71—88no—
301C4×D71#102116yescomplemented
302C4×D71C2×C4⋊C414yes—
303C4×D71#11714yes—
304C4×D71#12114yes—
305C4×D71C22⋊Q814yes—
306C8×C71—42no—
307C71⋊C8—42no—
308C22×C71—24no—
309C22×C71—42no—
310C22×C71—42no—
311C22×C71—42no—
312C22×C71—42no—
313C22×C71—42no—
314C22×C71—42no—
315C22×C71C22×C22⋊C411yescharacteristic
316C22×C71C2×#12111yescharacteristic
317C22×C71C2×C22⋊Q811yescharacteristic
318C22×C71C22×D811yescharacteristic
319C22×C71C22×SD1611yescharacteristic
320C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C71C2×#13711yescharacteristic
322C2×D71—24no—
323C2×D71—42no—
324C2×D71—42no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—42no—
328C2×D71—42no—
329C2×D71—432no—
330C2×D71#38014yes—
331C2×D71C2×#10214yes—
332C2×D71#41714yes—
333C2×D71#45914yes—
334C2×D71#46114yes—
335C2×D71#47414yes—
336C2×D71#47614yes—
337C4×C71—22no—
338C4×C71—42no—
339C4×C71—82no—
340C4×C71C2×#10214yescomplemented
341C4×C71C22×C4⋊C411yescharacteristic
342C4×C71C2×#11711yescharacteristic
343C4×C71C2×#12111yescharacteristic
344C4×C71C2×C22⋊Q811yescharacteristic
345Dic71—22no—
346Dic71—42no—
347Dic71—82no—
348Dic71#38014yes—
349Dic71C2×#10214yescomplemented
350C2×#1802—711nomaximal, Sylow
351C2×C71—44no—
352C2×C71C2×#38011yescharacteristic
353C2×C71C22×#10211yescharacteristic
354C2×C71C2×#41711yescharacteristic
355C2×C71C2×#45911yescharacteristic
356C2×C71C2×#46111yescharacteristic
357C2×C71C2×#47411yescharacteristic
358C2×C71C2×#47611yescharacteristic
359D71—44no—
360D71#180218yesdirect product factor
361C22×C4×D4—711no—
362C22×C4⋊C8—711no—
363C22×#102—712no—
364C2×#384—711no—
365#1802—711no—
366#1802—712no—
367#1802—711no—
368#1802—712no—
369#1802—711no—
370#1802D7111yescharacteristic, direct product factor
371C2×#340—712no—
372C71C2×#180211yescharacteristic, complemented, Sylow
373C23×D4—711no—
374C24×C4—1421no—
375C23×C8—712no—
376C2×C4×D4—711no—
377C2×C4×D4—718no—
378C2×C4×D4—711no—
379C2×C4×D4—711no—
380C2×C4×D4—1421no—
381C2×C4×D4—1424no—
382C2×C4×D4—1421no—
383C2×C4×D4C2×D7111yescharacteristic
384C22×C4⋊C4—711no—
385C22×C4⋊C4—712no—
386C22×C4⋊C4—1421no—
387C22×C4⋊C4—1421no—
388C22×C22⋊C4—1421no—
389C22×C42—711no—
390C2×C4⋊C8—712no—
391C2×C4⋊C8—711no—
392C2×C4⋊C8—1424no—
393C2×C4⋊C8C2×D7111yescharacteristic, complemented
394C2×#102—712no—
395C2×#102—712no—
396C2×#102—712no—
397C2×#102—1428no—
398C2×#102C2×D7112yes—
399#384—712no—
400#384—711no—
401#384—1421no—
402#384—1421no—
403#384C2×D7111yescharacteristic, complemented
404#340—712no—
405#340—712no—
406#340—712no—
407#340C2×D7112yescomplemented
408C25—1421no—
409C22×D4—714no—
410C22×D4—714no—
411C22×D4—714no—
412C22×D4—711no—
413C22×D4—1422no—
414C22×D4—1422no—
415C22×D4—1422no—
416C22×D4—1421no—
417C22×D4C22×D7111yescharacteristic
418C23×C4—21no—
419C23×C4—2844no—
420C23×C4—2844no—
421C23×C4—711no—
422C23×C4—711no—
423C23×C4—711no—
424C23×C4—1422no—
425C23×C4—1421no—
426C23×C4—1428no—
427C23×C4—1421no—
428C23×C4—1421no—
429C23×C4—1421no—
430C22×C8—712no—
431C22×C8—1424no—
432C22×C8—1424no—
433C22×C8—1424no—
434C22×C8C22×D7112yes—
435C4×D4—22no—
436C4×D4—714no—
437C4×D4—714no—
438C4×D4—714no—
439C4×D4—1428no—
440C4×D4—1422no—
441C4×D4—1428no—
442C4×D4—1422no—
443C4×D4—1422no—
444C4×D4C4×D7114yescomplemented
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—2844no—
448C2×C4⋊C4—2844no—
449C2×C4⋊C4—711no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—712no—
452C2×C4⋊C4—1424no—
453C2×C4⋊C4—1424no—
454C2×C4⋊C4—1422no—
455C2×C4⋊C4—1422no—
456C2×C4⋊C4—1422no—
457C2×C4⋊C4—1422no—
458C2×C4⋊C4—1421no—
459C2×C4⋊C4—1421no—
460C2×C4⋊C4—1421no—
461C2×C4⋊C4C22×D7112yes—
462C2×C4⋊C4C22×D7111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1428no—
465C2×C22⋊C4—1421no—
466C2×C22⋊C4—1421no—
467C2×C22⋊C4—1421no—
468C2×C42—711no—
469C2×C42—711no—
470C2×C42—711no—
471C2×C42—714no—
472C2×C42—714no—
473C2×C42C22×D7111yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—1424no—
476C4⋊C8—1422no—
477#102—24no—
478#102—1424no—
479#102—1424no—
480#102—1424no—
481C24—21no—
482C24—2842no—
483C24—2842no—
484C24—2842no—
485C24—2842no—
486C24—711no—
487C24—1424no—
488C24—1424no—
489C24—1424no—
490C24—1421no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—7116no—
495C2×D4—712no—
496C2×D4—712no—
497C2×D4—712no—
498C2×D4—1428no—
499C2×D4—1428no—
500C2×D4—1428no—
501C2×D4—1424no—
502C2×D4—1424no—
503C2×D4—1424no—
504C2×D4—1421no—
505C2×D4—1421no—
506C2×D4—1421no—
507C2×D4C2×C4×D7112yes—
508C2×D4D4×D7112yes—
509C2×D4Q8×D7112yes—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—2842no—
516C22×C4—2842no—
517C22×C4—2842no—
518C22×C4—2842no—
519C22×C4—28432no—
520C22×C4—2844no—
521C22×C4—2844no—
522C22×C4—2844no—
523C22×C4—2842no—
524C22×C4—2842no—
525C22×C4—2842no—
526C22×C4—2842no—
527C22×C4—711no—
528C22×C4—711no—
529C22×C4—712no—
530C22×C4—712no—
531C22×C4—712no—
532C22×C4—712no—
533C22×C4—712no—
534C22×C4—712no—
535C22×C4—714no—
536C22×C4—714no—
537C22×C4—714no—
538C22×C4—711no—
539C22×C4—714no—
540C22×C4—1424no—
541C22×C4—1424no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1422no—
545C22×C4—1424no—
546C22×C4—1421no—
547C22×C4—1424no—
548C22×C4D4×D7111yescharacteristic
549C22×C4D4×D7111yescharacteristic
550C22×C4C23×D7111yescharacteristic
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—2848no—
555C2×C8—1422no—
556C2×C8—1422no—
557C2×C8—1422no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—2842no—
564C4⋊C4—2844no—
565C4⋊C4—2844no—
566C4⋊C4—2844no—
567C4⋊C4—2842no—
568C4⋊C4—712no—
569C4⋊C4—1424no—
570C4⋊C4—1422no—
571C4⋊C4—1422no—
572C4⋊C4—1421no—
573C4⋊C4C2×C4×D7112yes—
574C22⋊C4—24no—
575C22⋊C4—1424no—
576C22⋊C4—1424no—
577C22⋊C4—1424no—
578C42—712no—
579C42—712no—
580C42—714no—
581C42—714no—
582C42C2×C4×D7112yes—
583C42D4×D7112yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—2848no—
592C23—2848no—
593C23—2848no—
594C23—2848no—
595C23—2848no—
596C23—2848no—
597C23—2841no—
598C23—2841no—
599C23—2841no—
600C23—2841no—
601C23—712no—
602C23—712no—
603C23—712no—
604C23—712no—
605C23—712no—
606C23—712no—
607C23—712no—
608C23—14216no—
609C23—1422no—
610C23—1422no—
611C23—1422no—
612C23C2×D4×D7111yescharacteristic
613D4—22no—
614D4—22no—
615D4—22no—
616D4—714no—
617D4—14216no—
618D4—1422no—
619D4—1422no—
620D4—1422no—
621D4C4⋊C4×D7114yescomplemented
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—48no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—2848no—
632C2×C4—2848no—
633C2×C4—2841no—
634C2×C4—2841no—
635C2×C4—2848no—
636C2×C4—2848no—
637C2×C4—2842no—
638C2×C4—2842no—
639C2×C4—2842no—
640C2×C4—5688no—
641C2×C4—712no—
642C2×C4—712no—
643C2×C4—712no—
644C2×C4—712no—
645C2×C4—712no—
646C2×C4—712no—
647C2×C4—714no—
648C2×C4—714no—
649C2×C4—714no—
650C2×C4—714no—
651C2×C4—7116no—
652C2×C4—712no—
653C2×C4—1428no—
654C2×C4—1422no—
655C2×C4—1421no—
656C2×C4—1421no—
657C2×C4C22⋊C4×D7112yes—
658C2×C4C22⋊C4×D7112yes—
659C2×C4D8×D7112yes—
660C2×C4SD16×D7112yes—
661C2×C4C22×C4×D7111yescharacteristic
662C2×C4C2×D4×D7111yescharacteristic
663C2×C4C2×D4×D7111yescharacteristic
664C2×C4C2×Q8×D7111yescharacteristic
665C2×C4#41×D7111yescharacteristic
666C2×C4#41×D7111yescharacteristic
667C8—42no—
668C8—2842no—
669C22—24no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—28432no—
677C22—2842no—
678C22—2842no—
679C22—2842no—
680C22—2842no—
681C22—2842no—
682C22—2842no—
683C22—714no—
684C22—714no—
685C22—714no—
686C22—714no—
687C22—714no—
688C22—714no—
689C22—714no—
690C22—1424no—
691C22C2×C22⋊C4×D7111yescharacteristic
692C22#121×D7111yescharacteristic
693C22C22⋊Q8×D7111yescharacteristic
694C22C2×D8×D7111yescharacteristic
695C22C2×SD16×D7111yescharacteristic
696C22AGL(1,ℤ/8)×D7111yescharacteristic
697C22#137×D7111yescharacteristic
698C4—22no—
699C4—42no—
700C4—82no—
701C4—2842no—
702C4—5682no—
703C4—714no—
704C4—714no—
705C4—1422no—
706C4#102×D7114yescomplemented
707C4C2×C4⋊C4×D7111yescharacteristic
708C4#117×D7111yescharacteristic
709C4#121×D7111yescharacteristic
710C4C22⋊Q8×D7111yescharacteristic
711C2—44no—
712C2—2844no—
713C2—718no—
714C2#380×D7111yescharacteristic
715C2C2×#102×D7111yescharacteristic
716C2#417×D7111yescharacteristic
717C2#459×D7111yescharacteristic
718C2#461×D7111yescharacteristic
719C2#474×D7111yescharacteristic
720C2#476×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1802C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
cosocleC22×C4×C71C24
hypercenter#1802D71
hypocenterC71C2×#1802
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D71C2semidirect
4. #384×D71C2semidirect
5. #22588341C2semidirect
6. #22588340C2semidirect
7. #22588339C2semidirect
8. #22588338C2semidirect
9. #22588337C2semidirect
10. #340×D71C2semidirect
11. C71×#1802C2semidirect
21. C4×D4×D71C4semidirect
28. C2×C4⋊(C71⋊C8)C22semidirect
29. C2×Dic71⋊C8C22semidirect
35. #17985869C22semidirect
38. #17985868C22semidirect
39. #17985762C22semidirect
40. #17985761C22semidirect
41. #17985761C22semidirect
43. C2×C4⋊C8×C71C22semidirect
45. #384×C71C22semidirect
46. #340×C71C22semidirect
72. C4×D284C2×C4semidirect
74. D4×Dic71C2×C4semidirect
76. #14556090C2×C4semidirect
111. C4×D4×C71C2×C4semidirect
141. D4×D71C4⋊C4semidirect
255. D4×C71C2×C4⋊C4semidirect
295. D284C2×C4⋊C4semidirect
301. C4×D71#102semidirect
340. C4×C71C2×#102semidirect
349. Dic71C2×#102semidirect
360. D71#1802direct (N × H)
370. #1802D71direct (N × H)
372. C71C2×#1802semidirect
393. C2×C4⋊C8C2×D71semidirect
403. #384C2×D71semidirect
407. #340C2×D71semidirect
444. C4×D4C4×D71semidirect
621. D4C4⋊C4×D71semidirect
706. C4#102×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D712
C2×C4⋊C8×D712
C2×#102×D712
#384×D712
#225883412
#225883402
#225883392
#225883382
#225883372
#340×D712
C71×#18022
C2×#180271