Finite Group Databasebeta

← #32015606

Subgroups — #32015606

Order 18176.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986041C211yesmaximal, characteristic, complemented
2C22×#14556060C211yesmaximal, characteristic, complemented
3#22591269C211yesmaximal, characteristic
4D4×C4⋊Dic71C211yesmaximal, characteristic
5#22589110C211yesmaximal, characteristic, complemented
6#22589104C211yesmaximal, characteristic, complemented
7#22588541C211yesmaximal, characteristic, complemented
8#22588535C211yesmaximal, characteristic, complemented
9#22588535C211yesmaximal, characteristic, complemented
10#22588530C211yesmaximal, characteristic, complemented
11#22588508C211yesmaximal, characteristic, complemented
12#22588373C211yesmaximal, characteristic, complemented
13#22588369C211yesmaximal, characteristic, complemented
14#22588237C211yesmaximal, characteristic, complemented
15C2×#435×C71C211yesmaximal, characteristic
16C2×D4×Dic71—21no—
17C2×#14556087C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21#17986041—24no—
22C2×#14556062C2211yescharacteristic
23C2×#14556062C2211yescharacteristic
24C2×#14556062C2211yescharacteristic
25C2×#14556062C2211yescharacteristic
26C2×#14556060—24no—
27C2×#14556060C2211yescharacteristic
28C2×#14556060C2211yescharacteristic
29C2×#14556060C2211yescharacteristic
30C2×#14556060C2211yescharacteristic
31C2×#14556060C2211yescharacteristic
32C2×#14556060C2211yescharacteristic
33#17985898—21no—
34#17985892—21no—
35#17985885—21no—
36#17985879—21no—
37#17985874—21no—
38#17985874—21no—
39#17985869C2211yescharacteristic
40#17985865C2211yescharacteristic
41#17985859C2211yescharacteristic
42#17985859C2211yescharacteristic
43#17985859C2211yescharacteristic
44#17985859C2211yescharacteristic
45C4×C4⋊Dic71C2211yescharacteristic
46C4×C4⋊Dic71C2211yescharacteristic
47C22⋊C4×Dic71—21no—
48#17985762C2211yescharacteristic
49#17985762C2211yescharacteristic
50#17985762C2211yescharacteristic
51#17985762C2211yescharacteristic
52#17985762C2211yescharacteristic
53#17985762C2211yescharacteristic
54C22×M16×C71C2211yescharacteristic
55C23×C8×C71C2211yescharacteristic
56C2×C4×D4×C71C2211yescharacteristic
57#435×C71C418yescomplemented
58C2×C4⋊C8×C71C2211yescharacteristic
59C2×C22⋊C8×C71C2211yescharacteristic
60C2×C22⋊C8×C71C2211yescharacteristic
61C2×#97×C71C2211yescharacteristic
62C23×Dic71—21no—
63C23×Dic71—21no—
64C23×Dic71—21no—
65D4×Dic71—44no—
66#14556087—22no—
67#14556087—41no—
68C2×C4⋊Dic71—22no—
69C2×C4⋊Dic71—22no—
70C2×C4⋊Dic71—22no—
71C2×C4⋊Dic71—21no—
72C2×C4⋊Dic71—21no—
73C2×C4⋊Dic71—21no—
74C2×C4⋊Dic71—21no—
75C2×C4⋊Dic71—21no—
76C2×C4⋊Dic71—41no—
77C2×C4⋊Dic71—41no—
78C2×C4⋊Dic71—41no—
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C4⋊Dic71C2311yescharacteristic
83C2×C4⋊Dic71C2311yescharacteristic
84C2×C4⋊Dic71C2311yescharacteristic
85C2×C4⋊Dic71C2311yescharacteristic
86C2×C4⋊Dic71C2311yescharacteristic
87C2×C22⋊Dic71—21no—
88C2×C22⋊Dic71—21no—
89C2×C22⋊Dic71—21no—
90C2×C22⋊Dic71—21no—
91C2×C22⋊Dic71—21no—
92C2×C4×Dic71—21no—
93C2×C4×Dic71—21no—
94C2×C4×Dic71—21no—
95#14556062—22no—
96#14556062—22no—
97#14556062—22no—
98#14556062—41no—
99#14556060—22no—
100#14556060—22no—
101#14556060—22no—
102#14556060—22no—
103#14556060—41no—
104#14556060D414yescomplemented
105C71⋊#95—21no—
106C71⋊#95—21no—
107C71⋊#95—21no—
108C71⋊#95—21no—
109C71⋊#95—21no—
110C71⋊#95—21no—
111C71⋊#95—21no—
112C71⋊#95—21no—
113C22×D4×C71D411yescharacteristic
114C23×C4×C71C2311yescharacteristic
115C23×C4×C71C2311yescharacteristic
116C2×M16×C71—22no—
117C2×M16×C71—22no—
118C2×M16×C71C2×C414yescomplemented
119C22×C8×C71—22no—
120C22×C8×C71—22no—
121C22×C8×C71C2×C414yescomplemented
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C22×C8×C71C2311yescharacteristic
125C22×C8×C71C2311yescharacteristic
126C4×D4×C71C2×C414yes—
127C4×D4×C71Q814yes—
128C2×C4⋊C4×C71D411yescharacteristic
129C2×C22⋊C4×C71D411yescharacteristic
130C2×C22⋊C4×C71D411yescharacteristic
131C2×C42×C71C2311yescharacteristic
132C4⋊C8×C71C2×C414yescomplemented
133C22⋊C8×C71C2×C414yescomplemented
134C22⋊C8×C71C2×C414yescomplemented
135#97×C71C2×C414yescomplemented
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—42no—
145C22×Dic71—42no—
146C22×Dic71—42no—
147C22×Dic71—42no—
148C22×Dic71—42no—
149C22×Dic71—42no—
150C22×Dic71—81no—
151C22×Dic71—81no—
152C22×Dic71—81no—
153C4⋊Dic71—21no—
154C4⋊Dic71—21no—
155C4⋊Dic71—21no—
156C4⋊Dic71—21no—
157C4⋊Dic71—21no—
158C4⋊Dic71—21no—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—42no—
168C4⋊Dic71—42no—
169C4⋊Dic71—42no—
170C4⋊Dic71—42no—
171C4⋊Dic71—81no—
172C4⋊Dic71C2×D412yes—
173C4⋊Dic71C2×D412yes—
174C22⋊Dic71—42no—
175C22⋊Dic71—42no—
176C22⋊Dic71—42no—
177C22⋊Dic71—42no—
178C22⋊Dic71—81no—
179C4×Dic71—42no—
180C4×Dic71—42no—
181C4×Dic71—81no—
182C24×C71C2×D411yescharacteristic
183C24×C71C2×D411yescharacteristic
184C2×D4×C71—22no—
185C2×D4×C71—22no—
186C2×D4×C71C4⋊C414yes—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71C22×C412yes—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C2×D411yescharacteristic
198C22×C4×C71C2×D411yescharacteristic
199C22×C4×C71C2×D411yescharacteristic
200C22×C4×C71C2×D411yescharacteristic
201C22×C4×C71C2×Q812yes—
202C22×C4×C71C2×Q812yes—
203C22×C4×C71C2411yescharacteristic
204M16×C71—28no—
205C2×C8×C71—21no—
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—21no—
209C2×C8×C71—21no—
210C2×C8×C71—21no—
211C2×C8×C71—28no—
212C2×C8×C71C22×C412yes—
213C2×C8×C71C22×C412yes—
214C2×C8×C71C22×C412yes—
215C2×C8×C71C22×C412yes—
216C2×C8×C71C2×D412yes—
217C2×C8×C71#4112yes—
218C4⋊C4×C71C4⋊C414yes—
219C22⋊C4×C71C4⋊C414yes—
220C22⋊C4×C71C4⋊C414yes—
221C42×C71C22×C412yes—
222C42×C71C2×Q812yes—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71C2×C4⋊C412yes—
234C23×C71C2×C4⋊C412yes—
235C23×C71AGL(1,ℤ/8)12yes—
236C23×C71#13712yes—
237C23×C71C22×D411yescharacteristic
238D4×C71—28no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71C2×C4⋊C412yes—
256C2×C4×C71C2×C4⋊C412yes—
257C2×C4×C71C2×C4⋊C412yes—
258C2×C4×C71C2×C4⋊C412yes—
259C2×C4×C71C23×C411yescharacteristic
260C2×C4×C71C22×D411yescharacteristic
261C2×C4×C71C22×Q811yescharacteristic
262C2×C4×C71C2×#4111yescharacteristic
263C2×C4×C71H(5,𝔽2)11yescharacteristic
264C2×C4×C712−1+411yescharacteristic
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—41no—
268C2×Dic71—41no—
269C2×Dic71—41no—
270C2×Dic71—41no—
271C2×Dic71—41no—
272C2×Dic71—41no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—84no—
290C2×Dic71—84no—
291C2×Dic71—84no—
292C8×C71—22no—
293C8×C71—22no—
294C8×C71—22no—
295C8×C71C4×D414yescomplemented
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—22no—
300C22×C71—22no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—41no—
306C22×C71—41no—
307C22×C71—41no—
308C22×C71—41no—
309C22×C71#42814yescomplemented
310C22×C71C22×C4⋊C411yescharacteristic
311C22×C71D4211yescharacteristic
312C22×C71#54711yescharacteristic
313C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C71C2×#13711yescharacteristic
315C22×C71#57711yescharacteristic
316C22×C71#57711yescharacteristic
317C4×C71—22no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—22no—
321C4×C71C2×C4×D411yescharacteristic
322C4×C71#52011yescharacteristic
323C4×C71D4×Q811yescharacteristic
324C4×C71#55411yescharacteristic
325Dic71—42no—
326Dic71—42no—
327Dic71—81no—
328Dic71—81no—
329Dic71—81no—
330Dic71—81no—
331Dic71—81no—
332Dic71—81no—
333#22659—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71—42no—
336C2×C71D4×C4⋊C411yescharacteristic
337C2×C71C2×#42811yescharacteristic
338C2×C71#291211yescharacteristic
339C2×C71#326511yescharacteristic
340C2×C71#326611yescharacteristic
341C2×C71#334411yescharacteristic
342C2×C71#334511yescharacteristic
343C2×#435D7111yescharacteristic
344C2×#428—711no—
345C22×#106—711no—
346#2352—711no—
347D4×C4⋊C4—711no—
348#1949—711no—
349#1948—711no—
350#1854—711no—
351#1853—711no—
352#1853—711no—
353#1852—711no—
354#1847—711no—
355#1809—711no—
356#1808—711no—
357#1776—711no—
358C71#2265911yescharacteristic, complemented, Sylow
359C22×M16C2×D7111yescharacteristic
360C23×C8C2×D7111yescharacteristic
361C2×C4×D4—1421no—
362C2×C4×D4C2×D7111yescharacteristic
363C2×#117—711no—
364C22×C4⋊C4—711no—
365C22×C4⋊C4—711no—
366C22×C4⋊C4—711no—
367#435Dic7118yescomplemented
368#428—1424no—
369C2×#107—711no—
370C2×#107—711no—
371C2×#107—711no—
372C2×#107—711no—
373C2×#106—711no—
374C2×#106—711no—
375C2×#106—711no—
376C2×#106—711no—
377C2×#106—711no—
378C2×#106—711no—
379C2×#106—1424no—
380C2×C4⋊C8C2×D7111yescharacteristic
381C2×C22⋊C8C2×D7111yescharacteristic
382C2×C22⋊C8C2×D7111yescharacteristic
383C2×#97C2×D7111yescharacteristic
384#389—1421no—
385#388—1421no—
386#387—1421no—
387#386—1421no—
388#385—1421no—
389#385—1421no—
390#384—711no—
391#382—711no—
392#380—711no—
393#380—711no—
394#380—711no—
395#380—711no—
396C4×C4⋊C4—711no—
397C4×C4⋊C4—711no—
398C4×C22⋊C4—1421no—
399#340—711no—
400#340—711no—
401#340—711no—
402#340—711no—
403#340—711no—
404#340—711no—
405C22×D4D28411yescharacteristic
406C23×C4—1421no—
407C23×C4—1421no—
408C23×C4—1421no—
409C23×C4C22×D7111yescharacteristic
410C23×C4C22×D7111yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×Dic7114yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×Dic7114yescomplemented
417C22×C8C22×D7111yescharacteristic
418C22×C8C22×D7111yescharacteristic
419C22×C8C22×D7111yescharacteristic
420C22×C8C22×D7111yescharacteristic
421C4×D4—2844no—
422C4×D4Dic14214yes—
423C4×D4C2×Dic7114yes—
424#117—2841no—
425#117—1422no—
426C2×C4⋊C4—2841no—
427C2×C4⋊C4—2841no—
428C2×C4⋊C4—2841no—
429C2×C4⋊C4—711no—
430C2×C4⋊C4—711no—
431C2×C4⋊C4—711no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—711no—
436C2×C4⋊C4—711no—
437C2×C4⋊C4—1421no—
438C2×C4⋊C4—1421no—
439C2×C4⋊C4—1421no—
440C2×C4⋊C4—1421no—
441C2×C4⋊C4—1422no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1422no—
444C2×C4⋊C4—1421no—
445C2×C4⋊C4D28411yescharacteristic
446C2×C22⋊C4—1421no—
447C2×C22⋊C4—1421no—
448C2×C22⋊C4—1421no—
449C2×C22⋊C4—1421no—
450C2×C22⋊C4—1421no—
451C2×C22⋊C4D28411yescharacteristic
452C2×C22⋊C4D28411yescharacteristic
453C2×C42—1421no—
454C2×C42—1421no—
455C2×C42—1421no—
456C2×C42C22×D7111yescharacteristic
457#107—2841no—
458#107—1422no—
459#107—1422no—
460#107—1422no—
461#106—2841no—
462#106—714no—
463#106—1422no—
464#106—1422no—
465#106—1422no—
466#106—1422no—
467C4⋊C8C2×Dic7114yescomplemented
468C22⋊C8C2×Dic7114yescomplemented
469C22⋊C8C2×Dic7114yescomplemented
470#97C2×Dic7114yescomplemented
471#95—1421no—
472#95—1421no—
473#95—1421no—
474#95—1421no—
475#95—1421no—
476#95—1421no—
477#95—1421no—
478#95—1421no—
479C24C2×D28411yescharacteristic
480C24C2×D28411yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊Dic7114yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—2842no—
493C22×C4—2842no—
494C22×C4—2842no—
495C22×C4—2842no—
496C22×C4—2842no—
497C22×C4—2842no—
498C22×C4—5681no—
499C22×C4—5681no—
500C22×C4—5681no—
501C22×C4—1421no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4C22×Dic7112yes—
510C22×C4C22×Dic7112yes—
511C22×C4C2×D28411yescharacteristic
512C22×C4C2×D28411yescharacteristic
513C22×C4C2×D28411yescharacteristic
514C22×C4C2×D28411yescharacteristic
515C22×C4C2×Dic14212yes—
516C22×C4C2×Dic14212yes—
517C22×C4C23×D7111yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8C22×Dic7112yes—
527C2×C8C22×Dic7112yes—
528C2×C8C22×Dic7112yes—
529C2×C8C22×Dic7112yes—
530C2×C8D4×D7112yes—
531C2×C8#1176586412yes—
532C4⋊C4—2842no—
533C4⋊C4—2842no—
534C4⋊C4—2842no—
535C4⋊C4—2842no—
536C4⋊C4—5681no—
537C4⋊C4—712no—
538C4⋊C4—712no—
539C4⋊C4—1421no—
540C4⋊C4—1421no—
541C4⋊C4—1421no—
542C4⋊C4—1421no—
543C4⋊C4—1421no—
544C4⋊C4—1421no—
545C4⋊C4—1421no—
546C4⋊C4—1421no—
547C4⋊C4—1421no—
548C4⋊C4—1421no—
549C4⋊C4—1421no—
550C4⋊C4—1421no—
551C4⋊C4—1421no—
552C4⋊C4—1421no—
553C4⋊C4C4⋊Dic7114yes—
554C22⋊C4—2842no—
555C22⋊C4—2842no—
556C22⋊C4—2842no—
557C22⋊C4—2842no—
558C22⋊C4—5681no—
559C22⋊C4C4⋊Dic7114yes—
560C22⋊C4C4⋊Dic7114yes—
561C42—2842no—
562C42—2842no—
563C42—5681no—
564C42C22×Dic7112yes—
565C42C2×Dic14212yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊Dic7112yes—
577C23C2×C4⋊Dic7112yes—
578C23#1455615612yes—
579C23#1455616112yes—
580C23C22×D28411yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—2841no—
599C2×C4—2841no—
600C2×C4—2841no—
601C2×C4—2841no—
602C2×C4—2841no—
603C2×C4—2841no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—2841no—
610C2×C4—2841no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—5684no—
621C2×C4—5684no—
622C2×C4—5684no—
623C2×C4—1422no—
624C2×C4—1422no—
625C2×C4C2×C4⋊Dic7112yes—
626C2×C4C2×C4⋊Dic7112yes—
627C2×C4C2×C4⋊Dic7112yes—
628C2×C4C2×C4⋊Dic7112yes—
629C2×C4C23×Dic7111yescharacteristic
630C2×C4C2×D4×D7111yescharacteristic
631C2×C4C22×Dic14211yescharacteristic
632C2×C4C2×#1176586411yescharacteristic
633C2×C4#1455617411yescharacteristic
634C2×C4#1455617511yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8D4×Dic7114yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1798604114yescomplemented
653C22C22×C4⋊Dic7111yescharacteristic
654C22D4×D28411yescharacteristic
655C22#1798665311yescharacteristic
656C22C2×#1455615611yescharacteristic
657C22C2×#1455616111yescharacteristic
658C22#1798681111yescharacteristic
659C22#1798681111yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—2842no—
665C4—2842no—
666C4—5681no—
667C4—5681no—
668C4—5681no—
669C4—5681no—
670C4—5681no—
671C4—5681no—
672C4C2×D4×Dic7111yescharacteristic
673C4#1798648211yescharacteristic
674C4D4×Dic14211yescharacteristic
675C4#1798670611yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊Dic7111yescharacteristic
679C2C2×#1798604111yescharacteristic
680C2#2259693511yescharacteristic
681C2#2259984011yescharacteristic
682C2#2259985511yescharacteristic
683C2#2260079711yescharacteristic
684C2#2260081211yescharacteristic
subgroupG/H
centerC23C22×D284
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenterC2×#435D71
hypocenterC71#22659
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986041C2semidirect
2. C22×#14556060C2semidirect
5. #22589110C2semidirect
6. #22589104C2semidirect
7. #22588541C2semidirect
8. #22588535C2semidirect
9. #22588535C2semidirect
10. #22588530C2semidirect
11. #22588508C2semidirect
12. #22588373C2semidirect
13. #22588369C2semidirect
14. #22588237C2semidirect
57. #435×C71C4semidirect
104. #14556060D4semidirect
118. C2×M16×C71C2×C4semidirect
121. C22×C8×C71C2×C4semidirect
132. C4⋊C8×C71C2×C4semidirect
133. C22⋊C8×C71C2×C4semidirect
134. C22⋊C8×C71C2×C4semidirect
135. #97×C71C2×C4semidirect
295. C8×C71C4×D4semidirect
309. C22×C71#428semidirect
358. C71#22659semidirect
367. #435Dic71semidirect
413. C2×M16C2×Dic71semidirect
416. C22×C8C2×Dic71semidirect
467. C4⋊C8C2×Dic71semidirect
468. C22⋊C8C2×Dic71semidirect
469. C22⋊C8C2×Dic71semidirect
470. #97C2×Dic71semidirect
638. C8D4×Dic71semidirect
652. C22#17986041semidirect

Maximal subgroups

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

subgroupindex
C2×#179860412
C22×#145560602
#225912692
D4×C4⋊Dic712
#225891102
#225891042
#225885412
#225885352
#225885302
#225885082
#225883732
#225883692
#225882372
C2×#435×C712
#2265971