Finite Group Databasebeta

← C2×#22598483 #32865569

Subgroups — C2×#22598483 #32865569

Order 18176.

2582 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986534C211yesmaximal, characteristic, complemented
2C2×C4×D4×D71C211yesmaximal, characteristic, complemented
3#22598483C2116yesmaximal, direct product factor
4C2×#17986331C211yesmaximal, characteristic, complemented
5C2×#17986314C211yesmaximal, characteristic, complemented
6C2×#17986296C211yesmaximal, characteristic, complemented
7C2×#17986215C211yesmaximal, characteristic, complemented
8C2×#17986214C211yesmaximal, characteristic, complemented
9C2×#17986151C211yesmaximal, characteristic, complemented
10C2×#17986134C211yesmaximal, characteristic
11C2×#17986110C211yesmaximal, characteristic, complemented
12C2×#17986108C211yesmaximal, characteristic, complemented
13C2×#17986098C211yesmaximal, characteristic, complemented
14C2×#17986096C211yesmaximal, characteristic, complemented
15C2×#17986055C211yesmaximal, characteristic, complemented
16C2×#478×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C23×C4×D71—21no—
19C22×#11765854C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21C22×D568C2211yescharacteristic
22C22×#11765850C2211yescharacteristic
23#17986534—24no—
24#17986534C2218yescomplemented
25C2×#14556123—21no—
26C2×#14556116C2211yescharacteristic, complemented
27C2×#14556113—21no—
28C2×#14556108C2211yescharacteristic
29C2×#14556103C2211yescharacteristic
30C2×#14556093C2211yescharacteristic, complemented
31C2×C4×D284C2211yescharacteristic
32C2×D4×Dic71C2211yescharacteristic
33C2×#14556090—21no—
34C2×#14556090C2211yescharacteristic
35C2×#14556090C2211yescharacteristic, complemented
36C2×C4×C22⋊D71—21no—
37C2×(C22⋊D71)⋊C4—21no—
38C4×D4×D71—24no—
39C4×D4×D71C2218yescomplemented
40C2×#14556086—21no—
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C22⋊C4×D71—21no—
43C2×C42×D71C2211yescharacteristic
44#17986331C2218yescomplemented
45#17986314C2218yescomplemented
46#17986296C2218yescomplemented
47#17986215C2218yescomplemented
48#17986214C2218yescomplemented
49#17986151C2218yescomplemented
50#17986134C2218yes—
51#17986110C2218yescomplemented
52#17986108C2218yescomplemented
53#17986098C2218yescomplemented
54#17986096C2218yescomplemented
55#17986055C2218yescomplemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556051C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic, complemented
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic, complemented
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×#14556038C2211yescharacteristic, complemented
68C2×#14556038C2211yescharacteristic, complemented
69C2×#125×C71C2211yescharacteristic, complemented
70C2×C4×D4×C71C2211yescharacteristic
71#478×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic, complemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×C4⋊C8×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284—21no—
80C22×D284C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C22⋊D71—21no—
83C2×D4×D71—24no—
84C2×D4×D71—22no—
85C2×D4×D71—24no—
86C2×D4×D71C2314yes—
87C23×Dic71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—28no—
92C22×C4×D71—21no—
93C22×C4×D71—48no—
94C22×C4×D71D411yescharacteristic
95C22×C4×D71D411yescharacteristic
96C22×C4×D71C2311yescharacteristic
97C2×#11765854—24no—
98C2×#11765854C2314yes—
99C2×#11765853—24no—
100C2×#11765853C2314yes—
101C2×D568—24no—
102C2×D568C2314yes—
103C2×#11765850—24no—
104C2×#11765850C2314yes—
105C22×C71⋊C8C2311yescharacteristic
106C22×C71⋊C8C2311yescharacteristic
107#14556123—28no—
108#14556116—22no—
109#14556116C2314yescomplemented
110#14556113—28no—
111#14556108—22no—
112#14556108C2314yes—
113#14556103—22no—
114#14556103C2314yes—
115#14556093—22no—
116#14556093C2314yescomplemented
117C4×D284—22no—
118C4×D284C2314yes—
119D4×Dic71—22no—
120D4×Dic71C2314yes—
121#14556090—28no—
122#14556090—22no—
123#14556090—22no—
124#14556090C2314yes—
125#14556090C2314yescomplemented
126C4×C22⋊D71—28no—
127(C22⋊D71)⋊C4—28no—
128#14556086—28no—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C4⋊C4×D71—22no—
134C4⋊C4×D71C2314yes—
135C2×C22⋊Dic71—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C22⋊C4×D71—28no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71D411yescharacteristic
146C2×C4×Dic71D411yescharacteristic
147C2×C4×Dic71C2311yescharacteristic
148C42×D71D414yes—
149C42×D71C2314yes—
150#14556061C2314yescomplemented
151#14556059C2314yescomplemented
152C4⋊(C71⋊C8)C2314yescomplemented
153#14556053C2314yescomplemented
154#14556051C2314yescomplemented
155#14556050C2314yescomplemented
156#14556048C2314yes—
157#14556048C2314yes—
158#14556048C2314yescomplemented
159(C2×D71)⋊C8C2314yes—
160(C2×D71)⋊C8C2314yes—
161#14556038C2314yescomplemented
162#14556038C2314yescomplemented
163C22×D4×C71C2311yescharacteristic
164C23×C4×C71—21no—
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167#125×C71—22no—
168#125×C71C2314yescomplemented
169C4×D4×C71—22no—
170C4×D4×C71C2314yes—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2311yescharacteristic
176C2×C22⋊C4×C71—21no—
177C2×C42×C71C2311yescharacteristic
178#107×C71C2314yescomplemented
179#106×C71C2314yescomplemented
180C4⋊C8×C71C2314yescomplemented
181#102×C71C2314yes—
182#102×C71C2314yes—
183C23×D71—28no—
184C23×D71—21no—
185C23×D71—24no—
186C23×D71—21no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71C2×D411yescharacteristic
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—21no—
193C2×Dic142C2412yes—
194C2×D284—21no—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—24no—
199C2×D284—21no—
200C2×D284—44no—
201C2×D284#4114yes—
202C2×D284C2412yes—
203C2×D284C2412yes—
204C2×C22⋊D71—28no—
205C2×C22⋊D71—24no—
206D4×D71—216no—
207D4×D71—28no—
208D4×D71—28no—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71—24no—
212C22×Dic71—44no—
213C22×Dic71C2×D411yescharacteristic
214C22×Dic71C2×D411yescharacteristic
215C22×Dic71C2×D411yescharacteristic
216C2×C4×D71—24no—
217C2×C4×D71—22no—
218C2×C4×D71—22no—
219C2×C4×D71—24no—
220C2×C4×D71—24no—
221C2×C4×D71—24no—
222C2×C4×D71—24no—
223C2×C4×D71—432no—
224C2×C4×D71—42no—
225C2×C4×D71—44no—
226C2×C4×D71—44no—
227C2×C4×D71—44no—
228C2×C4×D71—44no—
229C2×C4×D71C2×D414yes—
230C2×C4×D71C2×D412yes—
231C2×C4×D71C2×D414yes—
232C2×C4×D71C2412yes—
233#11765854—28no—
234#11765853—28no—
235D568—28no—
236#11765850—28no—
237C2×C71⋊C8—22no—
238C2×C71⋊C8—22no—
239C2×C71⋊C8C2412yes—
240C2×C71⋊C8C2412yes—
241C4⋊Dic71—21no—
242C4⋊Dic71—24no—
243C4⋊Dic71C2412yes—
244Dic71⋊C4—24no—
245Dic71⋊C4—24no—
246C22⋊Dic71—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4—24no—
254C4×Dic71—24no—
255C4×Dic71C2×D412yes—
256C4×Dic71C2×D414yes—
257C4×Dic71C2×D414yes—
258C4×Dic71C2412yes—
259C24×C71—21no—
260C2×D4×C71—21no—
261C2×D4×C71—22no—
262C2×D4×C71#4114yes—
263C2×D4×C71C2412yes—
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—24no—
268C22×C4×C71—44no—
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2411yescharacteristic
272C2×C8×C71—22no—
273C2×C8×C71—22no—
274C2×C8×C71C2412yes—
275C2×C8×C71C2412yes—
276C4⋊C4×C71—24no—
277C4⋊C4×C71—24no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71C2412yes—
282C4⋊C4×C71C2412yes—
283C4⋊C4×C71C2412yes—
284C22⋊C4×C71—24no—
285C42×C71C2×D412yes—
286C42×C71C2412yes—
287C23×C71—24no—
288C23×C71—22no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71C22×D411yescharacteristic
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—216no—
295C22×D71—24no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—432no—
299C22×D71—48no—
300C22×D71—42no—
301C22×D71—42no—
302C22×D71—48no—
303C22×D71—42no—
304C22×D71—42no—
305C22×D71—42no—
306C22×D71AGL(1,ℤ/8)14yes—
307C22×D71C22×D412yes—
308D4×C71—24no—
309D4×C71—22no—
310D4×C71C2×#4114yes—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—48no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71C22×D412yes—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D411yescharacteristic
323C2×C4×C71C2×#4112yes—
324C2×C4×C71C2×#4112yes—
325C2×C4×C71C2511yescharacteristic
326C22⋊D71—216no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—48no—
333C2×Dic71—42no—
334C2×Dic71—42no—
335C2×Dic71C22×D412yes—
336C2×Dic71C22×D412yes—
337C2×Dic71C22×D412yes—
338D284—24no—
339D284—22no—
340D284—22no—
341D284—22no—
342D284—48no—
343D284—42no—
344D284C2×#4114yes—
345C4×D71—28no—
346C4×D71—24no—
347C4×D71—22no—
348C4×D71—22no—
349C4×D71—44no—
350C4×D71—48no—
351C4×D71—48no—
352C4×D71—48no—
353C4×D71—48no—
354Dic142—22no—
355Dic142—22no—
356Dic142—42no—
357C8×C71—22no—
358C8×C71—22no—
359C71⋊C8—22no—
360C71⋊C8—22no—
361C22×C71—24no—
362C22×C71—48no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71#52512yes—
366C22×C71C2×AGL(1,ℤ/8)12yes—
367C22×C71#57512yes—
368C22×C71C23×D411yescharacteristic
369C2×D71—28no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—24no—
373C2×D71—432no—
374C2×D71—48no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—42no—
380C2×D71—84no—
381C2×D71C2×AGL(1,ℤ/8)14yes—
382C4×C71—22no—
383C4×C71—22no—
384C4×C71—42no—
385C4×C71—42no—
386C4×C71—42no—
387C4×C71#52512yes—
388C4×C71C22×#4111yescharacteristic
389C4×C71C22×#4111yescharacteristic
390Dic71—22no—
391Dic71—22no—
392Dic71—22no—
393Dic71—42no—
394Dic71—42no—
395C2×#3114—711nomaximal, Sylow
396C2×C71—44no—
397C2×C71#311414yescomplemented
398C2×C71C2×#52511yescharacteristic
399C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C71C2×#57511yescharacteristic
401D71—24no—
402D71—44no—
403D71—82no—
404C2×#529—711no—
405C22×C4×D4—711no—
406#3114—7116no—
407C2×#483—711no—
408C2×#480—711no—
409C2×#478—711no—
410C2×#478D7111yescharacteristic, complemented
411C2×#463—711no—
412C2×#463—711no—
413C2×#450—711no—
414C2×#447—711no—
415C2×#442—711no—
416C2×#442—711no—
417C2×#440—711no—
418C2×#440—711no—
419C2×#432—711no—
420C71C2×#311411yescharacteristic, complemented, Sylow
421C23×D4—711no—
422C24×C4—1421no—
423C22×SD16—711no—
424C22×SD16—711no—
425C22×D8—711no—
426C22×D8—711no—
427#529—718no—
428#529—1424no—
429C2×#126—1421no—
430C2×#125C2×D7111yescharacteristic, complemented
431C2×#124—711no—
432C2×#123—1421no—
433C2×C22⋊Q8—711no—
434C2×#121—711no—
435C2×C4×Q8—711no—
436C2×C4×D4—711no—
437C2×C4×D4—718no—
438C2×C4×D4—711no—
439C2×C4×D4—711no—
440C2×C4×D4—711no—
441C2×C4×D4—1421no—
442C2×C4×D4—1424no—
443C2×C4×D4—1421no—
444C2×C4×D4—1421no—
445C2×C4×D4C2×D7111yescharacteristic
446C2×#117—1421no—
447C22×C4⋊C4—711no—
448C22×C22⋊C4—1421no—
449C22×C42—711no—
450#483—718no—
451#480—718no—
452#478—718no—
453#478C2×D7118yescomplemented
454#463—718no—
455#463—718no—
456#450—718no—
457#447—718no—
458#442—718no—
459#442—718no—
460#440—718no—
461#440—718no—
462#432—718no—
463C2×#107—711no—
464C2×#107C2×D7111yescharacteristic, complemented
465C2×#106—711no—
466C2×#106C2×D7111yescharacteristic, complemented
467C2×C4⋊C8—711no—
468C2×C4⋊C8C2×D7111yescharacteristic, complemented
469C2×#103—711no—
470C2×#103—711no—
471C2×#102—711no—
472C2×#102—711no—
473C2×#102—711no—
474C2×#102—711no—
475C2×#102C2×D7111yescharacteristic
476C2×#102C2×D7111yescharacteristic
477C2×C22⋊C8—711no—
478C2×C22⋊C8—711no—
479C2×#97—711no—
480C2×#97—711no—
481C25—1421no—
482C22×Q8—711no—
483C22×D4—714no—
484C22×D4—711no—
485C22×D4—711no—
486C22×D4—1421no—
487C22×D4—1422no—
488C22×D4—1421no—
489C22×D4—1424no—
490C22×D4—1424no—
491C22×D4C22×D7111yescharacteristic
492C23×C4—21no—
493C23×C4—2848no—
494C23×C4—711no—
495C23×C4—711no—
496C23×C4—711no—
497C23×C4—1421no—
498C23×C4—1421no—
499C23×C4—1428no—
500C23×C4—1421no—
501C23×C4—1421no—
502C23×C4—1421no—
503C2×SD16—714no—
504C2×SD16—714no—
505C2×SD16—1424no—
506C2×SD16—1424no—
507C2×D8—714no—
508C2×D8—714no—
509C2×D8—1424no—
510C2×D8—1424no—
511C22×C8—711no—
512C22×C8—711no—
513C22×C8C22×D7111yescharacteristic
514C22×C8C22×D7111yescharacteristic
515#126—1428no—
516#125—22no—
517#125C22×D7114yescomplemented
518#124—714no—
519#124—1422no—
520#123—1428no—
521C22⋊Q8—714no—
522C22⋊Q8—1422no—
523#121—714no—
524#121—1422no—
525C4×Q8—714no—
526C4×Q8—1422no—
527C4×D4—22no—
528C4×D4—714no—
529C4×D4—714no—
530C4×D4—714no—
531C4×D4—714no—
532C4×D4—1428no—
533C4×D4—1422no—
534C4×D4—1422no—
535C4×D4—1428no—
536C4×D4—1422no—
537C4×D4—1428no—
538C4×D4—1422no—
539C4×D4C22×D7114yes—
540#117—1428no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—711no—
544C2×C4⋊C4—714no—
545C2×C4⋊C4—1422no—
546C2×C4⋊C4—1421no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4C22×D7111yescharacteristic
550C2×C4⋊C4C22×D7111yescharacteristic
551C2×C4⋊C4C22×D7111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1428no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4—1421no—
558C2×C22⋊C4—1421no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4—1421no—
562C2×C42—711no—
563C2×C42—711no—
564C2×C42—711no—
565C2×C42—714no—
566C2×C42—714no—
567C2×C42—1421no—
568C2×C42C22×D7111yescharacteristic
569#107—714no—
570#107C22×D7114yescomplemented
571#106—714no—
572#106C22×D7114yescomplemented
573C4⋊C8—714no—
574C4⋊C8C22×D7114yescomplemented
575#103—714no—
576#103—714no—
577#102—714no—
578#102—714no—
579#102—714no—
580#102—714no—
581#102C22×D7114yes—
582#102C22×D7114yes—
583C22⋊C8—714no—
584C22⋊C8—714no—
585#97—714no—
586#97—714no—
587C24—21no—
588C24—2844no—
589C24—2844no—
590C24—711no—
591C24—1424no—
592C24—1428no—
593C24—1421no—
594C24—1421no—
595C2×Q8—712no—
596C2×Q8—1422no—
597C2×Q8—1422no—
598C2×Q8—1421no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—2844no—
602C2×D4—714no—
603C2×D4—712no—
604C2×D4—712no—
605C2×D4—1424no—
606C2×D4—1424no—
607C2×D4—1428no—
608C2×D4—14216no—
609C2×D4—1428no—
610C2×D4—1428no—
611C2×D4—1421no—
612C2×D4—1421no—
613C2×D4—1422no—
614C2×D4—1422no—
615C2×D4—1422no—
616C2×D4#1176586614yes—
617C2×D4C23×D7112yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—2844no—
624C22×C4—2842no—
625C22×C4—2844no—
626C22×C4—28432no—
627C22×C4—2844no—
628C22×C4—2844no—
629C22×C4—2844no—
630C22×C4—714no—
631C22×C4—711no—
632C22×C4—711no—
633C22×C4—711no—
634C22×C4—712no—
635C22×C4—714no—
636C22×C4—712no—
637C22×C4—1424no—
638C22×C4—1424no—
639C22×C4—1424no—
640C22×C4—1424no—
641C22×C4—1424no—
642C22×C4—1421no—
643C22×C4—1421no—
644C22×C4—1424no—
645C22×C4—1422no—
646C22×C4—1422no—
647C22×C4D4×D7111yescharacteristic
648C22×C4D4×D7111yescharacteristic
649C22×C4C23×D7111yescharacteristic
650SD16—1428no—
651SD16—1428no—
652D8—1428no—
653D8—1428no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—712no—
657C2×C8—712no—
658C2×C8—1422no—
659C2×C8—1422no—
660C2×C8C23×D7112yes—
661C2×C8C23×D7112yes—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—712no—
668C4⋊C4—1424no—
669C4⋊C4—1424no—
670C4⋊C4—1424no—
671C4⋊C4—1421no—
672C4⋊C4C23×D7112yes—
673C4⋊C4C23×D7112yes—
674C4⋊C4C23×D7112yes—
675C22⋊C4—24no—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4—1424no—
683C22⋊C4—1424no—
684C42—714no—
685C42—712no—
686C42—714no—
687C42—712no—
688C42—1424no—
689C42D4×D7112yes—
690C42C23×D7112yes—
691C23—22no—
692C23—24no—
693C23—42no—
694C23—42no—
695C23—2848no—
696C23—2848no—
697C23—28432no—
698C23—2842no—
699C23—2842no—
700C23—2842no—
701C23—2842no—
702C23—2842no—
703C23—712no—
704C23—714no—
705C23—14216no—
706C23—1422no—
707C23—1422no—
708C23—1424no—
709C23—1422no—
710C23—1422no—
711C23C2×D4×D7111yescharacteristic
712Q8—2842no—
713Q8—1422no—
714Q8—1422no—
715D4—22no—
716D4—24no—
717D4—2848no—
718D4—2842no—
719D4—714no—
720D4—14216no—
721D4—1422no—
722D4—1422no—
723D4—1422no—
724D4—1424no—
725D4C2×#1176586614yes—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—2848no—
736C2×C4—2844no—
737C2×C4—2848no—
738C2×C4—2848no—
739C2×C4—2848no—
740C2×C4—2842no—
741C2×C4—2842no—
742C2×C4—2848no—
743C2×C4—712no—
744C2×C4—712no—
745C2×C4—712no—
746C2×C4—1428no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1422no—
754C2×C4—1424no—
755C2×C4C2×D4×D7112yes—
756C2×C4C2×D4×D7112yes—
757C2×C4C2×D4×D7111yescharacteristic
758C2×C4#41×D7112yes—
759C2×C4C2×#1176586612yes—
760C2×C4C24×D7111yescharacteristic
761C8—22no—
762C8—22no—
763C8—1422no—
764C8—1422no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—48no—
769C22—28432no—
770C22—2842no—
771C22—2842no—
772C22—2848no—
773C22—2842no—
774C22—2842no—
775C22—2842no—
776C22—5684no—
777C22—714no—
778C22—1424no—
779C22—1422no—
780C22—1428no—
781C22—1422no—
782C22#1798651212yes—
783C22AGL(1,ℤ/8)×D7112yes—
784C22#1798679612yes—
785C22C22×D4×D7111yescharacteristic
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—2842no—
792C4—2842no—
793C4—1422no—
794C4—1422no—
795C4—1422no—
796C4#1798651212yes—
797C4C2×#41×D7111yescharacteristic
798C4C22×#1176586611yescharacteristic
799C2—44no—
800C2—2844no—
801C2—5682no—
802C2—1424no—
803C2#2259848314yesdirect product factor
804C2C2×#1798651211yescharacteristic
805C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
806C2C2×#1798679611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#478×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986134C2
hypercenterC2×#478D71
hypocenterC71C2×#3114
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#17986534C2semidirect
2. C2×C4×D4×D71C2semidirect
3. #22598483C2direct (N × H)
4. C2×#17986331C2semidirect
5. C2×#17986314C2semidirect
6. C2×#17986296C2semidirect
7. C2×#17986215C2semidirect
8. C2×#17986214C2semidirect
9. C2×#17986151C2semidirect
11. C2×#17986110C2semidirect
12. C2×#17986108C2semidirect
13. C2×#17986098C2semidirect
14. C2×#17986096C2semidirect
15. C2×#17986055C2semidirect
16. C2×#478×C71C2semidirect
24. #17986534C22semidirect
26. C2×#14556116C22semidirect
30. C2×#14556093C22semidirect
35. C2×#14556090C22semidirect
39. C4×D4×D71C22semidirect
44. #17986331C22semidirect
45. #17986314C22semidirect
46. #17986296C22semidirect
47. #17986215C22semidirect
48. #17986214C22semidirect
49. #17986151C22semidirect
51. #17986110C22semidirect
52. #17986108C22semidirect
53. #17986098C22semidirect
54. #17986096C22semidirect
55. #17986055C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×C4⋊(C71⋊C8)C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556051C22semidirect
61. C2×#14556050C22semidirect
64. C2×#14556048C22semidirect
67. C2×#14556038C22semidirect
68. C2×#14556038C22semidirect
69. C2×#125×C71C22semidirect
71. #478×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×C4⋊C8×C71C22semidirect
109. #14556116C23semidirect
116. #14556093C23semidirect
125. #14556090C23semidirect
150. #14556061C23semidirect
151. #14556059C23semidirect
152. C4⋊(C71⋊C8)C23semidirect
153. #14556053C23semidirect
154. #14556051C23semidirect
155. #14556050C23semidirect
158. #14556048C23semidirect
161. #14556038C23semidirect
162. #14556038C23semidirect
168. #125×C71C23semidirect
178. #107×C71C23semidirect
179. #106×C71C23semidirect
180. C4⋊C8×C71C23semidirect
397. C2×C71#3114semidirect
410. C2×#478D71semidirect
420. C71C2×#3114semidirect
430. C2×#125C2×D71semidirect
453. #478C2×D71semidirect
464. C2×#107C2×D71semidirect
466. C2×#106C2×D71semidirect
468. C2×C4⋊C8C2×D71semidirect
517. #125C22×D71semidirect
570. #107C22×D71semidirect
572. #106C22×D71semidirect
574. C4⋊C8C22×D71semidirect
803. C2#22598483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865342
C2×C4×D4×D712
#225984832
C2×#179863312
C2×#179863142
C2×#179862962
C2×#179862152
C2×#179862142
C2×#179861512
C2×#179861342
C2×#179861102
C2×#179861082
C2×#179860982
C2×#179860962
C2×#179860552
C2×#478×C712
C2×#311471