Finite Group Databasebeta

← C2×#22598135 #32864961

Subgroups — C2×#22598135 #32864961

Order 18176.

2530 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986555C211yesmaximal, characteristic, complemented
2C2×C4×D4×D71C211yesmaximal, characteristic
3#22598135C2116yesmaximal, direct product factor
4C2×#17986300C211yesmaximal, characteristic, complemented
5C2×#17986299C211yesmaximal, characteristic, complemented
6C2×#17986296C211yesmaximal, characteristic, complemented
7C2×#17986288C211yesmaximal, characteristic, complemented
8C2×#17986287C211yesmaximal, characteristic, complemented
9C2×#17986278C211yesmaximal, characteristic, complemented
10C2×#17986277C211yesmaximal, characteristic, complemented
11C2×#17986040C211yesmaximal, characteristic, complemented
12C2×#17986038C211yesmaximal, characteristic, complemented
13C2×#17986021C211yesmaximal, characteristic, complemented
14C2×#17986002C211yesmaximal, characteristic
15C2×#17986002C211yesmaximal, characteristic
16C2×#478×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C23×C4×D71—21no—
19C22×#11765848C2211yescharacteristic
20C22×#11765848C2211yescharacteristic
21#17986555—24no—
22#17986555C2218yescomplemented
23C2×#14556127C2211yescharacteristic, complemented
24C2×#14556127C2211yescharacteristic, complemented
25C2×#14556120C2211yescharacteristic, complemented
26C2×#14556106—21no—
27C2×#14556106—21no—
28C2×#14556093—21no—
29C2×#14556093—21no—
30C2×C4×D284C2211yescharacteristic
31C2×D4×Dic71C2211yescharacteristic
32C2×#14556090C2211yescharacteristic
33C2×C4×C22⋊D71—21no—
34C2×(C22⋊D71)⋊C4—21no—
35C4×D4×D71—24no—
36C4×D4×D71C2218yes—
37C2×#14556086C2211yescharacteristic
38C2×#14556086C2211yescharacteristic
39C2×C4⋊C4×D71C2211yescharacteristic
40C2×C22⋊C4×D71—21no—
41C2×C42×D71C2211yescharacteristic
42#17986300C2218yescomplemented
43#17986299C2218yescomplemented
44#17986296C2218yescomplemented
45#17986288C2218yescomplemented
46#17986287C2218yescomplemented
47#17986278C2218yescomplemented
48#17986277C2218yescomplemented
49#17986040C2218yescomplemented
50#17986038C2218yescomplemented
51C2×#14556062C2211yescharacteristic, complemented
52C2×#14556061C2211yescharacteristic, complemented
53C2×#14556061C2211yescharacteristic, complemented
54C2×#14556060C2211yescharacteristic, complemented
55C2×#14556059C2211yescharacteristic, complemented
56C2×#14556059C2211yescharacteristic, complemented
57#17986021C2218yescomplemented
58C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×Dic71⋊C8C2211yescharacteristic, complemented
61#17986002C2218yes—
62#17986002C2218yes—
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556049C2211yescharacteristic
67C2×#14556048C2211yescharacteristic
68C2×#14556048C2211yescharacteristic
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×Dic142—21no—
79C22×Dic142—21no—
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C2×D4×D71—22no—
83C2×D4×D71—24no—
84C2×D4×D71Q818yescomplemented
85C2×D4×D71C2314yes—
86C23×Dic71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—28no—
90C22×C4×D71—21no—
91C22×C4×D71—48no—
92C22×C4×D71D411yescharacteristic
93C22×C4×D71D411yescharacteristic
94C22×C4×D71C2311yescharacteristic
95C2×#11765848—24no—
96C2×#11765848—24no—
97C2×#11765848C2314yes—
98C2×#11765848C2314yes—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101#14556127—22no—
102#14556127—22no—
103#14556127C2314yescomplemented
104#14556127C2314yescomplemented
105#14556120—22no—
106#14556120C2314yescomplemented
107#14556106—28no—
108#14556106—28no—
109#14556093—28no—
110#14556093—28no—
111C4×D284—22no—
112C4×D284C2314yes—
113D4×Dic71—22no—
114D4×Dic71C2314yes—
115#14556090—22no—
116#14556090C2314yes—
117C4×C22⋊D71—28no—
118(C22⋊D71)⋊C4—28no—
119#14556086—22no—
120#14556086—22no—
121#14556086C2314yes—
122#14556086C2314yes—
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C2×C22⋊Dic71—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C22⋊C4×D71—28no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71D411yescharacteristic
142C2×C4×Dic71D411yescharacteristic
143C2×C4×Dic71C2311yescharacteristic
144C42×D71D414yes—
145C42×D71C2314yes—
146#14556062C2314yescomplemented
147#14556061C2314yescomplemented
148#14556061C2314yescomplemented
149#14556060C2314yescomplemented
150#14556059C2314yescomplemented
151#14556059C2314yescomplemented
152C4⋊(C71⋊C8)C2314yescomplemented
153Dic71⋊C8C2314yescomplemented
154Dic71⋊C8C2314yescomplemented
155#14556050C2314yes—
156#14556050C2314yes—
157#14556049C2314yes—
158#14556049C2314yes—
159#14556048C2314yes—
160#14556048C2314yes—
161C22×D4×C71C2311yescharacteristic
162C23×C4×C71—21no—
163C22×C8×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165#125×C71—22no—
166#125×C71C2314yescomplemented
167C4×D4×C71—22no—
168C4×D4×C71C2314yes—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C42×C71C2311yescharacteristic
176#107×C71C2314yescomplemented
177#106×C71C2314yescomplemented
178C4⋊C8×C71C2314yescomplemented
179#102×C71C2314yes—
180#102×C71C2314yes—
181C23×D71—21no—
182C23×D71—28no—
183C23×D71—24no—
184C23×D71—44no—
185C23×D71—44no—
186C23×D71C2×D411yescharacteristic
187C2×Dic142—24no—
188C2×Dic142—24no—
189C2×Dic142—44no—
190C2×Dic142—44no—
191C2×D284—21no—
192C2×D284—22no—
193C2×D284C2×Q814yes—
194C2×D284C2412yes—
195C2×C22⋊D71—28no—
196C2×C22⋊D71—24no—
197D4×D71—216no—
198D4×D71—28no—
199D4×D71C2×Q8116yescomplemented
200C22×Dic71—21no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—24no—
204C22×Dic71—44no—
205C22×Dic71C2×D411yescharacteristic
206C22×Dic71C2×D411yescharacteristic
207C22×Dic71C2×D411yescharacteristic
208C2×C4×D71—24no—
209C2×C4×D71—24no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—432no—
213C2×C4×D71—42no—
214C2×C4×D71—44no—
215C2×C4×D71—44no—
216C2×C4×D71—44no—
217C2×C4×D71C2×D414yes—
218C2×C4×D71C2×D414yes—
219C2×C4×D71C2×D412yes—
220C2×C4×D71C2×Q814yes—
221C2×C4×D71#4114yes—
222C2×C4×D71C2412yes—
223#11765848—28no—
224#11765848—28no—
225C2×C71⋊C8—22no—
226C2×C71⋊C8—22no—
227C2×C71⋊C8C2412yes—
228C2×C71⋊C8C2412yes—
229C4⋊Dic71—21no—
230C4⋊Dic71—21no—
231C4⋊Dic71—21no—
232C4⋊Dic71C2412yes—
233C4⋊Dic71C2412yes—
234C4⋊Dic71C2412yes—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4—24no—
240C22⋊Dic71—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4—24no—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71C2×D412yes—
248C4×Dic71C2×D414yes—
249C4×Dic71C2×D414yes—
250C4×Dic71C2412yes—
251C24×C71—21no—
252C2×D4×C71—21no—
253C2×D4×C71—22no—
254C2×D4×C71C2×Q814yes—
255C2×D4×C71C2412yes—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—24no—
260C22×C4×C71—44no—
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2411yescharacteristic
264C2×C8×C71—22no—
265C2×C8×C71—22no—
266C2×C8×C71C2412yes—
267C2×C8×C71C2412yes—
268C4⋊C4×C71—24no—
269C4⋊C4×C71—24no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71C2412yes—
274C4⋊C4×C71C2412yes—
275C4⋊C4×C71C2412yes—
276C22⋊C4×C71—24no—
277C42×C71C2×D412yes—
278C42×C71C2412yes—
279C23×C71—24no—
280C23×C71—22no—
281C23×C71—42no—
282C23×C71—42no—
283C23×C71C22×D411yescharacteristic
284C22×D71—22no—
285C22×D71—22no—
286C22×D71—24no—
287C22×D71—22no—
288C22×D71—216no—
289C22×D71—48no—
290C22×D71—432no—
291C22×D71—48no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71C22⋊Q814yes—
295C22×D71C22×D412yes—
296D4×C71—24no—
297D4×C71—22no—
298D4×C71C22×Q814yes—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—48no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—42no—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D411yescharacteristic
311C2×C4×C71C22×Q812yes—
312C2×C4×C71C2×#4112yes—
313C2×C4×C71C2511yescharacteristic
314C22⋊D71—216no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—48no—
323C2×Dic71C22⋊Q814yes—
324C2×Dic71AGL(1,ℤ/8)14yes—
325C2×Dic71C22×D412yes—
326C2×Dic71C22×D412yes—
327C2×Dic71C22×D412yes—
328D284—24no—
329D284—22no—
330D284C22×Q814yes—
331C4×D71—28no—
332C4×D71—44no—
333C4×D71—48no—
334C4×D71—48no—
335C4×D71—48no—
336C4×D71C22⋊Q818yes—
337C4×D71C22×Q814yes—
338C4×D71C2×#4114yes—
339Dic142—48no—
340Dic142—48no—
341C8×C71—22no—
342C8×C71—22no—
343C71⋊C8—22no—
344C71⋊C8—22no—
345C22×C71—24no—
346C22×C71—48no—
347C22×C71—42no—
348C22×C71—42no—
349C22×C71C2×C22⋊Q812yes—
350C22×C71C2×AGL(1,ℤ/8)12yes—
351C22×C71#57512yes—
352C22×C71C23×D411yescharacteristic
353C2×D71—28no—
354C2×D71—22no—
355C2×D71—22no—
356C2×D71—24no—
357C2×D71—432no—
358C2×D71—48no—
359C2×D71—42no—
360C2×D71—42no—
361C2×D71C2×C22⋊Q814yes—
362C4×C71—22no—
363C4×C71—22no—
364C4×C71—42no—
365C4×C71—42no—
366C4×C71—42no—
367C4×C71C2×C22⋊Q812yes—
368C4×C71C23×Q811yescharacteristic
369C4×C71C22×#4111yescharacteristic
370Dic71—22no—
371Dic71—42no—
372Dic71—42no—
373Dic71—42no—
374Dic71C2×C22⋊Q814yes—
375Dic71C2×AGL(1,ℤ/8)14yes—
376C2×#3077—711nomaximal, Sylow
377C2×C71—44no—
378C2×C71#307714yescomplemented
379C2×C71C22×C22⋊Q811yescharacteristic
380C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
381C2×C71C2×#57511yescharacteristic
382D71—24no—
383D71—44no—
384C2×#533—711no—
385C22×C4×D4—711no—
386#3077—7116no—
387C2×#478—711no—
388C2×#478—711no—
389C2×#478—711no—
390C2×#478D7111yescharacteristic, complemented
391C2×#476—711no—
392C2×#476—711no—
393C2×#474—711no—
394C2×#474—711no—
395C2×#428—711no—
396C2×#428—711no—
397C2×#423—711no—
398C2×#418—711no—
399C2×#418—711no—
400C71C2×#307711yescharacteristic, complemented, Sylow
401C23×D4—711no—
402C24×C4—1421no—
403C22×M16—711no—
404C22×M16—711no—
405#533—718no—
406#533—1424no—
407C2×C4⋊Q8—711no—
408C2×C4⋊Q8—711no—
409C2×#125—711no—
410C2×#125C2×D7111yescharacteristic, complemented
411C2×C22⋊Q8—1421no—
412C2×C22⋊Q8—1421no—
413C2×C4×Q8—1421no—
414C2×C4×Q8—1421no—
415C2×C4×D4—711no—
416C2×C4×D4—718no—
417C2×C4×D4—711no—
418C2×C4×D4—711no—
419C2×C4×D4—1421no—
420C2×C4×D4—1424no—
421C2×C4×D4—1421no—
422C2×C4×D4C2×D7111yescharacteristic
423C2×#117—711no—
424C2×#117—711no—
425C22×C4⋊C4—711no—
426C22×C22⋊C4—1421no—
427C22×C42—711no—
428#478—718no—
429#478—718no—
430#478—718no—
431#478C2×D7118yescomplemented
432#476—718no—
433#476—718no—
434#474—718no—
435#474—718no—
436#428—718no—
437#428—718no—
438C2×#107—711no—
439C2×#107—711no—
440C2×#107—711no—
441C2×#107C2×D7111yescharacteristic, complemented
442C2×#106—711no—
443C2×#106—711no—
444C2×#106—711no—
445C2×#106C2×D7111yescharacteristic, complemented
446#423—718no—
447C2×C4⋊C8—711no—
448C2×C4⋊C8—711no—
449C2×C4⋊C8—711no—
450C2×C4⋊C8C2×D7111yescharacteristic, complemented
451#418—718no—
452#418—718no—
453C2×#102—711no—
454C2×#102—711no—
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×#102C2×D7111yescharacteristic
460C2×#102C2×D7111yescharacteristic
461C25—1421no—
462C22×Q8—1421no—
463C22×Q8—1421no—
464C22×D4—718no—
465C22×D4—714no—
466C22×D4—711no—
467C22×D4—1422no—
468C22×D4—1424no—
469C22×D4—1421no—
470C22×D4C22×D7111yescharacteristic
471C23×C4—21no—
472C23×C4—2848no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—1421no—
477C23×C4—1428no—
478C23×C4—1421no—
479C23×C4—1421no—
480C23×C4—1421no—
481C2×M16—714no—
482C2×M16—714no—
483C2×M16—1424no—
484C2×M16—1424no—
485C22×C8—711no—
486C22×C8—711no—
487C22×C8C22×D7111yescharacteristic
488C22×C8C22×D7111yescharacteristic
489C4⋊Q8—714no—
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492C4⋊Q8—1422no—
493#125—22no—
494#125—714no—
495#125—1422no—
496#125C22×D7114yescomplemented
497C22⋊Q8—1428no—
498C22⋊Q8—1428no—
499C4×Q8—1428no—
500C4×Q8—1428no—
501C4×D4—22no—
502C4×D4—714no—
503C4×D4—714no—
504C4×D4—714no—
505C4×D4—1428no—
506C4×D4—1422no—
507C4×D4—1428no—
508C4×D4—1422no—
509C4×D4—1422no—
510C4×D4C22×D7114yes—
511#117—714no—
512#117—714no—
513#117—1422no—
514#117—1422no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—711no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—714no—
521C2×C4⋊C4—1422no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4—1421no—
525C2×C4⋊C4—1421no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4C22×D7111yescharacteristic
528C2×C4⋊C4C22×D7111yescharacteristic
529C2×C4⋊C4C22×D7111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1428no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C22⋊C4—1421no—
535C2×C22⋊C4—1421no—
536C2×C22⋊C4—1421no—
537C2×C42—711no—
538C2×C42—711no—
539C2×C42—711no—
540C2×C42—714no—
541C2×C42—714no—
542C2×C42—1421no—
543C2×C42—1421no—
544C2×C42C22×D7111yescharacteristic
545#107—714no—
546#107—714no—
547#107—714no—
548#107C22×D7114yescomplemented
549#106—714no—
550#106—714no—
551#106—714no—
552#106C22×D7114yescomplemented
553C4⋊C8—714no—
554C4⋊C8—714no—
555C4⋊C8—714no—
556C4⋊C8C22×D7114yescomplemented
557#102—714no—
558#102—714no—
559#102—714no—
560#102—714no—
561#102—714no—
562#102—714no—
563#102C22×D7114yes—
564#102C22×D7114yes—
565C24—21no—
566C24—2844no—
567C24—2844no—
568C24—711no—
569C24—1424no—
570C24—1428no—
571C24—1421no—
572C2×Q8—2844no—
573C2×Q8—2844no—
574C2×Q8—1424no—
575C2×Q8—1424no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—7116no—
579C2×D4—714no—
580C2×D4—712no—
581C2×D4—1428no—
582C2×D4—14216no—
583C2×D4—1424no—
584C2×D4—1428no—
585C2×D4—1421no—
586C2×D4—1422no—
587C2×D4Q8×D7114yes—
588C2×D4C23×D7112yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—44no—
594C22×C4—2844no—
595C22×C4—2842no—
596C22×C4—2844no—
597C22×C4—2844no—
598C22×C4—28432no—
599C22×C4—2844no—
600C22×C4—714no—
601C22×C4—711no—
602C22×C4—711no—
603C22×C4—712no—
604C22×C4—714no—
605C22×C4—714no—
606C22×C4—712no—
607C22×C4—711no—
608C22×C4—714no—
609C22×C4—1424no—
610C22×C4—1424no—
611C22×C4—1424no—
612C22×C4—1424no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1424no—
617C22×C4D4×D7111yescharacteristic
618C22×C4D4×D7111yescharacteristic
619C22×C4C23×D7111yescharacteristic
620M16—1428no—
621M16—1428no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—712no—
625C2×C8—712no—
626C2×C8—1422no—
627C2×C8—1422no—
628C2×C8C23×D7112yes—
629C2×C8C23×D7112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—712no—
636C4⋊C4—712no—
637C4⋊C4—712no—
638C4⋊C4—1424no—
639C4⋊C4—1424no—
640C4⋊C4—1424no—
641C4⋊C4—1424no—
642C4⋊C4—1424no—
643C4⋊C4—1421no—
644C4⋊C4—1421no—
645C4⋊C4—1421no—
646C4⋊C4C23×D7112yes—
647C4⋊C4C23×D7112yes—
648C4⋊C4C23×D7112yes—
649C22⋊C4—24no—
650C22⋊C4—1424no—
651C22⋊C4—1424no—
652C22⋊C4—1424no—
653C22⋊C4—1424no—
654C22⋊C4—1424no—
655C42—714no—
656C42—714no—
657C42—712no—
658C42—712no—
659C42—1424no—
660C42—1424no—
661C42D4×D7112yes—
662C42C23×D7112yes—
663C23—22no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—2848no—
668C23—2848no—
669C23—28432no—
670C23—2842no—
671C23—2842no—
672C23—712no—
673C23—714no—
674C23—14216no—
675C23—1422no—
676C23—1424no—
677C23—1422no—
678C23—1422no—
679C23C2×D4×D7111yescharacteristic
680Q8—2848no—
681Q8—2848no—
682D4—22no—
683D4—24no—
684D4—714no—
685D4—14216no—
686D4—1422no—
687D4—1424no—
688D4C2×Q8×D7114yes—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—2848no—
699C2×C4—2844no—
700C2×C4—2848no—
701C2×C4—2848no—
702C2×C4—2842no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2848no—
706C2×C4—712no—
707C2×C4—712no—
708C2×C4—714no—
709C2×C4—714no—
710C2×C4—714no—
711C2×C4—714no—
712C2×C4—718no—
713C2×C4—712no—
714C2×C4—1428no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1422no—
719C2×C4C2×D4×D7112yes—
720C2×C4C2×D4×D7112yes—
721C2×C4C2×D4×D7111yescharacteristic
722C2×C4C2×Q8×D7112yes—
723C2×C4#41×D7112yes—
724C2×C4C24×D7111yescharacteristic
725C8—22no—
726C8—22no—
727C8—1422no—
728C8—1422no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—48no—
733C22—28432no—
734C22—2842no—
735C22—2842no—
736C22—2848no—
737C22—714no—
738C22—1424no—
739C22—1422no—
740C22—1422no—
741C22—1428no—
742C22C22⋊Q8×D7112yes—
743C22AGL(1,ℤ/8)×D7112yes—
744C22#1798679612yes—
745C22C22×D4×D7111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—2842no—
752C4—2842no—
753C4—2842no—
754C4—714no—
755C4—714no—
756C4—1422no—
757C4C22⋊Q8×D7112yes—
758C4C22×Q8×D7111yescharacteristic
759C4C2×#41×D7111yescharacteristic
760C2—44no—
761C2—2844no—
762C2—1424no—
763C2#2259813514yesdirect product factor
764C2C2×C22⋊Q8×D7111yescharacteristic
765C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
766C2C2×#1798679611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#478×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
hypercenterC2×#478D71
hypocenterC71C2×#3077
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×#17986555C2semidirect
3. #22598135C2direct (N × H)
4. C2×#17986300C2semidirect
5. C2×#17986299C2semidirect
6. C2×#17986296C2semidirect
7. C2×#17986288C2semidirect
8. C2×#17986287C2semidirect
9. C2×#17986278C2semidirect
10. C2×#17986277C2semidirect
11. C2×#17986040C2semidirect
12. C2×#17986038C2semidirect
13. C2×#17986021C2semidirect
16. C2×#478×C71C2semidirect
22. #17986555C22semidirect
23. C2×#14556127C22semidirect
24. C2×#14556127C22semidirect
25. C2×#14556120C22semidirect
42. #17986300C22semidirect
43. #17986299C22semidirect
44. #17986296C22semidirect
45. #17986288C22semidirect
46. #17986287C22semidirect
47. #17986278C22semidirect
48. #17986277C22semidirect
49. #17986040C22semidirect
50. #17986038C22semidirect
51. C2×#14556062C22semidirect
52. C2×#14556061C22semidirect
53. C2×#14556061C22semidirect
54. C2×#14556060C22semidirect
55. C2×#14556059C22semidirect
56. C2×#14556059C22semidirect
57. #17986021C22semidirect
58. C2×C4⋊(C71⋊C8)C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×Dic71⋊C8C22semidirect
69. C2×#125×C71C22semidirect
71. #478×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×C4⋊C8×C71C22semidirect
84. C2×D4×D71Q8semidirect
103. #14556127C23semidirect
104. #14556127C23semidirect
106. #14556120C23semidirect
146. #14556062C23semidirect
147. #14556061C23semidirect
148. #14556061C23semidirect
149. #14556060C23semidirect
150. #14556059C23semidirect
151. #14556059C23semidirect
152. C4⋊(C71⋊C8)C23semidirect
153. Dic71⋊C8C23semidirect
154. Dic71⋊C8C23semidirect
166. #125×C71C23semidirect
176. #107×C71C23semidirect
177. #106×C71C23semidirect
178. C4⋊C8×C71C23semidirect
199. D4×D71C2×Q8semidirect
378. C2×C71#3077semidirect
390. C2×#478D71semidirect
400. C71C2×#3077semidirect
410. C2×#125C2×D71semidirect
431. #478C2×D71semidirect
441. C2×#107C2×D71semidirect
445. C2×#106C2×D71semidirect
450. C2×C4⋊C8C2×D71semidirect
496. #125C22×D71semidirect
548. #107C22×D71semidirect
552. #106C22×D71semidirect
556. C4⋊C8C22×D71semidirect
763. C2#22598135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865552
C2×C4×D4×D712
#225981352
C2×#179863002
C2×#179862992
C2×#179862962
C2×#179862882
C2×#179862872
C2×#179862782
C2×#179862772
C2×#179860402
C2×#179860382
C2×#179860212
C2×#179860022
C2×#478×C712
C2×#307771