Finite Group Databasebeta

← C2×#22598527 #32865686

Subgroups — C2×#22598527 #32865686

Order 18176.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986622C211yesmaximal, characteristic, complemented
2C2×#17986473C211yesmaximal, characteristic, complemented
3#22598527C2116yesmaximal, direct product factor
4C2×#17986323C211yesmaximal, characteristic, complemented
5C2×#17986288C211yesmaximal, characteristic, complemented
6C2×#17986278C211yesmaximal, characteristic, complemented
7C2×#17986217C211yesmaximal, characteristic, complemented
8C2×#17986217C211yesmaximal, characteristic, complemented
9C2×#17986149C211yesmaximal, characteristic, complemented
10C2×#17986135C211yesmaximal, characteristic
11C2×#17986110C211yesmaximal, characteristic, complemented
12C2×#17986102C211yesmaximal, characteristic, complemented
13C2×#17986084C211yesmaximal, characteristic, complemented
14C2×#17986081C211yesmaximal, characteristic, complemented
15C2×#17986057C211yesmaximal, characteristic, complemented
16C2×#485×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×D568C2211yescharacteristic
21C22×D568C2211yescharacteristic
22#17986622—24no—
23#17986622C2218yescomplemented
24C2×#14556127C2211yescharacteristic, complemented
25C2×#14556123—21no—
26C2×#14556117C2211yescharacteristic, complemented
27C2×#14556114—21no—
28C2×#14556110—21no—
29C2×#14556108—21no—
30C2×#14556102C2211yescharacteristic
31#17986473—24no—
32#17986473C2218yescomplemented
33C2×Q8×Dic71C2211yescharacteristic, complemented
34C2×C4×D284—21no—
35C2×C4×D284—21no—
36C2×#14556090C2211yescharacteristic
37C2×#14556090C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×#14556090C2211yescharacteristic
40C2×#14556090C2211yescharacteristic, complemented
41C2×#14556087C2211yescharacteristic
42C2×C22⋊C4×D71—21no—
43C2×C22⋊C4×D71—21no—
44#17986323C2218yescomplemented
45#17986288C2218yescomplemented
46#17986278C2218yescomplemented
47#17986217C2218yescomplemented
48#17986217C2218yescomplemented
49#17986149C2218yescomplemented
50#17986135C2218yes—
51#17986110C2218yescomplemented
52#17986102C2218yescomplemented
53#17986084C2218yescomplemented
54#17986081C2218yescomplemented
55#17986057C2218yescomplemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556050C2211yescharacteristic
61C2×#14556050C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic, complemented
65C2×#14556048C2211yescharacteristic, complemented
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×#14556038C2211yescharacteristic, complemented
68C2×C8×Dic71C2211yescharacteristic, complemented
69C2×C22⋊Q8×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71#485×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic, complemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×C22⋊C8×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142—21no—
79C22×D284—24no—
80C22×D284—24no—
81C22×D284—21no—
82C22×D284—22no—
83C22×D284C2314yes—
84C22×D284C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×D284C2311yescharacteristic
87C22×C22⋊D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—21no—
93C2×#11765852—24no—
94C2×#11765852—24no—
95C2×#11765852C2314yes—
96C2×#11765852C2314yes—
97C2×D568—24no—
98C2×D568—24no—
99C2×D568C2314yes—
100C2×D568C2314yes—
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103#14556127—22no—
104#14556127C2314yescomplemented
105#14556123—28no—
106#14556117—22no—
107#14556117C2314yescomplemented
108#14556114—28no—
109#14556110—28no—
110#14556108—28no—
111#14556102—22no—
112#14556102C2314yes—
113Q8×Dic71—22no—
114Q8×Dic71C2314yescomplemented
115C4×D284—28no—
116C4×D284—28no—
117#14556090—22no—
118#14556090—22no—
119#14556090—22no—
120#14556090—22no—
121#14556090—22no—
122#14556090C2314yes—
123#14556090C2314yes—
124#14556090C2314yes—
125#14556090C2314yes—
126#14556090C2314yescomplemented
127#14556087D414yes—
128#14556087C2314yes—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71D411yescharacteristic
131C2×C4⋊Dic71D411yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×Dic71⋊C4—21no—
134C2×C22⋊Dic71D411yescharacteristic
135C2×C22⋊Dic71D411yescharacteristic
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—
143C2×(C2×D71)⋊C4—21no—
144C22⋊C4×D71—28no—
145C22⋊C4×D71—28no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71C2311yescharacteristic
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556059C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556050C2314yes—
154#14556050C2314yes—
155#14556048C2314yes—
156#14556048C2314yes—
157#14556048C2314yescomplemented
158#14556048C2314yescomplemented
159C22⋊(C71⋊C8)C2314yes—
160#14556038C2314yescomplemented
161C8×Dic71C2314yescomplemented
162C22×Q8×C71C2311yescharacteristic
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22⋊Q8×C71—22no—
167C22⋊Q8×C71C2314yes—
168#117×C71—22no—
169#117×C71C2314yes—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C42×C71—21no—
177#107×C71C2314yescomplemented
178#106×C71C2314yescomplemented
179#103×C71C2314yescomplemented
180#103×C71C2314yescomplemented
181C22⋊C8×C71C2314yes—
182C23×D71—21no—
183C23×D71—21no—
184C23×D71—28no—
185C23×D71—24no—
186C23×D71—21no—
187C23×D71—82no—
188C23×D71—82no—
189C2×Dic142—24no—
190C2×Dic142—82no—
191C2×D284—28no—
192C2×D284—216no—
193C2×D284—21no—
194C2×D284—21no—
195C2×D284—24no—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—28no—
199C2×D284—28no—
200C2×D284—22no—
201C2×D284—22no—
202C2×D284—21no—
203C2×D284#4114yes—
204C2×D284#4114yes—
205C2×D284C2412yes—
206C2×D284C2412yes—
207C2×D284C2412yes—
208C2×C22⋊D71—24no—
209C2×C22⋊D71—82no—
210C22×Dic71—21no—
211C22×Dic71C2×D411yescharacteristic
212C22×Dic71C2×D411yescharacteristic
213C22×Dic71C2×D411yescharacteristic
214C22×Dic71C2×D411yescharacteristic
215C2×C4×D71—24no—
216C2×C4×D71—24no—
217C2×C4×D71—24no—
218C2×C4×D71—24no—
219C2×C4×D71—24no—
220C2×C4×D71—82no—
221C2×C4×D71—82no—
222C2×C4×D71—82no—
223C2×C4×D71—82no—
224C2×C4×D71—82no—
225#11765852—28no—
226#11765852—28no—
227D568—28no—
228D568—28no—
229C2×C71⋊C8—22no—
230C2×C71⋊C8—22no—
231C2×C71⋊C8C2412yes—
232C2×C71⋊C8C2412yes—
233C4⋊Dic71—21no—
234C4⋊Dic71—24no—
235C4⋊Dic71C2×D414yes—
236C4⋊Dic71C2×D414yes—
237C4⋊Dic71C2412yes—
238Dic71⋊C4—24no—
239C22⋊Dic71C2×D414yes—
240C22⋊Dic71C2×D414yes—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4—24no—
245(C2×D71)⋊C4—24no—
246(C2×D71)⋊C4—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249C4×Dic71—24no—
250C4×Dic71C2×D412yes—
251C4×Dic71C2×D412yes—
252C4×Dic71C2412yes—
253C4×Dic71C2412yes—
254C24×C71C2×D411yescharacteristic
255C2×Q8×C71—21no—
256C2×Q8×C71—22no—
257C2×Q8×C71—22no—
258C2×Q8×C71C2412yes—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2411yescharacteristic
269C2×C8×C71—22no—
270C2×C8×C71—22no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C4⋊C4×C71—24no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71C2412yes—
278C4⋊C4×C71C2412yes—
279C4⋊C4×C71C2412yes—
280C22⋊C4×C71—24no—
281C22⋊C4×C71—24no—
282C42×C71—24no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71C22×D412yes—
287C23×C71C22×D411yescharacteristic
288C22×D71—24no—
289C22×D71—24no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—216no—
293C22×D71—22no—
294C22×D71—42no—
295C22×D71—42no—
296C22×D71—42no—
297C22×D71—42no—
298C22×D71—42no—
299C22×D71—42no—
300C22×D71—42no—
301C22×D71—84no—
302C22×D71—84no—
303C22×D71—816no—
304Q8×C71—22no—
305Q8×C71—22no—
306Q8×C71—42no—
307C2×C4×C71—22no—
308C2×C4×C71—24no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D411yescharacteristic
321C2×C4×C71C2×#4112yes—
322C2×C4×C71C2×#4112yes—
323C2×C4×C71C2511yescharacteristic
324C22⋊D71—84no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—42no—
331C2×Dic71C22×D412yes—
332C2×Dic71C22×D412yes—
333C2×Dic71C22×D412yes—
334C2×Dic71C22×D412yes—
335D284—216no—
336D284—24no—
337D284—24no—
338D284—22no—
339D284—22no—
340D284—22no—
341D284—22no—
342D284—42no—
343D284C2×#4114yes—
344D284C2×#4114yes—
345C4×D71—84no—
346C4×D71—84no—
347C4×D71—84no—
348C4×D71—84no—
349C4×D71—84no—
350Dic142—84no—
351C8×C71—22no—
352C8×C71—22no—
353C71⋊C8—22no—
354C71⋊C8—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71—44no—
359C22×C71#52512yes—
360C22×C71#57612yes—
361C22×C71#57712yes—
362C22×C71C23×D411yescharacteristic
363C2×D71—24no—
364C2×D71—24no—
365C2×D71—48no—
366C2×D71—48no—
367C2×D71—42no—
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—816no—
375C2×D71—84no—
376C4×C71—22no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71#52512yes—
382C4×C71C22×#4111yescharacteristic
383C4×C71C22×#4111yescharacteristic
384Dic71—22no—
385Dic71—22no—
386Dic71—22no—
387Dic71—22no—
388Dic71—42no—
389C2×#3118—711nomaximal, Sylow
390C2×C71—42no—
391C2×C71#311814yescomplemented
392C2×C71C2×#52511yescharacteristic
393C2×C71C2×#57611yescharacteristic
394C2×C71C2×#57711yescharacteristic
395D71—44no—
396D71—44no—
397D71—82no—
398C2×#542—711no—
399C2×#518—711no—
400#3118—7116no—
401C2×#485D7111yescharacteristic, complemented
402C2×#482—711no—
403C2×#476—711no—
404C2×#474—711no—
405C2×#463—711no—
406C2×#463—711no—
407C2×#450—711no—
408C2×#447—711no—
409C2×#442—711no—
410C2×#440—711no—
411C2×C4×SD16—711no—
412C2×C4×D8—711no—
413C2×#433—711no—
414C71C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—711no—
416C22×SD16—711no—
417C22×SD16—711no—
418C22×D8—711no—
419C22×D8—711no—
420#542—718no—
421#542—1424no—
422C2×C4⋊Q8—711no—
423C2×#126—1421no—
424C2×#124—711no—
425C2×#124—1421no—
426C2×#123—1421no—
427C2×C22⋊Q8—1421no—
428C2×C22⋊Q8C2×D7111yescharacteristic
429C2×#121—711no—
430#518—718no—
431#518—1424no—
432C2×C4×Q8—711no—
433C2×C4×D4—711no—
434C2×C4×D4—711no—
435C2×C4×D4—711no—
436C2×C4×D4—711no—
437C2×C4×D4—711no—
438C2×C4×D4—1421no—
439C2×C4×D4—1421no—
440C2×#117—711no—
441C2×#117C2×D7111yescharacteristic
442C22×C22⋊C4—1421no—
443C22×C22⋊C4—1421no—
444#485C2×D7118yescomplemented
445#482—718no—
446#476—718no—
447#474—718no—
448#463—718no—
449#463—718no—
450#450—718no—
451#447—718no—
452#442—718no—
453#440—718no—
454C4×SD16—718no—
455C4×D8—718no—
456#433—718no—
457C2×#107—711no—
458C2×#107C2×D7111yescharacteristic, complemented
459C2×#106—711no—
460C2×#106C2×D7111yescharacteristic, complemented
461C2×C4⋊C8—711no—
462C2×C4⋊C8—711no—
463C2×#103C2×D7111yescharacteristic, complemented
464C2×#103C2×D7111yescharacteristic, complemented
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×C22⋊C8—711no—
472C2×C22⋊C8C2×D7111yescharacteristic
473C2×#97—711no—
474C2×C4×C8—711no—
475C25—1421no—
476C22×Q8—1421no—
477C22×Q8C22×D7111yescharacteristic
478C22×D4—711no—
479C22×D4—711no—
480C22×D4—711no—
481C22×D4—714no—
482C22×D4—1424no—
483C22×D4—1424no—
484C22×D4—1421no—
485C22×D4—1421no—
486C22×D4—1422no—
487C23×C4—1421no—
488C23×C4—1421no—
489C23×C4—1421no—
490C23×C4—1421no—
491C23×C4—1421no—
492C23×C4C22×D7111yescharacteristic
493C2×SD16—714no—
494C2×SD16—714no—
495C2×SD16—1424no—
496C2×SD16—1424no—
497C2×D8—714no—
498C2×D8—714no—
499C2×D8—1424no—
500C2×D8—1424no—
501C22×C8—711no—
502C22×C8—711no—
503C22×C8C22×D7111yescharacteristic
504C22×C8C22×D7111yescharacteristic
505C4⋊Q8—714no—
506C4⋊Q8—1422no—
507#126—1428no—
508#124—714no—
509#124—1422no—
510#124—1428no—
511#123—1428no—
512C22⋊Q8—22no—
513C22⋊Q8—1428no—
514C22⋊Q8C22×D7114yes—
515#121—714no—
516#121—1422no—
517C4×Q8—714no—
518C4×Q8—1422no—
519C4×D4—714no—
520C4×D4—714no—
521C4×D4—714no—
522C4×D4—714no—
523C4×D4—714no—
524C4×D4—1428no—
525C4×D4—1428no—
526C4×D4—1422no—
527C4×D4—1422no—
528C4×D4—1422no—
529C4×D4—1422no—
530C4×D4—1422no—
531#117—22no—
532#117—714no—
533#117—714no—
534#117C22×D7114yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—711no—
538C2×C4⋊C4—711no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4C22×D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—711no—
547C2×C22⋊C4—711no—
548C2×C22⋊C4—1428no—
549C2×C22⋊C4—1428no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4—1421no—
558C2×C42—21no—
559C2×C42—711no—
560C2×C42—711no—
561C2×C42—1421no—
562#107—714no—
563#107C22×D7114yescomplemented
564#106—714no—
565#106C22×D7114yescomplemented
566C4⋊C8—714no—
567C4⋊C8—714no—
568#103C22×D7114yescomplemented
569#103C22×D7114yescomplemented
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576C22⋊C8—714no—
577C22⋊C8C22×D7114yes—
578#97—714no—
579C4×C8—714no—
580C24—5682no—
581C24—5682no—
582C24—1428no—
583C24—1421no—
584C24—1421no—
585C24—1421no—
586C24—1424no—
587C24D4×D7111yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—5682no—
592C2×Q8—1424no—
593C2×Q8C23×D7112yes—
594C2×D4—5682no—
595C2×D4—714no—
596C2×D4—714no—
597C2×D4—712no—
598C2×D4—712no—
599C2×D4—712no—
600C2×D4—1428no—
601C2×D4—1428no—
602C2×D4—1428no—
603C2×D4—14216no—
604C2×D4—1424no—
605C2×D4—1421no—
606C2×D4—1424no—
607C2×D4—1421no—
608C2×D4—1421no—
609C2×D4—1422no—
610C2×D4—1422no—
611C2×D4—1422no—
612C2×D4—1422no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—5682no—
620C22×C4—5682no—
621C22×C4—5682no—
622C22×C4—5682no—
623C22×C4—5682no—
624C22×C4—711no—
625C22×C4—711no—
626C22×C4—711no—
627C22×C4—711no—
628C22×C4—1424no—
629C22×C4—1424no—
630C22×C4—1424no—
631C22×C4—1424no—
632C22×C4—1424no—
633C22×C4—1421no—
634C22×C4D4×D7112yes—
635C22×C4D4×D7111yescharacteristic
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638SD16—1428no—
639SD16—1428no—
640D8—1428no—
641D8—1428no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—1422no—
647C2×C8—1422no—
648C2×C8C23×D7112yes—
649C2×C8C23×D7112yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—714no—
655C4⋊C4—714no—
656C4⋊C4—712no—
657C4⋊C4—1424no—
658C4⋊C4—1424no—
659C4⋊C4—1421no—
660C4⋊C4C23×D7112yes—
661C4⋊C4C23×D7112yes—
662C4⋊C4C23×D7112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—714no—
666C22⋊C4—714no—
667C22⋊C4—1424no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C22⋊C4—1424no—
671C22⋊C4—1424no—
672C22⋊C4—1424no—
673C22⋊C4—1424no—
674C22⋊C4—1424no—
675C42—24no—
676C42—712no—
677C42—712no—
678C42—712no—
679C42—712no—
680C42—1424no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—2842no—
685C23—2842no—
686C23—2842no—
687C23—2842no—
688C23—2842no—
689C23—2842no—
690C23—2842no—
691C23—5684no—
692C23—5684no—
693C23—56816no—
694C23—14216no—
695C23—1422no—
696C23—1422no—
697C23—1422no—
698C23—1424no—
699C23—1424no—
700C23C2×D4×D7112yes—
701C23C2×D4×D7111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—5684no—
706D4—2842no—
707D4—5684no—
708D4—714no—
709D4—714no—
710D4—14216no—
711D4—1422no—
712D4—1422no—
713D4—1422no—
714D4—1422no—
715D4—1424no—
716D4—1424no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—2842no—
730C2×C4—5684no—
731C2×C4—5684no—
732C2×C4—5684no—
733C2×C4—5684no—
734C2×C4—5684no—
735C2×C4—712no—
736C2×C4—712no—
737C2×C4—712no—
738C2×C4—712no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4C2×D4×D7112yes—
745C2×C4C2×D4×D7111yescharacteristic
746C2×C4#41×D7112yes—
747C2×C4#41×D7112yes—
748C2×C4C24×D7111yescharacteristic
749C8—22no—
750C8—22no—
751C8—1422no—
752C8—1422no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—2842no—
758C22—2842no—
759C22—2842no—
760C22—2842no—
761C22—2848no—
762C22—2848no—
763C22—2842no—
764C22—2842no—
765C22—2842no—
766C22—56816no—
767C22—5684no—
768C22—1424no—
769C22—1424no—
770C22#1798650712yes—
771C22#1798680112yes—
772C22#1798680812yes—
773C22C22×D4×D7111yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2842no—
780C4—1422no—
781C4—1422no—
782C4—1422no—
783C4—1422no—
784C4#1798650712yes—
785C4C2×#41×D7111yescharacteristic
786C4C2×#41×D7111yescharacteristic
787C2—42no—
788C2—2844no—
789C2—2844no—
790C2—5682no—
791C2#2259852714yesdirect product factor
792C2C2×#1798650711yescharacteristic
793C2C2×#1798680111yescharacteristic
794C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#485×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986135C2
hypercenterC2×#485D71
hypocenterC71C2×#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#17986622C2semidirect
2. C2×#17986473C2semidirect
3. #22598527C2direct (N × H)
4. C2×#17986323C2semidirect
5. C2×#17986288C2semidirect
6. C2×#17986278C2semidirect
7. C2×#17986217C2semidirect
8. C2×#17986217C2semidirect
9. C2×#17986149C2semidirect
11. C2×#17986110C2semidirect
12. C2×#17986102C2semidirect
13. C2×#17986084C2semidirect
14. C2×#17986081C2semidirect
15. C2×#17986057C2semidirect
16. C2×#485×C71C2semidirect
23. #17986622C22semidirect
24. C2×#14556127C22semidirect
26. C2×#14556117C22semidirect
32. #17986473C22semidirect
33. C2×Q8×Dic71C22semidirect
40. C2×#14556090C22semidirect
44. #17986323C22semidirect
45. #17986288C22semidirect
46. #17986278C22semidirect
47. #17986217C22semidirect
48. #17986217C22semidirect
49. #17986149C22semidirect
51. #17986110C22semidirect
52. #17986102C22semidirect
53. #17986084C22semidirect
54. #17986081C22semidirect
55. #17986057C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
64. C2×#14556048C22semidirect
65. C2×#14556048C22semidirect
67. C2×#14556038C22semidirect
68. C2×C8×Dic71C22semidirect
71. #485×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×#103×C71C22semidirect
75. C2×#103×C71C22semidirect
104. #14556127C23semidirect
107. #14556117C23semidirect
114. Q8×Dic71C23semidirect
126. #14556090C23semidirect
149. #14556061C23semidirect
150. #14556059C23semidirect
151. Dic71⋊C8C23semidirect
152. Dic71⋊C8C23semidirect
157. #14556048C23semidirect
158. #14556048C23semidirect
160. #14556038C23semidirect
161. C8×Dic71C23semidirect
177. #107×C71C23semidirect
178. #106×C71C23semidirect
179. #103×C71C23semidirect
180. #103×C71C23semidirect
391. C2×C71#3118semidirect
401. C2×#485D71semidirect
414. C71C2×#3118semidirect
444. #485C2×D71semidirect
458. C2×#107C2×D71semidirect
460. C2×#106C2×D71semidirect
463. C2×#103C2×D71semidirect
464. C2×#103C2×D71semidirect
563. #107C22×D71semidirect
565. #106C22×D71semidirect
568. #103C22×D71semidirect
569. #103C22×D71semidirect
791. C2#22598527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866222
C2×#179864732
#225985272
C2×#179863232
C2×#179862882
C2×#179862782
C2×#179862172
C2×#179861492
C2×#179861352
C2×#179861102
C2×#179861022
C2×#179860842
C2×#179860812
C2×#179860572
C2×#485×C712
C2×#311871