Finite Group Databasebeta

← C2×#22598526 #32865685

Subgroups — C2×#22598526 #32865685

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×#17986620C211yesmaximal, characteristic, complemented
2C2×#17986473C211yesmaximal, characteristic, complemented
3#22598526C2116yesmaximal, direct product factor
4C2×#17986341C211yesmaximal, characteristic, complemented
5C2×#17986324C211yesmaximal, characteristic, complemented
6C2×#17986290C211yesmaximal, characteristic, complemented
7C2×#17986280C211yesmaximal, characteristic, complemented
8C2×#17986215C211yesmaximal, characteristic, complemented
9C2×#17986215C211yesmaximal, characteristic, complemented
10C2×#17986152C211yesmaximal, characteristic, complemented
11C2×#17986135C211yesmaximal, characteristic
12C2×#17986112C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×C4×#11765854C211yesmaximal, characteristic, complemented
15C2×C4×D568C211yesmaximal, characteristic, complemented
16C2×#433×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×#11765854C2211yescharacteristic
19C22×#11765854C2211yescharacteristic
20C22×D568C2211yescharacteristic
21C22×D568C2211yescharacteristic
22#17986620—24no—
23#17986620C2218yescomplemented
24C2×#14556128C2211yescharacteristic, complemented
25C2×#14556123—21no—
26C2×#14556116C2211yescharacteristic, complemented
27C2×#14556114—21no—
28C2×#14556110—21no—
29C2×#14556107C2211yescharacteristic
30C2×#14556106—21no—
31C2×#14556102C2211yescharacteristic
32#17986473—24no—
33#17986473C2218yescomplemented
34C2×C4×Dic142C2211yescharacteristic, complemented
35C2×C4×D284C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37C2×C4×D284C2211yescharacteristic
38C2×C4×D284C2211yescharacteristic
39C2×C4×D284C2211yescharacteristic, complemented
40C2×#14556090—21no—
41C2×#14556090—21no—
42C2×#14556087C2211yescharacteristic
43C2×C22⋊C4×D71—21no—
44C2×C22⋊C4×D71—21no—
45#17986341C2218yescomplemented
46#17986324C2218yescomplemented
47#17986290C2218yescomplemented
48#17986280C2218yescomplemented
49#17986215C2218yescomplemented
50#17986215C2218yescomplemented
51#17986152C2218yescomplemented
52#17986135C2218yes—
53#17986112C2218yescomplemented
54#17986101C2218yescomplemented
55C4×#11765854C2218yescomplemented
56C4×D568C2218yescomplemented
57C2×#14556062C2211yescharacteristic, complemented
58C2×#14556062C2211yescharacteristic, complemented
59C2×#14556060C2211yescharacteristic, complemented
60C2×#14556060C2211yescharacteristic, complemented
61C2×#14556053C2211yescharacteristic, complemented
62C2×#14556053C2211yescharacteristic, complemented
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic, complemented
68C2×#14556050C2211yescharacteristic, complemented
69C2×#117×C71C2211yescharacteristic
70#433×C71C2218yescomplemented
71C2×C4⋊C8×C71C2211yescharacteristic, complemented
72C2×C4⋊C8×C71C2211yescharacteristic, complemented
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×#97×C71C2211yescharacteristic, complemented
76C2×C4×C8×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×D284—24no—
81C22×D284—24no—
82C22×D284—21no—
83C22×D284—22no—
84C22×D284C2314yes—
85C22×D284C2311yescharacteristic
86C22×D284C2311yescharacteristic
87C22×D284C2311yescharacteristic
88C22×C22⋊D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—21no—
93C22×C4×D71—21no—
94C2×#11765854—24no—
95C2×#11765854—24no—
96C2×#11765854C2314yes—
97C2×#11765854C2314yes—
98C2×D568—24no—
99C2×D568—24no—
100C2×D568C2314yes—
101C2×D568C2314yes—
102#14556128—22no—
103#14556128C2314yescomplemented
104#14556123—28no—
105#14556116—22no—
106#14556116C2314yescomplemented
107#14556114—28no—
108#14556110—28no—
109#14556107—22no—
110#14556107C2314yes—
111#14556106—28no—
112#14556102—22no—
113#14556102C2314yes—
114C4×Dic142—22no—
115C4×Dic142C2314yescomplemented
116C4×D284—22no—
117C4×D284—22no—
118C4×D284—22no—
119C4×D284—22no—
120C4×D284—22no—
121C4×D284C2314yes—
122C4×D284C2314yes—
123C4×D284C2314yes—
124C4×D284C2314yes—
125C4×D284C2314yescomplemented
126#14556090—28no—
127#14556090—28no—
128#14556087—22no—
129#14556087C2314yes—
130C2×C4⋊Dic71—21no—
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—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—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C22⋊C4×D71—28no—
148C22⋊C4×D71—28no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yescomplemented
152#14556062C2314yescomplemented
153#14556060C2314yescomplemented
154#14556060C2314yescomplemented
155#14556053C2314yescomplemented
156#14556053C2314yescomplemented
157#14556050C2314yes—
158#14556050C2314yes—
159#14556050C2314yes—
160#14556050C2314yes—
161#14556050C2314yescomplemented
162#14556050C2314yescomplemented
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168#117×C71D414yes—
169#117×C71C2314yes—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C4⋊C8×C71C2314yescomplemented
177C4⋊C8×C71C2314yescomplemented
178C22⋊C8×C71C2314yes—
179C22⋊C8×C71C2314yes—
180#97×C71C2314yescomplemented
181C4×C8×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—21no—
184C23×D71—28no—
185C23×D71—24no—
186C23×D71—21no—
187C23×D71—82no—
188C23×D71—82no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—21no—
192C2×Dic142—24no—
193C2×Dic142—82no—
194C2×Dic142C2412yes—
195C2×D284—28no—
196C2×D284—216no—
197C2×D284—24no—
198C2×D284—21no—
199C2×D284—21no—
200C2×D284—22no—
201C2×D284—22no—
202C2×D284—28no—
203C2×D284—28no—
204C2×D284—22no—
205C2×D284—22no—
206C2×D284—21no—
207C2×D284#4114yes—
208C2×D284#4114yes—
209C2×D284C2412yes—
210C2×D284C2412yes—
211C2×D284C2412yes—
212C2×C22⋊D71—24no—
213C2×C22⋊D71—82no—
214C22×Dic71—21no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C2×C4×D71—24no—
220C2×C4×D71—24no—
221C2×C4×D71—24no—
222C2×C4×D71—24no—
223C2×C4×D71—24no—
224C2×C4×D71—82no—
225C2×C4×D71—82no—
226C2×C4×D71—82no—
227C2×C4×D71—82no—
228C2×C4×D71—82no—
229#11765854—28no—
230#11765854—28no—
231D568—28no—
232D568—28no—
233C4⋊Dic71—24no—
234C4⋊Dic71—21no—
235C4⋊Dic71—21no—
236C4⋊Dic71—21no—
237C4⋊Dic71—21no—
238C4⋊Dic71C2412yes—
239C4⋊Dic71C2412yes—
240C4⋊Dic71C2412yes—
241C4⋊Dic71C2412yes—
242Dic71⋊C4—24no—
243Dic71⋊C4—24no—
244C22⋊Dic71—24no—
245C22⋊Dic71—24no—
246(C2×D71)⋊C4—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×Dic71—24no—
256C24×C71C2×D411yescharacteristic
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D412yes—
265C22×C4×C71C2412yes—
266C22×C4×C71C2411yescharacteristic
267C2×C8×C71—22no—
268C2×C8×C71—22no—
269C2×C8×C71—22no—
270C2×C8×C71—22no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C2×C8×C71C2412yes—
274C2×C8×C71C2412yes—
275C4⋊C4×C71C2×D414yes—
276C4⋊C4×C71C2×D414yes—
277C22⋊C4×C71C2×D414yes—
278C22⋊C4×C71C2×D414yes—
279C42×C71C2×D412yes—
280C42×C71C2×D412yes—
281C42×C71C2412yes—
282C42×C71C2412yes—
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—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—24no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D411yescharacteristic
318C2×C4×C71C2×#4112yes—
319C2×C4×C71C2×#4112yes—
320C2×C4×C71C2511yescharacteristic
321C22⋊D71—84no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71—42no—
332D284—216no—
333D284—24no—
334D284—24no—
335D284—22no—
336D284—22no—
337D284—22no—
338D284—22no—
339D284—42no—
340D284C2×#4114yes—
341D284C2×#4114yes—
342C4×D71—84no—
343C4×D71—84no—
344C4×D71—84no—
345C4×D71—84no—
346C4×D71—84no—
347Dic142—22no—
348Dic142—22no—
349Dic142—42no—
350Dic142—84no—
351C8×C71—22no—
352C8×C71—22no—
353C8×C71—22no—
354C8×C71—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—22no—
378C4×C71—22no—
379C4×C71—22no—
380C4×C71—22no—
381C4×C71#52512yes—
382C4×C71C22×#4111yescharacteristic
383C4×C71C22×#4111yescharacteristic
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387Dic71—42no—
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×#485—711no—
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×#433D7111yescharacteristic, complemented
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—711no—
428C2×C22⋊Q8—1421no—
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#485—718no—
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#433C2×D7118yescomplemented
457C2×#107—711no—
458C2×#107—711no—
459C2×#106—711no—
460C2×#106—711no—
461C2×C4⋊C8C2×D7111yescharacteristic, complemented
462C2×C4⋊C8C2×D7111yescharacteristic, complemented
463C2×#103—711no—
464C2×#103—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×C22⋊C8C2×D7111yescharacteristic
472C2×C22⋊C8C2×D7111yescharacteristic
473C2×#97C2×D7111yescharacteristic, complemented
474C2×C4×C8C2×D7111yescharacteristic, complemented
475C25—1421no—
476C22×Q8—711no—
477C22×Q8—1421no—
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×C8C22×D7111yescharacteristic
502C22×C8C22×D7111yescharacteristic
503C22×C8C22×D7111yescharacteristic
504C22×C8C22×D7111yescharacteristic
505C4⋊Q8—714no—
506C4⋊Q8—1422no—
507#126—1428no—
508#124—714no—
509#124—1428no—
510#124—1422no—
511#123—1428no—
512C22⋊Q8—714no—
513C22⋊Q8—1422no—
514C22⋊Q8—1428no—
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—714no—
532#117—1422no—
533#117D28414yes—
534#117C22×D7114yes—
535C2×C4⋊C4—711no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—711no—
538C2×C4⋊C4—711no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4D28411yescharacteristic
543C2×C4⋊C4D28411yescharacteristic
544C2×C22⋊C4—1421no—
545C2×C22⋊C4—1421no—
546C2×C22⋊C4—1421no—
547C2×C22⋊C4—1421no—
548C2×C22⋊C4—1421no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1428no—
555C2×C22⋊C4—1428no—
556C2×C22⋊C4D28411yescharacteristic
557C2×C22⋊C4D28411yescharacteristic
558C2×C42—1421no—
559C2×C42—1421no—
560C2×C42C22×D7111yescharacteristic
561C2×C42C22×D7111yescharacteristic
562#107—714no—
563#107—714no—
564#106—714no—
565#106—714no—
566C4⋊C8C22×D7114yescomplemented
567C4⋊C8C22×D7114yescomplemented
568#103—714no—
569#103—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576C22⋊C8C22×D7114yes—
577C22⋊C8C22×D7114yes—
578#97C22×D7114yescomplemented
579C4×C8C22×D7114yescomplemented
580C24—5682no—
581C24—5682no—
582C24—1428no—
583C24—1421no—
584C24—1421no—
585C24—1421no—
586C24—1424no—
587C24C2×D28411yescharacteristic
588C2×Q8—5682no—
589C2×Q8—712no—
590C2×Q8—1422no—
591C2×Q8—1422no—
592C2×Q8—1421no—
593C2×Q8—1424no—
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—5682no—
616C22×C4—5682no—
617C22×C4—5682no—
618C22×C4—5682no—
619C22×C4—5682no—
620C22×C4—1421no—
621C22×C4—1421no—
622C22×C4—1421no—
623C22×C4—1421no—
624C22×C4—1421no—
625C22×C4—1424no—
626C22×C4—1424no—
627C22×C4—1424no—
628C22×C4—1424no—
629C22×C4—1424no—
630C22×C4C2×D28412yes—
631C22×C4C2×D28411yescharacteristic
632C22×C4C2×D28411yescharacteristic
633C22×C4C2×D28411yescharacteristic
634C22×C4C2×D28411yescharacteristic
635C22×C4C2×D28411yescharacteristic
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638SD16—1428no—
639SD16—1428no—
640D8—1428no—
641D8—1428no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D7112yes—
647C2×C8C23×D7112yes—
648C2×C8C23×D7112yes—
649C2×C8C23×D7112yes—
650C4⋊C4—712no—
651C4⋊C4—712no—
652C4⋊C4—712no—
653C4⋊C4—712no—
654C4⋊C4—1424no—
655C4⋊C4—1424no—
656C4⋊C4—1421no—
657C4⋊C4—1421no—
658C4⋊C4—1421no—
659C4⋊C4—1421no—
660C4⋊C4—1424no—
661C4⋊C4C2×D28414yes—
662C4⋊C4C2×D28414yes—
663C22⋊C4—1424no—
664C22⋊C4—1424no—
665C22⋊C4—1424no—
666C22⋊C4—1424no—
667C22⋊C4—1424no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C22⋊C4—1424no—
671C22⋊C4—1424no—
672C22⋊C4—1424no—
673C22⋊C4C2×D28414yes—
674C22⋊C4C2×D28414yes—
675C42—1424no—
676C42—1424no—
677C42C2×D28412yes—
678C42C2×D28412yes—
679C42C23×D7112yes—
680C42C23×D7112yes—
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—
700C23C22×D28412yes—
701C23C22×D28411yescharacteristic
702Q8—2842no—
703Q8—5684no—
704Q8—1422no—
705Q8—1422no—
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—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—2842no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—2842no—
730C2×C4—5684no—
731C2×C4—5684no—
732C2×C4—5684no—
733C2×C4—5684no—
734C2×C4—5684no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4C22×D28412yes—
741C2×C4C22×D28412yes—
742C2×C4C22×D28412yes—
743C2×C4C22×D28412yes—
744C2×C4C22×D28412yes—
745C2×C4C22×D28411yescharacteristic
746C2×C4#41×D7112yes—
747C2×C4#41×D7112yes—
748C2×C4C24×D7111yescharacteristic
749C8—22no—
750C8—22no—
751C8—22no—
752C8—22no—
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#1798651112yes—
771C22#1798680412yes—
772C22#1798681112yes—
773C22C23×D28411yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2842no—
780C4—2842no—
781C4—2842no—
782C4—2842no—
783C4—2842no—
784C4#1798651112yes—
785C4C2×#41×D7111yescharacteristic
786C4C2×#41×D7111yescharacteristic
787C2—42no—
788C2—2844no—
789C2—2844no—
790C2—5682no—
791C2#2259852614yesdirect product factor
792C2C2×#1798651111yescharacteristic
793C2C2×#1798680411yescharacteristic
794C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986135C2
hypercenterC2×#433D71
hypocenterC71C2×#3118
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. C2×#17986473C2semidirect
3. #22598526C2direct (N × H)
4. C2×#17986341C2semidirect
5. C2×#17986324C2semidirect
6. C2×#17986290C2semidirect
7. C2×#17986280C2semidirect
8. C2×#17986215C2semidirect
9. C2×#17986215C2semidirect
10. C2×#17986152C2semidirect
12. C2×#17986112C2semidirect
13. C2×#17986101C2semidirect
14. C2×C4×#11765854C2semidirect
15. C2×C4×D568C2semidirect
16. C2×#433×C71C2semidirect
23. #17986620C22semidirect
24. C2×#14556128C22semidirect
26. C2×#14556116C22semidirect
33. #17986473C22semidirect
34. C2×C4×Dic142C22semidirect
39. C2×C4×D284C22semidirect
45. #17986341C22semidirect
46. #17986324C22semidirect
47. #17986290C22semidirect
48. #17986280C22semidirect
49. #17986215C22semidirect
50. #17986215C22semidirect
51. #17986152C22semidirect
53. #17986112C22semidirect
54. #17986101C22semidirect
55. C4×#11765854C22semidirect
56. C4×D568C22semidirect
57. C2×#14556062C22semidirect
58. C2×#14556062C22semidirect
59. C2×#14556060C22semidirect
60. C2×#14556060C22semidirect
61. C2×#14556053C22semidirect
62. C2×#14556053C22semidirect
67. C2×#14556050C22semidirect
68. C2×#14556050C22semidirect
70. #433×C71C22semidirect
71. C2×C4⋊C8×C71C22semidirect
72. C2×C4⋊C8×C71C22semidirect
75. C2×#97×C71C22semidirect
76. C2×C4×C8×C71C22semidirect
103. #14556128C23semidirect
106. #14556116C23semidirect
115. C4×Dic142C23semidirect
125. C4×D284C23semidirect
151. #14556062C23semidirect
152. #14556062C23semidirect
153. #14556060C23semidirect
154. #14556060C23semidirect
155. #14556053C23semidirect
156. #14556053C23semidirect
161. #14556050C23semidirect
162. #14556050C23semidirect
176. C4⋊C8×C71C23semidirect
177. C4⋊C8×C71C23semidirect
180. #97×C71C23semidirect
181. C4×C8×C71C23semidirect
391. C2×C71#3118semidirect
413. C2×#433D71semidirect
414. C71C2×#3118semidirect
456. #433C2×D71semidirect
461. C2×C4⋊C8C2×D71semidirect
462. C2×C4⋊C8C2×D71semidirect
473. C2×#97C2×D71semidirect
474. C2×C4×C8C2×D71semidirect
566. C4⋊C8C22×D71semidirect
567. C4⋊C8C22×D71semidirect
578. #97C22×D71semidirect
579. C4×C8C22×D71semidirect
791. C2#22598526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
C2×#179864732
#225985262
C2×#179863412
C2×#179863242
C2×#179862902
C2×#179862802
C2×#179862152
C2×#179861522
C2×#179861352
C2×#179861122
C2×#179861012
C2×C4×#117658542
C2×C4×D5682
C2×#433×C712
C2×#311871