Finite Group Databasebeta

← C2×#22599640 #32869691

Subgroups — C2×#22599640 #32869691

Order 18176.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986627C211yesmaximal, characteristic, complemented
2C2×#17986620C211yesmaximal, characteristic
3#22599640C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986397C211yesmaximal, characteristic, complemented
6C2×#17986359C211yesmaximal, characteristic, complemented
7C2×#17986354C211yesmaximal, characteristic, complemented
8C2×#17986318C211yesmaximal, characteristic
9C2×#17986341C211yesmaximal, characteristic, complemented
10C2×#17986324C211yesmaximal, characteristic
11C2×#17986330C211yesmaximal, characteristic, complemented
12C2×#17986307C211yesmaximal, characteristic, complemented
13C2×#17986285C211yesmaximal, characteristic, complemented
14C2×#17986300C211yesmaximal, characteristic, complemented
15C2×#17986290C211yesmaximal, characteristic, complemented
16C2×#433×C71C211yesmaximal, characteristic, complemented
17#17986627—24no—
18#17986627C2218yescomplemented
19#17986620—24no—
20#17986620C2218yes—
21C2×#14556128C2211yescharacteristic
22C2×#14556128C2211yescharacteristic
23C2×#14556128C2211yescharacteristic
24C2×#14556127—21no—
25C2×#14556123—21no—
26C2×#14556120C2211yescharacteristic
27C2×#14556120C2211yescharacteristic
28C2×#14556119—21no—
29C2×#14556116C2211yescharacteristic
30C2×#14556114—21no—
31C2×#14556110—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556106—21no—
34C2×#14556105—21no—
35C2×#14556105—21no—
36C2×#14556102C2211yescharacteristic
37C2×C4×Dic142C2211yescharacteristic
38C2×C4×D284C2211yescharacteristic
39C2×#14556087C2211yescharacteristic
40C22×C4⋊Dic71C2211yescharacteristic
41#17986408C2218yescomplemented
42#17986397C2218yescomplemented
43#17986359C2218yescomplemented
44#17986354C2218yescomplemented
45#17986341C2218yescomplemented
46#17986330C2218yescomplemented
47#17986324C2218yes—
48#17986318C2218yes—
49#17986307C2218yescomplemented
50#17986300C2218yescomplemented
51#17986290C2218yescomplemented
52#17986285C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556060C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C2×#117×C71C2211yescharacteristic
70#433×C71C2218yescomplemented
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C4⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×#97×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142—21no—
80C22×Dic142C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C22⋊D71—21no—
83C23×Dic71—21no—
84C22×C4×D71—21no—
85#14556128—22no—
86#14556128—22no—
87#14556128—22no—
88#14556128C2314yes—
89#14556128C2314yes—
90#14556128C2314yes—
91#14556127—28no—
92#14556123—28no—
93#14556120—22no—
94#14556120—22no—
95#14556120C2314yes—
96#14556120C2314yes—
97#14556119—28no—
98#14556116—22no—
99#14556116C2314yes—
100#14556114—28no—
101#14556110—28no—
102#14556107—22no—
103#14556107C2314yes—
104#14556106—28no—
105#14556105—28no—
106#14556105—28no—
107#14556102—22no—
108#14556102C2314yes—
109C4×Dic142—22no—
110C4×Dic142C2314yes—
111C4×D284—22no—
112C4×D284C2314yes—
113#14556087—22no—
114#14556087C2314yes—
115C2×C4⋊Dic71—22no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71C2314yes—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141#14556062C2314yes—
142#14556062C2314yes—
143#14556060C2314yes—
144#14556060C2314yes—
145#14556060C2314yes—
146#14556060C2314yes—
147#14556060C2314yes—
148#14556060C2314yes—
149#14556053C2314yes—
150#14556053C2314yes—
151#14556053C2314yes—
152#14556053C2314yes—
153#14556050C2314yes—
154#14556050C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157C23×C4×C71C2311yescharacteristic
158C22×C8×C71C2311yescharacteristic
159C22×C8×C71C2311yescharacteristic
160C22×C8×C71C2311yescharacteristic
161C22×C8×C71C2311yescharacteristic
162#117×C71D414yes—
163#117×C71C2314yes—
164C2×C4⋊C4×C71D411yescharacteristic
165C2×C4⋊C4×C71D411yescharacteristic
166C2×C22⋊C4×C71D411yescharacteristic
167C2×C22⋊C4×C71D411yescharacteristic
168C2×C42×C71C2311yescharacteristic
169C2×C42×C71C2311yescharacteristic
170C4⋊C8×C71C2314yes—
171C4⋊C8×C71C2314yes—
172C22⋊C8×C71C2314yes—
173C22⋊C8×C71C2314yes—
174#97×C71C2314yes—
175C4×C8×C71C2314yes—
176C23×D71—21no—
177C2×Dic142—22no—
178C2×Dic142—22no—
179C2×Dic142—21no—
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—24no—
183C2×Dic142—82no—
184C2×Dic142—82no—
185C2×Dic142—82no—
186C2×Dic142C2412yes—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—21no—
190C2×D284C2412yes—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—82no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—24no—
201C22×Dic71—82no—
202C2×C4×D71—24no—
203C2×C4×D71—82no—
204C4⋊Dic71—24no—
205C4⋊Dic71—21no—
206C4⋊Dic71—21no—
207C4⋊Dic71—24no—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226C22⋊Dic71—24no—
227C22⋊Dic71—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232C4×Dic71—24no—
233C4×Dic71—24no—
234C24×C71C2×D411yescharacteristic
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2×D411yescharacteristic
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2411yescharacteristic
245C2×C8×C71—22no—
246C2×C8×C71—22no—
247C2×C8×C71—22no—
248C2×C8×C71—22no—
249C2×C8×C71C2412yes—
250C2×C8×C71C2412yes—
251C2×C8×C71C2412yes—
252C2×C8×C71C2412yes—
253C4⋊C4×C71C2×D414yes—
254C4⋊C4×C71C2×D414yes—
255C22⋊C4×C71C2×D414yes—
256C22⋊C4×C71C2×D414yes—
257C42×C71C2×D412yes—
258C42×C71C2×D412yes—
259C42×C71C2412yes—
260C42×C71C2412yes—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71C22×D412yes—
265C23×C71C22×D411yescharacteristic
266C22×D71—22no—
267C22×D71—42no—
268C22×D71—42no—
269C22×D71—42no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—24no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71C22×D412yes—
279C2×C4×C71C22×D412yes—
280C2×C4×C71C22×D412yes—
281C2×C4×C71C22×D412yes—
282C2×C4×C71C22×D412yes—
283C2×C4×C71C22×D411yescharacteristic
284C2×C4×C712−1+412yes—
285C2×C4×C712−1+412yes—
286C2×C4×C71C2511yescharacteristic
287C22⋊D71—84no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71—84no—
303D284—22no—
304D284—22no—
305D284—42no—
306C4×D71—84no—
307Dic142—22no—
308Dic142—22no—
309Dic142—42no—
310Dic142—84no—
311Dic142—84no—
312Dic142—84no—
313C8×C71—22no—
314C8×C71—22no—
315C8×C71—22no—
316C8×C71—22no—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—44no—
321C22×C71#53612yes—
322C22×C71#57712yes—
323C22×C71#57712yes—
324C22×C71C23×D411yescharacteristic
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—42no—
328C2×D71—84no—
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71#53612yes—
335C4×C71C2×2−1+411yescharacteristic
336C4×C71C2×2−1+411yescharacteristic
337Dic71—42no—
338Dic71—42no—
339Dic71—42no—
340Dic71—42no—
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344C2×#3244—711nomaximal, Sylow
345C2×C71—42no—
346C2×C71#324414yescomplemented
347C2×C71C2×#53611yescharacteristic
348C2×C71C2×#57711yescharacteristic
349C2×C71C2×#57711yescharacteristic
350D71—82no—
351C2×#544—711no—
352C2×#542—711no—
353#3244—7116no—
354C2×#501—711no—
355C2×#498—711no—
356C2×#489—711no—
357C2×#488—711no—
358C2×#481—711no—
359C2×#485—711no—
360C2×#482—711no—
361C2×#483—711no—
362C2×#479—711no—
363C2×#475—711no—
364C2×#478—711no—
365C2×#476—711no—
366C2×#433D7111yescharacteristic, complemented
367C71C2×#324411yescharacteristic, complemented, Sylow
368#544—718no—
369#544—1424no—
370#542—718no—
371#542—1424no—
372C2×C4⋊Q8—711no—
373C2×C4⋊Q8—711no—
374C2×C4⋊Q8—711no—
375C2×C4⋊Q8—1421no—
376C2×#126—1421no—
377C2×#125—711no—
378C2×#125—711no—
379C2×#125—1421no—
380C2×#124—711no—
381C2×#124—1421no—
382C2×#123—1421no—
383C2×C22⋊Q8—711no—
384C2×C22⋊Q8—1421no—
385C2×C22⋊Q8—1421no—
386C2×C22⋊Q8—1421no—
387C2×#121—711no—
388C2×C4×Q8—711no—
389C2×C4×D4—711no—
390C2×#117—711no—
391C2×#117C2×D7111yescharacteristic
392C22×C4⋊C4—711no—
393#501—718no—
394#498—718no—
395#489—718no—
396#488—718no—
397#485—718no—
398#483—718no—
399#482—718no—
400#481—718no—
401#479—718no—
402#478—718no—
403#476—718no—
404#475—718no—
405#433C2×D7118yescomplemented
406C2×#107—711no—
407C2×#107—711no—
408C2×#106—711no—
409C2×#106—711no—
410C2×#106—711no—
411C2×#106—711no—
412C2×#106—711no—
413C2×#106—711no—
414C2×C4⋊C8C2×D7111yescharacteristic
415C2×C4⋊C8C2×D7111yescharacteristic
416C2×#103—711no—
417C2×#103—711no—
418C2×#103—711no—
419C2×#103—711no—
420C2×#102—711no—
421C2×#102—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×C22⋊C8C2×D7111yescharacteristic
425C2×C22⋊C8C2×D7111yescharacteristic
426C2×#97C2×D7111yescharacteristic
427C2×C4×C8C2×D7111yescharacteristic
428C22×Q8—711no—
429C22×Q8—1421no—
430C22×Q8—1421no—
431C22×Q8—1421no—
432C22×D4—711no—
433C22×D4—1421no—
434C23×C4—1421no—
435C23×C4—1421no—
436C23×C4C22×D7111yescharacteristic
437C22×C8C22×D7111yescharacteristic
438C22×C8C22×D7111yescharacteristic
439C22×C8C22×D7111yescharacteristic
440C22×C8C22×D7111yescharacteristic
441C4⋊Q8—714no—
442C4⋊Q8—714no—
443C4⋊Q8—714no—
444C4⋊Q8—1428no—
445C4⋊Q8—1422no—
446C4⋊Q8—1422no—
447C4⋊Q8—1422no—
448#126—1428no—
449#125—714no—
450#125—714no—
451#125—1428no—
452#125—1422no—
453#125—1422no—
454#124—714no—
455#124—1428no—
456#124—1422no—
457#123—1428no—
458C22⋊Q8—714no—
459C22⋊Q8—1422no—
460C22⋊Q8—1428no—
461C22⋊Q8—1428no—
462C22⋊Q8—1428no—
463#121—714no—
464#121—1422no—
465C4×Q8—714no—
466C4×Q8—1422no—
467C4×D4—714no—
468C4×D4—1422no—
469#117—714no—
470#117—1422no—
471#117D28414yes—
472#117C22×D7114yes—
473C2×C4⋊C4—711no—
474C2×C4⋊C4—711no—
475C2×C4⋊C4—714no—
476C2×C4⋊C4—711no—
477C2×C4⋊C4—711no—
478C2×C4⋊C4—711no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—1421no—
481C2×C4⋊C4—1422no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4—1421no—
487C2×C4⋊C4—1421no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4D28411yescharacteristic
492C2×C4⋊C4D28411yescharacteristic
493C2×C22⋊C4—1421no—
494C2×C22⋊C4—1421no—
495C2×C22⋊C4—1421no—
496C2×C22⋊C4—1421no—
497C2×C22⋊C4—1421no—
498C2×C22⋊C4—1421no—
499C2×C22⋊C4D28411yescharacteristic
500C2×C22⋊C4D28411yescharacteristic
501C2×C42—1421no—
502C2×C42—1421no—
503C2×C42C22×D7111yescharacteristic
504C2×C42C22×D7111yescharacteristic
505#107—714no—
506#107—714no—
507#106—714no—
508#106—714no—
509#106—714no—
510#106—714no—
511#106—714no—
512#106—714no—
513C4⋊C8C22×D7114yes—
514C4⋊C8C22×D7114yes—
515#103—714no—
516#103—714no—
517#103—714no—
518#103—714no—
519#102—714no—
520#102—714no—
521#102—714no—
522#102—714no—
523C22⋊C8C22×D7114yes—
524C22⋊C8C22×D7114yes—
525#97C22×D7114yes—
526C4×C8C22×D7114yes—
527C24—1421no—
528C24C2×D28411yescharacteristic
529C2×Q8—5682no—
530C2×Q8—5682no—
531C2×Q8—5682no—
532C2×Q8—712no—
533C2×Q8—1422no—
534C2×Q8—1422no—
535C2×Q8—1421no—
536C2×Q8—1424no—
537C2×Q8—1424no—
538C2×Q8—1424no—
539C2×D4—5682no—
540C2×D4—712no—
541C2×D4—1424no—
542C2×D4—1421no—
543C2×D4—1422no—
544C2×D4—1422no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—5682no—
548C22×C4—5682no—
549C22×C4—1421no—
550C22×C4—1421no—
551C22×C4—1421no—
552C22×C4—1421no—
553C22×C4—1421no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1424no—
557C22×C4—1424no—
558C22×C4C2×D28412yes—
559C22×C4C2×D28411yescharacteristic
560C22×C4C2×D28411yescharacteristic
561C22×C4C2×D28411yescharacteristic
562C22×C4C2×D28411yescharacteristic
563C22×C4C2×D28411yescharacteristic
564C22×C4C23×D7112yes—
565C22×C4C23×D7111yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8C23×D7112yes—
571C2×C8C23×D7112yes—
572C2×C8C23×D7112yes—
573C2×C8C23×D7112yes—
574C4⋊C4—712no—
575C4⋊C4—712no—
576C4⋊C4—712no—
577C4⋊C4—712no—
578C4⋊C4—712no—
579C4⋊C4—712no—
580C4⋊C4—1424no—
581C4⋊C4—1424no—
582C4⋊C4—1424no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1424no—
586C4⋊C4—1424no—
587C4⋊C4—1421no—
588C4⋊C4—1421no—
589C4⋊C4—1421no—
590C4⋊C4—1421no—
591C4⋊C4—1421no—
592C4⋊C4—1421no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4C2×D28414yes—
597C4⋊C4C2×D28414yes—
598C22⋊C4—1424no—
599C22⋊C4—1424no—
600C22⋊C4—1424no—
601C22⋊C4—1424no—
602C22⋊C4—1424no—
603C22⋊C4—1424no—
604C22⋊C4C2×D28414yes—
605C22⋊C4C2×D28414yes—
606C42—1424no—
607C42—1424no—
608C42C2×D28412yes—
609C42C2×D28412yes—
610C42C23×D7112yes—
611C42C23×D7112yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—2842no—
616C23—2842no—
617C23—2842no—
618C23—1422no—
619C23C22×D28412yes—
620C23C22×D28411yescharacteristic
621Q8—2842no—
622Q8—5684no—
623Q8—5684no—
624Q8—5684no—
625Q8—1422no—
626Q8—1422no—
627D4—2842no—
628D4—5684no—
629D4—1422no—
630D4—1422no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—2842no—
640C2×C4—2842no—
641C2×C4—2842no—
642C2×C4—2842no—
643C2×C4—2842no—
644C2×C4—2842no—
645C2×C4—2842no—
646C2×C4—5684no—
647C2×C4—5684no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4C22×D28412yes—
656C2×C4C22×D28412yes—
657C2×C4C22×D28412yes—
658C2×C4C22×D28412yes—
659C2×C4C22×D28412yes—
660C2×C4C22×D28411yescharacteristic
661C2×C4#1455617512yes—
662C2×C4#1455617512yes—
663C2×C4C24×D7111yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—2842no—
673C22—2842no—
674C22—2842no—
675C22—5684no—
676C22#1798657512yes—
677C22#1798681112yes—
678C22#1798681112yes—
679C22C23×D28411yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—2842no—
686C4—2842no—
687C4—2842no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4—2842no—
692C4#1798657512yes—
693C4C2×#1455617511yescharacteristic
694C4C2×#1455617511yescharacteristic
695C2—42no—
696C2—5682no—
697C2#2259964014yesdirect product factor
698C2C2×#1798657511yescharacteristic
699C2C2×#1798681111yescharacteristic
700C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
hypercenterC2×#433D71
hypocenterC71C2×#3244
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×#17986627C2semidirect
3. #22599640C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986397C2semidirect
6. C2×#17986359C2semidirect
7. C2×#17986354C2semidirect
9. C2×#17986341C2semidirect
11. C2×#17986330C2semidirect
12. C2×#17986307C2semidirect
13. C2×#17986285C2semidirect
14. C2×#17986300C2semidirect
15. C2×#17986290C2semidirect
16. C2×#433×C71C2semidirect
18. #17986627C22semidirect
41. #17986408C22semidirect
42. #17986397C22semidirect
43. #17986359C22semidirect
44. #17986354C22semidirect
45. #17986341C22semidirect
46. #17986330C22semidirect
49. #17986307C22semidirect
50. #17986300C22semidirect
51. #17986290C22semidirect
52. #17986285C22semidirect
70. #433×C71C22semidirect
346. C2×C71#3244semidirect
366. C2×#433D71semidirect
367. C71C2×#3244semidirect
405. #433C2×D71semidirect
697. C2#22599640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866272
C2×#179866202
#225996402
C2×#179864082
C2×#179863972
C2×#179863592
C2×#179863542
C2×#179863182
C2×#179863412
C2×#179863242
C2×#179863302
C2×#179863072
C2×#179862852
C2×#179863002
C2×#179862902
C2×#433×C712
C2×#324471