Finite Group Databasebeta

← C2×#21435374 #29460905

Subgroups — C2×#21435374 #29460905

Order 15104.

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×#16838029C211yesmaximal, characteristic, complemented
2C2×#16838021C211yesmaximal, characteristic
3#21435374C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837805C211yesmaximal, characteristic, complemented
6C2×#16837756C211yesmaximal, characteristic, complemented
7C2×#16837736C211yesmaximal, characteristic, complemented
8C2×#16837741C211yesmaximal, characteristic, complemented
9C2×#16837725C211yesmaximal, characteristic
10C2×#16837714C211yesmaximal, characteristic
11C2×#16837707C211yesmaximal, characteristic, complemented
12C2×#16837695C211yesmaximal, characteristic, complemented
13C2×#16837704C211yesmaximal, characteristic, complemented
14C2×#16837680C211yesmaximal, characteristic, complemented
15C2×#16837464C211yesmaximal, characteristic, complemented
16C2×C59×#489C211yesmaximal, characteristic, complemented
17#16838029—24no—
18#16838029C2218yescomplemented
19#16838021—24no—
20#16838021C2218yes—
21C2×#14273727C2211yescharacteristic
22C2×#14273726C2211yescharacteristic
23C2×#14273725—21no—
24C2×#14273720—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273717—21no—
28C2×#14273713—21no—
29C2×#14273711—21no—
30C2×#14273705—21no—
31C2×#14273704—21no—
32C2×#14273703—21no—
33C2×#14273703C2211yescharacteristic
34C2×#14273698C2211yescharacteristic
35C2×Q8×Dic59C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273684C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40#16837811C2218yescomplemented
41#16837805C2218yescomplemented
42#16837756C2218yescomplemented
43#16837741C2218yescomplemented
44#16837736C2218yescomplemented
45#16837725C2218yes—
46#16837714C2218yes—
47#16837707C2218yescomplemented
48#16837704C2218yescomplemented
49#16837695C2218yescomplemented
50#16837680C2218yescomplemented
51#16837464C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C59×#489C2218yescomplemented
72C2×#103×C59C2211yescharacteristic
73C2×#103×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81C22×C4×D59—21no—
82C22×C4×D59C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273727—22no—
86#14273727C2314yes—
87#14273726—22no—
88#14273726C2314yes—
89#14273725—28no—
90#14273720—28no—
91#14273719—22no—
92#14273719C2314yes—
93#14273718—22no—
94#14273718C2314yes—
95#14273717—28no—
96#14273713—28no—
97#14273711—28no—
98#14273705—28no—
99#14273704—28no—
100#14273703—22no—
101#14273703—28no—
102#14273703C2314yes—
103#14273698—22no—
104#14273698C2314yes—
105Q8×Dic59—22no—
106Q8×Dic59C2314yes—
107D4×Dic59—22no—
108D4×Dic59C2314yes—
109#14273685—22no—
110#14273685C2314yes—
111#14273684D414yes—
112#14273684C2314yes—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59C2311yescharacteristic
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×Dic59⋊C4—21no—
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4D411yescharacteristic
127C2×Dic59⋊C4D411yescharacteristic
128C4⋊C4×D59—22no—
129C4⋊C4×D59C2314yes—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4D411yescharacteristic
135C2×(C2×D59)⋊C4D411yescharacteristic
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59C2311yescharacteristic
139#14273661C2314yes—
140#14273661C2314yes—
141#14273660C2314yes—
142#14273660C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273651C2314yes—
150#14273651C2314yes—
151#14273648C2314yes—
152#14273648C2314yes—
153(C2×D59)⋊C8C2314yes—
154(C2×D59)⋊C8C2314yes—
155C4×C59⋊C8C2314yes—
156C22×Q8×C59—21no—
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59C2311yescharacteristic
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C4⋊Q8×C59—22no—
162C4⋊Q8×C59C2314yes—
163#124×C59—22no—
164#124×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C42×C59C2311yescharacteristic
171#103×C59C2314yes—
172#103×C59C2314yes—
173#102×C59C2314yes—
174#102×C59C2314yes—
175#97×C59C2314yes—
176C24×C59—21no—
177C23×D59C2×D411yescharacteristic
178C2×Q8×C59—21no—
179C2×Q8×C59—24no—
180C2×Q8×C59—22no—
181C2×Q8×C59—22no—
182C2×Q8×C59—82no—
183C2×Q8×C59C2412yes—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59C2412yes—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2411yescharacteristic
194C2×C22⋊D59—24no—
195C2×C22⋊D59—82no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—24no—
201C22×Dic59—82no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205C2×C4×D59—22no—
206C2×C4×D59—22no—
207C2×C4×D59—24no—
208C2×C4×D59—82no—
209C2×C4×D59C2×D412yes—
210C2×C4×D59C2412yes—
211C2×Dic118—24no—
212C2×Dic118—24no—
213C2×Dic118—82no—
214C2×Dic118—82no—
215C2×C8×C59—22no—
216C2×C8×C59—22no—
217C2×C8×C59C2412yes—
218C2×C8×C59C2412yes—
219C4⋊C4×C59—24no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59C2412yes—
223C4⋊C4×C59C2412yes—
224C22⋊C4×C59—24no—
225C22⋊C4×C59—24no—
226C42×C59C2×D412yes—
227C42×C59C2412yes—
228C22⋊Dic59—24no—
229C22⋊Dic59—24no—
230(C2×D59)⋊C4—24no—
231(C2×D59)⋊C4—24no—
232(C2×D59)⋊C4C2×D414yes—
233(C2×D59)⋊C4C2×D414yes—
234C4⋊Dic59—21no—
235C4⋊Dic59—24no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—24no—
240C4⋊Dic59—24no—
241C4⋊Dic59C2412yes—
242C4⋊Dic59C2412yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4C2×D414yes—
252Dic59⋊C4C2×D414yes—
253C4×Dic59—24no—
254C4×Dic59—24no—
255C4×Dic59C2×D412yes—
256C4×Dic59C2412yes—
257C2×C59⋊C8—22no—
258C2×C59⋊C8—22no—
259C2×C59⋊C8C2412yes—
260C2×C59⋊C8C2412yes—
261C23×C59—22no—
262C23×C59—42no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59C22×D411yescharacteristic
266C22×D59—22no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59C22×D412yes—
270Q8×C59—22no—
271Q8×C59—22no—
272Q8×C59—42no—
273Q8×C59—84no—
274D4×C59—22no—
275D4×C59—22no—
276D4×C59—42no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C592−1+412yes—
289C2×C4×C592−1+412yes—
290C2×C4×C59C2511yescharacteristic
291C22⋊D59—84no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—84no—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307C4×D59—24no—
308C4×D59—22no—
309C4×D59—22no—
310C4×D59—84no—
311Dic118—84no—
312Dic118—84no—
313C8×C59—22no—
314C8×C59—22no—
315C59⋊C8—22no—
316C59⋊C8—22no—
317C2×#3243—591nomaximal, Sylow
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—84no—
322C22×C59#53612yes—
323C22×C59#57612yes—
324C22×C59#57812yes—
325C22×C59C23×D411yescharacteristic
326C2×D59—22no—
327C2×D59—22no—
328C2×D59—22no—
329C2×D59—44no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—42no—
333C4×C59—42no—
334C4×C59—42no—
335C4×C59#53612yes—
336C4×C59C2×2−1+411yescharacteristic
337C4×C59C2×2−1+411yescharacteristic
338Dic59—22no—
339Dic59—22no—
340Dic59—22no—
341Dic59—42no—
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345C2×#544—591no—
346C2×#542—591no—
347#3243—5916no—
348C2×#501—591no—
349C2×#500—591no—
350C2×#489D5911yescharacteristic, complemented
351C2×#488—591no—
352C2×#484—591no—
353C2×#485—591no—
354C2×#482—591no—
355C2×#480—591no—
356C2×#479—591no—
357C2×#477—591no—
358C2×#478—591no—
359C2×#474—591no—
360C2×#433—591no—
361C2×C59—82no—
362C2×C59#324314yescomplemented
363C2×C59C2×#53611yescharacteristic
364C2×C59C2×#57611yescharacteristic
365C2×C59C2×#57811yescharacteristic
366D59—42no—
367#544—598no—
368#544—1184no—
369#542—598no—
370#542—1184no—
371C2×C4⋊Q8—591no—
372C2×C4⋊Q8—591no—
373C2×C4⋊Q8—1181no—
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×#126—1181no—
376C2×#125—591no—
377C2×#125—591no—
378C2×#125—1181no—
379C2×#124—1181no—
380C2×#124C2×D5911yescharacteristic
381C2×#123—1181no—
382C2×C22⋊Q8—591no—
383C2×C22⋊Q8—1181no—
384C2×C22⋊Q8—1181no—
385C2×C22⋊Q8—1181no—
386C2×#121—591no—
387C2×C4×Q8—591no—
388C2×C4×D4—591no—
389C2×#117—591no—
390C2×#117—591no—
391C22×C4⋊C4—591no—
392#501—598no—
393#500—598no—
394#489C2×D5918yescomplemented
395#488—598no—
396#485—598no—
397#484—598no—
398#482—598no—
399#480—598no—
400#479—598no—
401#478—598no—
402#477—598no—
403#474—598no—
404#433—598no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#107—591no—
408C2×#107—591no—
409C2×#107—591no—
410C2×#107—591no—
411C2×#106—591no—
412C2×#106—591no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103C2×D5911yescharacteristic
418C2×#103C2×D5911yescharacteristic
419C2×#102—591no—
420C2×#102—591no—
421C2×#102C2×D5911yescharacteristic
422C2×#102C2×D5911yescharacteristic
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×#97C2×D5911yescharacteristic
426C2×C4×C8—591no—
427C59C2×#324311yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—1181no—
430C22×Q8—1181no—
431C22×Q8C22×D5911yescharacteristic
432C22×D4—1181no—
433C22×D4C22×D5911yescharacteristic
434C23×C4—591no—
435C23×C4—1181no—
436C23×C4—1181no—
437C22×C8—591no—
438C22×C8—591no—
439C22×C8C22×D5911yescharacteristic
440C22×C8C22×D5911yescharacteristic
441C4⋊Q8—22no—
442C4⋊Q8—594no—
443C4⋊Q8—594no—
444C4⋊Q8—1182no—
445C4⋊Q8—1188no—
446C4⋊Q8—1182no—
447C4⋊Q8C22×D5914yes—
448#126—1188no—
449#125—594no—
450#125—594no—
451#125—1182no—
452#125—1188no—
453#125—1182no—
454#124—22no—
455#124—1188no—
456#124C22×D5914yes—
457#123—1188no—
458C22⋊Q8—594no—
459C22⋊Q8—1188no—
460C22⋊Q8—1188no—
461C22⋊Q8—1188no—
462C22⋊Q8—1182no—
463#121—594no—
464#121—1182no—
465C4×Q8—594no—
466C4×Q8—1182no—
467C4×D4—594no—
468C4×D4—1182no—
469#117—594no—
470#117—594no—
471#117—594no—
472#117—1182no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—1182no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C4⋊C4C22×D5911yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—591no—
496C2×C22⋊C4—591no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C42—591no—
502C2×C42—1181no—
503C2×C42—1181no—
504C2×C42C22×D5911yescharacteristic
505#107—594no—
506#107—594no—
507#107—594no—
508#107—594no—
509#107—594no—
510#107—594no—
511#106—594no—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515#103—594no—
516#103—594no—
517#103C22×D5914yes—
518#103C22×D5914yes—
519#102—594no—
520#102—594no—
521#102C22×D5914yes—
522#102C22×D5914yes—
523C22⋊C8—594no—
524C22⋊C8—594no—
525#97C22×D5914yes—
526C4×C8—594no—
527C24—21no—
528C24—591no—
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—1184no—
535C2×Q8—1184no—
536C2×Q8—4722no—
537C2×Q8—4722no—
538C2×Q8C23×D5912yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—1184no—
543C2×D4—4722no—
544C2×D4C23×D5912yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—591no—
549C22×C4—591no—
550C22×C4—591no—
551C22×C4—592no—
552C22×C4—592no—
553C22×C4—1184no—
554C22×C4—1184no—
555C22×C4—1182no—
556C22×C4—1182no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—4722no—
562C22×C4—4722no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1182no—
571C2×C8—1182no—
572C2×C8C23×D5912yes—
573C2×C8C23×D5912yes—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—594no—
578C4⋊C4—594no—
579C4⋊C4—592no—
580C4⋊C4—592no—
581C4⋊C4—592no—
582C4⋊C4—592no—
583C4⋊C4—1184no—
584C4⋊C4—1184no—
585C4⋊C4—1184no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1184no—
594C4⋊C4—1184no—
595C4⋊C4—1184no—
596C4⋊C4C23×D5912yes—
597C4⋊C4C23×D5912yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—594no—
601C22⋊C4—594no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4—1184no—
605C22⋊C4—1184no—
606C42—592no—
607C42—592no—
608C42—1184no—
609C42—1184no—
610C42D4×D5912yes—
611C42C23×D5912yes—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—592no—
617C23—1182no—
618C23—1182no—
619C23—1182no—
620C23C2×D4×D5911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—4724no—
626Q8—4724no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—4724no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—592no—
640C2×C4—592no—
641C2×C4—592no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—1182no—
645C2×C4—1184no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—4724no—
653C2×C4—4724no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4—2362no—
657C2×C4—2362no—
658C2×C4C2×D4×D5912yes—
659C2×C4C2×D4×D5912yes—
660C2×C4C2×D4×D5911yescharacteristic
661C2×C4#1427377412yes—
662C2×C4#1427377412yes—
663C2×C4C24×D5911yescharacteristic
664C8—22no—
665C8—22no—
666C8—1182no—
667C8—1182no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—84no—
672C22—1182no—
673C22—1182no—
674C22—1182no—
675C22—2364no—
676C22#1683797212yes—
677C22#1683820612yes—
678C22#1683821812yes—
679C22C22×D4×D5911yescharacteristic
680C4—22no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—1182no—
686C4—1182no—
687C4—1182no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4—2362no—
692C4#1683797212yes—
693C4C2×#1427377411yescharacteristic
694C4C2×#1427377411yescharacteristic
695C2—82no—
696C2—2362no—
697C2#2143537414yesdirect product factor
698C2C2×#1683797211yescharacteristic
699C2C2×#1683820611yescharacteristic
700C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#489C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC2×#489D59
hypocenterC59C2×#3243
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16838029C2semidirect
3. #21435374C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837805C2semidirect
6. C2×#16837756C2semidirect
7. C2×#16837736C2semidirect
8. C2×#16837741C2semidirect
11. C2×#16837707C2semidirect
12. C2×#16837695C2semidirect
13. C2×#16837704C2semidirect
14. C2×#16837680C2semidirect
15. C2×#16837464C2semidirect
16. C2×C59×#489C2semidirect
18. #16838029C22semidirect
40. #16837811C22semidirect
41. #16837805C22semidirect
42. #16837756C22semidirect
43. #16837741C22semidirect
44. #16837736C22semidirect
47. #16837707C22semidirect
48. #16837704C22semidirect
49. #16837695C22semidirect
50. #16837680C22semidirect
51. #16837464C22semidirect
71. C59×#489C22semidirect
350. C2×#489D59semidirect
362. C2×C59#3243semidirect
394. #489C2×D59semidirect
427. C59C2×#3243semidirect
697. C2#21435374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380292
C2×#168380212
#214353742
C2×#168378112
C2×#168378052
C2×#168377562
C2×#168377362
C2×#168377412
C2×#168377252
C2×#168377142
C2×#168377072
C2×#168376952
C2×#168377042
C2×#168376802
C2×#168374642
C2×C59×#4892
C2×#324359