Finite Group Databasebeta

← C2×#20287251 #28262725

Subgroups — C2×#20287251 #28262725

Order 13568.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811344C211yesmaximal, characteristic
2C2×#16811307C211yesmaximal, characteristic
3#20287251C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810963C211yesmaximal, characteristic, complemented
7C2×#16810961C211yesmaximal, characteristic, complemented
8C2×#16810961C211yesmaximal, characteristic, complemented
9C2×#16810932C211yesmaximal, characteristic, complemented
10C2×#16810916C211yesmaximal, characteristic, complemented
11C2×#16810878C211yesmaximal, characteristic, complemented
12C2×#16810730C211yesmaximal, characteristic, complemented
13C2×#16810694C211yesmaximal, characteristic
14C2×#16810664C211yesmaximal, characteristic, complemented
15C2×#16810661C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18#16811344—24no—
19#16811344C2218yes—
20#16811307—24no—
21#16811307C2218yes—
22C2×#13133216C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133210—21no—
25C2×#13133210—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133207—21no—
28C2×#13133203—21no—
29C2×#13133199—21no—
30C2×#13133193C2211yescharacteristic
31C2×#13133193C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×#13133182—21no—
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133176C2211yescharacteristic
37C2×#13133176C2211yescharacteristic
38C2×#13133175—21no—
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811031C2218yescomplemented
42#16810963C2218yescomplemented
43#16810961C2218yescomplemented
44#16810961C2218yescomplemented
45#16810957C2218yescomplemented
46#16810932C2218yescomplemented
47#16810916C2218yescomplemented
48#16810878C2218yescomplemented
49#16810730C2218yescomplemented
50#16810694C2218yes—
51#16810664C2218yescomplemented
52#16810661C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#467C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×C22⋊D53D411yescharacteristic
79C22×C4×D53—21no—
80C22×C4×D53C2311yescharacteristic
81C2×#11719912—24no—
82C2×#11719912C2314yes—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85#13133216—22no—
86#13133216C2314yes—
87#13133212—28no—
88#13133210—28no—
89#13133210—28no—
90#13133208—22no—
91#13133208C2314yes—
92#13133207—28no—
93#13133203—28no—
94#13133199—28no—
95#13133193—22no—
96#13133193—22no—
97#13133193C2314yes—
98#13133193C2314yes—
99Q8×Dic53—22no—
100Q8×Dic53—22no—
101Q8×Dic53C2314yes—
102Q8×Dic53C2314yes—
103#13133182—28no—
104C4×C22⋊D53D414yes—
105C4×C22⋊D53C2314yes—
106#13133176—22no—
107#13133176—22no—
108#13133176C2314yes—
109#13133176C2314yes—
110#13133175—28no—
111#13133175—22no—
112#13133175C2314yes—
113C2×C4⋊Dic53—21no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53C2311yescharacteristic
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×#11719919—21no—
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919D411yescharacteristic
126C4⋊C4×D53—22no—
127C4⋊C4×D53C2314yes—
128C2×C22⋊Dic53—21no—
129C2×C22⋊Dic53—21no—
130C2×C22⋊Dic53D411yescharacteristic
131C2×#11719921—21no—
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921D411yescharacteristic
135C2×C4×Dic53—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133150C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154C22⋊#88322C2314yes—
155#13133129C2314yes—
156#13133127C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×Q8×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C2×Q16×C53—24no—
161C2×Q16×C53C2314yes—
162C22×C8×C53—24no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169C22⋊Q8×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176#107×C53C2314yes—
177#103×C53C2314yes—
178#103×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C2×Q8×C53C2412yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—42no—
200C2×C22⋊D53C2×D414yes—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—24no—
211C2×C4×D53—44no—
212C2×C4×D53C2×D412yes—
213C2×C4×D53C2412yes—
214C2×Dic106—24no—
215C2×Dic106—44no—
216Q16×C53—28no—
217C2×C8×C53—22no—
218C2×C8×C53—28no—
219C2×C8×C53#4114yes—
220C2×C8×C53C2412yes—
221C2×C8×C53C2412yes—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53C2412yes—
227C4⋊C4×C53C2412yes—
228C22⋊C4×C53—24no—
229C22⋊C4×C53—24no—
230C22⋊Dic53—24no—
231C22⋊Dic53—24no—
232C22⋊Dic53C2×D414yes—
233#11719921—24no—
234#11719921—24no—
235#11719921—24no—
236#11719921C2×D414yes—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53—21no—
241C4⋊Dic53—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53—24no—
244C4⋊Dic53C2412yes—
245C4⋊Dic53C2412yes—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248#11719919—24no—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919C2×D414yes—
254C4×Dic53—24no—
255C4×Dic53—24no—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53—24no—
259C4×Dic53C2×D412yes—
260C4×Dic53C2412yes—
261C2×#88322—22no—
262C2×#88322—22no—
263C2×#88322C2412yes—
264C2×#88322C2412yes—
265#11719912—28no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53C22×D412yes—
270C23×C53C22×D411yescharacteristic
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53C22×D412yes—
275Q8×C53—22no—
276Q8×C53—22no—
277Q8×C53—22no—
278Q8×C53—22no—
279Q8×C53—42no—
280Q8×C53—42no—
281C2×C4×C53—22no—
282C2×C4×C53—24no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4112yes—
296C2×C4×C532−1+412yes—
297C2×C4×C53C2511yescharacteristic
298C22⋊D53—44no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313C4×D53—24no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—48no—
317Dic106—48no—
318C8×C53—22no—
319C8×C53C2×#4114yes—
320#88322—22no—
321#88322—22no—
322C2×#3349—531nomaximal, Sylow
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—44no—
327C22×C53#54712yes—
328C22×C53#57512yes—
329C22×C53#57812yes—
330C22×C53C23×D411yescharacteristic
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—22no—
334C2×D53—44no—
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53#54712yes—
341C4×C53C22×#4111yescharacteristic
342C4×C53C2×2−1+411yescharacteristic
343Dic53—22no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350C2×#556—531no—
351C2×#552—531no—
352#3349—5316no—
353C2×#501—531no—
354C2×#484—531no—
355C2×#485—531no—
356C2×#485—531no—
357C2×#485—531no—
358C2×#479—531no—
359C2×#477—531no—
360C2×#470—531no—
361C2×#467D5311yescharacteristic, complemented
362C2×#441—531no—
363C2×#435—531no—
364C2×#428—531no—
365C2×#427—531no—
366C2×C53—42no—
367C2×C53#334914yescomplemented
368C2×C53C2×#54711yescharacteristic
369C2×C53C2×#57511yescharacteristic
370C2×C53C2×#57811yescharacteristic
371D53—42no—
372C22×Q16C2×D5311yescharacteristic
373C22×M16—531no—
374C23×C8C2×D5311yescharacteristic
375#556—538no—
376#556—1064no—
377#552—538no—
378#552—1064no—
379C2×C4⋊Q8—531no—
380C2×#126—1061no—
381C2×#126—1061no—
382C2×#126—1061no—
383C2×#125—531no—
384C2×#125—1061no—
385C2×#124—1061no—
386C2×#123—1061no—
387C2×C22⋊Q8—531no—
388C2×C22⋊Q8—531no—
389C2×C22⋊Q8C2×D5311yescharacteristic
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×C4×Q8—531no—
392C2×C4×Q8—531no—
393C2×C4×Q8—1061no—
394C2×C4×D4—531no—
395C2×#117—531no—
396C2×#117—531no—
397C2×#117—531no—
398C2×#117—1061no—
399C22×C4⋊C4—531no—
400#501—538no—
401#485—538no—
402#485—538no—
403#485—538no—
404#484—538no—
405#479—538no—
406#477—538no—
407#470—538no—
408#467C2×D5318yescomplemented
409#441—538no—
410#435—538no—
411#428—538no—
412#427—538no—
413C2×#107—531no—
414C2×#107—531no—
415C2×#107—531no—
416C2×#107—531no—
417C2×#107C2×D5311yescharacteristic
418C2×#106—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103C2×D5311yescharacteristic
428C2×#103C2×D5311yescharacteristic
429C2×C22⋊C8—531no—
430C2×C22⋊C8—531no—
431C2×#97—531no—
432C53C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—1061no—
434C22×Q8C22×D5311yescharacteristic
435C22×Q8C22×D5311yescharacteristic
436C22×D4—531no—
437C23×C4—531no—
438C23×C4—1061no—
439C23×C4C22×D5311yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D5314yes—
442C2×M16—534no—
443C2×M16—1064no—
444C22×C8—24no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8C22×D5311yescharacteristic
448C22×C8C22×D5314yes—
449C22×C8C22×D5311yescharacteristic
450C4⋊Q8—534no—
451C4⋊Q8—1062no—
452#126—1068no—
453#126—1068no—
454#126—1068no—
455#125—534no—
456#125—1062no—
457#125—1068no—
458#124—1068no—
459#123—1068no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—534no—
463C22⋊Q8—534no—
464C22⋊Q8—1062no—
465C22⋊Q8—1062no—
466C22⋊Q8C22×D5314yes—
467C22⋊Q8C22×D5314yes—
468C4×Q8—534no—
469C4×Q8—534no—
470C4×Q8—1062no—
471C4×Q8—1062no—
472C4×Q8—1068no—
473C4×D4—534no—
474C4×D4—534no—
475#117—534no—
476#117—534no—
477#117—534no—
478#117—1068no—
479#117—1062no—
480#117—1062no—
481#117—1062no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—531no—
504C2×C22⋊C4—531no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C42—531no—
511C2×C42—1061no—
512C2×C42—1061no—
513C2×C42—1061no—
514C2×C42—1061no—
515C2×C42—1061no—
516#107—534no—
517#107—534no—
518#107—534no—
519#107—534no—
520#107C22×D5314yes—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526#103—534no—
527#103—534no—
528#103—534no—
529#103—534no—
530#103C22×D5314yes—
531#103C22×D5314yes—
532C22⋊C8—534no—
533C22⋊C8—534no—
534#97—534no—
535C24—531no—
536C24D4×D5311yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—1064no—
544C2×Q8—2124no—
545C2×Q8C23×D5312yes—
546C2×Q8C23×D5312yes—
547C2×D4—534no—
548C2×D4—2122no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—1064no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—2124no—
568C22×C4D4×D5312yes—
569C22×C4D4×D5311yescharacteristic
570C22×C4C23×D5312yes—
571C22×C4C23×D5311yescharacteristic
572Q16—28no—
573M16—1068no—
574C2×C8—22no—
575C2×C8—28no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1062no—
579C2×C8—1062no—
580C2×C8#1171994714yes—
581C2×C8C23×D5312yes—
582C2×C8C23×D5312yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—534no—
588C4⋊C4—532no—
589C4⋊C4—532no—
590C4⋊C4—532no—
591C4⋊C4—532no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4C23×D5312yes—
605C4⋊C4C23×D5312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—534no—
609C22⋊C4—534no—
610C22⋊C4—1064no—
611C22⋊C4—1064no—
612C22⋊C4—1064no—
613C22⋊C4—1064no—
614C22⋊C4—1064no—
615C42—532no—
616C42—532no—
617C42—1064no—
618C42—1064no—
619C42—1064no—
620C42—1064no—
621C42—1064no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—532no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23C2×D4×D5312yes—
630C23C2×D4×D5311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637Q8—2128no—
638D4—2124no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—532no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1064no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—2128no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4C2×D4×D5312yes—
670C2×C4C2×D4×D5311yescharacteristic
671C2×C4C2×#1171994712yes—
672C2×C4#1313326412yes—
673C2×C4C24×D5311yescharacteristic
674C8—22no—
675C8—1062no—
676C8—1062no—
677C8C2×#1171994714yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—1062no—
683C22—1062no—
684C22—1062no—
685C22—2124no—
686C22#1681127312yes—
687C22#1681142012yes—
688C22#1681143612yes—
689C22C22×D4×D5311yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1062no—
696C4—1062no—
697C4—1062no—
698C4—2122no—
699C4—2122no—
700C4—2122no—
701C4—2122no—
702C4#1681127312yes—
703C4C22×#1171994711yescharacteristic
704C4C2×#1313326411yescharacteristic
705C2—42no—
706C2—2122no—
707C2#2028725114yesdirect product factor
708C2C2×#1681127311yescharacteristic
709C2C2×#1681142011yescharacteristic
710C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#467D53
hypocenterC53C2×#3349
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #20287251C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810963C2semidirect
7. C2×#16810961C2semidirect
8. C2×#16810961C2semidirect
9. C2×#16810932C2semidirect
10. C2×#16810916C2semidirect
11. C2×#16810878C2semidirect
12. C2×#16810730C2semidirect
14. C2×#16810664C2semidirect
15. C2×#16810661C2semidirect
16. C2×C53×#467C2semidirect
41. #16811031C22semidirect
42. #16810963C22semidirect
43. #16810961C22semidirect
44. #16810961C22semidirect
45. #16810957C22semidirect
46. #16810932C22semidirect
47. #16810916C22semidirect
48. #16810878C22semidirect
49. #16810730C22semidirect
51. #16810664C22semidirect
52. #16810661C22semidirect
73. C53×#467C22semidirect
361. C2×#467D53semidirect
367. C2×C53#3349semidirect
408. #467C2×D53semidirect
432. C53C2×#3349semidirect
707. C2#20287251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113442
C2×#168113072
#202872512
C2×#168110312
C2×#168109572
C2×#168109632
C2×#168109612
C2×#168109322
C2×#168109162
C2×#168108782
C2×#168107302
C2×#168106942
C2×#168106642
C2×#168106612
C2×C53×#4672
C2×#334953