Finite Group Databasebeta

← C2×#20287408 #28263713

Subgroups — C2×#20287408 #28263713

Order 13568.

1894 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811355C211yesmaximal, characteristic
2C2×#16811350C211yesmaximal, characteristic, complemented
3#20287408C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810968C211yesmaximal, characteristic
6C2×#16810906C211yesmaximal, characteristic, complemented
7C2×#16810925C211yesmaximal, characteristic, complemented
8C2×#16810920C211yesmaximal, characteristic, complemented
9C2×#16810848C211yesmaximal, characteristic, complemented
10C2×#16810842C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic
12C2×C8×Dic106C211yesmaximal, characteristic, complemented
13C2×#16810715C211yesmaximal, characteristic, complemented
14C2×#16810714C211yesmaximal, characteristic, complemented
15C2×C4×#11719913C211yesmaximal, characteristic, complemented
16C2×C53×#488C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20#16811355—24no—
21#16811355C2218yes—
22#16811350—24no—
23#16811350C2218yescomplemented
24C2×#13133216—21no—
25C2×#13133216C2211yescharacteristic
26C2×#13133213C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133207—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133203—21no—
32C2×#13133201—21no—
33C2×#13133199—21no—
34C2×Q8×Dic53C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182—21no—
38C2×#13133182C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×D4×Dic53C2211yescharacteristic
42C2×#13133177—21no—
43#16810979C2218yescomplemented
44#16810968C2218yes—
45#16810925C2218yescomplemented
46#16810920C2218yescomplemented
47#16810906C2218yescomplemented
48#16810848C2218yescomplemented
49#16810842C2218yescomplemented
50#16810822C2218yes—
51C8×Dic106C2218yescomplemented
52#16810715C2218yescomplemented
53#16810714C2218yescomplemented
54C4×#11719913C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C53×#488C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C22×C4×D53—21no—
85C2×#11719925—24no—
86C2×#11719925C2314yes—
87C2×#11719913—24no—
88C2×#11719913C2314yes—
89C2×#11719923—24no—
90C2×#11719923C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133216—22no—
94#13133216—28no—
95#13133216C2314yes—
96#13133213—22no—
97#13133213C2314yes—
98#13133208—22no—
99#13133208C2314yes—
100#13133207—28no—
101#13133207—28no—
102#13133206—22no—
103#13133206C2314yes—
104#13133203—28no—
105#13133201—28no—
106#13133199—28no—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109C4×Dic106—22no—
110C4×Dic106D414yes—
111C4×Dic106C2314yes—
112C4×Dic106C2314yes—
113#13133182—28no—
114#13133182—22no—
115#13133182—22no—
116#13133182C2314yes—
117#13133182C2314yes—
118C4×D212—22no—
119C4×D212C2314yes—
120D4×Dic53—22no—
121D4×Dic53C2314yes—
122#13133177—28no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53D411yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148C4⋊#88322C2314yes—
149#13133146C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133139C2314yes—
154#13133138C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157C8×Dic53C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#125×C53—22no—
164#125×C53C2314yes—
165#124×C53—22no—
166#124×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#103×C53C2314yes—
175#103×C53C2314yes—
176#102×C53C2314yes—
177#102×C53C2314yes—
178C4×C8×C53C2314yes—
179C24×C53—21no—
180C23×D53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53—24no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53—82no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—24no—
203C22×Dic53—82no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—21no—
211C2×D212C2412yes—
212C2×C4×D53—24no—
213C2×C4×D53—82no—
214C2×Dic106—21no—
215C2×Dic106—22no—
216C2×Dic106—24no—
217C2×Dic106—24no—
218C2×Dic106—44no—
219C2×Dic106C2×D414yes—
220C2×Dic106#4114yes—
221C2×Dic106C2412yes—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53C2412yes—
225C2×C8×C53C2412yes—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—24no—
234C42×C53C2×D412yes—
235C42×C53C2412yes—
236C22⋊Dic53—24no—
237#11719925—28no—
238#11719923—28no—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53C2×D414yes—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919C2×D414yes—
255#11719919C2×D414yes—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53C2×D412yes—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268#11719913—28no—
269C23×C53—22no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—42no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—42no—
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×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4112yes—
296C2×C4×C532−1+412yes—
297C2×C4×C53C2511yescharacteristic
298C22⋊D53—48no—
299C22⋊D53—84no—
300C2×Dic53—24no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—84no—
310C2×Dic53#13514yes—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315D212—22no—
316D212—22no—
317D212—42no—
318C4×D53—84no—
319Dic106—24no—
320Dic106—22no—
321Dic106—28no—
322Dic106—48no—
323Dic106C2×#4114yes—
324C8×C53—22no—
325C8×C53—22no—
326#88322—22no—
327#88322—22no—
328C2×#3365—531nomaximal, Sylow
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—84no—
333C22×C53#54812yes—
334C22×C53C2×#13512yes—
335C22×C53#57712yes—
336C22×C53C23×D411yescharacteristic
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53#54812yes—
347C4×C53C22×#4111yescharacteristic
348C4×C53C2×2−1+411yescharacteristic
349Dic53—24no—
350Dic53—22no—
351Dic53—22no—
352Dic53—22no—
353Dic53—42no—
354Dic53—42no—
355Dic53C2×#13514yes—
356C2×#559—531no—
357C2×#557—531no—
358#3365—5316no—
359C2×#488—531no—
360C2×#488D5311yescharacteristic, complemented
361C2×#486—531no—
362C2×#475—531no—
363C2×#478—531no—
364C2×#478—531no—
365C2×#464—531no—
366C2×#464—531no—
367C2×#460—531no—
368C2×C8×Q8—531no—
369C2×C4×Q16—531no—
370C2×C4×SD16—531no—
371C2×C4×SD16—531no—
372C2×C53—82no—
373C2×C53#336514yescomplemented
374C2×C53C2×#54811yescharacteristic
375C2×C53C22×#13511yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—82no—
378C22×Q16—531no—
379C22×SD16—531no—
380C22×SD16—531no—
381#559—538no—
382#559—1064no—
383#557—538no—
384#557—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8—1061no—
387C2×#127—531no—
388C2×#125—531no—
389C2×#125—1061no—
390C2×#125—1061no—
391C2×#125C2×D5311yescharacteristic
392C2×#124—531no—
393C2×#124—1061no—
394C2×#124C2×D5311yescharacteristic
395C2×#123—1061no—
396C2×#123—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8—531no—
400C2×C4×Q8—531no—
401C2×C4×Q8—531no—
402C2×C4×Q8—1061no—
403C2×C4×D4—531no—
404C2×C4×D4—531no—
405C2×C4×D4—1061no—
406#488—538no—
407#488C2×D5318yescomplemented
408#486—538no—
409#478—538no—
410#478—538no—
411#475—538no—
412#464—538no—
413#464—538no—
414#460—538no—
415C8×Q8—538no—
416C4×Q16—538no—
417C4×SD16—538no—
418C4×SD16—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×C4⋊C8—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103C2×D5311yescharacteristic
428C2×#103C2×D5311yescharacteristic
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102C2×D5311yescharacteristic
434C2×#102C2×D5311yescharacteristic
435C2×C4×C8—531no—
436C2×C4×C8—531no—
437C2×C4×C8C2×D5311yescharacteristic
438C53C2×#336511yescharacteristic, complemented, Sylow
439C22×Q8—531no—
440C22×Q8—531no—
441C22×Q8—1061no—
442C22×Q8C22×D5311yescharacteristic
443C22×D4—531no—
444C22×D4—1061no—
445C22×D4—1061no—
446C22×D4C22×D5311yescharacteristic
447C23×C4—1061no—
448C23×C4—1061no—
449C2×Q16—534no—
450C2×Q16—1064no—
451C2×SD16—534no—
452C2×SD16—534no—
453C2×SD16—1064no—
454C2×SD16—1064no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8C22×D5311yescharacteristic
458C22×C8C22×D5311yescharacteristic
459C4⋊Q8—534no—
460C4⋊Q8—1062no—
461C4⋊Q8—1068no—
462#127—534no—
463#127—1062no—
464#125—22no—
465#125—534no—
466#125—1062no—
467#125—1068no—
468#125—1068no—
469#125C22×D5314yes—
470#124—22no—
471#124—534no—
472#124—1062no—
473#124—1068no—
474#124C22×D5314yes—
475#123—1068no—
476#123—1068no—
477C4×Q8—534no—
478C4×Q8—534no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×Q8—534no—
482C4×Q8—534no—
483C4×Q8—1062no—
484C4×Q8—1062no—
485C4×Q8—1062no—
486C4×Q8—1068no—
487C4×Q8—1062no—
488C4×D4—534no—
489C4×D4—534no—
490C4×D4—1062no—
491C4×D4—1068no—
492C4×D4—1062no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—531no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8—534no—
528#103—534no—
529#103—534no—
530#103C22×D5314yes—
531#103C22×D5314yes—
532#102—534no—
533#102—534no—
534#102—534no—
535#102—534no—
536#102C22×D5314yes—
537#102C22×D5314yes—
538C4×C8—534no—
539C4×C8—534no—
540C4×C8C22×D5314yes—
541C24—21no—
542C24—1061no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—534no—
547C2×Q8—534no—
548C2×Q8—532no—
549C2×Q8—1064no—
550C2×Q8—1064no—
551C2×Q8—1061no—
552C2×Q8—1062no—
553C2×Q8—2124no—
554C2×Q8C23×D5312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—532no—
559C2×D4—1064no—
560C2×D4—1064no—
561C2×D4—1061no—
562C2×D4—1062no—
563C2×D4—1062no—
564C2×D4—4242no—
565C2×D4—2124no—
566C2×D4C23×D5312yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—531no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—1064no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1064no—
579C22×C4—4242no—
580C22×C4—4242no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584Q16—1068no—
585SD16—1068no—
586SD16—1068no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8C23×D5312yes—
594C2×C8C23×D5312yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—534no—
600C4⋊C4—534no—
601C4⋊C4—534no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1064no—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C42—532no—
622C42—532no—
623C42—532no—
624C42—532no—
625C42—1064no—
626C42—1064no—
627C42—1064no—
628C42—1064no—
629C42D4×D5312yes—
630C42C23×D5312yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—1062no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23C2×D4×D5311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—534no—
644Q8—1068no—
645Q8—1064no—
646Q8—1062no—
647Q8—2128no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—1062no—
652D4—1062no—
653D4—4244no—
654D4—2128no—
655D4—2122no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—534no—
665C2×C4—532no—
666C2×C4—532no—
667C2×C4—532no—
668C2×C4—532no—
669C2×C4—1064no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—4244no—
677C2×C4—4244no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4C2×D4×D5312yes—
681C2×C4C2×D4×D5312yes—
682C2×C4C2×D4×D5311yescharacteristic
683C2×C4#41×D5312yes—
684C2×C4#1313326412yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—4244no—
695C22—2122no—
696C22—2122no—
697C22—2122no—
698C22#1681128112yes—
699C22#135×D5312yes—
700C22#1681143012yes—
701C22C22×D4×D5311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—534no—
708C4—1062no—
709C4—1064no—
710C4—1062no—
711C4—1062no—
712C4—2122no—
713C4—2122no—
714C4#1681128112yes—
715C4C2×#41×D5311yescharacteristic
716C4C2×#1313326411yescharacteristic
717C2—82no—
718C2—4242no—
719C2#2028740814yesdirect product factor
720C2C2×#1681128111yescharacteristic
721C2C2×#135×D5311yescharacteristic
722C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#488C2
socleC23×C53C22×D4
prime radicalC2×#13133213C22
hypercenterC2×#488D53
hypocenterC53C2×#3365
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
2. C2×#16811350C2semidirect
3. #20287408C2direct (N × H)
4. C2×#16810979C2semidirect
6. C2×#16810906C2semidirect
7. C2×#16810925C2semidirect
8. C2×#16810920C2semidirect
9. C2×#16810848C2semidirect
10. C2×#16810842C2semidirect
12. C2×C8×Dic106C2semidirect
13. C2×#16810715C2semidirect
14. C2×#16810714C2semidirect
15. C2×C4×#11719913C2semidirect
16. C2×C53×#488C2semidirect
23. #16811350C22semidirect
43. #16810979C22semidirect
45. #16810925C22semidirect
46. #16810920C22semidirect
47. #16810906C22semidirect
48. #16810848C22semidirect
49. #16810842C22semidirect
51. C8×Dic106C22semidirect
52. #16810715C22semidirect
53. #16810714C22semidirect
54. C4×#11719913C22semidirect
71. C53×#488C22semidirect
360. C2×#488D53semidirect
373. C2×C53#3365semidirect
407. #488C2×D53semidirect
438. C53C2×#3365semidirect
719. C2#20287408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113552
C2×#168113502
#202874082
C2×#168109792
C2×#168109682
C2×#168109062
C2×#168109252
C2×#168109202
C2×#168108482
C2×#168108422
C2×#168108222
C2×C8×Dic1062
C2×#168107152
C2×#168107142
C2×C4×#117199132
C2×C53×#4882
C2×#336553