Finite Group Databasebeta

← C2×#20275995 #27411930

Subgroups — C2×#20275995 #27411930

Order 13568.

1322 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133247C211yesmaximal, characteristic
2C2×#16810671C211yesmaximal, characteristic, complemented
3C2×#16810640C211yesmaximal, characteristic
4C2×#16810633C211yesmaximal, characteristic, complemented
5C22×#13133135C211yesmaximal, characteristic, complemented
6#20275995C218yesmaximal, direct product factor
7C2×#16810394C211yesmaximal, characteristic, complemented
8C2×C53×#413C211yesmaximal, characteristic
9C23×Dic106C2211yescharacteristic
10C2×#13133247—22no—
11C2×#13133247—22no—
12C2×#13133247—22no—
13C2×#13133247—22no—
14C2×#13133247—22no—
15C2×#13133247C2214yes—
16C22×#11719925—21no—
17C22×#11719923—21no—
18C22×#11719917C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810671—22no—
22#16810671C2214yescomplemented
23C2×#13133152—22no—
24#16810640—22no—
25#16810640C2214yes—
26C2×#13133144—22no—
27#16810633—22no—
28#16810633C2214yescomplemented
29C2×#13133142—22no—
30C2×#13133135—22no—
31C2×#13133135—22no—
32C2×#13133135C2214yescomplemented
33#16810394C2214yescomplemented
34C22×#41×C53C2211yescharacteristic
35C22×M16×C53C2211yescharacteristic
36C22×M16×C53C2211yescharacteristic
37C53×#413—22no—
38C53×#413C2214yes—
39C2×#101×C53—21no—
40C2×#100×C53—21no—
41C22×Dic106—21no—
42C22×Dic106—21no—
43C22×Dic106—21no—
44C22×Dic106—21no—
45C22×Dic106—21no—
46C22×Dic106—21no—
47C22×Dic106—21no—
48C22×Dic106—21no—
49C22×Dic106—21no—
50C22×Dic106—21no—
51C22×Dic106—21no—
52C22×Dic106D412yes—
53C22×Dic106D412yes—
54C22×Dic106C2312yes—
55C23×Dic53—21no—
56#13133247—28no—
57#13133247—28no—
58#13133247—28no—
59#13133247—28no—
60C2×#11719925—24no—
61C2×#11719925—24no—
62C2×#11719925—24no—
63C2×#11719923—24no—
64C2×#11719923—24no—
65C2×#11719923—24no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917—21no—
72C2×#11719917D412yes—
73C2×#11719917D412yes—
74C2×#11719917D412yes—
75C2×#11719917D412yes—
76C2×#11719917C2312yes—
77C2×#11719917C2312yes—
78C22×#88322—21no—
79C22×#88322—21no—
80#13133176—21no—
81#13133176—21no—
82#13133176—21no—
83#13133176C2312yes—
84C2×C4⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C4×Dic53—21no—
87#13133152—28no—
88#13133144—28no—
89#13133142—28no—
90#13133135—28no—
91C2×#41×C53—21no—
92C2×#41×C53—21no—
93C2×#41×C53—21no—
94C2×#41×C53—21no—
95C2×#41×C53—21no—
96C2×#41×C53—21no—
97C2×#41×C53—21no—
98C2×#41×C53—21no—
99C2×#41×C53—21no—
100C2×#41×C53—21no—
101C2×#41×C53D412yes—
102C2×#41×C53C2312yes—
103C22×Q8×C53D411yescharacteristic
104C22×D4×C53—21no—
105C22×D4×C53D411yescharacteristic
106C23×C4×C53—21no—
107C23×C4×C53C2311yescharacteristic
108C2×M16×C53—21no—
109C2×M16×C53—21no—
110C2×M16×C53—21no—
111C2×M16×C53—21no—
112C2×M16×C53—21no—
113C2×M16×C53—21no—
114C2×M16×C53—21no—
115C2×M16×C53—21no—
116C2×M16×C53—21no—
117C2×M16×C53—21no—
118C2×M16×C53C2312yes—
119C2×M16×C53C2312yes—
120C22×C8×C53—21no—
121C22×C8×C53—21no—
122#101×C53—24no—
123#100×C53—24no—
124C24×C53—21no—
125C24×C53#4111yescharacteristic
126#41×C53—22no—
127#41×C53—22no—
128#41×C53—22no—
129#41×C53—22no—
130#41×C53—22no—
131#41×C53—22no—
132#41×C53—22no—
133#41×C53—22no—
134#41×C53—41no—
135#41×C53—41no—
136#41×C53—41no—
137#41×C53—41no—
138#41×C53—41no—
139#41×C53—41no—
140#41×C53—41no—
141#41×C53—41no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53C2×D412yes—
148C2×D4×C53—22no—
149C2×D4×C53—22no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—41no—
156C2×D4×C53—41no—
157C2×D4×C53—41no—
158C2×D4×C53—41no—
159C2×D4×C53C2×D412yes—
160C22×C4×C53—21no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—41no—
164C22×C4×C53—41no—
165C22×C4×C53—41no—
166C22×C4×C53—41no—
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53#4111yescharacteristic
176C22×C4×C53#4111yescharacteristic
177C22×C4×C53#4111yescharacteristic
178C22×C4×C53#4111yescharacteristic
179C22×C4×C53#4111yescharacteristic
180C22×C4×C53C2411yescharacteristic
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—41no—
185C22×Dic53—41no—
186C22×Dic53—41no—
187C22×Dic53—41no—
188C22×Dic53—41no—
189C2×Dic106—22no—
190C2×Dic106—22no—
191C2×Dic106—22no—
192C2×Dic106—22no—
193C2×Dic106—22no—
194C2×Dic106—22no—
195C2×Dic106—22no—
196C2×Dic106—22no—
197C2×Dic106—22no—
198C2×Dic106—22no—
199C2×Dic106—22no—
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—22no—
203C2×Dic106—22no—
204C2×Dic106—41no—
205C2×Dic106—41no—
206C2×Dic106—41no—
207C2×Dic106—41no—
208C2×Dic106—41no—
209C2×Dic106—41no—
210C2×Dic106—41no—
211C2×Dic106—41no—
212C2×Dic106—41no—
213C2×Dic106—41no—
214C2×Dic106—41no—
215C2×Dic106—41no—
216C2×Dic106C2×D414yes—
217M16×C53—22no—
218M16×C53—22no—
219M16×C53—22no—
220M16×C53—22no—
221M16×C53—41no—
222M16×C53—41no—
223M16×C53—41no—
224M16×C53—41no—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53—41no—
228C2×C8×C53—41no—
229C2×C8×C53—41no—
230C2×C8×C53—41no—
231C22⋊Dic53—22no—
232C22⋊Dic53—41no—
233#11719925—216no—
234#11719923—216no—
235C4⋊Dic53—22no—
236C4⋊Dic53—41no—
237C4×Dic53—22no—
238C4×Dic53—41no—
239#11719917—22no—
240#11719917—22no—
241#11719917—22no—
242#11719917—22no—
243#11719917—22no—
244#11719917—22no—
245#11719917C2×D414yes—
246#11719917C2×D414yes—
247C2×#88322—22no—
248C2×#88322—22no—
249C2×#88322—22no—
250C2×#88322—22no—
251C2×#88322—22no—
252C2×#88322—22no—
253C23×C53—22no—
254C23×C53—42no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—82no—
258C23×C53#12111yescharacteristic
259C23×C53#12111yescharacteristic
260C23×C53#12311yescharacteristic
261C23×C53#12311yescharacteristic
262C23×C53#12411yescharacteristic
263C23×C53#12411yescharacteristic
264C23×C53C2×#4111yescharacteristic
265Q8×C53—22no—
266Q8×C53—22no—
267Q8×C53—41no—
268Q8×C53—41no—
269D4×C53—22no—
270D4×C53—22no—
271D4×C53—42no—
272D4×C53—42no—
273D4×C53—42no—
274D4×C53—42no—
275D4×C53—41no—
276D4×C53—41no—
277C2×C4×C53—22no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—42no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53#12011yescharacteristic
285C2×C4×C53#12011yescharacteristic
286C2×C4×C53#12011yescharacteristic
287C2×C4×C53#12011yescharacteristic
288C2×C4×C53#12111yescharacteristic
289C2×C4×C53#12111yescharacteristic
290C2×C4×C53#12111yescharacteristic
291C2×C4×C53#12111yescharacteristic
292C2×C4×C53#12111yescharacteristic
293C2×C4×C53#12111yescharacteristic
294C2×C4×C53#12111yescharacteristic
295C2×C4×C53#12111yescharacteristic
296C2×C4×C53#12111yescharacteristic
297C2×C4×C53#12111yescharacteristic
298C2×C4×C53#12311yescharacteristic
299C2×C4×C53#12311yescharacteristic
300C2×C4×C53#12311yescharacteristic
301C2×C4×C53#12311yescharacteristic
302C2×C4×C53#12311yescharacteristic
303C2×C4×C53#12311yescharacteristic
304C2×C4×C53#12411yescharacteristic
305C2×C4×C53#12411yescharacteristic
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×Dic53—24no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—82no—
321Dic106—24no—
322Dic106—24no—
323Dic106—42no—
324Dic106—42no—
325Dic106—42no—
326Dic106—42no—
327Dic106—42no—
328Dic106—42no—
329C8×C53—42no—
330C8×C53—42no—
331#88322—24no—
332#88322—24no—
333C2×#2049—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—82no—
343C22×C53—82no—
344C22×C53—82no—
345C22×C53#39411yescharacteristic
346C22×C53#39411yescharacteristic
347C22×C53#39411yescharacteristic
348C22×C53#39411yescharacteristic
349C22×C53C2×#12111yescharacteristic
350C22×C53C2×#12311yescharacteristic
351C22×C53C2×#12411yescharacteristic
352C4×C53—42no—
353C4×C53#39411yescharacteristic
354C4×C53#39411yescharacteristic
355C4×C53#39411yescharacteristic
356C4×C53#39411yescharacteristic
357C4×C53C2×#12011yescharacteristic
358C4×C53C2×#12111yescharacteristic
359C4×C53C2×#12111yescharacteristic
360C4×C53C2×#12311yescharacteristic
361Dic53—44no—
362Dic53—82no—
363C22×#137—531no—
364C2×#430—531no—
365C2×#421—531no—
366C2×#419—531no—
367C2×#413D5311yescharacteristic
368C22×#101—531no—
369#2049—538no—
370C2×#344—531no—
371C2×C53—21no—
372C2×C53—21no—
373C2×C53—21no—
374C2×C53—21no—
375C2×C53—21no—
376C2×C53—21no—
377C2×C53—82no—
378C2×C53#204912yescomplemented
379C2×C53C2×#39411yescharacteristic
380C22×#41C2×D5311yescharacteristic
381C23×Q8—531no—
382C2×#137—534no—
383C2×#137—1062no—
384C2×#137—1062no—
385C2×#137—1062no—
386C2×#137—1062no—
387C2×#137—1062no—
388C22×Q16—1061no—
389C22×SD16—1061no—
390C22×M16—531no—
391C22×M16—531no—
392C22×M16C2×D5311yescharacteristic
393C22×M16C2×D5311yescharacteristic
394C2×#117—531no—
395#430—534no—
396#430—1062no—
397C2×#108—1062no—
398#421—534no—
399#421—1062no—
400C2×#104—1062no—
401#419—534no—
402#419—1062no—
403C2×#103—1062no—
404#413—22no—
405#413C2×D5314yes—
406C2×#101—21no—
407C2×#101—534no—
408C2×#101—1062no—
409C2×#101—1062no—
410C2×#100—21no—
411#344—534no—
412C53C2×#204911yescharacteristic, complemented, Sylow
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41C22⋊D5312yes—
424C2×#41C22×D5312yes—
425C22×Q8—532no—
426C22×Q8—532no—
427C22×Q8—532no—
428C22×Q8—1061no—
429C22×Q8—1061no—
430C22×Q8—1061no—
431C22×Q8—1061no—
432C22×Q8—1061no—
433C22×Q8—1061no—
434C22×Q8—1061no—
435C22×Q8—1061no—
436C22×Q8—1061no—
437C22×Q8—1061no—
438C22×Q8—1061no—
439C22×Q8C22⋊D5311yescharacteristic
440C22×D4—21no—
441C22×D4C22⋊D5311yescharacteristic
442C23×C4—21no—
443C23×C4—1061no—
444C23×C4C22×D5311yescharacteristic
445#137—1068no—
446#137—1068no—
447#137—1068no—
448#137—1068no—
449C2×Q16—1064no—
450C2×Q16—1064no—
451C2×Q16—1064no—
452C2×SD16—1064no—
453C2×SD16—1064no—
454C2×SD16—1064no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—532no—
466C2×M16—532no—
467C2×M16—532no—
468C2×M16—532no—
469C2×M16—532no—
470C2×M16—532no—
471C2×M16—1061no—
472C2×M16—1061no—
473C2×M16—1061no—
474C2×M16—1061no—
475C2×M16—1061no—
476C2×M16—1061no—
477C2×M16C22×D5312yes—
478C2×M16C22×D5312yes—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—1061no—
482C22×C8—1061no—
483#117—532no—
484#117—1061no—
485#117—1061no—
486#117—1061no—
487C2×C4⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C42—1061no—
490#108—1068no—
491#104—1068no—
492#103—1068no—
493#101—24no—
494#101—1068no—
495#100—24no—
496C24—21no—
497C24#1171994511yescharacteristic
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—534no—
520C2×Q8—1062no—
521C2×Q8—1062no—
522C2×Q8—1062no—
523C2×Q8—1062no—
524C2×Q8—1062no—
525C2×Q8—1062no—
526C2×Q8—1062no—
527C2×Q8—1062no—
528C2×Q8—1062no—
529C2×Q8—1062no—
530C2×Q8—1062no—
531C2×Q8—1062no—
532C2×Q8—1062no—
533C2×Q8—1062no—
534C2×Q8—1062no—
535C2×Q8—2121no—
536C2×Q8—2121no—
537C2×Q8—2121no—
538C2×Q8—2121no—
539C2×Q8—2121no—
540C2×Q8—2121no—
541C2×Q8—2121no—
542C2×Q8—2121no—
543C2×Q8—2121no—
544C2×Q8—2121no—
545C2×Q8—2121no—
546C2×Q8—2121no—
547C2×Q8C2×C22⋊D5312yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×C22⋊D5312yes—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—2121no—
571C22×C4—2121no—
572C22×C4—2121no—
573C22×C4—2121no—
574C22×C4—2121no—
575C22×C4#1171994511yescharacteristic
576C22×C4#1171994511yescharacteristic
577C22×C4#1171994511yescharacteristic
578C22×C4D4×D5311yescharacteristic
579C22×C4D4×D5311yescharacteristic
580C22×C4D4×D5311yescharacteristic
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4D4×D5311yescharacteristic
584C22×C4#1171994711yescharacteristic
585C22×C4#1171994711yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C23×D5311yescharacteristic
589Q16—10616no—
590SD16—10616no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—22no—
595M16—41no—
596M16—41no—
597M16—41no—
598M16—41no—
599M16—534no—
600M16—534no—
601M16—1062no—
602M16—1062no—
603M16—1062no—
604M16—1062no—
605M16—1062no—
606M16—1062no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—1062no—
614C2×C8—1062no—
615C2×C8—1062no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—1062no—
619C4⋊C4—1062no—
620C4⋊C4—2121no—
621C22⋊C4—1062no—
622C22⋊C4—2121no—
623C42—1062no—
624C42—2121no—
625C23—22no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—82no—
630C23#1313319011yescharacteristic
631C23#1313319011yescharacteristic
632C23#1313320011yescharacteristic
633C23#1313320011yescharacteristic
634C23#1313320311yescharacteristic
635C23#1313320311yescharacteristic
636C23C2×#1171994511yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—1064no—
642Q8—1064no—
643Q8—2122no—
644Q8—2122no—
645Q8—2122no—
646Q8—2122no—
647Q8—2122no—
648Q8—2122no—
649D4—22no—
650D4—22no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—41no—
656D4—41no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—1064no—
665C2×C4—4242no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4#1313318511yescharacteristic
674C2×C4#1313318511yescharacteristic
675C2×C4#1313318511yescharacteristic
676C2×C4#1313318511yescharacteristic
677C2×C4#1313318911yescharacteristic
678C2×C4#1313318911yescharacteristic
679C2×C4#1313318911yescharacteristic
680C2×C4#1313318911yescharacteristic
681C2×C4#1313319011yescharacteristic
682C2×C4#1313319011yescharacteristic
683C2×C4#1313319011yescharacteristic
684C2×C4#1313319011yescharacteristic
685C2×C4#1313319011yescharacteristic
686C2×C4#1313319011yescharacteristic
687C2×C4#1313319911yescharacteristic
688C2×C4#1313319911yescharacteristic
689C2×C4#1313319911yescharacteristic
690C2×C4#1313319911yescharacteristic
691C2×C4#1313320011yescharacteristic
692C2×C4#1313320011yescharacteristic
693C2×C4#1313320311yescharacteristic
694C2×C4#1313320311yescharacteristic
695C2×C4C2×D4×D5311yescharacteristic
696C2×C4C2×D4×D5311yescharacteristic
697C2×C4C2×D4×D5311yescharacteristic
698C2×C4C22×C22⋊D5311yescharacteristic
699C2×C4C2×#1171994711yescharacteristic
700C2×C4C2×#1171994511yescharacteristic
701C8—42no—
702C8—42no—
703C8—1064no—
704C8—1064no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22#1681053811yescharacteristic
717C22#1681053811yescharacteristic
718C22#1681053811yescharacteristic
719C22#1681053811yescharacteristic
720C22C2×#1313319011yescharacteristic
721C22C2×#1313320011yescharacteristic
722C22C2×#1313320311yescharacteristic
723C4—42no—
724C4—4242no—
725C4—2124no—
726C4#1681053811yescharacteristic
727C4#1681053811yescharacteristic
728C4#1681053811yescharacteristic
729C4#1681053811yescharacteristic
730C4C2×#1313318511yescharacteristic
731C4C2×#1313318911yescharacteristic
732C4C2×#1313319011yescharacteristic
733C4C2×#1313319911yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2#2027599512yesdirect product factor
742C2C2×#1681053811yescharacteristic
subgroupG/H
centerC22#16810538
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#413C2
socleC22×C53#394
prime radicalC22×#41×C53C22
hypercenterC2×#413D53
hypocenterC53C2×#2049
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#16810671C2semidirect
4. C2×#16810633C2semidirect
5. C22×#13133135C2semidirect
6. #20275995C2direct (N × H)
7. C2×#16810394C2semidirect
22. #16810671C22semidirect
28. #16810633C22semidirect
32. C2×#13133135C22semidirect
33. #16810394C22semidirect
378. C2×C53#2049semidirect
412. C53C2×#2049semidirect
741. C2#20275995direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332472
C2×#168106712
C2×#168106402
C2×#168106332
C22×#131331352
#202759952
C2×#168103942
C2×C53×#4132
C2×#204953