Finite Group Databasebeta

← C2×#20285017 #28252450

Subgroups — C2×#20285017 #28252450

Order 13568.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811236C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic
3#20285017C2116yesmaximal, direct product factor
4C2×#16810967C211yesmaximal, characteristic
5C2×#16810966C211yesmaximal, characteristic
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810834C211yesmaximal, characteristic, complemented
8C2×#16810833C211yesmaximal, characteristic, complemented
9C2×#16810780C211yesmaximal, characteristic
10C2×#16810780C211yesmaximal, characteristic
11C2×#16810729C211yesmaximal, characteristic, complemented
12C2×#16810727C211yesmaximal, characteristic, complemented
13C2×#16810717C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic
16C2×C53×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22#16811236—24no—
23#16811236C2218yes—
24C2×#13133217C2211yescharacteristic
25C2×#13133212—21no—
26C2×#13133212—21no—
27C2×#13133208—21no—
28C2×#13133208—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133197C2211yescharacteristic
31#16811099—24no—
32#16811099C2218yes—
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×#13133182—21no—
37C2×#13133182C2211yescharacteristic
38C2×#13133182C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×#13133175—21no—
41C2×#13133175C2211yescharacteristic
42C2×#13133174—21no—
43C2×#13133174C2211yescharacteristic
44#16810967C2218yes—
45#16810966C2218yes—
46#16810927C2218yescomplemented
47#16810834C2218yescomplemented
48#16810833C2218yescomplemented
49#16810780C2218yes—
50#16810780C2218yes—
51#16810729C2218yescomplemented
52#16810727C2218yescomplemented
53#16810717C2218yescomplemented
54#16810715C2218yescomplemented
55#16810683C2218yes—
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#479C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—24no—
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53C2314yes—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C2×Dic212—24no—
88C2×Dic212—24no—
89C2×Dic212C2314yes—
90C2×Dic212C2314yes—
91C2×#11719925—24no—
92C2×#11719925—24no—
93C2×#11719925C2314yes—
94C2×#11719925C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133217—22no—
98#13133217C2314yes—
99#13133212—28no—
100#13133212—28no—
101#13133208—28no—
102#13133208—28no—
103#13133197—22no—
104#13133197—22no—
105#13133197C2314yes—
106#13133197C2314yes—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109C4×Dic106—22no—
110C4×Dic106—28no—
111C4×Dic106C2314yes—
112#13133182—28no—
113#13133182—22no—
114#13133182—22no—
115#13133182—22no—
116#13133182C2314yes—
117#13133182C2314yes—
118#13133182C2314yes—
119#13133175—28no—
120#13133175—22no—
121#13133175C2314yes—
122#13133174—28no—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×#11719919D411yescharacteristic
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921D411yescharacteristic
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#125×C53—22no—
166#125×C53C2314yes—
167C4×Q8×C53—22no—
168C4×Q8×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53#4114yes—
186C2×Q8×C53C2412yes—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2411yescharacteristic
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201Q8×D53—216no—
202Q8×D53—28no—
203Q8×D53—28no—
204C2×C4×D53—28no—
205C2×C4×D53—24no—
206C2×C4×D53—22no—
207C2×C4×D53—22no—
208C2×C4×D53C2×D412yes—
209C2×C4×D53C2412yes—
210C2×Dic106—28no—
211C2×Dic106—21no—
212C2×Dic106—22no—
213C2×Dic106—24no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—21no—
219C2×Dic106—21no—
220C2×Dic106#4114yes—
221C2×Dic106C2412yes—
222C2×Dic106C2412yes—
223C2×Dic106C2412yes—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C42×C53—24no—
238C42×C53C2×D412yes—
239C42×C53C2412yes—
240#11719925—28no—
241#11719925—28no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921C2×D414yes—
246#11719921C2×D414yes—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919C2×D414yes—
259#11719919C2×D414yes—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53C2×D412yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272Dic212—28no—
273Dic212—28no—
274C23×C53C22×D411yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53C22×D412yes—
279Q8×C53—24no—
280Q8×C53—22no—
281Q8×C53C2×#4114yes—
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×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4112yes—
296C2×C4×C53C2×#4112yes—
297C2×C4×C53C2511yescharacteristic
298C2×Dic53—22no—
299C2×Dic53—24no—
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×Dic53C22×D412yes—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C4×D53—216no—
313C4×D53—24no—
314C4×D53—22no—
315C4×D53—22no—
316Dic106—216no—
317Dic106—24no—
318Dic106—22no—
319Dic106—22no—
320Dic106—22no—
321Dic106—22no—
322Dic106—22no—
323Dic106—42no—
324Dic106—42no—
325Dic106C2×#4114yes—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322—22no—
330C2×#3127—531nomaximal, Sylow
331C22×C53#52512yes—
332C22×C53#57812yes—
333C22×C53#57812yes—
334C22×C53C23×D411yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—44no—
339C4×C53—24no—
340C4×C53—22no—
341C4×C53—22no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53#52512yes—
346C4×C53C22×#4111yescharacteristic
347C4×C53C22×#4111yescharacteristic
348Dic53—22no—
349Dic53—24no—
350Dic53—22no—
351Dic53—22no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355C2×#541—531no—
356C2×#519—531no—
357#3127—5316no—
358C2×#485—531no—
359C2×#485—531no—
360C2×#479—531no—
361C2×#479D5311yescharacteristic, complemented
362C2×#462—531no—
363C2×#462—531no—
364C2×#451—531no—
365C2×#451—531no—
366C2×#441—531no—
367C2×#441—531no—
368C2×C4×Q16—531no—
369C2×C4×Q16—531no—
370C2×#433—531no—
371C2×C53#312714yescomplemented
372C2×C53C2×#52511yescharacteristic
373C2×C53C2×#57811yescharacteristic
374C2×C53C2×#57811yescharacteristic
375D53—42no—
376C23×Q8—531no—
377C22×Q16—531no—
378C22×Q16—531no—
379C22×Q16—531no—
380C22×Q16—531no—
381#541—538no—
382#541—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#125—1061no—
387C2×#125—1061no—
388C2×#125C2×D5311yescharacteristic
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391#519—538no—
392#519—1064no—
393C2×C4×Q8—531no—
394C2×C4×Q8—531no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×Q8—531no—
398C2×C4×Q8—1061no—
399C2×C4×Q8—1061no—
400C2×C4×Q8C2×D5311yescharacteristic
401C2×#117—531no—
402C2×#117—531no—
403C2×#117—1061no—
404C2×#117—1061no—
405#485—538no—
406#485—538no—
407#479—538no—
408#479C2×D5318yescomplemented
409#462—538no—
410#462—538no—
411#451—538no—
412#451—538no—
413#441—538no—
414#441—538no—
415C4×Q16—538no—
416C4×Q16—538no—
417#433—538no—
418C2×#107—531no—
419C2×#107C2×D5311yescharacteristic
420C2×#106—531no—
421C2×#106C2×D5311yescharacteristic
422C2×C4⋊C8—531no—
423C2×C4⋊C8C2×D5311yescharacteristic
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103C2×D5311yescharacteristic
431C2×#103C2×D5311yescharacteristic
432C2×C22⋊C8—531no—
433C2×C22⋊C8—531no—
434C2×#97—531no—
435C2×C4×C8—531no—
436C53C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—534no—
438C22×Q8—531no—
439C22×Q8—531no—
440C22×Q8—531no—
441C22×Q8—1061no—
442C22×Q8—1062no—
443C22×Q8—1064no—
444C22×Q8—1064no—
445C22×Q8C22×D5311yescharacteristic
446C23×C4—531no—
447C23×C4—1061no—
448C2×Q16—534no—
449C2×Q16—534no—
450C2×Q16—534no—
451C2×Q16—534no—
452C2×Q16—1064no—
453C2×Q16—1064no—
454C2×Q16—1064no—
455C2×Q16—1064no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8C22×D5311yescharacteristic
459C22×C8C22×D5311yescharacteristic
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462#126—1068no—
463#126—1068no—
464#125—22no—
465#125—1068no—
466#125—1068no—
467#125C22×D5314yes—
468C22⋊Q8—534no—
469C22⋊Q8—534no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C4×Q8—22no—
473C4×Q8—534no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×Q8—1068no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×Q8—1068no—
484C4×Q8—1062no—
485C4×Q8C22×D5314yes—
486#117—534no—
487#117—534no—
488#117—534no—
489#117—1068no—
490#117—1068no—
491#117—1062no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
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×C4⋊C4C22×D5311yescharacteristic
510C2×C22⋊C4—531no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—21no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42C22×D5311yescharacteristic
524#107—534no—
525#107C22×D5314yes—
526#106—534no—
527#106C22×D5314yes—
528C4⋊C8—534no—
529C4⋊C8C22×D5314yes—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536#103C22×D5314yes—
537#103C22×D5314yes—
538C22⋊C8—534no—
539C22⋊C8—534no—
540#97—534no—
541C4×C8—534no—
542C24—531no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—534no—
546C2×Q8—532no—
547C2×Q8—532no—
548C2×Q8—532no—
549C2×Q8—1064no—
550C2×Q8—1068no—
551C2×Q8—1068no—
552C2×Q8—10616no—
553C2×Q8—1068no—
554C2×Q8—1061no—
555C2×Q8—1061no—
556C2×Q8—1061no—
557C2×Q8—1062no—
558C2×Q8—1062no—
559C2×Q8—1062no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8#1171994914yes—
563C2×Q8C23×D5312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—1064no—
574C22×C4—1068no—
575C22×C4—1061no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584Q16—1068no—
585Q16—1068no—
586Q16—1068no—
587Q16—1068no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—532no—
591C2×C8—532no—
592C2×C8—1062no—
593C2×C8—1062no—
594C2×C8C23×D5312yes—
595C2×C8C23×D5312yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—534no—
603C4⋊C4—534no—
604C4⋊C4—532no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1061no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4C23×D5312yes—
616C4⋊C4C23×D5312yes—
617C4⋊C4C23×D5312yes—
618C22⋊C4—534no—
619C22⋊C4—534no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—24no—
624C42—532no—
625C42—532no—
626C42—1064no—
627C42—1064no—
628C42—1064no—
629C42—1064no—
630C42—1064no—
631C42—1064no—
632C42D4×D5312yes—
633C42C23×D5312yes—
634C23—532no—
635C23—1062no—
636C23—1062no—
637C23—1062no—
638C23C2×D4×D5311yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—534no—
642Q8—10616no—
643Q8—1064no—
644Q8—1062no—
645Q8—1062no—
646Q8—1062no—
647Q8—1062no—
648Q8—1062no—
649Q8—2122no—
650Q8—2122no—
651Q8C2×#1171994914yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—532no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—10616no—
666C2×C4—1062no—
667C2×C4—1064no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1064no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4C2×D4×D5312yes—
681C2×C4C2×D4×D5312yes—
682C2×C4C2×D4×D5311yescharacteristic
683C2×C4#41×D5312yes—
684C2×C4C2×#1171994912yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—1062no—
691C22—1062no—
692C22—1062no—
693C22—2124no—
694C22#1681113612yes—
695C22#1681143712yes—
696C22#1681143912yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—1062no—
705C4—1062no—
706C4—1062no—
707C4—1064no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4#1681113612yes—
712C4C2×#41×D5311yescharacteristic
713C4C22×#1171994911yescharacteristic
714C2—2122no—
715C2#2028501714yesdirect product factor
716C2C2×#1681113611yescharacteristic
717C2C2×#1681143711yescharacteristic
718C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#479C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#479D53
hypocenterC53C2×#3127
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #20285017C2direct (N × H)
6. C2×#16810927C2semidirect
7. C2×#16810834C2semidirect
8. C2×#16810833C2semidirect
11. C2×#16810729C2semidirect
12. C2×#16810727C2semidirect
13. C2×#16810717C2semidirect
14. C2×#16810715C2semidirect
16. C2×C53×#479C2semidirect
46. #16810927C22semidirect
47. #16810834C22semidirect
48. #16810833C22semidirect
51. #16810729C22semidirect
52. #16810727C22semidirect
53. #16810717C22semidirect
54. #16810715C22semidirect
71. C53×#479C22semidirect
361. C2×#479D53semidirect
371. C2×C53#3127semidirect
408. #479C2×D53semidirect
436. C53C2×#3127semidirect
715. C2#20285017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112362
C2×#168110992
#202850172
C2×#168109672
C2×#168109662
C2×#168109272
C2×#168108342
C2×#168108332
C2×#168107802
C2×#168107292
C2×#168107272
C2×#168107172
C2×#168107152
C2×#168106832
C2×C53×#4792
C2×#312753