Finite Group Databasebeta

← C2×#20283808 #28249046

Subgroups — C2×#20283808 #28249046

Order 13568.

1750 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic
2#20283808C2116yesmaximal, direct product factor
3C2×#16810754C211yesmaximal, characteristic, complemented
4C2×#16810752C211yesmaximal, characteristic, complemented
5C2×#16810752C211yesmaximal, characteristic, complemented
6C2×#16810751C211yesmaximal, characteristic, complemented
7C2×#16810751C211yesmaximal, characteristic, complemented
8C2×C8×Dic106C211yesmaximal, characteristic, complemented
9C2×#16810747C211yesmaximal, characteristic, complemented
10C2×#16810685C211yesmaximal, characteristic
11C2×#16810683C211yesmaximal, characteristic
12C2×#16810683C211yesmaximal, characteristic
13C2×#16810682C211yesmaximal, characteristic
14C2×#16810678C211yesmaximal, characteristic
15C2×#16810675C211yesmaximal, characteristic
16C2×C53×#446C211yesmaximal, characteristic, complemented
17#16811177C418yes—
18#16811177C2218yes—
19C2×#13133216C411yescharacteristic
20C2×#13133215C411yescharacteristic
21C2×#13133207C411yescharacteristic
22C2×#13133207C411yescharacteristic
23C2×#13133197C411yescharacteristic
24C2×#13133195C411yescharacteristic
25C2×#13133195C411yescharacteristic
26C2×#13133193C411yescharacteristic
27C2×C4×Dic106C2211yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×Dic106C2211yescharacteristic
30C2×#13133174C2211yescharacteristic
31C2×#13133174C2211yescharacteristic
32C2×C42×D53C2211yescharacteristic
33#16810754C2218yescomplemented
34#16810752C2218yescomplemented
35#16810752C2218yescomplemented
36#16810751C2218yescomplemented
37#16810751C2218yescomplemented
38C8×Dic106C2218yescomplemented
39#16810747C2218yescomplemented
40#16810685C2218yes—
41#16810683C2218yes—
42#16810683C2218yes—
43#16810682C2218yes—
44#16810678C2218yes—
45#16810675C2218yes—
46C2×C4⋊#88322C2211yescharacteristic
47C2×C4⋊#88322C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×#13133146C2211yescharacteristic
50C2×#13133146C2211yescharacteristic
51C2×#13133146C2211yescharacteristic
52C2×#13133146C2211yescharacteristic
53C2×#13133146C2211yescharacteristic
54C2×#13133146C2211yescharacteristic
55C2×#13133129C2211yescharacteristic
56C2×#13133129C2211yescharacteristic
57C2×#13133129C2211yescharacteristic
58C2×#13133129C2211yescharacteristic
59C2×#13133128C2211yescharacteristic
60C2×#13133128C2211yescharacteristic
61C2×#13133127C2211yescharacteristic
62C2×#13133127C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C2×C8×Dic53C2211yescharacteristic
65C2×C8×Dic53C2211yescharacteristic
66C2×C8×Dic53C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C4×Q8×C53C2211yescharacteristic
69C53×#446C2218yescomplemented
70C2×C4⋊C8×C53C2211yescharacteristic
71C2×C4⋊C8×C53C2211yescharacteristic
72C2×C4⋊C8×C53C2211yescharacteristic
73C2×#97×C53C2211yescharacteristic
74C2×#97×C53C2211yescharacteristic
75C2×C4×C8×C53C2211yescharacteristic
76C22×Dic106C2×C411yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×Dic106C2×C411yescharacteristic
79C22×C4×D53C2×C411yescharacteristic
80C22×C4×D53C2×C411yescharacteristic
81C22×C4×D53C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86#13133216C2×C418yes—
87#13133215C2×C418yes—
88#13133207C2×C418yes—
89#13133207C2×C418yes—
90#13133197C2×C418yes—
91#13133195C2×C418yes—
92#13133195C2×C418yes—
93#13133193C2×C418yes—
94C4×Dic106C2×C414yes—
95C4×Dic106C2×C414yes—
96C4×Dic106C2×C414yes—
97C4×Dic106C2314yes—
98C4×Dic106C2314yes—
99C4×Dic106C2314yes—
100#13133174C2×C414yes—
101#13133174C2×C414yes—
102#13133174C2314yes—
103#13133174C2314yes—
104C2×C4⋊Dic53C2×C411yescharacteristic
105C2×C4⋊Dic53C2×C411yescharacteristic
106C2×C4⋊Dic53C2×C411yescharacteristic
107C2×#11719919C2×C411yescharacteristic
108C2×#11719919C2×C411yescharacteristic
109C2×#11719919C2×C411yescharacteristic
110C2×#11719919C2×C411yescharacteristic
111C2×#11719919C2×C411yescharacteristic
112C2×#11719919C2×C411yescharacteristic
113C2×#11719919C2×C411yescharacteristic
114C2×#11719919C2×C411yescharacteristic
115C2×#11719919C2×C411yescharacteristic
116C2×#11719919C2×C411yescharacteristic
117C2×#11719921C2×C411yescharacteristic
118C2×#11719921C2×C411yescharacteristic
119C2×#11719921C2×C411yescharacteristic
120C2×#11719921C2×C411yescharacteristic
121C2×C4×Dic53C2×C411yescharacteristic
122C2×C4×Dic53C2×C411yescharacteristic
123C2×C4×Dic53C2311yescharacteristic
124C2×C4×Dic53C2311yescharacteristic
125C2×C4×Dic53C2311yescharacteristic
126C42×D53C2×C414yes—
127C42×D53C2314yes—
128C4⋊#88322C2314yes—
129C4⋊#88322C2314yes—
130C4⋊#88322C2314yes—
131#13133146C2314yes—
132#13133146C2314yes—
133#13133146C2314yes—
134#13133146C2314yes—
135#13133146C2314yes—
136#13133146C2314yes—
137#13133129C2314yes—
138#13133129C2314yes—
139#13133129C2314yes—
140#13133129C2314yes—
141#13133128C2314yes—
142#13133128C2314yes—
143#13133127C2314yes—
144#13133127C2314yes—
145C4×#88322C2314yes—
146C8×Dic53C2314yes—
147C8×Dic53C2314yes—
148C8×Dic53C2314yes—
149C8×Dic53C2314yes—
150C22×Q8×C53C2×C411yescharacteristic
151C22×C8×C53C2311yescharacteristic
152C22×C8×C53C2311yescharacteristic
153C22×C8×C53C2311yescharacteristic
154C22×C8×C53C2311yescharacteristic
155C4×Q8×C53C2×C414yes—
156C4×Q8×C53C2314yes—
157C2×C4⋊C4×C53C2×C411yescharacteristic
158C2×C4⋊C4×C53C2×C411yescharacteristic
159C2×C4⋊C4×C53C2×C411yescharacteristic
160C2×C42×C53C2311yescharacteristic
161C2×C42×C53C2311yescharacteristic
162C2×C42×C53C2311yescharacteristic
163C4⋊C8×C53C2314yes—
164C4⋊C8×C53C2314yes—
165C4⋊C8×C53C2314yes—
166#97×C53C2314yes—
167#97×C53C2314yes—
168C4×C8×C53C2314yes—
169C23×D53C22×C411yescharacteristic
170C2×Q8×C53—42no—
171C2×Q8×C53C22×C414yes—
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C22×C411yescharacteristic
176C22×C4×C53C22×C411yescharacteristic
177C22×C4×C53C22×C411yescharacteristic
178C22×C4×C53C2411yescharacteristic
179C22×Dic53C22×C411yescharacteristic
180C22×Dic53C22×C411yescharacteristic
181C22×Dic53C22×C411yescharacteristic
182C22×Dic53C22×C411yescharacteristic
183C22×Dic53C22×C411yescharacteristic
184C22×Dic53C22×C411yescharacteristic
185C22×Dic53C22×C411yescharacteristic
186C2×C4×D53—22no—
187C2×C4×D53—22no—
188C2×C4×D53—24no—
189C2×C4×D53—42no—
190C2×C4×D53C22×C412yes—
191C2×C4×D53C22×C414yes—
192C2×C4×D53C22×C414yes—
193C2×C4×D53C2412yes—
194C2×Dic106—24no—
195C2×Dic106—24no—
196C2×Dic106—42no—
197C2×Dic106C22×C414yes—
198C2×Dic106C22×C414yes—
199C2×Dic106C22×C414yes—
200C2×C8×C53—22no—
201C2×C8×C53—22no—
202C2×C8×C53—22no—
203C2×C8×C53—22no—
204C2×C8×C53C2412yes—
205C2×C8×C53C2412yes—
206C2×C8×C53C2412yes—
207C2×C8×C53C2412yes—
208C4⋊C4×C53C22×C414yes—
209C4⋊C4×C53C22×C414yes—
210C4⋊C4×C53C22×C414yes—
211C42×C53C22×C412yes—
212C42×C53C22×C412yes—
213C42×C53C22×C412yes—
214C42×C53C2412yes—
215C42×C53C2412yes—
216C42×C53C2412yes—
217#11719921C22×C414yes—
218#11719921C22×C414yes—
219#11719921C22×C414yes—
220#11719921C22×C414yes—
221C4⋊Dic53C22×C414yes—
222C4⋊Dic53C22×C414yes—
223C4⋊Dic53C22×C414yes—
224#11719919C22×C414yes—
225#11719919C22×C414yes—
226#11719919C22×C414yes—
227#11719919C22×C414yes—
228#11719919C22×C414yes—
229#11719919C22×C414yes—
230#11719919C22×C414yes—
231#11719919C22×C414yes—
232#11719919C22×C414yes—
233#11719919C22×C414yes—
234C4×Dic53C22×C412yes—
235C4×Dic53C22×C414yes—
236C4×Dic53C22×C414yes—
237C4×Dic53C22×C412yes—
238C4×Dic53C22×C412yes—
239C4×Dic53C2412yes—
240C4×Dic53C2412yes—
241C4×Dic53C2412yes—
242C2×#88322—22no—
243C2×#88322—22no—
244C2×#88322—22no—
245C2×#88322—22no—
246C2×#88322C2412yes—
247C2×#88322C2412yes—
248C2×#88322C2412yes—
249C2×#88322C2412yes—
250C23×C53C23×C411yescharacteristic
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53C23×C412yes—
255Q8×C53—44no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53C23×C412yes—
263C2×C4×C53C23×C412yes—
264C2×C4×C53C23×C412yes—
265C2×C4×C53C23×C412yes—
266C2×C4×C53C23×C412yes—
267C2×C4×C53C23×C412yes—
268C2×C4×C53C23×C411yescharacteristic
269C2×C4×C532−1+412yes—
270C2×C4×C532−1+412yes—
271C2×C4×C53C2511yescharacteristic
272C2×Dic53—22no—
273C2×Dic53—22no—
274C2×Dic53—22no—
275C2×Dic53—22no—
276C2×Dic53—22no—
277C2×Dic53—22no—
278C2×Dic53#13114yes—
279C2×Dic53C23×C412yes—
280C2×Dic53C23×C412yes—
281C2×Dic53C23×C412yes—
282C2×Dic53C23×C412yes—
283C2×Dic53C23×C412yes—
284C2×Dic53C23×C412yes—
285C2×Dic53C23×C412yes—
286C4×D53—24no—
287C4×D53—22no—
288C4×D53—22no—
289C4×D53—28no—
290C4×D53—44no—
291Dic106—28no—
292Dic106—28no—
293Dic106—44no—
294C8×C53—22no—
295C8×C53—22no—
296C8×C53—22no—
297C8×C53—22no—
298#88322—22no—
299#88322—22no—
300#88322—22no—
301#88322—22no—
302C2×#2985—531nomaximal, Sylow
303C22×C53#51912yes—
304C22×C53C2×#13112yes—
305C22×C53#56812yes—
306C22×C53C24×C411yescharacteristic
307C2×D53—22no—
308C2×D53—22no—
309C2×D53—22no—
310C2×D53—44no—
311C4×C53—22no—
312C4×C53—22no—
313C4×C53—22no—
314C4×C53—22no—
315C4×C53—22no—
316C4×C53—22no—
317C4×C53#51912yes—
318C4×C53C2×2−1+411yescharacteristic
319C4×C53C2×2−1+411yescharacteristic
320Dic53—22no—
321Dic53—22no—
322Dic53—22no—
323Dic53—22no—
324Dic53—22no—
325Dic53—22no—
326Dic53C2×#13114yes—
327C2×#533—531no—
328#2985—5316no—
329C2×#446—531no—
330C2×#446—531no—
331C2×#446—531no—
332C2×#446—531no—
333C2×#446—531no—
334C2×#446D5311yescharacteristic, complemented
335C2×C8×Q8—531no—
336C2×C8×Q8—531no—
337C2×#433—531no—
338C2×#433—531no—
339C2×#433—531no—
340C2×#433—531no—
341C2×#432—531no—
342C2×#431—531no—
343C2×C53#298514yescomplemented
344C2×C53C2×#51911yescharacteristic
345C2×C53C22×#13111yescharacteristic
346C2×C53C2×#56811yescharacteristic
347D53—42no—
348#533—538no—
349#533—538no—
350C2×C4⋊Q8—531no—
351C2×C4⋊Q8—531no—
352C2×#125—531no—
353C2×#125—531no—
354C2×C22⋊Q8—531no—
355C2×C22⋊Q8—531no—
356C2×C22⋊Q8—531no—
357C2×C22⋊Q8—531no—
358C2×C4×Q8—531no—
359C2×C4×Q8—531no—
360C2×C4×Q8—531no—
361C2×C4×Q8C2×D5311yescharacteristic
362C2×#117—531no—
363C2×#117—531no—
364C22×C42—531no—
365#446—538no—
366#446—538no—
367#446—538no—
368#446—538no—
369#446—538no—
370#446C2×D5318yescomplemented
371C8×Q8—538no—
372C8×Q8—538no—
373#433—538no—
374#433—538no—
375#433—538no—
376#433—538no—
377#432—538no—
378#431—538no—
379C2×C4⋊C8—531no—
380C2×C4⋊C8—531no—
381C2×C4⋊C8—531no—
382C2×C4⋊C8—531no—
383C2×C4⋊C8—531no—
384C2×C4⋊C8—531no—
385C2×C4⋊C8—531no—
386C2×C4⋊C8—531no—
387C2×C4⋊C8—531no—
388C2×C4⋊C8C2×D5311yescharacteristic
389C2×C4⋊C8C2×D5311yescharacteristic
390C2×C4⋊C8C2×D5311yescharacteristic
391C2×C22⋊C8—531no—
392C2×C22⋊C8—531no—
393C2×C22⋊C8—531no—
394C2×C22⋊C8—531no—
395C2×#97—531no—
396C2×#97—531no—
397C2×#97—531no—
398C2×#97—531no—
399C2×#97C2×D5311yescharacteristic
400C2×#97C2×D5311yescharacteristic
401C2×C4×C8—531no—
402C2×C4×C8—531no—
403C2×C4×C8—531no—
404C2×C4×C8—531no—
405C2×C4×C8—531no—
406C2×C4×C8C2×D5311yescharacteristic
407C53C2×#298511yescharacteristic, complemented, Sylow
408C22×Q8—531no—
409C22×Q8—531no—
410C22×Q8—531no—
411C22×Q8C4×D5311yescharacteristic
412C23×C4—531no—
413C23×C4—531no—
414C23×C4—531no—
415C22×C8—531no—
416C22×C8—531no—
417C22×C8—531no—
418C22×C8—531no—
419C22×C8C22×D5311yescharacteristic
420C22×C8C22×D5311yescharacteristic
421C22×C8C22×D5311yescharacteristic
422C22×C8C22×D5311yescharacteristic
423C4⋊Q8—538no—
424C4⋊Q8—538no—
425#125—538no—
426#125—538no—
427C22⋊Q8—538no—
428C22⋊Q8—538no—
429C22⋊Q8—538no—
430C22⋊Q8—538no—
431C4×Q8—534no—
432C4×Q8—534no—
433C4×Q8—534no—
434C4×Q8—534no—
435C4×Q8—534no—
436C4×Q8—534no—
437C4×Q8C4×D5314yes—
438C4×Q8C22×D5314yes—
439#117—534no—
440#117—534no—
441#117—534no—
442#117—534no—
443C2×C4⋊C4—531no—
444C2×C4⋊C4—531no—
445C2×C4⋊C4—531no—
446C2×C4⋊C4—531no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—531no—
450C2×C4⋊C4—531no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—531no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4C4×D5311yescharacteristic
457C2×C4⋊C4C4×D5311yescharacteristic
458C2×C4⋊C4C4×D5311yescharacteristic
459C2×C22⋊C4—531no—
460C2×C22⋊C4—531no—
461C2×C22⋊C4—531no—
462C2×C22⋊C4—531no—
463C2×C42—531no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—531no—
467C2×C42—531no—
468C2×C42—534no—
469C2×C42—534no—
470C2×C42C22×D5311yescharacteristic
471C2×C42C22×D5311yescharacteristic
472C2×C42C22×D5311yescharacteristic
473C4⋊C8—534no—
474C4⋊C8—534no—
475C4⋊C8—534no—
476C4⋊C8—534no—
477C4⋊C8—534no—
478C4⋊C8—534no—
479C4⋊C8—534no—
480C4⋊C8—534no—
481C4⋊C8—534no—
482C4⋊C8C22×D5314yes—
483C4⋊C8C22×D5314yes—
484C4⋊C8C22×D5314yes—
485C22⋊C8—534no—
486C22⋊C8—534no—
487C22⋊C8—534no—
488C22⋊C8—534no—
489#97—534no—
490#97—534no—
491#97—534no—
492#97—534no—
493#97C22×D5314yes—
494#97C22×D5314yes—
495C4×C8—534no—
496C4×C8—534no—
497C4×C8—534no—
498C4×C8—534no—
499C4×C8—534no—
500C4×C8C22×D5314yes—
501C24—531no—
502C2×Q8—42no—
503C2×Q8—534no—
504C2×Q8—534no—
505C2×Q8—534no—
506C2×Q8—1064no—
507C2×Q8—1064no—
508C2×Q8—2122no—
509C2×Q8C2×C4×D5314yes—
510C22×C4—531no—
511C22×C4—531no—
512C22×C4—531no—
513C22×C4—531no—
514C22×C4—531no—
515C22×C4—531no—
516C22×C4—531no—
517C22×C4—532no—
518C22×C4—534no—
519C22×C4—532no—
520C22×C4—534no—
521C22×C4—1064no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—2122no—
525C22×C4C2×C4×D5311yescharacteristic
526C22×C4C2×C4×D5311yescharacteristic
527C22×C4C2×C4×D5311yescharacteristic
528C22×C4C2×C4×D5311yescharacteristic
529C22×C4C2×C4×D5311yescharacteristic
530C22×C4C2×C4×D5311yescharacteristic
531C22×C4C23×D5311yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—532no—
537C2×C8—532no—
538C2×C8—532no—
539C2×C8—532no—
540C2×C8—1062no—
541C2×C8—1062no—
542C2×C8—1062no—
543C2×C8—1062no—
544C2×C8C23×D5312yes—
545C2×C8C23×D5312yes—
546C2×C8C23×D5312yes—
547C2×C8C23×D5312yes—
548C4⋊C4—534no—
549C4⋊C4—534no—
550C4⋊C4—534no—
551C4⋊C4—534no—
552C4⋊C4—534no—
553C4⋊C4—534no—
554C4⋊C4—534no—
555C4⋊C4—534no—
556C4⋊C4—534no—
557C4⋊C4—534no—
558C4⋊C4—534no—
559C4⋊C4—534no—
560C4⋊C4—534no—
561C4⋊C4C2×C4×D5314yes—
562C4⋊C4C2×C4×D5314yes—
563C4⋊C4C2×C4×D5314yes—
564C22⋊C4—534no—
565C22⋊C4—534no—
566C22⋊C4—534no—
567C22⋊C4—534no—
568C42—532no—
569C42—534no—
570C42—534no—
571C42—532no—
572C42—532no—
573C42—532no—
574C42—532no—
575C42—532no—
576C42C2×C4×D5312yes—
577C42C2×C4×D5312yes—
578C42C2×C4×D5312yes—
579C42C23×D5312yes—
580C42C23×D5312yes—
581C42C23×D5312yes—
582C23—532no—
583C23—1062no—
584C23—1062no—
585C23—1062no—
586C23C22×C4×D5311yescharacteristic
587Q8—44no—
588Q8—1068no—
589Q8—1068no—
590Q8—2124no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—534no—
598C2×C4—532no—
599C2×C4—532no—
600C2×C4—532no—
601C2×C4—532no—
602C2×C4—532no—
603C2×C4—532no—
604C2×C4—532no—
605C2×C4—1068no—
606C2×C4—1062no—
607C2×C4—1062no—
608C2×C4—1062no—
609C2×C4—1062no—
610C2×C4—1062no—
611C2×C4—1062no—
612C2×C4—1064no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—2124no—
616C2×C4C22×C4×D5312yes—
617C2×C4C22×C4×D5312yes—
618C2×C4C22×C4×D5312yes—
619C2×C4C22×C4×D5312yes—
620C2×C4C22×C4×D5312yes—
621C2×C4C22×C4×D5312yes—
622C2×C4C22×C4×D5311yescharacteristic
623C2×C4#1313326412yes—
624C2×C4#1313326512yes—
625C2×C4C24×D5311yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—1062no—
631C8—1062no—
632C8—1062no—
633C8—1062no—
634C22—1062no—
635C22—1062no—
636C22—1062no—
637C22—2124no—
638C22#1681109912yes—
639C22#131×D5312yes—
640C22#1681138912yes—
641C22C23×C4×D5311yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—534no—
649C4—1062no—
650C4—1062no—
651C4—1062no—
652C4—1062no—
653C4—1062no—
654C4—1062no—
655C4#1681109912yes—
656C4C2×#1313326411yescharacteristic
657C4C2×#1313326511yescharacteristic
658C2—2122no—
659C2#2028380814yesdirect product factor
660C2C2×#1681109911yescharacteristic
661C2C2×#131×D5311yescharacteristic
662C2C2×#1681138911yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutatorC22×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C53×#446C2
socleC23×C53C23×C4
prime radicalC23×D53C22×C4
cosocleC2×C4×C53C25
hypercenterC2×#446D53
hypocenterC53C2×#2985
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #20283808C2direct (N × H)
3. C2×#16810754C2semidirect
4. C2×#16810752C2semidirect
5. C2×#16810752C2semidirect
6. C2×#16810751C2semidirect
7. C2×#16810751C2semidirect
8. C2×C8×Dic106C2semidirect
9. C2×#16810747C2semidirect
16. C2×C53×#446C2semidirect
33. #16810754C22semidirect
34. #16810752C22semidirect
35. #16810752C22semidirect
36. #16810751C22semidirect
37. #16810751C22semidirect
38. C8×Dic106C22semidirect
39. #16810747C22semidirect
69. C53×#446C22semidirect
334. C2×#446D53semidirect
343. C2×C53#2985semidirect
370. #446C2×D53semidirect
407. C53C2×#2985semidirect
659. C2#20283808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
#202838082
C2×#168107542
C2×#168107522
C2×#168107512
C2×C8×Dic1062
C2×#168107472
C2×#168106852
C2×#168106832
C2×#168106822
C2×#168106782
C2×#168106752
C2×C53×#4462
C2×#298553