Finite Group Databasebeta

← C2×#20285387 #28253964

Subgroups — C2×#20285387 #28253964

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811245C211yesmaximal, characteristic
2C2×#16811231C211yesmaximal, characteristic, complemented
3#20285387C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811016C211yesmaximal, characteristic, complemented
6C2×#16810979C211yesmaximal, characteristic, complemented
7C2×#16810972C211yesmaximal, characteristic, complemented
8C2×#16810878C211yesmaximal, characteristic, complemented
9C2×#16810870C211yesmaximal, characteristic
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810855C211yesmaximal, characteristic
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810721C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×#16810577C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811245—24no—
23#16811245C2218yes—
24#16811231—24no—
25#16811231C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133215C2211yescharacteristic
28C2×#13133212—21no—
29C2×#13133211—21no—
30C2×#13133211—21no—
31C2×#13133209—21no—
32C2×#13133208C2211yescharacteristic
33C2×#13133207—21no—
34C2×#13133206C2211yescharacteristic
35C2×#13133205—21no—
36C2×#13133202—21no—
37C2×#13133197C2211yescharacteristic
38C2×#13133195—21no—
39C2×#13133193C2211yescharacteristic
40C2×#13133193C2211yescharacteristic
41C2×#13133192C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×C4×D212C2211yescharacteristic
44C2×#13133174C2211yescharacteristic
45#16811031C2218yescomplemented
46#16811016C2218yescomplemented
47#16810979C2218yescomplemented
48#16810972C2218yescomplemented
49#16810878C2218yescomplemented
50#16810870C2218yes—
51#16810863C2218yescomplemented
52#16810855C2218yes—
53#16810728C2218yescomplemented
54#16810721C2218yescomplemented
55C4×#11719913C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810577C2218yescomplemented
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C4×Q16×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C2×#11719925—24no—
84C2×#11719925C2314yes—
85C2×#11719913—24no—
86C2×#11719913C2314yes—
87C2×#11719924—24no—
88C2×#11719924C2314yes—
89C2×#11719912—24no—
90C2×#11719912C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C2×C8×D53—24no—
94C2×C8×D53C2314yes—
95#13133216—22no—
96#13133216C2314yes—
97#13133215—22no—
98#13133215C2314yes—
99#13133212—28no—
100#13133211—28no—
101#13133211—28no—
102#13133209—28no—
103#13133208—22no—
104#13133208C2314yes—
105#13133207—28no—
106#13133206—22no—
107#13133206C2314yes—
108#13133205—28no—
109#13133202—28no—
110#13133197—22no—
111#13133197C2314yes—
112#13133195—28no—
113#13133193—22no—
114#13133193—22no—
115#13133193C2314yes—
116#13133193C2314yes—
117#13133192—22no—
118#13133192C2314yes—
119C4×Dic106—22no—
120C4×Dic106C2314yes—
121C4×D212—22no—
122C4×D212C2314yes—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×#11719919D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133149C2314yes—
151#13133148C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133128C2314yes—
159#13133127C2314yes—
160C8×Dic53C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×Q8×C53—22no—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×Q8×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C4×C8×C53C2314yes—
182C23×D53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—21no—
208C2×D212—24no—
209C2×D212—82no—
210C2×D212C2412yes—
211C2×C4×D53—22no—
212C2×C4×D53—22no—
213C2×C4×D53—24no—
214C2×C4×D53—82no—
215C2×C4×D53C2×D412yes—
216C2×C4×D53C2412yes—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—21no—
220C2×Dic106—24no—
221C2×Dic106—82no—
222C2×Dic106C2412yes—
223Q16×C53—28no—
224C2×C8×C53—22no—
225C2×C8×C53#4114yes—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C42×C53—24no—
235C42×C53—24no—
236C42×C53C2×D412yes—
237C42×C53C2412yes—
238#11719925—28no—
239#11719924—28no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921C2×D414yes—
248#11719921C2×D414yes—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919C2×D414yes—
263#11719919C2×D414yes—
264C4×Dic53—24no—
265C4×Dic53C2×D412yes—
266C4×Dic53C2412yes—
267C2×#88322—22no—
268C2×#88322#4114yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271#11719913—28no—
272#11719912—28no—
273C8×D53—28no—
274C23×C53C22×D411yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53C22×D412yes—
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—42no—
288Q8×C53—42no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4112yes—
303C2×C4×C53C2×#4112yes—
304C2×C4×C53C2511yescharacteristic
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317D212—22no—
318D212—22no—
319D212—42no—
320D212—84no—
321C4×D53—24no—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—84no—
325Dic106—22no—
326Dic106—22no—
327Dic106—42no—
328Dic106—84no—
329C8×C53—22no—
330C8×C53C2×#4114yes—
331#88322—22no—
332#88322C2×#4114yes—
333C2×#3178—531nomaximal, Sylow
334C22×C53#53212yes—
335C22×C53#57712yes—
336C22×C53#57812yes—
337C22×C53C23×D411yescharacteristic
338C2×D53—22no—
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—44no—
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—84no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#53212yes—
353C4×C53C22×#4111yescharacteristic
354C4×C53C22×#4111yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#542—531no—
362C2×#541—531no—
363#3178—5316no—
364C2×#501—531no—
365C2×#497—531no—
366C2×#488—531no—
367C2×#487—531no—
368C2×#470—531no—
369C2×#468—531no—
370C2×#467—531no—
371C2×#465—531no—
372C2×#441—531no—
373C2×#440—531no—
374C2×C4×Q16D5311yescharacteristic, complemented
375C2×C4×SD16—531no—
376C2×#405—531no—
377C2×C53#317814yescomplemented
378C2×C53C2×#53211yescharacteristic
379C2×C53C2×#57711yescharacteristic
380C2×C53C2×#57811yescharacteristic
381D53—42no—
382D53—82no—
383C22×Q16—531no—
384C22×Q16C2×D5311yescharacteristic
385C22×SD16—531no—
386C22×SD16—531no—
387C22×M16—531no—
388C23×C8—531no—
389#542—538no—
390#542—1064no—
391#541—538no—
392#541—1064no—
393C2×C4⋊Q8—531no—
394C2×C4⋊Q8—531no—
395C2×#126—1061no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×#124—531no—
402C2×#124—1061no—
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×Q8C2×D5311yescharacteristic
412C2×C4×D4—531no—
413C2×#117—531no—
414#501—538no—
415#497—538no—
416#488—538no—
417#487—538no—
418#470—538no—
419#468—538no—
420#467—538no—
421#465—538no—
422#441—538no—
423#440—538no—
424C4×Q16C2×D5318yescomplemented
425C4×SD16—538no—
426C2×#107—531no—
427C2×#107C2×D5311yescharacteristic
428C2×#106—531no—
429C2×#106—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103C2×D5311yescharacteristic
435C2×#103C2×D5311yescharacteristic
436C2×#102—531no—
437C2×#102—531no—
438#405—538no—
439C2×#97—531no—
440C2×#97—531no—
441C2×C4×C8—531no—
442C2×C4×C8C2×D5311yescharacteristic
443C53C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—531no—
445C22×Q8—1061no—
446C22×Q8C22×D5311yescharacteristic
447C22×Q8C22×D5311yescharacteristic
448C22×D4—531no—
449C22×D4—1061no—
450C23×C4—531no—
451C23×C4—1061no—
452C2×Q16—24no—
453C2×Q16—534no—
454C2×Q16—1064no—
455C2×Q16C22×D5314yes—
456C2×SD16—534no—
457C2×SD16—534no—
458C2×SD16—1064no—
459C2×SD16—1064no—
460C2×M16—534no—
461C2×M16—1064no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—534no—
465C22×C8—1064no—
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C4⋊Q8—534no—
469C4⋊Q8—534no—
470C4⋊Q8—1062no—
471C4⋊Q8—1062no—
472#126—1068no—
473#126—1068no—
474#126—1068no—
475#125—534no—
476#125—1068no—
477#125—1062no—
478#125—1068no—
479#124—534no—
480#124—1068no—
481#124—1062no—
482#123—1068no—
483C22⋊Q8—534no—
484C22⋊Q8—534no—
485C22⋊Q8—534no—
486C22⋊Q8—1068no—
487C22⋊Q8—1062no—
488C22⋊Q8—1062no—
489C22⋊Q8—1062no—
490#121—534no—
491#121—1062no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×Q8C22×D5314yes—
497C4×Q8C22×D5314yes—
498C4×D4—534no—
499C4×D4—1062no—
500#117—534no—
501#117—534no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C22⋊C4—531no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—531no—
531C2×C42—1061no—
532C2×C42C22×D5311yescharacteristic
533#107—534no—
534#107C22×D5314yes—
535#106—534no—
536#106—534no—
537#103—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#103C22×D5314yes—
542#103C22×D5314yes—
543#102—534no—
544#102—534no—
545#97—534no—
546#97—534no—
547C4×C8—534no—
548C4×C8C22×D5314yes—
549C24—531no—
550C24—1061no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—532no—
558C2×Q8—1064no—
559C2×Q8—1061no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—4242no—
563C2×Q8C23×D5312yes—
564C2×Q8C23×D5312yes—
565C2×D4—532no—
566C2×D4—1064no—
567C2×D4—1061no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—4242no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—531no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1064no—
586C22×C4—4242no—
587C22×C4D4×D5311yescharacteristic
588C22×C4D4×D5311yescharacteristic
589C22×C4C23×D5311yescharacteristic
590Q16—28no—
591Q16—1068no—
592SD16—1068no—
593SD16—1068no—
594M16—1068no—
595C2×C8—22no—
596C2×C8—534no—
597C2×C8—532no—
598C2×C8—532no—
599C2×C8—1068no—
600C2×C8—1062no—
601C2×C8#1171994514yes—
602C2×C8C23×D5312yes—
603C2×C8C23×D5312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—534no—
609C4⋊C4—534no—
610C4⋊C4—532no—
611C4⋊C4—532no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1064no—
623C4⋊C4C23×D5312yes—
624C4⋊C4C23×D5312yes—
625C22⋊C4—534no—
626C22⋊C4—534no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C42—24no—
635C42—24no—
636C42—532no—
637C42—532no—
638C42—1064no—
639C42D4×D5312yes—
640C42C23×D5312yes—
641C23—532no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—2122no—
647C23—2122no—
648C23—2122no—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—1062no—
657Q8—1062no—
658Q8—4244no—
659Q8—2122no—
660D4—1062no—
661D4—1062no—
662D4—4244no—
663D4—2122no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1064no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—4244no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4C2×D4×D5312yes—
691C2×C4C2×D4×D5312yes—
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#41×D5312yes—
694C2×C4C2×#1171994512yes—
695C2×C4C24×D5311yescharacteristic
696C8—22no—
697C8—534no—
698C8—1062no—
699C8C2×#1171994514yes—
700C22—1062no—
701C22—1062no—
702C22—1062no—
703C22—4244no—
704C22—2122no—
705C22—2122no—
706C22—2122no—
707C22—2124no—
708C22#1681117012yes—
709C22#1681143012yes—
710C22#1681143612yes—
711C22C22×D4×D5311yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—1062no—
719C4—1062no—
720C4—1062no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4#1681117012yes—
725C4C2×#41×D5311yescharacteristic
726C4C22×#1171994511yescharacteristic
727C2—4242no—
728C2—2122no—
729C2#2028538714yesdirect product factor
730C2C2×#1681117011yescharacteristic
731C2C2×#1681143011yescharacteristic
732C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133192C22
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3178
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#16811231C2semidirect
3. #20285387C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811016C2semidirect
6. C2×#16810979C2semidirect
7. C2×#16810972C2semidirect
8. C2×#16810878C2semidirect
10. C2×#16810863C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810721C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×#16810577C2semidirect
16. C2×C4×Q16×C53C2semidirect
25. #16811231C22semidirect
45. #16811031C22semidirect
46. #16811016C22semidirect
47. #16810979C22semidirect
48. #16810972C22semidirect
49. #16810878C22semidirect
51. #16810863C22semidirect
53. #16810728C22semidirect
54. #16810721C22semidirect
55. C4×#11719913C22semidirect
65. #16810577C22semidirect
72. C4×Q16×C53C22semidirect
374. C2×C4×Q16D53semidirect
377. C2×C53#3178semidirect
424. C4×Q16C2×D53semidirect
443. C53C2×#3178semidirect
729. C2#20285387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112452
C2×#168112312
#202853872
C2×#168110312
C2×#168110162
C2×#168109792
C2×#168109722
C2×#168108782
C2×#168108702
C2×#168108632
C2×#168108552
C2×#168107282
C2×#168107212
C2×C4×#117199132
C2×#168105772
C2×C4×Q16×C532
C2×#317853