Finite Group Databasebeta

← C2×#20287090 #28262535

Subgroups — C2×#20287090 #28262535

Order 13568.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811321C211yesmaximal, characteristic
2C2×#16811308C211yesmaximal, characteristic, complemented
3#20287090C2116yesmaximal, direct product factor
4C2×#16811023C211yesmaximal, characteristic, complemented
5C2×#16810958C211yesmaximal, characteristic, complemented
6C2×#16810967C211yesmaximal, characteristic, complemented
7C2×#16810949C211yesmaximal, characteristic, complemented
8C2×#16810936C211yesmaximal, characteristic, complemented
9C2×#16810933C211yesmaximal, characteristic, complemented
10C2×#16810922C211yesmaximal, characteristic, complemented
11C2×#16810853C211yesmaximal, characteristic, complemented
12C2×#16810852C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
15C2×#16810658C211yesmaximal, characteristic, complemented
16C22×#106×C53C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811321—24no—
20#16811321C2218yes—
21#16811308—24no—
22#16811308C2218yescomplemented
23C2×#13133212—21no—
24C2×#13133212—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133208C2211yescharacteristic
27C2×#13133207—21no—
28C2×#13133202—21no—
29C2×#13133200—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133196C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133191—21no—
34C2×#13133191C2211yescharacteristic
35C2×#13133182C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133176—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42#16811023C2218yescomplemented
43#16810967C2218yescomplemented
44#16810958C2218yescomplemented
45#16810949C2218yescomplemented
46#16810936C2218yescomplemented
47#16810933C2218yescomplemented
48#16810922C2218yescomplemented
49#16810853C2218yescomplemented
50#16810852C2218yescomplemented
51#16810710C2218yescomplemented
52C8×C22⋊D53C2218yescomplemented
53#16810658C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×C8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#106×C53C2218yescomplemented
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53D411yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53C2311yescharacteristic
84C2×#11719913—24no—
85C2×#11719913C2314yes—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C2×C8×D53—24no—
89C2×C8×D53C2314yes—
90#13133212—28no—
91#13133212—28no—
92#13133208—22no—
93#13133208—22no—
94#13133208C2314yes—
95#13133208C2314yes—
96#13133207—28no—
97#13133202—28no—
98#13133200—28no—
99#13133197—22no—
100#13133197C2314yes—
101#13133196—22no—
102#13133196C2314yes—
103#13133192—22no—
104#13133192C2314yes—
105#13133191—22no—
106#13133191—28no—
107#13133191C2314yes—
108#13133182—22no—
109#13133182C2314yes—
110#13133179—22no—
111#13133179C2314yes—
112C4×C22⋊D53—28no—
113C4×C22⋊D53D414yes—
114C4×C22⋊D53C2314yes—
115#13133176—28no—
116#13133175—22no—
117#13133175—22no—
118#13133175C2314yes—
119#13133175C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53D411yescharacteristic
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53C2311yescharacteristic
143#13133150C2314yes—
144#13133150C2314yes—
145#13133150C2314yes—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133140C2314yes—
151#13133140C2314yes—
152#13133139C2314yes—
153#13133137C2314yes—
154#13133137C2314yes—
155C22⋊#88322C2314yes—
156#13133129C2314yes—
157C8×Dic53C2314yes—
158C23×C4×C53—21no—
159C23×C4×C53—21no—
160C23×C4×C53C2311yescharacteristic
161C22×C8×C53—24no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2314yes—
164C22×C8×C53C2311yescharacteristic
165C2×C4⋊C4×C53—22no—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175#106×C53C2314yes—
176#106×C53C2314yes—
177#106×C53C2314yes—
178#106×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53—21no—
181C23×D53C2×D411yescharacteristic
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—24no—
189C22×C4×C53—24no—
190C22×C4×C53—44no—
191C22×C4×C53—82no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—44no—
199C2×C22⋊D53C2×D414yes—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C2×D212—22no—
207C2×D212—22no—
208C2×D212—21no—
209C2×D212—24no—
210C2×D212—82no—
211C2×D212C2412yes—
212C2×C4×D53—22no—
213C2×C4×D53—22no—
214C2×C4×D53—24no—
215C2×C4×D53—82no—
216C2×C4×D53C2×D412yes—
217C2×C4×D53C2412yes—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—21no—
221C2×Dic106C2412yes—
222C2×C8×C53—22no—
223C2×C8×C53—28no—
224C2×C8×C53#4114yes—
225C2×C8×C53C2412yes—
226C2×C8×C53C2412yes—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊Dic53—24no—
238C22⋊Dic53C2×D414yes—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921C2×D414yes—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919C2×D414yes—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267#11719913—28no—
268C8×D53—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53#13514yes—
272C23×C53C22×D412yes—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53C22×D412yes—
282C2×C4×C53—22no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—48no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—84no—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4112yes—
299C2×C4×C532−1+412yes—
300C2×C4×C53C2511yescharacteristic
301C22⋊D53—28no—
302C22⋊D53—48no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315D212—22no—
316D212—22no—
317D212—42no—
318D212—84no—
319C4×D53—24no—
320C4×D53—22no—
321C4×D53—22no—
322C4×D53—84no—
323Dic106—22no—
324Dic106—22no—
325Dic106—42no—
326C8×C53—22no—
327C8×C53C2×#4114yes—
328#88322—22no—
329#88322—22no—
330C2×#3337—531nomaximal, Sylow
331C22×C53—28no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53#54712yes—
335C22×C53C2×#13514yes—
336C22×C53C2×#13512yes—
337C22×C53#57712yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—44no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#54712yes—
353C4×C53C22×#4111yescharacteristic
354C4×C53C2×2−1+411yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#553—531no—
362C2×#552—531no—
363#3337—5316no—
364C2×#499—531no—
365C2×#484—531no—
366C2×#485—531no—
367C2×#482—531no—
368C2×#480—531no—
369C2×#479—531no—
370C2×#478—531no—
371C2×#465—531no—
372C2×#465—531no—
373C2×C4×SD16—531no—
374C2×C8×D4—531no—
375C2×#427—531no—
376C22×#106D5311yescharacteristic, complemented
377C2×C53—24no—
378C2×C53#333714yescomplemented
379C2×C53C2×#54711yescharacteristic
380C2×C53C22×#13511yescharacteristic
381C2×C53C2×#57711yescharacteristic
382D53—42no—
383D53—82no—
384C22×SD16—531no—
385C23×C8—531no—
386C23×C8C2×D5311yescharacteristic
387#553—538no—
388#553—1064no—
389#552—538no—
390#552—1064no—
391C2×#126—1061no—
392C2×#126—1061no—
393C2×#125—531no—
394C2×#125—531no—
395C2×#125—1061no—
396C2×#123—1061no—
397C2×#123—1061no—
398C2×C22⋊Q8—531no—
399C2×C22⋊Q8—531no—
400C2×#121—531no—
401C2×#121—531no—
402C2×#121—1061no—
403C2×C4×Q8—531no—
404C2×C4×D4—531no—
405C2×C4×D4—531no—
406C2×C4×D4—1061no—
407C2×#117—531no—
408C2×#117—531no—
409C2×#117—1061no—
410C22×C4⋊C4C2×D5311yescharacteristic
411C22×C4⋊C4C2×D5311yescharacteristic
412#499—538no—
413#485—538no—
414#484—538no—
415#482—538no—
416#480—538no—
417#479—538no—
418#478—538no—
419#465—538no—
420#465—538no—
421C4×SD16—538no—
422C8×D4—538no—
423#427—538no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#106—531no—
429C2×#106C2×D5311yescharacteristic
430C2×#106C2×D5311yescharacteristic
431C2×#106C2×D5311yescharacteristic
432C2×#106C2×D5311yescharacteristic
433C2×#106C2×D5318yescomplemented
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C4×C8—531no—
444C53C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—531no—
446C22×D4—531no—
447C22×D4—531no—
448C22×D4—1061no—
449C22×D4—1061no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—531no—
453C23×C4—1061no—
454C23×C4C22×D5311yescharacteristic
455C2×SD16—534no—
456C2×SD16—1064no—
457C22×C8—24no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—534no—
461C22×C8—1064no—
462C22×C8C22×D5311yescharacteristic
463C22×C8C22×D5314yes—
464C22×C8C22×D5311yescharacteristic
465#126—1068no—
466#126—1068no—
467#125—534no—
468#125—534no—
469#125—1062no—
470#125—1062no—
471#125—1068no—
472#123—1068no—
473#123—1068no—
474C22⋊Q8—534no—
475C22⋊Q8—534no—
476C22⋊Q8—1062no—
477C22⋊Q8—1062no—
478#121—534no—
479#121—534no—
480#121—1062no—
481#121—1068no—
482#121—1062no—
483C4×Q8—534no—
484C4×Q8—1062no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—534no—
488C4×D4—1062no—
489C4×D4—1068no—
490#117—534no—
491#117—534no—
492#117—1068no—
493#117—1062no—
494#117—1062no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4C22×D5311yescharacteristic
510C2×C4⋊C4C22×D5311yescharacteristic
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5314yes—
514C2×C4⋊C4C22×D5314yes—
515C2×C22⋊C4—531no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C42—531no—
525C2×C42—1061no—
526C2×C42—1061no—
527C2×C42—1061no—
528#107—534no—
529#107—534no—
530#107—534no—
531#107—534no—
532#106—534no—
533#106C22×D5314yes—
534#106C22×D5314yes—
535#106C22×D5314yes—
536#106C22×D5314yes—
537C4⋊C8—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#102—534no—
542#102—534no—
543#102—534no—
544C22⋊C8—534no—
545C22⋊C8—534no—
546C4×C8—534no—
547C24—531no—
548C24—1061no—
549C24D4×D5311yescharacteristic
550C2×Q8—532no—
551C2×Q8—1061no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×D4—534no—
555C2×D4—532no—
556C2×D4—1064no—
557C2×D4—1064no—
558C2×D4—1064no—
559C2×D4—1061no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—4242no—
563C2×D4—2124no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—82no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—1064no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—4242no—
586C22×C4D4×D5312yes—
587C22×C4D4×D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—1062no—
596C2×C8—1062no—
597C2×C8—1068no—
598C2×C8#1171994514yes—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—534no—
608C4⋊C4—532no—
609C4⋊C4—532no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—1064no—
619C4⋊C4C23×D5312yes—
620C4⋊C4C23×D5312yes—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C22⋊C4—534no—
624C22⋊C4—534no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C42—532no—
633C42—532no—
634C42—1064no—
635C42—1064no—
636C42—1064no—
637C23—22no—
638C23—22no—
639C23—532no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—2122no—
645C23—2122no—
646C23—2122no—
647C23#1313323814yes—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—1062no—
651Q8—1062no—
652Q8—2122no—
653D4—1068no—
654D4—1062no—
655D4—1062no—
656D4—4244no—
657D4—2128no—
658D4—2122no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—532no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1064no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—4244no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4C2×D4×D5312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×#1171994512yes—
692C2×C4#1313326512yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—1062no—
696C8—1062no—
697C8C2×#1171994514yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—1062no—
702C22—1062no—
703C22—1062no—
704C22—4244no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22—2124no—
709C22#1681127412yes—
710C22C2×#1313323814yes—
711C22C2×#1313323812yes—
712C22#1681142912yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1062no—
720C4—1062no—
721C4—1062no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127412yes—
726C4C22×#1171994511yescharacteristic
727C4C2×#1313326511yescharacteristic
728C2—24no—
729C2—4242no—
730C2—2122no—
731C2#2028709014yesdirect product factor
732C2C2×#1681127411yescharacteristic
733C2C22×#1313323811yescharacteristic
734C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#106×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811321C2
hypercenterC22×#106D53
hypocenterC53C2×#3337
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#16811308C2semidirect
3. #20287090C2direct (N × H)
4. C2×#16811023C2semidirect
5. C2×#16810958C2semidirect
6. C2×#16810967C2semidirect
7. C2×#16810949C2semidirect
8. C2×#16810936C2semidirect
9. C2×#16810933C2semidirect
10. C2×#16810922C2semidirect
11. C2×#16810853C2semidirect
12. C2×#16810852C2semidirect
13. C2×#16810710C2semidirect
14. C2×C8×C22⋊D53C2semidirect
15. C2×#16810658C2semidirect
16. C22×#106×C53C2semidirect
22. #16811308C22semidirect
42. #16811023C22semidirect
43. #16810967C22semidirect
44. #16810958C22semidirect
45. #16810949C22semidirect
46. #16810936C22semidirect
47. #16810933C22semidirect
48. #16810922C22semidirect
49. #16810853C22semidirect
50. #16810852C22semidirect
51. #16810710C22semidirect
52. C8×C22⋊D53C22semidirect
53. #16810658C22semidirect
76. C2×#106×C53C22semidirect
376. C22×#106D53semidirect
378. C2×C53#3337semidirect
433. C2×#106C2×D53semidirect
444. C53C2×#3337semidirect
731. C2#20287090direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113212
C2×#168113082
#202870902
C2×#168110232
C2×#168109582
C2×#168109672
C2×#168109492
C2×#168109362
C2×#168109332
C2×#168109222
C2×#168108532
C2×#168108522
C2×#168107102
C2×C8×C22⋊D532
C2×#168106582
C22×#106×C532
C2×#333753