Finite Group Databasebeta

← C2×#20284578 #28251686

Subgroups — C2×#20284578 #28251686

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811253C211yesmaximal, characteristic, complemented
2C2×#16811102C211yesmaximal, characteristic
3#20284578C2116yesmaximal, direct product factor
4C2×#16810929C211yesmaximal, characteristic, complemented
5C2×#16810927C211yesmaximal, characteristic, complemented
6C2×#16810909C211yesmaximal, characteristic, complemented
7C2×#16810907C211yesmaximal, characteristic, complemented
8C2×#16810925C211yesmaximal, characteristic, complemented
9C2×#16810913C211yesmaximal, characteristic, complemented
10C2×#16810911C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic, complemented
12C2×#106×D53C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic
15C2×#16810616C211yesmaximal, characteristic
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811253—24no—
21#16811253C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133216—21no—
24C2×#13133216C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133197—21no—
28C2×#13133195—21no—
29#16811102—24no—
30#16811102C2218yes—
31C2×C4×Dic106C2211yescharacteristic
32C2×#13133182C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×C4×C22⋊D53—21no—
35C2×#13133177—21no—
36C2×#13133175C2211yescharacteristic
37C2×#13133174C2211yescharacteristic
38C2×#13133173—21no—
39C22×#11719919—21no—
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810929C2218yescomplemented
43#16810927C2218yescomplemented
44#16810925C2218yescomplemented
45#16810913C2218yescomplemented
46#16810911C2218yescomplemented
47#16810909C2218yescomplemented
48#16810907C2218yescomplemented
49#16810664C2218yescomplemented
50C2×#13133150C2211yescharacteristic
51C2×#13133149C2211yescharacteristic
52C2×#13133149C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56#106×D53C2218yescomplemented
57#16810648C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61#16810621C2218yes—
62#16810616C2218yes—
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133138C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—22no—
78C2×#11719947—24no—
79C2×#11719947Q818yescomplemented
80C2×#11719947C2314yes—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×C22⋊D53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53C2311yescharacteristic
90C2×#11719912—24no—
91C2×#11719912C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C2×C8×D53—24no—
95C2×C8×D53C2314yes—
96#13133217—22no—
97#13133217C2314yes—
98#13133216—28no—
99#13133216—22no—
100#13133216C2314yes—
101#13133208—22no—
102#13133208C2314yes—
103#13133207—28no—
104#13133197—28no—
105#13133195—28no—
106C4×Dic106—22no—
107C4×Dic106C2314yes—
108#13133182—22no—
109#13133182C2314yes—
110D4×Dic53—22no—
111D4×Dic53C2314yes—
112C4×C22⋊D53—28no—
113#13133177—28no—
114#13133175—22no—
115#13133175C2314yes—
116#13133174D414yes—
117#13133174C2314yes—
118#13133173—28no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—28no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—22no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C4⋊C4×D53C2314yes—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×#11719921D411yescharacteristic
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133149C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53—21no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164#125×C53—22no—
165#125×C53C2314yes—
166C4×D4×C53—22no—
167C4×D4×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#106×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C23×D53C2×D411yescharacteristic
182C2×D4×C53—21no—
183C2×D4×C53—22no—
184C2×D4×C53C2×Q814yes—
185C2×D4×C53C2412yes—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—24no—
190C22×C4×C53—82no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—28no—
195C2×C22⋊D53—24no—
196C22×Dic53—21no—
197C22×Dic53—28no—
198C22×Dic53—24no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—24no—
203C22×Dic53—82no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207#11719947—216no—
208#11719947—28no—
209#11719947C2×Q8116yescomplemented
210C2×C4×D53—24no—
211C2×C4×D53—24no—
212C2×C4×D53—82no—
213C2×C4×D53—82no—
214C2×C4×D53C2×D412yes—
215C2×C4×D53C2×Q814yes—
216C2×C4×D53#4114yes—
217C2×C4×D53C2412yes—
218C2×Dic106—21no—
219C2×Dic106—22no—
220C2×Dic106—24no—
221C2×Dic106—24no—
222C2×Dic106—82no—
223C2×Dic106—82no—
224C2×Dic106C2×Q814yes—
225C2×Dic106C2412yes—
226C2×C8×C53—22no—
227C2×C8×C53—22no—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242#11719921—24no—
243#11719921C2×D414yes—
244#11719921C2×D414yes—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—24no—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919C2×D414yes—
260#11719919C2×D414yes—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719912—28no—
271C8×D53—28no—
272C23×C53—24no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53C22⋊Q814yes—
280C22×D53C22×D412yes—
281D4×C53—24no—
282D4×C53—22no—
283D4×C53C22×Q814yes—
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×C53—84no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C22×Q812yes—
297C2×C4×C53C2×#4112yes—
298C2×C4×C53C2511yescharacteristic
299C22⋊D53—216no—
300C2×Dic53—24no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—216no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—84no—
312C2×Dic53C22⋊Q814yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C4×D53—84no—
317C4×D53—84no—
318C4×D53C22⋊Q818yes—
319C4×D53C22×Q814yes—
320C4×D53C2×#4114yes—
321Dic106—24no—
322Dic106—22no—
323Dic106—84no—
324Dic106—84no—
325Dic106C22×Q814yes—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322—22no—
330C2×#3084—531nomaximal, Sylow
331C22×C53—24no—
332C22×C53—48no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53C2×C22⋊Q812yes—
336C22×C53#57712yes—
337C22×C53#57712yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—28no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53C2×C22⋊Q814yes—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53—42no—
348C4×C53C2×C22⋊Q812yes—
349C4×C53C23×Q811yescharacteristic
350C4×C53C22×#4111yescharacteristic
351Dic53—24no—
352Dic53—22no—
353Dic53—22no—
354Dic53—42no—
355Dic53—42no—
356Dic53—42no—
357Dic53C2×C22⋊Q814yes—
358C2×#544—531no—
359C2×#520—531no—
360#3084—5316no—
361C2×#479—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#475—531no—
365C2×#478—531no—
366C2×#478D5311yescharacteristic, complemented
367C2×#476—531no—
368C2×#476—531no—
369C2×#428—531no—
370C22×#106—531no—
371C2×#424—531no—
372C2×#417—531no—
373C2×#416—531no—
374C2×C53—44no—
375C2×C53#308414yescomplemented
376C2×C53C22×C22⋊Q811yescharacteristic
377C2×C53C2×#57711yescharacteristic
378C2×C53C2×#57711yescharacteristic
379D53—24no—
380C22×#41—531no—
381C22×M16—531no—
382C23×C8—531no—
383#544—538no—
384#544—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8—531no—
387C2×C4⋊Q8—1061no—
388C2×#125—531no—
389C2×#125—1061no—
390C2×#125C2×D5311yescharacteristic
391C2×C22⋊Q8—1061no—
392C2×C22⋊Q8—1061no—
393#520—538no—
394#520—1064no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×D4—531no—
398C2×C4×D4—1061no—
399C2×C4×D4—1061no—
400C2×C4×D4C2×D5311yescharacteristic
401C2×#117—531no—
402C2×#117—531no—
403C2×#117—1061no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—1061no—
407#479—538no—
408#479—538no—
409#478—538no—
410#478C2×D5318yescomplemented
411#476—538no—
412#476—538no—
413#475—538no—
414#475—538no—
415#428—538no—
416C2×#107—531no—
417C2×#107C2×D5311yescharacteristic
418C2×#106—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—538no—
424C2×#106C2×D5311yescharacteristic
425#424—538no—
426C2×C4⋊C8—531no—
427C2×C4⋊C8—531no—
428C2×C4⋊C8—531no—
429C2×C4⋊C8C2×D5311yescharacteristic
430#417—538no—
431#416—538no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#102—531no—
437C2×#102—531no—
438C2×#102C2×D5311yescharacteristic
439C2×#102C2×D5311yescharacteristic
440C53C2×#308411yescharacteristic, complemented, Sylow
441C2×#41—538no—
442C2×#41—534no—
443C2×#41—1062no—
444C2×#41—1064no—
445C22×Q8—531no—
446C22×Q8—1061no—
447C22×Q8—1061no—
448C22×D4—1061no—
449C22×D4C22×D5311yescharacteristic
450C23×C4—21no—
451C23×C4—531no—
452C23×C4—1061no—
453C23×C4—1061no—
454C23×C4—1061no—
455C23×C4—1061no—
456C2×M16—534no—
457C2×M16—1064no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—534no—
461C22×C8—1064no—
462C22×C8C22×D5311yescharacteristic
463C22×C8C22×D5311yescharacteristic
464C4⋊Q8—534no—
465C4⋊Q8—534no—
466C4⋊Q8—1062no—
467C4⋊Q8—1068no—
468C4⋊Q8—1062no—
469#125—22no—
470#125—534no—
471#125—1062no—
472#125—1068no—
473#125C22×D5314yes—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×Q8—1062no—
479C4×Q8—1062no—
480C4×D4—22no—
481C4×D4—534no—
482C4×D4—1062no—
483C4×D4—1068no—
484C4×D4—1068no—
485C4×D4C22×D5314yes—
486#117—534no—
487#117—534no—
488#117—534no—
489#117—1068no—
490#117—1062no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1062no—
502C2×C4⋊C4—1068no—
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⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—531no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C42—531no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42C22×D5311yescharacteristic
524#107—534no—
525#107C22×D5314yes—
526#106—534no—
527#106—534no—
528#106—534no—
529#106—534no—
530#106—534no—
531#106C22×D5314yes—
532C4⋊C8—534no—
533C4⋊C8—534no—
534C4⋊C8—534no—
535C4⋊C8C22×D5314yes—
536#103—534no—
537#103—534no—
538#103—534no—
539#103—534no—
540#102—534no—
541#102—534no—
542#102C22×D5314yes—
543#102C22×D5314yes—
544C24—21no—
545C24—531no—
546#41—5316no—
547#41—10616no—
548#41—1068no—
549C2×Q8—534no—
550C2×Q8—532no—
551C2×Q8—1064no—
552C2×Q8—1061no—
553C2×Q8—1064no—
554C2×Q8—1062no—
555C2×Q8—4242no—
556C2×Q8—4242no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—1064no—
560C2×D4—1068no—
561C2×D4Q8×D5314yes—
562C2×D4C23×D5312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—531no—
569C22×C4—532no—
570C22×C4—534no—
571C22×C4—534no—
572C22×C4—532no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—1064no—
576C22×C4—1064no—
577C22×C4—1064no—
578C22×C4—1068no—
579C22×C4—1064no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—4242no—
585C22×C4—4242no—
586C22×C4—4242no—
587C22×C4D4×D5311yescharacteristic
588C22×C4D4×D5311yescharacteristic
589C22×C4C23×D5311yescharacteristic
590M16—1068no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—1068no—
596C2×C8—1062no—
597C2×C8—1062no—
598C2×C8C23×D5312yes—
599C2×C8C23×D5312yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—534no—
606C4⋊C4—534no—
607C4⋊C4—532no—
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—1061no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C4⋊C4C23×D5312yes—
624C22⋊C4—24no—
625C22⋊C4—534no—
626C22⋊C4—534no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C42—532no—
630C42—532no—
631C42—1064no—
632C42—1064no—
633C42—1064no—
634C42D4×D5312yes—
635C42C23×D5312yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—534no—
641C23—532no—
642C23—1062no—
643C23—1062no—
644C23C2×D4×D5311yescharacteristic
645Q8—534no—
646Q8—1064no—
647Q8—1062no—
648Q8—4244no—
649Q8—4244no—
650D4—24no—
651D4—22no—
652D4—10616no—
653D4C2×Q8×D5314yes—
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—84no—
663C2×C4—534no—
664C2×C4—532no—
665C2×C4—538no—
666C2×C4—534no—
667C2×C4—534no—
668C2×C4—532no—
669C2×C4—532no—
670C2×C4—10616no—
671C2×C4—1064no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—4244no—
679C2×C4—4244no—
680C2×C4—4244no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4C2×D4×D5312yes—
685C2×C4C2×D4×D5312yes—
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4C2×Q8×D5312yes—
688C2×C4#41×D5312yes—
689C2×C4C24×D5311yescharacteristic
690C8—22no—
691C8—22no—
692C8—1062no—
693C8—1062no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—534no—
699C22—1068no—
700C22—1062no—
701C22—1062no—
702C22C22⋊Q8×D5312yes—
703C22#1681143012yes—
704C22#1681143312yes—
705C22C22×D4×D5311yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—534no—
712C4—1062no—
713C4—1062no—
714C4—1064no—
715C4—2122no—
716C4—2122no—
717C4—2122no—
718C4C22⋊Q8×D5312yes—
719C4C22×Q8×D5311yescharacteristic
720C4C2×#41×D5311yescharacteristic
721C2—44no—
722C2—1064no—
723C2#2028457814yesdirect product factor
724C2C2×C22⋊Q8×D5311yescharacteristic
725C2C2×#1681143011yescharacteristic
726C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
hypercenterC2×#478D53
hypocenterC53C2×#3084
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811253C2semidirect
3. #20284578C2direct (N × H)
4. C2×#16810929C2semidirect
5. C2×#16810927C2semidirect
6. C2×#16810909C2semidirect
7. C2×#16810907C2semidirect
8. C2×#16810925C2semidirect
9. C2×#16810913C2semidirect
10. C2×#16810911C2semidirect
11. C2×#16810664C2semidirect
12. C2×#106×D53C2semidirect
13. C2×#16810648C2semidirect
16. C2×C53×#478C2semidirect
21. #16811253C22semidirect
42. #16810929C22semidirect
43. #16810927C22semidirect
44. #16810925C22semidirect
45. #16810913C22semidirect
46. #16810911C22semidirect
47. #16810909C22semidirect
48. #16810907C22semidirect
49. #16810664C22semidirect
56. #106×D53C22semidirect
57. #16810648C22semidirect
71. C53×#478C22semidirect
79. C2×#11719947Q8semidirect
209. #11719947C2×Q8semidirect
366. C2×#478D53semidirect
375. C2×C53#3084semidirect
410. #478C2×D53semidirect
440. C53C2×#3084semidirect
723. C2#20284578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112532
C2×#168111022
#202845782
C2×#168109292
C2×#168109272
C2×#168109092
C2×#168109072
C2×#168109252
C2×#168109132
C2×#168109112
C2×#168106642
C2×#106×D532
C2×#168106482
C2×#168106212
C2×#168106162
C2×C53×#4782
C2×#308453