Finite Group Databasebeta

← C2×#20284539 #28251644

Subgroups — C2×#20284539 #28251644

Order 13568.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811250C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic
3#20284539C2116yesmaximal, direct product factor
4C2×#16810926C211yesmaximal, characteristic, complemented
5C2×#16810924C211yesmaximal, characteristic, complemented
6C2×#16810923C211yesmaximal, characteristic, complemented
7C2×#16810921C211yesmaximal, characteristic, complemented
8C2×#16810911C211yesmaximal, characteristic, complemented
9C2×#16810910C211yesmaximal, characteristic, complemented
10C2×#16810902C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic, complemented
12C2×#16810660C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810626C211yesmaximal, characteristic
15C2×#102×D53C211yesmaximal, characteristic
16C2×C53×#474C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811250—24no—
21#16811250C2218yescomplemented
22C2×#13133216C2211yescharacteristic, complemented
23C2×#13133215—21no—
24C2×#13133209C2211yescharacteristic, complemented
25C2×#13133208C2211yescharacteristic, complemented
26C2×#13133207—21no—
27C2×#13133195—21no—
28C2×#13133193—21no—
29#16811095—24no—
30#16811095C2218yes—
31C2×C4×D212C2211yescharacteristic
32C2×D4×Dic53C2211yescharacteristic
33C2×#13133179C2211yescharacteristic
34C2×C4×C22⋊D53—21no—
35C2×#13133177—21no—
36C2×#13133175C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133174C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C22×#11719921—21no—
41C2×C22⋊C4×D53—21no—
42#16810926C2218yescomplemented
43#16810924C2218yescomplemented
44#16810923C2218yescomplemented
45#16810921C2218yescomplemented
46#16810911C2218yescomplemented
47#16810910C2218yescomplemented
48#16810902C2218yescomplemented
49#16810664C2218yescomplemented
50#16810660C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133150C2211yescharacteristic, complemented
53C2×#13133149C2211yescharacteristic, complemented
54C2×#13133148C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810648C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133146C2211yescharacteristic, complemented
61#16810626C2218yes—
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68#102×D53C2218yes—
69C2×C4⋊Q8×C53C2211yescharacteristic, complemented
70C2×C4×D4×C53C2211yescharacteristic
71C53×#474C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106—21no—
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C2×D4×D53—22no—
82C2×D4×D53—24no—
83C2×D4×D53Q818yescomplemented
84C2×D4×D53C2314yes—
85C23×Dic53—21no—
86C22×C4×D53—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#13133216—22no—
97#13133216C2314yescomplemented
98#13133215—28no—
99#13133209—22no—
100#13133209C2314yescomplemented
101#13133208—22no—
102#13133208C2314yescomplemented
103#13133207—28no—
104#13133195—28no—
105#13133193—28no—
106C4×D212—22no—
107C4×D212C2314yes—
108D4×Dic53—22no—
109D4×Dic53C2314yes—
110#13133179—22no—
111#13133179C2314yes—
112C4×C22⋊D53—28no—
113#13133177—28no—
114#13133175—22no—
115#13133175—22no—
116#13133175C2314yes—
117#13133175C2314yes—
118#13133174D414yes—
119#13133174C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×#11719921—28no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×#11719921D411yescharacteristic
141C22⋊C4×D53—28no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yescomplemented
146#13133150C2314yescomplemented
147#13133149C2314yescomplemented
148#13133148C2314yescomplemented
149#13133148C2314yescomplemented
150#13133148C2314yescomplemented
151C4⋊#88322C2314yescomplemented
152#13133146C2314yescomplemented
153#13133146C2314yescomplemented
154#13133139C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133137C2314yes—
160C22×Q8×C53—21no—
161C22×D4×C53C2311yescharacteristic
162C23×C4×C53—21no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4⋊Q8×C53—22no—
166C4⋊Q8×C53C2314yescomplemented
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
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×C53C2314yescomplemented
176#107×C53C2314yescomplemented
177C4⋊C8×C53C2314yescomplemented
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C23×D53—21no—
182C23×D53—28no—
183C23×D53—24no—
184C23×D53—82no—
185C23×D53—82no—
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—24no—
188C2×Q8×C53—82no—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53C2×Q814yes—
192C2×D4×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—82no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—28no—
202C2×C22⋊D53—24no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—24no—
207C22×Dic53—82no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211D4×D53—216no—
212D4×D53—28no—
213D4×D53C2×Q8116yescomplemented
214C2×D212—21no—
215C2×D212—22no—
216C2×D212C2×Q814yes—
217C2×D212C2412yes—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C2×C4×D53—82no—
223C2×C4×D53—82no—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2×Q814yes—
226C2×C4×D53#4114yes—
227C2×C4×D53C2412yes—
228C2×Dic106—24no—
229C2×Dic106—82no—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C22⋊C4×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921C2×D414yes—
250#11719921C2×D414yes—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919C2×D414yes—
264#11719919C2×D414yes—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273#11719912—28no—
274C8×D53—28no—
275C23×C53—24no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53C22×D411yescharacteristic
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—24no—
283C22×D53—22no—
284C22×D53—216no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—816no—
288C22×D53—84no—
289C22×D53—84no—
290C22×D53C22⋊Q814yes—
291C22×D53C22×D412yes—
292Q8×C53—84no—
293D4×C53—24no—
294D4×C53—22no—
295D4×C53C22×Q814yes—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—84no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C22×Q812yes—
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2511yescharacteristic
311C22⋊D53—216no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—84no—
321C2×Dic53C22⋊Q814yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—24no—
326D212—22no—
327D212C22×Q814yes—
328C4×D53—84no—
329C4×D53—84no—
330C4×D53—84no—
331C4×D53C22⋊Q818yes—
332C4×D53C22×Q814yes—
333C4×D53C2×#4114yes—
334Dic106—84no—
335C8×C53—22no—
336C8×C53—22no—
337#88322—22no—
338#88322—22no—
339C2×#3081—531nomaximal, Sylow
340C22×C53—24no—
341C22×C53—48no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53C2×C22⋊Q812yes—
345C22×C53#57612yes—
346C22×C53#57712yes—
347C22×C53C23×D411yescharacteristic
348C2×D53—28no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—24no—
352C2×D53—48no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—816no—
356C2×D53C2×C22⋊Q814yes—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53C2×C22⋊Q812yes—
363C4×C53C23×Q811yescharacteristic
364C4×C53C22×#4111yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—42no—
368Dic53—42no—
369Dic53—42no—
370Dic53C2×C22⋊Q814yes—
371C2×#544—531no—
372C2×#518—531no—
373#3081—5316no—
374C2×#478—531no—
375C2×#478—531no—
376C2×#478—531no—
377C2×#478—531no—
378C2×#476—531no—
379C2×#476—531no—
380C2×#474—531no—
381C2×#474D5311yescharacteristic, complemented
382C2×#428—531no—
383C2×#427—531no—
384C2×#424—531no—
385C2×#418—531no—
386C22×#102—531no—
387C2×C53—44no—
388C2×C53#308114yescomplemented
389C2×C53C22×C22⋊Q811yescharacteristic
390C2×C53C2×#57611yescharacteristic
391C2×C53C2×#57711yescharacteristic
392D53—24no—
393D53—44no—
394C23×D4—531no—
395C22×M16—531no—
396C23×C8—531no—
397#544—538no—
398#544—1064no—
399C2×C4⋊Q8—531no—
400C2×C4⋊Q8—1061no—
401C2×C4⋊Q8C2×D5311yescharacteristic, complemented
402C2×#125—531no—
403C2×#125—531no—
404C2×#125—1061no—
405C2×C22⋊Q8—1061no—
406C2×C22⋊Q8—1061no—
407#518—538no—
408#518—1064no—
409C2×C4×D4—531no—
410C2×C4×D4—531no—
411C2×C4×D4—531no—
412C2×C4×D4—1061no—
413C2×C4×D4—1061no—
414C2×C4×D4C2×D5311yescharacteristic
415C2×#117—531no—
416C2×#117—531no—
417C2×#117—531no—
418C22×C4⋊C4—531no—
419C22×C22⋊C4—1061no—
420C22×C22⋊C4—1061no—
421#478—538no—
422#478—538no—
423#478—538no—
424#478—538no—
425#476—538no—
426#476—538no—
427#474—538no—
428#474C2×D5318yescomplemented
429#428—538no—
430#427—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107C2×D5311yescharacteristic, complemented
434C2×#107C2×D5311yescharacteristic, complemented
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×#106—531no—
439#424—538no—
440C2×C4⋊C8—531no—
441C2×C4⋊C8—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8C2×D5311yescharacteristic, complemented
444#418—538no—
445C2×#102—531no—
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102—538no—
452C2×#102C2×D5311yescharacteristic
453C2×#102C2×D5311yescharacteristic
454C53C2×#308111yescharacteristic, complemented, Sylow
455C25—1061no—
456C22×Q8—21no—
457C22×Q8—1061no—
458C22×D4—538no—
459C22×D4—534no—
460C22×D4—531no—
461C22×D4—1062no—
462C22×D4—1064no—
463C22×D4—1061no—
464C22×D4C22×D5311yescharacteristic
465C23×C4—21no—
466C23×C4—531no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4—1061no—
470C23×C4—1061no—
471C2×M16—534no—
472C2×M16—1064no—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8—534no—
476C22×C8—1064no—
477C22×C8C22×D5311yescharacteristic
478C22×C8C22×D5311yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—534no—
481C4⋊Q8—1062no—
482C4⋊Q8—1068no—
483C4⋊Q8C22×D5314yescomplemented
484#125—534no—
485#125—534no—
486#125—1062no—
487#125—1068no—
488#125—1062no—
489C22⋊Q8—1068no—
490C22⋊Q8—1068no—
491C4×D4—22no—
492C4×D4—534no—
493C4×D4—534no—
494C4×D4—534no—
495C4×D4—1062no—
496C4×D4—1062no—
497C4×D4—1068no—
498C4×D4—1068no—
499C4×D4—1062no—
500C4×D4C22×D5314yes—
501#117—534no—
502#117—534no—
503#117—534no—
504#117—534no—
505#117—1062no—
506#117—1062no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—1062no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—1068no—
528C2×C22⋊C4—1068no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C42—531no—
535C2×C42—1061no—
536C2×C42—1061no—
537C2×C42C22×D5311yescharacteristic
538#107—534no—
539#107—534no—
540#107C22×D5314yescomplemented
541#107C22×D5314yescomplemented
542#106—534no—
543#106—534no—
544#106—534no—
545#106—534no—
546C4⋊C8—534no—
547C4⋊C8—534no—
548C4⋊C8—534no—
549C4⋊C8C22×D5314yescomplemented
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102—534no—
556#102C22×D5314yes—
557#102C22×D5314yes—
558C24—21no—
559C24—531no—
560C24—1064no—
561C24—1068no—
562C24—1061no—
563C24—4242no—
564C24—4242no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—1064no—
568C2×Q8—4242no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—5316no—
572C2×D4—534no—
573C2×D4—532no—
574C2×D4—10616no—
575C2×D4—1068no—
576C2×D4—1064no—
577C2×D4—1068no—
578C2×D4—1061no—
579C2×D4—1062no—
580C2×D4Q8×D5314yes—
581C2×D4C23×D5312yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—531no—
588C22×C4—532no—
589C22×C4—534no—
590C22×C4—534no—
591C22×C4—532no—
592C22×C4—531no—
593C22×C4—531no—
594C22×C4—1064no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1064no—
601C22×C4—4242no—
602C22×C4—4242no—
603C22×C4—4242no—
604C22×C4—4242no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608M16—1068no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—532no—
612C2×C8—532no—
613C2×C8—1068no—
614C2×C8—1062no—
615C2×C8—1062no—
616C2×C8C23×D5312yes—
617C2×C8C23×D5312yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—534no—
623C4⋊C4—534no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1061no—
632C4⋊C4—1061no—
633C4⋊C4—1061no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C4⋊C4C23×D5312yes—
639C22⋊C4—24no—
640C22⋊C4—534no—
641C22⋊C4—534no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C42—532no—
648C42—532no—
649C42—1064no—
650C42—1064no—
651C42D4×D5312yes—
652C42C23×D5312yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—534no—
658C23—532no—
659C23—10616no—
660C23—1062no—
661C23—1062no—
662C23—1064no—
663C23—1062no—
664C23—42416no—
665C23—4244no—
666C23—4244no—
667C23—2122no—
668C23—2122no—
669C23C2×D4×D5311yescharacteristic
670Q8—84no—
671Q8—4244no—
672D4—24no—
673D4—22no—
674D4—534no—
675D4—10616no—
676D4—1064no—
677D4—1062no—
678D4C2×Q8×D5314yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—534no—
689C2×C4—532no—
690C2×C4—538no—
691C2×C4—534no—
692C2×C4—534no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—4244no—
701C2×C4—4244no—
702C2×C4—4244no—
703C2×C4—4244no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4C2×D4×D5312yes—
708C2×C4C2×D4×D5312yes—
709C2×C4C2×D4×D5311yescharacteristic
710C2×C4C2×Q8×D5312yes—
711C2×C4#41×D5312yes—
712C2×C4C24×D5311yescharacteristic
713C8—22no—
714C8—22no—
715C8—1062no—
716C8—1062no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—534no—
722C22—1068no—
723C22—1062no—
724C22—1062no—
725C22—1064no—
726C22—42416no—
727C22—2128no—
728C22—2122no—
729C22—2122no—
730C22C22⋊Q8×D5312yes—
731C22#1681142412yes—
732C22#1681143212yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—534no—
740C4—1062no—
741C4—1062no—
742C4—2122no—
743C4—2122no—
744C4—2122no—
745C4C22⋊Q8×D5312yes—
746C4C22×Q8×D5311yescharacteristic
747C4C2×#41×D5311yescharacteristic
748C2—44no—
749C2—1064no—
750C2—2124no—
751C2#2028453914yesdirect product factor
752C2C2×C22⋊Q8×D5311yescharacteristic
753C2C2×#1681142411yescharacteristic
754C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#474C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×#474D53
hypocenterC53C2×#3081
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16811250C2semidirect
3. #20284539C2direct (N × H)
4. C2×#16810926C2semidirect
5. C2×#16810924C2semidirect
6. C2×#16810923C2semidirect
7. C2×#16810921C2semidirect
8. C2×#16810911C2semidirect
9. C2×#16810910C2semidirect
10. C2×#16810902C2semidirect
11. C2×#16810664C2semidirect
12. C2×#16810660C2semidirect
13. C2×#16810648C2semidirect
16. C2×C53×#474C2semidirect
21. #16811250C22semidirect
22. C2×#13133216C22semidirect
24. C2×#13133209C22semidirect
25. C2×#13133208C22semidirect
42. #16810926C22semidirect
43. #16810924C22semidirect
44. #16810923C22semidirect
45. #16810921C22semidirect
46. #16810911C22semidirect
47. #16810910C22semidirect
48. #16810902C22semidirect
49. #16810664C22semidirect
50. #16810660C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133150C22semidirect
53. C2×#13133149C22semidirect
54. C2×#13133148C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810648C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133146C22semidirect
69. C2×C4⋊Q8×C53C22semidirect
71. C53×#474C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#107×C53C22semidirect
74. C2×C4⋊C8×C53C22semidirect
83. C2×D4×D53Q8semidirect
97. #13133216C23semidirect
100. #13133209C23semidirect
102. #13133208C23semidirect
145. #13133151C23semidirect
146. #13133150C23semidirect
147. #13133149C23semidirect
148. #13133148C23semidirect
149. #13133148C23semidirect
150. #13133148C23semidirect
151. C4⋊#88322C23semidirect
152. #13133146C23semidirect
153. #13133146C23semidirect
166. C4⋊Q8×C53C23semidirect
175. #107×C53C23semidirect
176. #107×C53C23semidirect
177. C4⋊C8×C53C23semidirect
213. D4×D53C2×Q8semidirect
381. C2×#474D53semidirect
388. C2×C53#3081semidirect
401. C2×C4⋊Q8C2×D53semidirect
428. #474C2×D53semidirect
433. C2×#107C2×D53semidirect
434. C2×#107C2×D53semidirect
443. C2×C4⋊C8C2×D53semidirect
454. C53C2×#3081semidirect
483. C4⋊Q8C22×D53semidirect
540. #107C22×D53semidirect
541. #107C22×D53semidirect
549. C4⋊C8C22×D53semidirect
751. C2#20284539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112502
C2×#168110952
#202845392
C2×#168109262
C2×#168109242
C2×#168109232
C2×#168109212
C2×#168109112
C2×#168109102
C2×#168109022
C2×#168106642
C2×#168106602
C2×#168106482
C2×#168106262
C2×#102×D532
C2×C53×#4742
C2×#308153