Finite Group Databasebeta

← C2×#20287200 #28262671

Subgroups — C2×#20287200 #28262671

Order 13568.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811330C211yesmaximal, characteristic, complemented
2#20287200C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16810958C211yesmaximal, characteristic, complemented
5C2×#16810939C211yesmaximal, characteristic, complemented
6C2×#16810964C211yesmaximal, characteristic, complemented
7C2×#16810934C211yesmaximal, characteristic, complemented
8C2×#16810927C211yesmaximal, characteristic, complemented
9C2×#16810903C211yesmaximal, characteristic, complemented
10C2×#16810867C211yesmaximal, characteristic, complemented
11C2×#16810850C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810666C211yesmaximal, characteristic, complemented
15C22×#13133150C211yesmaximal, characteristic, complemented
16C2×C53×#553C211yesmaximal, characteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811330—24no—
21#16811330C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133208—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133196C2211yescharacteristic
26C2×#13133194—21no—
27C2×#13133194—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×D4×Dic53—21no—
30C22×C4⋊Dic53C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811033C2218yescomplemented
33#16810964C2218yescomplemented
34#16810958C2218yescomplemented
35#16810939C2218yescomplemented
36#16810934C2218yescomplemented
37#16810927C2218yescomplemented
38#16810903C2218yescomplemented
39#16810867C2218yescomplemented
40#16810850C2218yescomplemented
41#16810723C2218yescomplemented
42#16810695C2218yescomplemented
43#16810666C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133150C2211yescharacteristic
50C2×#13133150C2218yescomplemented
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#553—24no—
65C53×#553C2218yes—
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic
68C2×#123×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×D4×C53—21no—
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C23×Dic53—21no—
80C23×Dic53—21no—
81C2×#11719923—24no—
82C2×#11719923C2314yes—
83C2×#11719917—24no—
84C2×#11719917C2314yes—
85C22×#88322—24no—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2314yes—
90C22×#88322C2311yescharacteristic
91#13133217—22no—
92#13133217C2314yes—
93#13133208—28no—
94#13133196—22no—
95#13133196—22no—
96#13133196C2314yes—
97#13133196C2314yes—
98#13133194—28no—
99#13133194—28no—
100C4×Dic106—22no—
101C4×Dic106C2314yes—
102D4×Dic53—28no—
103C2×C4⋊Dic53—22no—
104C2×C4⋊Dic53—22no—
105C2×C4⋊Dic53—21no—
106C2×C4⋊Dic53—21no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2314yes—
110C2×C4⋊Dic53C2314yes—
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×C22⋊Dic53—21no—
117C2×C22⋊Dic53—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128C4⋊#88322C2314yes—
129#13133140C2314yes—
130#13133140C2314yes—
131#13133140C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137#13133128C2314yes—
138C22×D4×C53—21no—
139C22×D4×C53—21no—
140C22×D4×C53D411yescharacteristic
141C22×D4×C53C2311yescharacteristic
142C23×C4×C53—21no—
143C23×C4×C53—21no—
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146#126×C53—28no—
147#125×C53—22no—
148#125×C53C2314yes—
149#123×C53—28no—
150#121×C53—28no—
151#121×C53—22no—
152#121×C53—22no—
153#121×C53C2314yes—
154#121×C53C2314yes—
155C4×D4×C53—28no—
156C4×D4×C53—22no—
157C4×D4×C53D414yes—
158C4×D4×C53C2314yes—
159C4×D4×C53C2314yes—
160#117×C53—22no—
161#117×C53C2314yes—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—22no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C24×C53C2×D411yescharacteristic
181C24×C53C2×D411yescharacteristic
182C2×D4×C53—24no—
183C2×D4×C53—24no—
184C2×D4×C53—24no—
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53—44no—
189C2×D4×C53—82no—
190C2×D4×C53C2×D414yes—
191C2×D4×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—24no—
201C22×C4×C53—82no—
202C22×C4×C53—82no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D412yes—
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2411yescharacteristic
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—24no—
218C22×Dic53—82no—
219C22×Dic53—82no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—21no—
223C2×Dic106—24no—
224C2×Dic106—82no—
225C2×Dic106C2412yes—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2×D414yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C22⋊C4×C53C2×D414yes—
241C22⋊C4×C53C2×D414yes—
242C42×C53—24no—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247#11719923—28no—
248C4⋊Dic53—21no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260C4×Dic53—24no—
261#11719917—28no—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322—28no—
266C2×#88322#4114yes—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53#13714yes—
281C23×C53C22×D412yes—
282C23×C53C22×D412yes—
283C23×C53C22×D411yescharacteristic
284D4×C53—28no—
285D4×C53—22no—
286D4×C53—22no—
287D4×C53—48no—
288D4×C53—42no—
289D4×C53—84no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—84no—
307C2×C4×C53—84no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4112yes—
314C2×C4×C532−1+412yes—
315C2×C4×C53C2511yescharacteristic
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—84no—
325C2×Dic53—84no—
326Dic106—22no—
327Dic106—22no—
328Dic106—42no—
329Dic106—84no—
330#88322—22no—
331#88322—22no—
332#88322—22no—
333#88322C2×#4114yes—
334C2×#3346—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—44no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—84no—
346C22×C53#54712yes—
347C22×C53C2×#13714yes—
348C22×C53C2×#13712yes—
349C22×C53#57612yes—
350C22×C53C23×D411yescharacteristic
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53#54712yes—
359C4×C53C22×#4111yescharacteristic
360C4×C53C2×2−1+411yescharacteristic
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#554—531no—
366C2×#553D5311yescharacteristic
367#3346—5316no—
368C2×#501—531no—
369C2×#484—531no—
370C2×#481—531no—
371C2×#485—531no—
372C2×#480—531no—
373C2×#479—531no—
374C2×#474—531no—
375C2×#468—531no—
376C2×#465—531no—
377C2×#440—531no—
378C2×#435—531no—
379C2×#428—531no—
380C22×#107—531no—
381C2×C53—24no—
382C2×C53—42no—
383C2×C53—82no—
384C2×C53#334614yescomplemented
385C2×C53C2×#54711yescharacteristic
386C2×C53C22×#13711yescharacteristic
387C2×C53C2×#57611yescharacteristic
388C22×SD16—531no—
389C22×M16—531no—
390C23×C8—531no—
391#554—538no—
392#554—1064no—
393#553—24no—
394#553C2×D5318yes—
395C2×C4⋊Q8—531no—
396C2×#126—21no—
397C2×#125—1061no—
398C2×#125C2×D5311yescharacteristic
399C2×#123—21no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8—1061no—
404C2×#121—21no—
405C2×#121C2×D5311yescharacteristic
406C2×#121C2×D5311yescharacteristic
407C2×C4×Q8—531no—
408C2×C4×D4—21no—
409C2×C4×D4—1061no—
410C2×C4×D4C2×D5311yescharacteristic
411C2×C4×D4C2×D5311yescharacteristic
412C2×#117C2×D5311yescharacteristic
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4C2×D5311yescharacteristic
416#501—538no—
417#485—538no—
418#484—538no—
419#481—538no—
420#480—538no—
421#479—538no—
422#474—538no—
423#468—538no—
424#465—538no—
425#440—538no—
426#435—538no—
427#428—538no—
428C2×#107—531no—
429C2×#107—531no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—538no—
433C2×#107—531no—
434C2×#107—531no—
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×C4⋊C8—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×#97—531no—
448C53C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—531no—
450C22×Q8—1061no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C22⋊D5311yescharacteristic
454C22×D4C22×D5311yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C2×SD16—534no—
462C2×SD16—1064no—
463C2×M16—534no—
464C2×M16—1064no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—534no—
468C22×C8—531no—
469C22×C8—531no—
470C22×C8—1064no—
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#126—28no—
474#125—22no—
475#125—1068no—
476#125C22×D5314yes—
477#123—28no—
478C22⋊Q8—534no—
479C22⋊Q8—534no—
480C22⋊Q8—1062no—
481C22⋊Q8—1062no—
482C22⋊Q8—1068no—
483C22⋊Q8—1068no—
484#121—28no—
485#121—22no—
486#121—22no—
487#121C22×D5314yes—
488#121C22×D5314yes—
489C4×Q8—534no—
490C4×Q8—1062no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—1068no—
494C4×D4C22⋊D5314yes—
495C4×D4C22×D5314yes—
496C4×D4C22×D5314yes—
497#117—22no—
498#117C22×D5314yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1062no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4C22⋊D5311yescharacteristic
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5314yes—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4C22⋊D5311yescharacteristic
528C2×C22⋊C4C22⋊D5311yescharacteristic
529C2×C42—21no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532#107—534no—
533#107—534no—
534#107—534no—
535#107—534no—
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540#106—534no—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548C22⋊C8—534no—
549C22⋊C8—534no—
550#97—534no—
551C24—21no—
552C24C2×C22⋊D5311yescharacteristic
553C24C2×C22⋊D5311yescharacteristic
554C2×Q8—532no—
555C2×Q8—1064no—
556C2×Q8—1061no—
557C2×Q8—1062no—
558C2×Q8—1062no—
559C2×Q8—4242no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×C22⋊D5314yes—
569C2×D4C23×D5312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—1064no—
582C22×C4—1064no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—4242no—
588C22×C4—4242no—
589C22×C4C2×C22⋊D5312yes—
590C22×C4C2×C22⋊D5312yes—
591C22×C4C2×C22⋊D5311yescharacteristic
592C22×C4C2×C22⋊D5311yescharacteristic
593C22×C4C2×C22⋊D5311yescharacteristic
594C22×C4C2×C22⋊D5311yescharacteristic
595C22×C4C23×D5312yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5311yescharacteristic
598SD16—1068no—
599M16—1068no—
600C2×C8—534no—
601C2×C8—532no—
602C2×C8—532no—
603C2×C8—532no—
604C2×C8—532no—
605C2×C8—1068no—
606C2×C8—1062no—
607C2×C8—1062no—
608C2×C8—1062no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—532no—
618C4⋊C4—1061no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4C2×C22⋊D5314yes—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4C2×C22⋊D5314yes—
638C22⋊C4C2×C22⋊D5314yes—
639C42—24no—
640C42—1064no—
641C42C2×C22⋊D5312yes—
642C42C23×D5312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#1313324714yes—
653C23C22×C22⋊D5312yes—
654C23C22×C22⋊D5312yes—
655C23C22×C22⋊D5311yescharacteristic
656Q8—1062no—
657Q8—1062no—
658Q8—4244no—
659Q8—2122no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—4244no—
689C2×C4—4244no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4C22×C22⋊D5312yes—
695C2×C4C22×C22⋊D5312yes—
696C2×C4C22×C22⋊D5312yes—
697C2×C4C22×C22⋊D5312yes—
698C2×C4C22×C22⋊D5311yescharacteristic
699C2×C4#41×D5312yes—
700C2×C4#1313326412yes—
701C2×C4C24×D5311yescharacteristic
702C8—534no—
703C8—1062no—
704C8—1062no—
705C8—1062no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22#1681127212yes—
718C22C2×#1313324714yes—
719C22C2×#1313324712yes—
720C22#1681142612yes—
721C22C23×C22⋊D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681127212yes—
734C4C2×#41×D5311yescharacteristic
735C4C2×#1313326411yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#2028720014yesdirect product factor
740C2C2×#1681127211yescharacteristic
741C2C22×#1313324711yescharacteristic
742C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53C2×#3346
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16811330C2semidirect
2. #20287200C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16810958C2semidirect
5. C2×#16810939C2semidirect
6. C2×#16810964C2semidirect
7. C2×#16810934C2semidirect
8. C2×#16810927C2semidirect
9. C2×#16810903C2semidirect
10. C2×#16810867C2semidirect
11. C2×#16810850C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810666C2semidirect
15. C22×#13133150C2semidirect
21. #16811330C22semidirect
32. #16811033C22semidirect
33. #16810964C22semidirect
34. #16810958C22semidirect
35. #16810939C22semidirect
36. #16810934C22semidirect
37. #16810927C22semidirect
38. #16810903C22semidirect
39. #16810867C22semidirect
40. #16810850C22semidirect
41. #16810723C22semidirect
42. #16810695C22semidirect
43. #16810666C22semidirect
50. C2×#13133150C22semidirect
384. C2×C53#3346semidirect
448. C53C2×#3346semidirect
739. C2#20287200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113302
#202872002
C2×#168110332
C2×#168109582
C2×#168109392
C2×#168109642
C2×#168109342
C2×#168109272
C2×#168109032
C2×#168108672
C2×#168108502
C2×#168107232
C2×#168106952
C2×#168106662
C22×#131331502
C2×C53×#5532
C2×#334653