Finite Group Databasebeta

← C2×#20284945 #28252372

Subgroups — C2×#20284945 #28252372

Order 13568.

2058 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×#16811246C211yesmaximal, characteristic
2C2×#16811101C211yesmaximal, characteristic, complemented
3#20284945C2116yesmaximal, direct product factor
4C2×#16810961C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic
6C2×#16810916C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810847C211yesmaximal, characteristic, complemented
9C2×#16810847C211yesmaximal, characteristic, complemented
10C2×#16810762C211yesmaximal, characteristic
11C2×#16810730C211yesmaximal, characteristic, complemented
12C2×#16810726C211yesmaximal, characteristic, complemented
13C2×Q16×Dic53C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#451C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19#16811246—24no—
20#16811246C2218yes—
21C2×#13133216C2211yescharacteristic
22C2×#13133212—21no—
23C2×#13133206C2211yescharacteristic
24C2×#13133203—21no—
25C2×#13133199—21no—
26C2×#13133197—21no—
27C2×#13133191C2211yescharacteristic
28#16811101—24no—
29#16811101C2218yescomplemented
30C2×Q8×Dic53—21no—
31C2×Q8×Dic53—21no—
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133176—21no—
39C2×#13133176—21no—
40C2×#13133176C2211yescharacteristic
41C2×#13133176C2211yescharacteristic
42#16810961C2218yescomplemented
43#16810948C2218yes—
44#16810916C2218yescomplemented
45#16810906C2218yescomplemented
46#16810847C2218yescomplemented
47#16810847C2218yescomplemented
48#16810762C2218yes—
49#16810730C2218yescomplemented
50#16810726C2218yescomplemented
51Q16×Dic53C2218yescomplemented
52#16810708C2218yescomplemented
53#16810681C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#451C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81C2×#11719924—24no—
82C2×#11719924—24no—
83C2×#11719924C2314yes—
84C2×#11719924C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133216—22no—
88#13133216C2314yes—
89#13133212—28no—
90#13133206—22no—
91#13133206C2314yes—
92#13133203—28no—
93#13133199—28no—
94#13133197—28no—
95#13133191—22no—
96#13133191C2314yes—
97Q8×Dic53—28no—
98Q8×Dic53—28no—
99Q8×Dic53—22no—
100Q8×Dic53—22no—
101Q8×Dic53—22no—
102Q8×Dic53—22no—
103Q8×Dic53—22no—
104Q8×Dic53C2314yes—
105Q8×Dic53C2314yes—
106Q8×Dic53C2314yes—
107Q8×Dic53C2314yes—
108Q8×Dic53C2314yes—
109#13133179—22no—
110#13133179C2314yes—
111#13133176—28no—
112#13133176—28no—
113#13133176—22no—
114#13133176D414yes—
115#13133176C2314yes—
116#13133176C2314yes—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53D411yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×C22⋊Dic53—21no—
129C2×C22⋊Dic53D411yescharacteristic
130C2×C22⋊Dic53D411yescharacteristic
131C2×#11719921—21no—
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×C4×Dic53—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133141C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155C22⋊#88322C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53—24no—
159C22×Q8×C53—24no—
160C22×Q8×C53—21no—
161C22×Q8×C53—22no—
162C22×Q8×C53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C2×Q16×C53—24no—
169C2×Q16×C53—24no—
170C2×Q16×C53C2314yes—
171C2×Q16×C53C2314yes—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22⋊Q8×C53—22no—
175C22⋊Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×Q8×C53—216no—
185C2×Q8×C53—28no—
186C2×Q8×C53—28no—
187C2×Q8×C53—28no—
188C2×Q8×C53—24no—
189C2×Q8×C53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53#4114yes—
197C2×Q8×C53#4114yes—
198C2×Q8×C53C2412yes—
199C2×Q8×C53C2412yes—
200C2×Q8×C53C2412yes—
201C22×C4×C53—28no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—82no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—21no—
225C2×D212C2412yes—
226C2×C4×D53—24no—
227C2×C4×D53—82no—
228C2×Dic106—24no—
229C2×Dic106—82no—
230Q16×C53—28no—
231Q16×C53—28no—
232C2×C8×C53—22no—
233C2×C8×C53—22no—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53C2×D414yes—
242C22⋊Dic53C2×D414yes—
243#11719924—28no—
244#11719924—28no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2×D414yes—
258C4⋊Dic53C2×D414yes—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D412yes—
271C4×Dic53C2412yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286Q8×C53—216no—
287Q8×C53—24no—
288Q8×C53—24no—
289Q8×C53—22no—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—22no—
293Q8×C53—42no—
294Q8×C53C2×#4114yes—
295Q8×C53C2×#4114yes—
296C2×C4×C53—216no—
297C2×C4×C53—24no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—84no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329D212—22no—
330D212—22no—
331D212—42no—
332C4×D53—84no—
333Dic106—84no—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3121—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—44no—
343C22×C53#52512yes—
344C22×C53#57712yes—
345C22×C53#57812yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—84no—
351C4×C53—24no—
352C4×C53—24no—
353C4×C53—22no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53#52512yes—
357C4×C53C22×#4111yescharacteristic
358C4×C53C22×#4111yescharacteristic
359Dic53—22no—
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366C2×#542—531no—
367C2×#519—531no—
368#3121—5316no—
369C2×#485—531no—
370C2×#482—531no—
371C2×#477—531no—
372C2×#475—531no—
373C2×#464—531no—
374C2×#464—531no—
375C2×#451D5311yescharacteristic, complemented
376C2×#448—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—42no—
383C2×C53#312114yescomplemented
384C2×C53C2×#52511yescharacteristic
385C2×C53C2×#57711yescharacteristic
386C2×C53C2×#57811yescharacteristic
387D53—82no—
388C23×Q8C2×D5311yescharacteristic
389C22×Q16C2×D5311yescharacteristic
390C22×Q16C2×D5311yescharacteristic
391C22×SD16—531no—
392C22×SD16—531no—
393#542—538no—
394#542—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#124—531no—
398C2×#124—1061no—
399C2×#123—1061no—
400C2×C22⋊Q8—1061no—
401C2×C22⋊Q8C2×D5311yescharacteristic
402C2×#121—531no—
403#519—538no—
404#519—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—1061no—
411C2×C4×Q8—1061no—
412C2×C4×D4—531no—
413C2×#117—531no—
414C2×#117—531no—
415C2×#117—1061no—
416C2×#117—1061no—
417#485—538no—
418#482—538no—
419#477—538no—
420#475—538no—
421#464—538no—
422#464—538no—
423#451C2×D5318yescomplemented
424#448—538no—
425#441—538no—
426#440—538no—
427C4×Q16—538no—
428C4×SD16—538no—
429#433—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#106—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8C2×D5311yescharacteristic
446C2×#97—531no—
447C2×C4×C8—531no—
448C53C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—1061no—
454C22×Q8C22×D5311yescharacteristic
455C22×Q8C22×D5314yes—
456C22×Q8C22×D5311yescharacteristic
457C22×Q8C22×D5311yescharacteristic
458C22×D4—531no—
459C22×D4—1061no—
460C23×C4—21no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×Q16—24no—
464C2×Q16—24no—
465C2×Q16C22×D5314yes—
466C2×Q16C22×D5314yes—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—1064no—
470C2×SD16—1064no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#124—534no—
479#124—1062no—
480#124—1068no—
481#123—1068no—
482C22⋊Q8—22no—
483C22⋊Q8—1068no—
484C22⋊Q8C22×D5314yes—
485#121—534no—
486#121—1062no—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—534no—
492C4×Q8—1062no—
493C4×Q8—1062no—
494C4×Q8—1062no—
495C4×Q8—1062no—
496C4×Q8—1062no—
497C4×Q8—1068no—
498C4×Q8—1068no—
499C4×D4—534no—
500C4×D4—1062no—
501#117—534no—
502#117—534no—
503#117—534no—
504#117—1068no—
505#117—1068no—
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—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—1061no—
531C2×C42—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42—1061no—
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540C4⋊C8—534no—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103C22×D5314yes—
547#103C22×D5314yes—
548#102—534no—
549#102—534no—
550C22⋊C8—534no—
551C22⋊C8C22×D5314yes—
552#97—534no—
553C4×C8—534no—
554C24—1061no—
555C24D4×D5311yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—1064no—
569C2×Q8—4242no—
570C2×Q8#1171994714yes—
571C2×Q8#1171994714yes—
572C2×Q8C23×D5312yes—
573C2×Q8C23×D5312yes—
574C2×Q8C23×D5312yes—
575C2×D4—532no—
576C2×D4—1064no—
577C2×D4—1061no—
578C2×D4—1062no—
579C2×D4—1062no—
580C2×D4—4242no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—531no—
592C22×C4—531no—
593C22×C4—1064no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—4242no—
598C22×C4D4×D5312yes—
599C22×C4D4×D5311yescharacteristic
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602Q16—28no—
603Q16—28no—
604SD16—1068no—
605SD16—1068no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8C23×D5312yes—
613C2×C8C23×D5312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—534no—
617C4⋊C4—534no—
618C4⋊C4—532no—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—534no—
633C22⋊C4—534no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—532no—
640C42—532no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42—1064no—
646C42—1064no—
647C42—1064no—
648C42—1064no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1062no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23C2×D4×D5312yes—
657C23C2×D4×D5311yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—4244no—
667Q8C2×#1171994714yes—
668Q8C2×#1171994714yes—
669D4—1062no—
670D4—1062no—
671D4—4244no—
672D4—2122no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—532no—
689C2×C4—532no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—4244no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4—2122no—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994712yes—
704C2×C4C2×#1171994712yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—4244no—
715C22—2122no—
716C22—2122no—
717C22—2122no—
718C22#1681112912yes—
719C22#1681143212yes—
720C22#1681143612yes—
721C22C22×D4×D5311yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—1062no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C4#1681112912yes—
735C4C22×#1171994711yescharacteristic
736C4C22×#1171994711yescharacteristic
737C2—42no—
738C2—4242no—
739C2#2028494514yesdirect product factor
740C2C2×#1681112911yescharacteristic
741C2C2×#1681143211yescharacteristic
742C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#451D53
hypocenterC53C2×#3121
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#16811101C2semidirect
3. #20284945C2direct (N × H)
4. C2×#16810961C2semidirect
6. C2×#16810916C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810847C2semidirect
9. C2×#16810847C2semidirect
11. C2×#16810730C2semidirect
12. C2×#16810726C2semidirect
13. C2×Q16×Dic53C2semidirect
14. C2×#16810708C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#451C2semidirect
29. #16811101C22semidirect
42. #16810961C22semidirect
44. #16810916C22semidirect
45. #16810906C22semidirect
46. #16810847C22semidirect
47. #16810847C22semidirect
49. #16810730C22semidirect
50. #16810726C22semidirect
51. Q16×Dic53C22semidirect
52. #16810708C22semidirect
53. #16810681C22semidirect
73. C53×#451C22semidirect
375. C2×#451D53semidirect
383. C2×C53#3121semidirect
423. #451C2×D53semidirect
448. C53C2×#3121semidirect
739. C2#20284945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112462
C2×#168111012
#202849452
C2×#168109612
C2×#168109482
C2×#168109162
C2×#168109062
C2×#168108472
C2×#168107622
C2×#168107302
C2×#168107262
C2×Q16×Dic532
C2×#168107082
C2×#168106812
C2×C53×#4512
C2×#312153