Finite Group Databasebeta

← C2×#20284926 #28252352

Subgroups — C2×#20284926 #28252352

Order 13568.

2070 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×#16811234C211yesmaximal, characteristic, complemented
2C2×#16811102C211yesmaximal, characteristic
3#20284926C2116yesmaximal, direct product factor
4C2×#16810957C211yesmaximal, characteristic, complemented
5C2×#16810952C211yesmaximal, characteristic, complemented
6C2×#16810931C211yesmaximal, characteristic, complemented
7C2×#16810923C211yesmaximal, characteristic, complemented
8C2×#16810830C211yesmaximal, characteristic, complemented
9C2×#16810782C211yesmaximal, characteristic
10C2×#16810782C211yesmaximal, characteristic
11C2×#16810727C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810715C211yesmaximal, characteristic, complemented
14C2×SD16×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#461C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20#16811234—24no—
21#16811234C2218yescomplemented
22C2×#13133212—21no—
23C2×#13133212—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133207—21no—
27C2×#13133193C2211yescharacteristic
28C2×#13133193C2211yescharacteristic
29#16811102—24no—
30#16811102C2218yes—
31C2×Q8×Dic53C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×C4×Dic106C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×C4×C22⋊D53—21no—
37C2×#13133177—21no—
38C2×#13133174C2211yescharacteristic
39C2×#13133173—21no—
40C22×#11719919—21no—
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810957C2218yescomplemented
43#16810952C2218yescomplemented
44#16810931C2218yescomplemented
45#16810923C2218yescomplemented
46#16810830C2218yescomplemented
47#16810782C2218yes—
48#16810782C2218yes—
49#16810727C2218yescomplemented
50#16810724C2218yescomplemented
51#16810715C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53#16810683C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#461C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#11719947—24no—
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C2×#11719925—24no—
88C2×#11719925—24no—
89C2×#11719925C2314yes—
90C2×#11719925C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133212—28no—
94#13133212—28no—
95#13133209—22no—
96#13133209C2314yes—
97#13133207—28no—
98#13133207—28no—
99#13133193—22no—
100#13133193—22no—
101#13133193C2314yes—
102#13133193C2314yes—
103Q8×Dic53—22no—
104Q8×Dic53—22no—
105Q8×Dic53C2314yes—
106Q8×Dic53C2314yes—
107C4×Dic106—22no—
108C4×Dic106C2314yes—
109#13133182—22no—
110#13133182C2314yes—
111D4×Dic53—22no—
112D4×Dic53C2314yes—
113C4×C22⋊D53—28no—
114#13133177—28no—
115#13133174D414yes—
116#13133174C2314yes—
117#13133173—28no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—28no—
124C2×#11719919—21no—
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×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×#11719921D411yescharacteristic
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149C4⋊#88322C2314yes—
150#13133142C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C2×SD16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4⋊Q8×C53—22no—
171C4⋊Q8×C53C2314yes—
172C4×D4×C53—22no—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53#4114yes—
195C2×D4×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—82no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—28no—
205C2×C22⋊D53—24no—
206C22×Dic53—28no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—24no—
213C22×Dic53—82no—
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217#11719947—216no—
218#11719947—28no—
219#11719947—28no—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—82no—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2412yes—
226C2×Dic106—21no—
227C2×Dic106—22no—
228C2×Dic106#4114yes—
229C2×Dic106C2412yes—
230SD16×C53—28no—
231SD16×C53—28no—
232C2×C8×C53—22no—
233C2×C8×C53—22no—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244#11719925—28no—
245#11719925—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921C2×D414yes—
249#11719921C2×D414yes—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
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#11719919—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53C2×D412yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277C23×C53—24no—
278C23×C53—22no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53C22×D412yes—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291Q8×C53—42no—
292D4×C53—24no—
293D4×C53—22no—
294D4×C53C2×#4114yes—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—84no—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C2×#4112yes—
308C2×C4×C53C2×#4112yes—
309C2×C4×C53C2511yescharacteristic
310C22⋊D53—216no—
311C2×Dic53—216no—
312C2×Dic53—24no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—84no—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C4×D53—24no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—84no—
331Dic106—24no—
332Dic106—22no—
333Dic106C2×#4114yes—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3120—531nomaximal, Sylow
339C22×C53—24no—
340C22×C53—48no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53#52512yes—
344C22×C53#57712yes—
345C22×C53#57812yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—44no—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53#52512yes—
357C4×C53C22×#4111yescharacteristic
358C4×C53C22×#4111yescharacteristic
359Dic53—24no—
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366C2×#541—531no—
367C2×#520—531no—
368#3120—5316no—
369C2×#484—531no—
370C2×#483—531no—
371C2×#479—531no—
372C2×#478—531no—
373C2×#462—531no—
374C2×#461D5311yescharacteristic, complemented
375C2×#452—531no—
376C2×#452—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—44no—
383C2×C53#312014yescomplemented
384C2×C53C2×#52511yescharacteristic
385C2×C53C2×#57711yescharacteristic
386C2×C53C2×#57811yescharacteristic
387D53—42no—
388C22×#41—531no—
389C22×Q16—531no—
390C22×Q16—531no—
391C22×SD16C2×D5311yescharacteristic
392C22×SD16C2×D5311yescharacteristic
393#541—538no—
394#541—1064no—
395C2×C4⋊Q8C2×D5311yescharacteristic
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8—531no—
403#520—538no—
404#520—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×D4—531no—
410C2×C4×D4—1061no—
411C2×C4×D4—1061no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—1061no—
417#484—538no—
418#483—538no—
419#479—538no—
420#478—538no—
421#462—538no—
422#461C2×D5318yescomplemented
423#452—538no—
424#452—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⋊C8C2×D5311yescharacteristic
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⋊C8—531no—
446C2×#97—531no—
447C2×C4×C8—531no—
448C53C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—534no—
450C2×#41—1062no—
451C2×#41—1064no—
452C2×#41—1064no—
453C22×Q8—531no—
454C22×Q8C22×D5311yescharacteristic
455C22×Q8C22×D5311yescharacteristic
456C22×D4—1061no—
457C22×D4C22×D5311yescharacteristic
458C23×C4—21no—
459C23×C4—531no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C2×Q16—534no—
464C2×Q16—534no—
465C2×Q16—1064no—
466C2×Q16—1064no—
467C2×SD16—24no—
468C2×SD16—24no—
469C2×SD16C22×D5314yes—
470C2×SD16C22×D5314yes—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C22×D5314yes—
477#126—1068no—
478#126—1068no—
479#125—534no—
480#125—1068no—
481#125—1068no—
482#125—1062no—
483C22⋊Q8—534no—
484C22⋊Q8—534no—
485C22⋊Q8—1062no—
486C22⋊Q8—1062no—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×Q8—1062no—
494C4×Q8—1062no—
495C4×D4—22no—
496C4×D4—534no—
497C4×D4—1062no—
498C4×D4—1068no—
499C4×D4—1068no—
500C4×D4C22×D5314yes—
501#117—534no—
502#117—534no—
503#117—1068no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1068no—
514C2×C4⋊C4—1061no—
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⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—531no—
531C2×C42—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42C22×D5311yescharacteristic
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540C4⋊C8—534no—
541C4⋊C8C22×D5314yes—
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⋊C8—534no—
552#97—534no—
553C4×C8—534no—
554C24—21no—
555C24—531no—
556#41—1068no—
557#41—10616no—
558#41—1068no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—534no—
566C2×Q8—532no—
567C2×Q8—1061no—
568C2×Q8—1062no—
569C2×Q8C23×D5312yes—
570C2×Q8C23×D5312yes—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—1064no—
574C2×D4—1068no—
575C2×D4#1171994714yes—
576C2×D4C23×D5312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—531no—
583C22×C4—531no—
584C22×C4—531no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—1064no—
588C22×C4—1064no—
589C22×C4—1064no—
590C22×C4—1068no—
591C22×C4—1061no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—4242no—
598C22×C4—4242no—
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602Q16—1068no—
603Q16—1068no—
604SD16—28no—
605SD16—28no—
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—24no—
616C4⋊C4—21no—
617C4⋊C4—534no—
618C4⋊C4—534no—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1061no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—534no—
637C22⋊C4—534no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42—1064no—
646C42—1064no—
647C42D4×D5312yes—
648C42C23×D5312yes—
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—532no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23C2×D4×D5311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—534no—
665Q8—1064no—
666Q8—1062no—
667D4—24no—
668D4—22no—
669D4—10616no—
670D4C2×#1171994714yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—10616no—
684C2×C4—1062no—
685C2×C4—1064no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1064no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—4244no—
696C2×C4—4244no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4C2×#1171994712yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—1062no—
715C22—1062no—
716C22—1062no—
717C22—2124no—
718C22#1681113312yes—
719C22#1681142912yes—
720C22#1681143912yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—1064no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C4#1681113312yes—
735C4C2×#41×D5311yescharacteristic
736C4C22×#1171994711yescharacteristic
737C2—44no—
738C2—2122no—
739C2#2028492614yesdirect product factor
740C2C2×#1681113311yescharacteristic
741C2C2×#1681142911yescharacteristic
742C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#461C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
hypercenterC2×#461D53
hypocenterC53C2×#3120
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16811234C2semidirect
3. #20284926C2direct (N × H)
4. C2×#16810957C2semidirect
5. C2×#16810952C2semidirect
6. C2×#16810931C2semidirect
7. C2×#16810923C2semidirect
8. C2×#16810830C2semidirect
11. C2×#16810727C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810715C2semidirect
14. C2×SD16×Dic53C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#461C2semidirect
21. #16811234C22semidirect
42. #16810957C22semidirect
43. #16810952C22semidirect
44. #16810931C22semidirect
45. #16810923C22semidirect
46. #16810830C22semidirect
49. #16810727C22semidirect
50. #16810724C22semidirect
51. #16810715C22semidirect
52. SD16×Dic53C22semidirect
53. #16810683C22semidirect
73. C53×#461C22semidirect
374. C2×#461D53semidirect
383. C2×C53#3120semidirect
422. #461C2×D53semidirect
448. C53C2×#3120semidirect
739. C2#20284926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112342
C2×#168111022
#202849262
C2×#168109572
C2×#168109522
C2×#168109312
C2×#168109232
C2×#168108302
C2×#168107822
C2×#168107272
C2×#168107242
C2×#168107152
C2×SD16×Dic532
C2×#168106832
C2×C53×#4612
C2×#312053