Finite Group Databasebeta

← C2×#20284922 #28252348

Subgroups — C2×#20284922 #28252348

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×#16811233C211yesmaximal, characteristic, complemented
2C2×#16811106C211yesmaximal, characteristic
3#20284922C2116yesmaximal, direct product factor
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810954C211yesmaximal, characteristic, complemented
6C2×#16810928C211yesmaximal, characteristic, complemented
7C2×#16810925C211yesmaximal, characteristic, complemented
8C2×#16810831C211yesmaximal, characteristic, complemented
9C2×#16810826C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic
11C2×#16810730C211yesmaximal, characteristic, complemented
12C2×#16810720C211yesmaximal, characteristic, complemented
13C2×#16810715C211yesmaximal, characteristic, complemented
14C2×SD16×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19#16811233—24no—
20#16811233C2218yescomplemented
21C2×#13133215C2211yescharacteristic
22C2×#13133210—21no—
23C2×#13133210—21no—
24C2×#13133208—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133196C2211yescharacteristic
28#16811106—24no—
29#16811106C2218yes—
30C2×Q8×Dic53C2211yescharacteristic
31C2×Q8×Dic53C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×#13133182C2211yescharacteristic
34C2×D4×Dic53—21no—
35C2×D4×Dic53—21no—
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×#13133176—21no—
39C2×#13133176C2211yescharacteristic
40C22×C4⋊Dic53—21no—
41C22×C4⋊Dic53C2211yescharacteristic
42#16810956C2218yescomplemented
43#16810954C2218yescomplemented
44#16810928C2218yescomplemented
45#16810925C2218yescomplemented
46#16810831C2218yescomplemented
47#16810826C2218yescomplemented
48#16810785C2218yes—
49#16810730C2218yescomplemented
50#16810720C2218yescomplemented
51#16810715C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53#16810681C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yes—
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C23×Dic53—21no—
79C23×Dic53—21no—
80C23×Dic53—21no—
81C2×#11719925—24no—
82C2×#11719925C2314yes—
83C2×#11719923—24no—
84C2×#11719923C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133215—22no—
88#13133215C2314yes—
89#13133210—28no—
90#13133210—28no—
91#13133208—28no—
92#13133208—22no—
93#13133208C2314yes—
94#13133207—28no—
95#13133196—22no—
96#13133196C2314yes—
97Q8×Dic53—22no—
98Q8×Dic53—22no—
99Q8×Dic53—22no—
100Q8×Dic53C2314yes—
101Q8×Dic53C2314yes—
102Q8×Dic53C2314yes—
103#13133182—22no—
104#13133182C2314yes—
105D4×Dic53—28no—
106D4×Dic53—28no—
107D4×Dic53—22no—
108D4×Dic53—22no—
109D4×Dic53C2314yes—
110D4×Dic53C2314yes—
111#13133176—28no—
112#13133176D414yes—
113#13133176C2314yes—
114C2×C4⋊Dic53—28no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—22no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2314yes—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53D411yescharacteristic
136C2×C22⋊Dic53D411yescharacteristic
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133150C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133142C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C2×#41×C53—24no—
159C2×#41×C53—24no—
160C2×#41×C53—22no—
161C2×#41×C53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53—21no—
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C2×Q16×C53—24no—
169C2×Q16×C53C2314yes—
170C2×SD16×C53—24no—
171C2×SD16×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#102×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184#41×C53—216no—
185#41×C53—28no—
186#41×C53—28no—
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53#4114yes—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C2×D4×C53—28no—
196C2×D4×C53—24no—
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53#4114yes—
200C2×D4×C53C2412yes—
201C22×C4×C53—28no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
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—24no—
219C22×Dic53—82no—
220C22×Dic53—82no—
221C22×Dic53—82no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—21no—
229C2×Dic106C2412yes—
230Q16×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—21no—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53C2×D414yes—
244C22⋊Dic53C2×D414yes—
245#11719925—28no—
246#11719923—28no—
247C4⋊Dic53—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2×D414yes—
256C4⋊Dic53C2×D414yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—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—24no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D412yes—
285C23×C53C22×D411yescharacteristic
286Q8×C53—24no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291Q8×C53C2×#4114yes—
292D4×C53—216no—
293D4×C53—24no—
294D4×C53—22no—
295D4×C53C2×#4114yes—
296C2×C4×C53—216no—
297C2×C4×C53—22no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2×#4112yes—
311C2×C4×C53C2511yescharacteristic
312C2×Dic53—22no—
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—42no—
324C2×Dic53—84no—
325C2×Dic53—84no—
326C2×Dic53—84no—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331Dic106—22no—
332Dic106—22no—
333Dic106—42no—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3120—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—24no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—44no—
344C22×C53—48no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53#52512yes—
348C22×C53#57712yes—
349C22×C53#57812yes—
350C22×C53C23×D411yescharacteristic
351C4×C53—22no—
352C4×C53—24no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#52512yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C22×#4111yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—22no—
362Dic53—42no—
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×#461—531no—
375C2×#452—531no—
376C2×#452D5311yescharacteristic
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—42no—
383C2×C53—44no—
384C2×C53#312014yescomplemented
385C2×C53C2×#52511yescharacteristic
386C2×C53C2×#57711yescharacteristic
387C2×C53C2×#57811yescharacteristic
388C22×#41C2×D5311yescharacteristic
389C22×Q16—531no—
390C22×Q16C2×D5311yescharacteristic
391C22×SD16—531no—
392C22×SD16C2×D5311yescharacteristic
393#541—538no—
394#541—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8C2×D5311yescharacteristic
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—531no—
411C2×C4×D4—1061no—
412C2×C4×D4—1061no—
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#461—538no—
423#452—538no—
424#452C2×D5318yes—
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×#103—531no—
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102C2×D5311yescharacteristic
444C2×C22⋊C8—531no—
445C2×C22⋊C8C2×D5311yescharacteristic
446C2×#97—531no—
447C2×C4×C8—531no—
448C53C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—22no—
452C2×#41C22×D5314yes—
453C22×Q8—531no—
454C22×Q8C22×D5311yescharacteristic
455C22×Q8C22×D5311yescharacteristic
456C22×D4—21no—
457C22×D4C22×D5311yescharacteristic
458C23×C4—21no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×Q16—24no—
464C2×Q16—534no—
465C2×Q16—1064no—
466C2×Q16C22×D5314yes—
467C2×SD16—24no—
468C2×SD16—534no—
469C2×SD16—1064no—
470C2×SD16C22×D5314yes—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#126—1068no—
479#125—534no—
480#125—1062no—
481#125—1068no—
482#125—1068no—
483C22⋊Q8—22no—
484C22⋊Q8—534no—
485C22⋊Q8—1062no—
486C22⋊Q8C22×D5314yes—
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—534no—
496C4×D4—534no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1068no—
500C4×D4—1068no—
501#117—534no—
502#117—534no—
503#117—1068no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—1068no—
512C2×C4⋊C4—1061no—
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⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1062no—
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—531no—
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#103—534no—
547#103C22×D5314yes—
548#102—534no—
549#102C22×D5314yes—
550C22⋊C8—534no—
551C22⋊C8C22×D5314yes—
552#97—534no—
553C4×C8—534no—
554C24—21no—
555C24D4×D5311yescharacteristic
556#41—216no—
557#41—28no—
558#41—28no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—532no—
565C2×Q8—1061no—
566C2×Q8—1062no—
567C2×Q8—1062no—
568C2×Q8#1171994714yes—
569C2×Q8C23×D5312yes—
570C2×Q8C23×D5312yes—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4#1171994714yes—
576C2×D4C23×D5312yes—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—1064no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—4242no—
596C22×C4—4242no—
597C22×C4—4242no—
598C22×C4D4×D5312yes—
599C22×C4D4×D5311yescharacteristic
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602Q16—28no—
603Q16—1068no—
604SD16—28no—
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—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1061no—
631C4⋊C4—1061no—
632C4⋊C4—1061no—
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—532no—
644C42—532no—
645C42—1064no—
646C42—1064no—
647C42—1064no—
648C42—1064no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C2×D4×D5312yes—
657C23C2×D4×D5311yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—1062no—
664Q8—1062no—
665Q8—2122no—
666Q8C2×#1171994714yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#1171994714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—532no—
683C2×C4—532no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—4244no—
695C2×C4—4244no—
696C2×C4—4244no—
697C2×C4—2122no—
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—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1681112912yes—
719C22#1681143012yes—
720C22#1681143912yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—1062no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C4#1681112912yes—
735C4C22×#1171994711yescharacteristic
736C4C22×#1171994711yescharacteristic
737C2—42no—
738C2—44no—
739C2#2028492214yesdirect product factor
740C2C2×#1681112911yescharacteristic
741C2C2×#1681143011yescharacteristic
742C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
hypercenterC2×#452D53
hypocenterC53C2×#3120
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811233C2semidirect
3. #20284922C2direct (N × H)
4. C2×#16810956C2semidirect
5. C2×#16810954C2semidirect
6. C2×#16810928C2semidirect
7. C2×#16810925C2semidirect
8. C2×#16810831C2semidirect
9. C2×#16810826C2semidirect
11. C2×#16810730C2semidirect
12. C2×#16810720C2semidirect
13. C2×#16810715C2semidirect
14. C2×SD16×Dic53C2semidirect
15. C2×#16810681C2semidirect
20. #16811233C22semidirect
42. #16810956C22semidirect
43. #16810954C22semidirect
44. #16810928C22semidirect
45. #16810925C22semidirect
46. #16810831C22semidirect
47. #16810826C22semidirect
49. #16810730C22semidirect
50. #16810720C22semidirect
51. #16810715C22semidirect
52. SD16×Dic53C22semidirect
53. #16810681C22semidirect
384. C2×C53#3120semidirect
448. C53C2×#3120semidirect
739. C2#20284922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168111062
#202849222
C2×#168109562
C2×#168109542
C2×#168109282
C2×#168109252
C2×#168108312
C2×#168108262
C2×#168107852
C2×#168107302
C2×#168107202
C2×#168107152
C2×SD16×Dic532
C2×#168106812
C2×C53×#4522
C2×#312053