Finite Group Databasebeta

← C2×#20284781 #28252160

Subgroups — C2×#20284781 #28252160

Order 13568.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811175C211yesmaximal, characteristic, complemented
2C2×#16811091C211yesmaximal, characteristic
3#20284781C2116yesmaximal, direct product factor
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810907C211yesmaximal, characteristic, complemented
6C2×#16810902C211yesmaximal, characteristic, complemented
7C2×#16810832C211yesmaximal, characteristic, complemented
8C2×#16810827C211yesmaximal, characteristic, complemented
9C2×#16810787C211yesmaximal, characteristic
10C2×#16810783C211yesmaximal, characteristic
11C2×#16810717C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810673C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811175—24no—
23#16811175C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133215C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133196C2211yescharacteristic
28C2×#13133194—21no—
29#16811091—24no—
30#16811091C2218yes—
31C2×Q8×Dic53C2211yescharacteristic
32C2×#13133182—21no—
33C2×#13133182C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C2×#13133182C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133177—21no—
39C2×#13133177—21no—
40C2×#13133174—21no—
41C2×#13133173—21no—
42C22×C4×Dic53C2211yescharacteristic
43C2×C42×D53—21no—
44#16810964C2218yescomplemented
45#16810907C2218yescomplemented
46#16810902C2218yescomplemented
47#16810832C2218yescomplemented
48#16810827C2218yescomplemented
49#16810787C2218yes—
50#16810783C2218yes—
51#16810717C2218yescomplemented
52#16810715C2218yescomplemented
53#16810710C2218yescomplemented
54#16810708C2218yescomplemented
55#16810673C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C23×Dic53D411yescharacteristic
87C23×Dic53D411yescharacteristic
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C2×Dic212—24no—
92C2×Dic212C2314yes—
93C2×#11719925—24no—
94C2×#11719925C2314yes—
95C2×#11719913—24no—
96C2×#11719913C2314yes—
97C2×#11719924—24no—
98C2×#11719924C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133216—22no—
102#13133216C2314yes—
103#13133215—22no—
104#13133215C2314yes—
105#13133207—28no—
106#13133196—22no—
107#13133196C2314yes—
108#13133194—28no—
109Q8×Dic53—22no—
110Q8×Dic53C2314yes—
111#13133182—28no—
112#13133182—22no—
113#13133182—22no—
114#13133182—22no—
115#13133182C2314yes—
116#13133182C2314yes—
117#13133182C2314yes—
118#13133179—22no—
119#13133179—22no—
120#13133179C2314yes—
121#13133179C2314yes—
122#13133177—28no—
123#13133177—28no—
124#13133174—28no—
125#13133173—28no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53D414yes—
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147C2×C4×Dic53C2314yes—
148C42×D53—28no—
149#13133150C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133139C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160C8×Dic53C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53C2314yes—
168#117×C53—22no—
169#117×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yes—
178#106×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—28no—
199C2×C22⋊D53—24no—
200C22×Dic53—21no—
201C22×Dic53—24no—
202C22×Dic53—24no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D414yes—
208C22×Dic53C2×D414yes—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211#11719945—216no—
212#11719945—28no—
213#11719945—28no—
214C2×D212—21no—
215C2×D212—22no—
216C2×D212#4114yes—
217C2×D212C2412yes—
218C2×C4×D53—28no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—44no—
223C2×C4×D53—44no—
224C2×Dic106—21no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—21no—
229C2×Dic106—24no—
230C2×Dic106—44no—
231C2×Dic106#4114yes—
232C2×Dic106C2412yes—
233C2×Dic106C2412yes—
234C2×C8×C53—22no—
235C2×C8×C53—22no—
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C42×C53—24no—
248C22⋊Dic53—24no—
249#11719925—28no—
250#11719924—28no—
251#11719921—24no—
252#11719921—24no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D414yes—
268C4×Dic53C2×D414yes—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D412yes—
271C4×Dic53C2412yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277Dic212—28no—
278#11719913—28no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53C22×D412yes—
283C23×C53C22×D411yescharacteristic
284C22×D53—24no—
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291C2×C4×C53—22no—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C53C2×#4112yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—216no—
309C2×Dic53—24no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—28no—
314C2×Dic53—28no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53#13514yes—
320C2×Dic53#13714yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—24no—
326D212—22no—
327D212C2×#4114yes—
328C4×D53—216no—
329C4×D53—48no—
330C4×D53—48no—
331Dic106—24no—
332Dic106—22no—
333Dic106—22no—
334Dic106—22no—
335Dic106—42no—
336Dic106—48no—
337Dic106C2×#4114yes—
338C8×C53—22no—
339C8×C53—22no—
340#88322—22no—
341#88322—22no—
342C2×#3107—531nomaximal, Sylow
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—22no—
346C22×C53—44no—
347C22×C53#52512yes—
348C22×C53C2×#13512yes—
349C22×C53C2×#13712yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—24no—
352C2×D53—48no—
353C2×D53—42no—
354C2×D53—42no—
355C4×C53—22no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53#52512yes—
361C4×C53C22×#4111yescharacteristic
362C4×C53C22×#4111yescharacteristic
363Dic53—24no—
364Dic53—22no—
365Dic53—22no—
366Dic53—42no—
367Dic53—42no—
368Dic53C2×#13514yes—
369Dic53C2×#13714yes—
370C2×#533—531no—
371C2×C4×#41—531no—
372#3107—5316no—
373C2×#485—531no—
374C2×#485D5311yescharacteristic, complemented
375C2×#475—531no—
376C2×#474—531no—
377C2×#462—531no—
378C2×#461—531no—
379C2×#452—531no—
380C2×#452—531no—
381C2×C4×Q16—531no—
382C2×C4×Q16—531no—
383C2×C4×SD16—531no—
384C2×C4×SD16—531no—
385C2×#431—531no—
386C2×C53—42no—
387C2×C53#310714yescomplemented
388C2×C53C2×#52511yescharacteristic
389C2×C53C22×#13511yescharacteristic
390C2×C53C22×#13711yescharacteristic
391D53—44no—
392C22×#41—531no—
393C22×Q16—531no—
394C22×Q16—531no—
395C22×SD16—531no—
396C22×SD16—531no—
397#533—538no—
398#533—1064no—
399C2×C4⋊Q8—531no—
400C2×C4⋊Q8—531no—
401C2×#125—1061no—
402C2×C22⋊Q8—531no—
403C2×C22⋊Q8—1061no—
404C2×C22⋊Q8C2×D5311yescharacteristic
405C4×#41—538no—
406C4×#41—1064no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—1061no—
412C2×C4×D4—531no—
413C2×C4×D4—531no—
414C2×C4×D4—1061no—
415C2×C4×D4—1061no—
416C2×#117—1061no—
417C2×#117—1061no—
418C2×#117C2×D5311yescharacteristic
419C22×C42—531no—
420C22×C42—1061no—
421#485—538no—
422#485C2×D5318yescomplemented
423#475—538no—
424#474—538no—
425#462—538no—
426#461—538no—
427#452—538no—
428#452—538no—
429C4×Q16—538no—
430C4×Q16—538no—
431C4×SD16—538no—
432C4×SD16—538no—
433#431—538no—
434C2×#107—531no—
435C2×#107C2×D5311yescharacteristic
436C2×#106—531no—
437C2×#106C2×D5311yescharacteristic
438C2×C4⋊C8—531no—
439C2×C4⋊C8—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103C2×D5311yescharacteristic
445C2×#103C2×D5311yescharacteristic
446C2×#102—531no—
447C2×#102—531no—
448C2×C22⋊C8—531no—
449C2×C22⋊C8C2×D5311yescharacteristic
450C2×C4×C8—531no—
451C2×C4×C8—531no—
452C53C2×#310711yescharacteristic, complemented, Sylow
453C2×#41—534no—
454C2×#41—1064no—
455C2×#41—1064no—
456C2×#41—1062no—
457C22×Q8—531no—
458C22×Q8—531no—
459C22×Q8—1061no—
460C22×Q8C22×D5311yescharacteristic
461C22×D4—531no—
462C22×D4—1061no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4—1061no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4C22×D5311yescharacteristic
469C2×Q16—534no—
470C2×Q16—534no—
471C2×Q16—1064no—
472C2×Q16—1064no—
473C2×SD16—534no—
474C2×SD16—534no—
475C2×SD16—1064no—
476C2×SD16—1064no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8C22×D5311yescharacteristic
480C22×C8C22×D5311yescharacteristic
481C4⋊Q8—534no—
482C4⋊Q8—534no—
483C4⋊Q8—1062no—
484C4⋊Q8—1062no—
485#125—1068no—
486C22⋊Q8—22no—
487C22⋊Q8—534no—
488C22⋊Q8—1068no—
489C22⋊Q8—1062no—
490C22⋊Q8C22×D5314yes—
491C4×Q8—534no—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×Q8—1062no—
497C4×Q8—1062no—
498C4×Q8—1068no—
499C4×Q8—1062no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1068no—
505C4×D4—1068no—
506#117—22no—
507#117—1068no—
508#117—1068no—
509#117C22×D5314yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—531no—
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⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—534no—
532C2×C42—531no—
533C2×C42—531no—
534C2×C42—534no—
535C2×C42—1068no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540#107—534no—
541#107C22×D5314yes—
542#106—534no—
543#106C22×D5314yes—
544C4⋊C8—534no—
545C4⋊C8—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103—534no—
550#103C22×D5314yes—
551#103C22×D5314yes—
552#102—534no—
553#102—534no—
554C22⋊C8—534no—
555C22⋊C8C22×D5314yes—
556C4×C8—534no—
557C4×C8—534no—
558C24—1061no—
559C24D4×D5311yescharacteristic
560#41—1068no—
561#41—1068no—
562#41—10616no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—534no—
567C2×Q8—532no—
568C2×Q8—532no—
569C2×Q8—1064no—
570C2×Q8—1061no—
571C2×Q8—1061no—
572C2×Q8—1062no—
573C2×Q8—1062no—
574C2×Q8—1062no—
575C2×Q8—2124no—
576C2×Q8C23×D5312yes—
577C2×D4—534no—
578C2×D4—532no—
579C2×D4—1068no—
580C2×D4—1064no—
581C2×D4—1061no—
582C2×D4—1062no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—534no—
592C22×C4—534no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1068no—
598C22×C4—1064no—
599C22×C4—1064no—
600C22×C4—1061no—
601C22×C4—1064no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—2124no—
605C22×C4—2124no—
606C22×C4D4×D5312yes—
607C22×C4D4×D5311yescharacteristic
608C22×C4C23×D5312yes—
609C22×C4C23×D5311yescharacteristic
610Q16—1068no—
611Q16—1068no—
612SD16—1068no—
613SD16—1068no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—532no—
617C2×C8—532no—
618C2×C8—1062no—
619C2×C8—1062no—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—532no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1061no—
635C4⋊C4—1064no—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C4⋊C4C23×D5312yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C42—24no—
645C42—534no—
646C42—534no—
647C42—532no—
648C42—532no—
649C42—532no—
650C42—532no—
651C42—1064no—
652C42—1064no—
653C42—1064no—
654C42—1064no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1064no—
659C23—1062no—
660C23—2122no—
661C23—2122no—
662C23C2×D4×D5312yes—
663C23C2×D4×D5311yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—534no—
668Q8—1064no—
669Q8—1062no—
670Q8—1062no—
671Q8—1062no—
672Q8—2128no—
673Q8—2122no—
674D4—534no—
675D4—10616no—
676D4—1064no—
677D4—1062no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—534no—
691C2×C4—534no—
692C2×C4—532no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—10616no—
697C2×C4—1068no—
698C2×C4—1068no—
699C2×C4—1064no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—2128no—
706C2×C4—2128no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4#41×D5312yes—
712C2×C4#41×D5312yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—22no—
716C8—1062no—
717C8—1062no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—1064no—
723C22—2128no—
724C22—2122no—
725C22—2122no—
726C22#1681113112yes—
727C22#135×D5312yes—
728C22#137×D5312yes—
729C22C22×D4×D5311yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—534no—
736C4—534no—
737C4—1062no—
738C4—1062no—
739C4—1064no—
740C4—2122no—
741C4—2122no—
742C4#1681113112yes—
743C4C2×#41×D5311yescharacteristic
744C4C2×#41×D5311yescharacteristic
745C2—42no—
746C2—2124no—
747C2#2028478114yesdirect product factor
748C2C2×#1681113111yescharacteristic
749C2C2×#135×D5311yescharacteristic
750C2C2×#137×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#485D53
hypocenterC53C2×#3107
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16811175C2semidirect
3. #20284781C2direct (N × H)
4. C2×#16810964C2semidirect
5. C2×#16810907C2semidirect
6. C2×#16810902C2semidirect
7. C2×#16810832C2semidirect
8. C2×#16810827C2semidirect
11. C2×#16810717C2semidirect
12. C2×#16810715C2semidirect
13. C2×#16810710C2semidirect
14. C2×#16810708C2semidirect
15. C2×#16810673C2semidirect
16. C2×C53×#485C2semidirect
23. #16811175C22semidirect
44. #16810964C22semidirect
45. #16810907C22semidirect
46. #16810902C22semidirect
47. #16810832C22semidirect
48. #16810827C22semidirect
51. #16810717C22semidirect
52. #16810715C22semidirect
53. #16810710C22semidirect
54. #16810708C22semidirect
55. #16810673C22semidirect
71. C53×#485C22semidirect
374. C2×#485D53semidirect
387. C2×C53#3107semidirect
422. #485C2×D53semidirect
452. C53C2×#3107semidirect
747. C2#20284781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111752
C2×#168110912
#202847812
C2×#168109642
C2×#168109072
C2×#168109022
C2×#168108322
C2×#168108272
C2×#168107872
C2×#168107832
C2×#168107172
C2×#168107152
C2×#168107102
C2×#168107082
C2×#168106732
C2×C53×#4852
C2×#310753