Finite Group Databasebeta

← C2×#20284727 #28252101

Subgroups — C2×#20284727 #28252101

Order 13568.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11719945C211yesmaximal, characteristic, complemented
2#20284727C2116yesmaximal, direct product factor
3C2×#16810961C211yesmaximal, characteristic, complemented
4C2×#16810944C211yesmaximal, characteristic, complemented
5C2×#16810927C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810835C211yesmaximal, characteristic, complemented
9C2×#16810783C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic
11C2×C4×#11719925C211yesmaximal, characteristic, complemented
12C2×C4×#11719924C211yesmaximal, characteristic, complemented
13C2×C4×#11719923C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810676C211yesmaximal, characteristic, complemented
16C2×C53×#529C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C4×#11719945—24no—
23C4×#11719945C2218yescomplemented
24C2×C4×Dic106C2211yescharacteristic
25C2×C4×Dic106C2211yescharacteristic
26C2×C4×D212C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C2×C4×C22⋊D53—21no—
29C2×C4×C22⋊D53—21no—
30C2×#13133176C2211yescharacteristic
31C2×#13133174—21no—
32C2×C42×D53—21no—
33#16810961C2218yescomplemented
34#16810944C2218yescomplemented
35#16810927C2218yescomplemented
36#16810920C2218yescomplemented
37#16810842C2218yescomplemented
38#16810835C2218yescomplemented
39#16810783C2218yescomplemented
40#16810766C2218yes—
41C4×#11719925C2218yescomplemented
42C4×#11719924C2218yescomplemented
43C4×#11719923C2218yescomplemented
44C4×#11719922C2218yescomplemented
45#16810676C2218yescomplemented
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C4×#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#529—24no—
65C53×#529C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic
68C2×#124×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C2×#117×C53—21no—
76C22×C42×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C2×#11719925—24no—
88C2×#11719925C2314yes—
89C2×#11719923—24no—
90C2×#11719923C2314yes—
91C2×#11719924—24no—
92C2×#11719924C2314yes—
93C2×#11719922—24no—
94C2×#11719922C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C4×Dic106—22no—
100C4×Dic106—22no—
101C4×Dic106C2314yes—
102C4×Dic106C2314yes—
103C4×D212—22no—
104C4×D212—22no—
105C4×D212C2314yes—
106C4×D212C2314yes—
107C4×C22⋊D53—28no—
108C4×C22⋊D53—28no—
109#13133176—22no—
110#13133176C2314yes—
111#13133174—28no—
112C2×C4⋊Dic53C2311yescharacteristic
113C2×C4⋊Dic53C2311yescharacteristic
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×C22⋊Dic53—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×C4×Dic53—21no—
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122C42×D53—28no—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127C4⋊#88322C2314yes—
128C4⋊#88322C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133140C2314yes—
132#13133140C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135#13133137C2314yes—
136#13133137C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139C4×#88322C2314yes—
140C4×#88322C2314yes—
141C22×Q8×C53C2311yescharacteristic
142C22×D4×C53—21no—
143C22×D4×C53C2311yescharacteristic
144C23×C4×C53—21no—
145C23×C4×C53D411yescharacteristic
146C23×C4×C53D411yescharacteristic
147C23×C4×C53C2311yescharacteristic
148#126×C53—28no—
149#125×C53—22no—
150#125×C53C2314yes—
151#124×C53—22no—
152#124×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—22no—
155C22⋊Q8×C53C2314yes—
156#121×C53—22no—
157#121×C53C2314yes—
158C4×Q8×C53—22no—
159C4×Q8×C53C2314yes—
160C4×D4×C53—22no—
161C4×D4×C53—28no—
162C4×D4×C53C2314yes—
163#117×C53—28no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53—21no—
176C2×C42×C53D411yescharacteristic
177C2×C42×C53D411yescharacteristic
178C2×C42×C53D414yes—
179C2×C42×C53C2311yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C2×D4×C53—24no—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—44no—
194C2×D4×C53C2412yes—
195C22×C4×C53—24no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—42no—
203C22×C4×C53—44no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D414yes—
210C22×C4×C53C2×D414yes—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—28no—
215C2×C22⋊D53—24no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219#11719945—216no—
220#11719945—28no—
221#11719945—28no—
222C2×D212—21no—
223C2×D212—22no—
224C2×D212#4114yes—
225C2×D212C2412yes—
226C2×C4×D53—28no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—44no—
231C2×C4×D53—44no—
232C2×Dic106—21no—
233C2×Dic106—22no—
234C2×Dic106#4114yes—
235C2×Dic106C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53—24no—
249C42×C53—24no—
250C42×C53C2×D414yes—
251C42×C53C2×D412yes—
252C42×C53C2×D412yes—
253C42×C53C2×D414yes—
254C42×C53C2412yes—
255C42×C53C2412yes—
256C22⋊Dic53—24no—
257#11719925—28no—
258#11719924—28no—
259#11719923—28no—
260#11719922—28no—
261#11719921—24no—
262#11719921—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53C2412yes—
266C4⋊Dic53C2412yes—
267#11719919—24no—
268#11719919—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—24no—
290C22×D53—22no—
291C22×D53—42no—
292C22×D53—42no—
293Q8×C53—22no—
294Q8×C53—22no—
295Q8×C53—42no—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—48no—
299D4×C53—42no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—24no—
305C2×C4×C53—28no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—44no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—48no—
316C2×C4×C53#13514yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D411yescharacteristic
322C2×C4×C53C22×D412yes—
323C2×C4×C53C2×#4112yes—
324C2×C4×C53C2×#4112yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—216no—
327C2×Dic53—24no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333D212—24no—
334D212—22no—
335D212C2×#4114yes—
336C4×D53—216no—
337C4×D53—48no—
338C4×D53—48no—
339Dic106—24no—
340Dic106—22no—
341Dic106C2×#4114yes—
342#88322—22no—
343#88322—22no—
344#88322—22no—
345#88322—22no—
346C2×#3102—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—44no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—84no—
355C22×C53#52512yes—
356C22×C53C2×#13512yes—
357C22×C53#57512yes—
358C22×C53C23×D411yescharacteristic
359C2×D53—24no—
360C2×D53—48no—
361C2×D53—42no—
362C2×D53—42no—
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#52512yes—
371C4×C53C2×#13514yes—
372C4×C53C22×#4111yescharacteristic
373C4×C53C22×#4111yescharacteristic
374Dic53—24no—
375Dic53—42no—
376Dic53—42no—
377C2×#529D5311yescharacteristic, complemented
378C2×C4×#41—531no—
379#3102—5316no—
380C2×#485—531no—
381C2×#482—531no—
382C2×#479—531no—
383C2×#478—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#452—531no—
387C2×#449—531no—
388C2×C4×Q16—531no—
389C2×C4×SD16—531no—
390C2×C4×SD16—531no—
391C2×C4×D8—531no—
392C2×#431—531no—
393C2×C53—42no—
394C2×C53—82no—
395C2×C53#310214yescomplemented
396C2×C53C2×#52511yescharacteristic
397C2×C53C22×#13511yescharacteristic
398C2×C53C2×#57511yescharacteristic
399D53—44no—
400C22×#41—531no—
401C22×Q16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
404C22×D8—531no—
405#529—24no—
406#529C2×D5318yescomplemented
407C2×#126—21no—
408C2×#125C2×D5311yescharacteristic
409C2×#124C2×D5311yescharacteristic
410C2×#123—21no—
411C2×C22⋊Q8C2×D5311yescharacteristic
412C2×#121C2×D5311yescharacteristic
413C4×#41—538no—
414C4×#41—1064no—
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8C2×D5311yescharacteristic
418C2×C4×D4—21no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×C4×D4C2×D5311yescharacteristic
424C2×#117—21no—
425C2×#117—531no—
426C2×#117—1061no—
427C22×C42—1061no—
428C22×C42C2×D5311yescharacteristic
429#485—538no—
430#482—538no—
431#479—538no—
432#478—538no—
433#464—538no—
434#463—538no—
435#452—538no—
436#449—538no—
437C4×Q16—538no—
438C4×SD16—538no—
439C4×SD16—538no—
440C4×D8—538no—
441#431—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×C4×C8—531no—
459C2×C4×C8—531no—
460C53C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—534no—
462C2×#41—1064no—
463C2×#41—1064no—
464C2×#41—1062no—
465C22×Q8—531no—
466C22×Q8C22×D5311yescharacteristic
467C22×D4—21no—
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4C22×D5311yescharacteristic
471C23×C4—21no—
472C23×C4—1061no—
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4C22⋊D5311yescharacteristic
476C23×C4C22⋊D5311yescharacteristic
477C23×C4C22×D5311yescharacteristic
478C2×Q16—534no—
479C2×Q16—1064no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×D8—534no—
485C2×D8—1064no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8—531no—
489C22×C8—531no—
490#126—28no—
491#125—22no—
492#125C22×D5314yes—
493#124—22no—
494#124C22×D5314yes—
495#123—28no—
496C22⋊Q8—22no—
497C22⋊Q8C22×D5314yes—
498#121—22no—
499#121C22×D5314yes—
500C4×Q8—22no—
501C4×Q8—534no—
502C4×Q8—534no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8C22×D5314yes—
506C4×D4—28no—
507C4×D4—22no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1068no—
511C4×D4—1068no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4C22×D5314yes—
515#117—28no—
516#117—534no—
517#117—1062no—
518#117—1068no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—21no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—1061no—
541C2×C42—1068no—
542C2×C42C22⋊D5311yescharacteristic
543C2×C42C22⋊D5314yes—
544C2×C42C22⋊D5311yescharacteristic
545C2×C42C22×D5311yescharacteristic
546C2×C42C22×D5314yes—
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107—534no—
550#106—534no—
551#106—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562C22⋊C8—534no—
563C22⋊C8—534no—
564C4×C8—534no—
565C4×C8—534no—
566C24—21no—
567C24—1061no—
568C24C2×C22⋊D5311yescharacteristic
569#41—1068no—
570#41—1068no—
571#41—10616no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—534no—
576C2×Q8—532no—
577C2×Q8—1061no—
578C2×Q8—1062no—
579C2×Q8C23×D5312yes—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—534no—
586C2×D4—532no—
587C2×D4—1068no—
588C2×D4—1064no—
589C2×D4—1061no—
590C2×D4—1062no—
591C2×D4C23×D5312yes—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—1068no—
602C22×C4—1061no—
603C22×C4—1064no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4C2×C22⋊D5311yescharacteristic
611C22×C4C2×C22⋊D5311yescharacteristic
612C22×C4C2×C22⋊D5312yes—
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5314yes—
616C22×C4C2×C22⋊D5314yes—
617C22×C4C2×C22⋊D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620Q16—1068no—
621SD16—1068no—
622SD16—1068no—
623D8—1068no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8—1062no—
631C2×C8—1062no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—532no—
639C4⋊C4—532no—
640C4⋊C4—1061no—
641C4⋊C4—1061no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4C23×D5312yes—
645C4⋊C4C23×D5312yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C42—24no—
655C42—1064no—
656C42—1064no—
657C42—1064no—
658C42C2×C22⋊D5314yes—
659C42C2×C22⋊D5314yes—
660C42C2×C22⋊D5312yes—
661C42C2×C22⋊D5312yes—
662C42C23×D5312yes—
663C42C23×D5312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1064no—
672C23—1062no—
673C23—2122no—
674C23—2122no—
675C23C22×C22⋊D5312yes—
676C23C22×C22⋊D5311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—534no—
681Q8—1064no—
682Q8—1062no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—534no—
688D4—10616no—
689D4—1064no—
690D4—1062no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—48no—
707C2×C4—10616no—
708C2×C4—1064no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—2128no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2128no—
716C2×C4#1313323714yes—
717C2×C4C22×C22⋊D5312yes—
718C2×C4C22×C22⋊D5312yes—
719C2×C4C22×C22⋊D5312yes—
720C2×C4C22×C22⋊D5312yes—
721C2×C4C22×C22⋊D5311yescharacteristic
722C2×C4C22×C22⋊D5312yes—
723C2×C4#41×D5312yes—
724C2×C4#41×D5312yes—
725C2×C4C24×D5311yescharacteristic
726C8—1062no—
727C8—1062no—
728C8—1062no—
729C8—1062no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—1064no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22#1681113012yes—
743C22C2×#1313323712yes—
744C22#1681142112yes—
745C22C23×C22⋊D5311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—1064no—
754C4—2122no—
755C4—2122no—
756C4#1681113012yes—
757C4C2×#1313323714yes—
758C4C2×#41×D5311yescharacteristic
759C4C2×#41×D5311yescharacteristic
760C2—42no—
761C2—82no—
762C2—2124no—
763C2#2028472714yesdirect product factor
764C2C2×#1681113011yescharacteristic
765C2C22×#1313323711yescharacteristic
766C2C2×#1681142111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#529C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
hypercenterC2×#529D53
hypocenterC53C2×#3102
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11719945C2semidirect
2. #20284727C2direct (N × H)
3. C2×#16810961C2semidirect
4. C2×#16810944C2semidirect
5. C2×#16810927C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810835C2semidirect
9. C2×#16810783C2semidirect
11. C2×C4×#11719925C2semidirect
12. C2×C4×#11719924C2semidirect
13. C2×C4×#11719923C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810676C2semidirect
16. C2×C53×#529C2semidirect
23. C4×#11719945C22semidirect
33. #16810961C22semidirect
34. #16810944C22semidirect
35. #16810927C22semidirect
36. #16810920C22semidirect
37. #16810842C22semidirect
38. #16810835C22semidirect
39. #16810783C22semidirect
41. C4×#11719925C22semidirect
42. C4×#11719924C22semidirect
43. C4×#11719923C22semidirect
44. C4×#11719922C22semidirect
45. #16810676C22semidirect
65. C53×#529C22semidirect
377. C2×#529D53semidirect
395. C2×C53#3102semidirect
406. #529C2×D53semidirect
460. C53C2×#3102semidirect
763. C2#20284727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117199452
#202847272
C2×#168109612
C2×#168109442
C2×#168109272
C2×#168109202
C2×#168108422
C2×#168108352
C2×#168107832
C2×#168107662
C2×C4×#117199252
C2×C4×#117199242
C2×C4×#117199232
C2×C4×#117199222
C2×#168106762
C2×C53×#5292
C2×#310253