Finite Group Databasebeta

← C2×#20284632 #28251863

Subgroups — C2×#20284632 #28251863

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811135C211yesmaximal, characteristic
2C2×#117×D53C211yesmaximal, characteristic, complemented
3#20284632C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810967C211yesmaximal, characteristic, complemented
7C2×#16810966C211yesmaximal, characteristic, complemented
8C2×#16810950C211yesmaximal, characteristic, complemented
9C2×#16810949C211yesmaximal, characteristic, complemented
10C2×#16810955C211yesmaximal, characteristic, complemented
11C2×#16810938C211yesmaximal, characteristic, complemented
12C2×#16810659C211yesmaximal, characteristic, complemented
13C2×#16810620C211yesmaximal, characteristic, complemented
14C2×#16810617C211yesmaximal, characteristic, complemented
15C22×#13133129C211yesmaximal, characteristic, complemented
16C2×C53×#427C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811135—24no—
21#16811135C2218yes—
22C2×#13133201—21no—
23C2×#13133197C2211yescharacteristic
24C2×#13133197C2211yescharacteristic
25C2×#13133192C2211yescharacteristic
26C2×#13133192C2211yescharacteristic
27C2×#13133187—21no—
28C2×C4×D212—21no—
29C2×C4×D212—21no—
30C2×#13133176C2211yescharacteristic
31C2×#13133175C2211yescharacteristic
32C2×#13133175C2211yescharacteristic
33C2×#13133174—21no—
34C2×#13133173—21no—
35#117×D53—24no—
36#117×D53C2218yescomplemented
37C2×C4⋊C4×D53C2211yescharacteristic
38C2×C4⋊C4×D53C2211yescharacteristic
39C2×C22⋊C4×D53—21no—
40C2×C42×D53—21no—
41#16810967C2218yescomplemented
42#16810966C2218yescomplemented
43#16810960C2218yescomplemented
44#16810955C2218yescomplemented
45#16810950C2218yescomplemented
46#16810949C2218yescomplemented
47#16810943C2218yescomplemented
48#16810938C2218yescomplemented
49#16810659C2218yescomplemented
50C2×#13133150C2211yescharacteristic, complemented
51C2×#13133150C2211yescharacteristic, complemented
52C2×#13133148C2211yescharacteristic, complemented
53C2×#13133148C2211yescharacteristic, complemented
54#16810620C2218yescomplemented
55#16810617C2218yescomplemented
56C2×#13133142C2211yescharacteristic, complemented
57C2×#13133142C2211yescharacteristic, complemented
58C2×#13133140C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133129C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2218yescomplemented
69C23×C8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C2×#117×C53C2211yescharacteristic
72C53×#427C2218yescomplemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#107×C53C2211yescharacteristic, complemented
75C2×#106×C53C2211yescharacteristic, complemented
76C2×#106×C53C2211yescharacteristic, complemented
77C24×D53D411yescharacteristic
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—24no—
81C2×#11719945C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212—21no—
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C23×Dic53D411yescharacteristic
88C22×C4×D53—24no—
89C22×C4×D53—24no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53D411yescharacteristic
94C22×C4×D53D414yes—
95C22×C4×D53D411yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C22×C4×D53C2314yes—
98C22×C4×D53C2311yescharacteristic
99C22×#88322—24no—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C22×#88322C2314yes—
103#13133201—28no—
104#13133197—22no—
105#13133197—22no—
106#13133197C2314yes—
107#13133197C2314yes—
108#13133192—22no—
109#13133192—22no—
110#13133192C2314yes—
111#13133192C2314yes—
112#13133187—28no—
113C4×D212—28no—
114C4×D212—28no—
115#13133176—22no—
116#13133176C2314yes—
117#13133175—22no—
118#13133175—22no—
119#13133175C2314yes—
120#13133175C2314yes—
121#13133174—28no—
122#13133173—28no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53C2314yes—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C22⋊C4×D53—28no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C42×D53—28no—
145#13133150C2314yescomplemented
146#13133150C2314yescomplemented
147#13133148C2314yescomplemented
148#13133148C2314yescomplemented
149#13133142C2314yescomplemented
150#13133142C2314yescomplemented
151#13133140C2314yescomplemented
152#13133140C2314yescomplemented
153#13133139C2314yescomplemented
154#13133139C2314yescomplemented
155#13133137C2314yescomplemented
156#13133137C2314yescomplemented
157#13133129C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133129C2314yes—
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53—24no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2314yes—
166#117×C53—22no—
167#117×C53—22no—
168#117×C53C2314yes—
169#117×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
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—
177C2×C42×C53—21no—
178#107×C53C2314yescomplemented
179#107×C53C2314yescomplemented
180#106×C53C2314yescomplemented
181#106×C53C2314yescomplemented
182C24×C53C2×D411yescharacteristic
183C23×D53—24no—
184C23×D53—24no—
185C23×D53—21no—
186C23×D53—42no—
187C23×D53C2×D411yescharacteristic
188C23×D53C2×D414yes—
189C23×D53C2×D411yescharacteristic
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53#4114yes—
197C22×C4×C53#4114yes—
198C22×C4×C53C2411yescharacteristic
199C22×C4×C53C2412yes—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—44no—
202C22×Dic53—24no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D414yes—
209#11719945—28no—
210#11719945—28no—
211#11719945—48no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—24no—
215C2×D212—24no—
216C2×D212—21no—
217C2×D212—44no—
218C2×D212—44no—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—216no—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—28no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—28no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—44no—
233C2×C4×D53—44no—
234C2×C4×D53—44no—
235C2×C4×D53C2×D414yes—
236C2×C4×D53C2×D412yes—
237C2×C4×D53C2×D414yes—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2412yes—
240C2×C4×D53C2412yes—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—21no—
244C2×Dic106C2412yes—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53—28no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C42×C53—24no—
261C42×C53—24no—
262C22⋊Dic53—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—28no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53#12314yes—
288C23×C53C22×D412yes—
289C23×C53C22×D411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—28no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—28no—
297C22×D53—22no—
298C22×D53—44no—
299C22×D53—416no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53#13514yes—
304C22×D53C22×D412yes—
305C22×D53C22×D412yes—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53#12314yes—
315C2×C4×C53#12318yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C22×D412yes—
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2×#4114yes—
320C2×C4×C53C2×#4112yes—
321C2×C4×C53C2×#4114yes—
322C2×C4×C53C2511yescharacteristic
323C22⋊D53—48no—
324C2×Dic53—28no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—22no—
336D212—22no—
337D212—48no—
338D212—48no—
339D212—42no—
340C4×D53—24no—
341C4×D53—24no—
342C4×D53—28no—
343C4×D53—28no—
344C4×D53—22no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—22no—
348C4×D53—48no—
349C4×D53—48no—
350C4×D53—48no—
351Dic106—22no—
352Dic106—22no—
353Dic106—42no—
354C8×C53—22no—
355C8×C53—22no—
356#88322—22no—
357#88322—22no—
358C2×#3091—531nomaximal, Sylow
359C22×C53—28no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53C2×#12314yes—
363C22×C53C2×#12312yes—
364C22×C53C2×#13512yes—
365C22×C53#57512yes—
366C22×C53C23×D411yescharacteristic
367C2×D53—28no—
368C2×D53—22no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—416no—
374C2×D53—44no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—84no—
379C2×D53C2×#13514yes—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53C2×#12312yes—
385C4×C53C2×#12314yes—
386C4×C53C22×#4111yescharacteristic
387C4×C53C22×#4111yescharacteristic
388Dic53—22no—
389Dic53—22no—
390Dic53—42no—
391Dic53—42no—
392Dic53—42no—
393C2×#525—531no—
394C22×#117—531no—
395#3091—5316no—
396C2×#484—531no—
397C2×#481—531no—
398C2×#485—531no—
399C2×#485—531no—
400C2×#482—531no—
401C2×#482—531no—
402C2×#483—531no—
403C2×#480—531no—
404C2×#427—531no—
405C2×#427D5311yescharacteristic, complemented
406C2×#416—531no—
407C2×#416—531no—
408C22×C22⋊C8—531no—
409C2×C53—24no—
410C2×C53#309114yescomplemented
411C2×C53C22×#12311yescharacteristic
412C2×C53C22×#13511yescharacteristic
413C2×C53C2×#57511yescharacteristic
414D53—24no—
415D53—42no—
416D53—82no—
417C22×#41—531no—
418C24×C4—531no—
419C23×C8—531no—
420C23×C8C2×D5311yescharacteristic
421#525—538no—
422#525—1064no—
423C2×#123—1061no—
424C2×C22⋊Q8—531no—
425C2×C22⋊Q8—531no—
426C2×#121—531no—
427C2×#121—531no—
428C2×#120—1061no—
429C2×C4×D4—1061no—
430C2×C4×D4—1061no—
431C2×#117—531no—
432C2×#117—538no—
433C2×#117—531no—
434C2×#117—531no—
435C2×#117—1061no—
436C2×#117—1061no—
437C2×#117—1064no—
438C2×#117C2×D5311yescharacteristic
439C2×#117C2×D5311yescharacteristic
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442C22×C22⋊C4—1061no—
443C22×C42—1061no—
444#485—538no—
445#485—538no—
446#484—538no—
447#483—538no—
448#482—538no—
449#482—538no—
450#481—538no—
451#480—538no—
452#427—538no—
453#427C2×D5318yescomplemented
454C2×#107—531no—
455C2×#107—531no—
456C2×#107C2×D5311yescharacteristic, complemented
457C2×#107C2×D5311yescharacteristic, complemented
458C2×#106—531no—
459C2×#106—531no—
460C2×#106C2×D5311yescharacteristic, complemented
461C2×#106C2×D5311yescharacteristic, complemented
462#416—538no—
463#416—538no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×C22⋊C8—531no—
473C2×C22⋊C8—531no—
474C2×C22⋊C8—531no—
475C2×C22⋊C8—531no—
476C2×C22⋊C8—538no—
477C53C2×#309111yescharacteristic, complemented, Sylow
478C25—531no—
479C2×#41—534no—
480C2×#41—1062no—
481C2×#41—1064no—
482C2×#41—1064no—
483C22×Q8—531no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4—1061no—
488C23×C4—531no—
489C23×C4—534no—
490C23×C4—531no—
491C23×C4—531no—
492C23×C4—531no—
493C23×C4—531no—
494C23×C4—534no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1064no—
498C23×C4—1064no—
499C23×C4—1061no—
500C23×C4C22×D5311yescharacteristic
501C22×C8—24no—
502C22×C8—531no—
503C22×C8—531no—
504C22×C8—534no—
505C22×C8—1064no—
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C22×C8C22×D5314yes—
509#123—1068no—
510C22⋊Q8—534no—
511C22⋊Q8—534no—
512C22⋊Q8—1062no—
513C22⋊Q8—1062no—
514#121—534no—
515#121—534no—
516#121—1062no—
517#121—1062no—
518#120—1068no—
519C4×D4—1068no—
520C4×D4—1068no—
521#117—22no—
522#117—22no—
523#117—534no—
524#117—534no—
525#117—534no—
526#117—1068no—
527#117—1068no—
528#117—1062no—
529#117—1062no—
530#117—1062no—
531#117C22×D5314yes—
532#117C22×D5314yes—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—534no—
536C2×C4⋊C4—534no—
537C2×C4⋊C4—1062no—
538C2×C4⋊C4—1062no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1068no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1068no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42—1061no—
563#107—534no—
564#107—534no—
565#107C22×D5314yescomplemented
566#107C22×D5314yescomplemented
567#106—534no—
568#106—534no—
569#106C22×D5314yescomplemented
570#106C22×D5314yescomplemented
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#102—534no—
576#102—534no—
577#102—534no—
578#102—534no—
579C22⋊C8—534no—
580C22⋊C8—534no—
581C22⋊C8—534no—
582C22⋊C8—534no—
583C24—531no—
584C24—531no—
585C24—534no—
586C24—1064no—
587C24—1064no—
588C24—1061no—
589C24—2122no—
590C24D4×D5311yescharacteristic
591#41—1068no—
592#41—1068no—
593#41—2128no—
594C2×Q8—532no—
595C2×Q8—1061no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×D4—532no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1061no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—2124no—
606C2×D4—2124no—
607C2×D4—2124no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—531no—
613C22×C4—531no—
614C22×C4—534no—
615C22×C4—534no—
616C22×C4—532no—
617C22×C4—534no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—532no—
621C22×C4—1064no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—10616no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1068no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1068no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1064no—
637C22×C4—2124no—
638C22×C4—2124no—
639C22×C4—2124no—
640C22×C4#1171994514yes—
641C22×C4D4×D5312yes—
642C22×C4D4×D5311yescharacteristic
643C22×C4#1171994914yes—
644C22×C4C23×D5311yescharacteristic
645C22×C4C23×D5312yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—532no—
650C2×C8—532no—
651C2×C8—1062no—
652C2×C8—1062no—
653C2×C8—1068no—
654C2×C8C23×D5312yes—
655C2×C8C23×D5312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—532no—
661C4⋊C4—532no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4C23×D5312yes—
669C4⋊C4C23×D5312yes—
670C4⋊C4C23×D5312yes—
671C4⋊C4C23×D5312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C42—24no—
682C42—24no—
683C42—1064no—
684C42—1064no—
685C42—1064no—
686C23—22no—
687C23—22no—
688C23—534no—
689C23—532no—
690C23—532no—
691C23—1068no—
692C23—1062no—
693C23—1062no—
694C23—1068no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—2124no—
700C23—21216no—
701C23—2122no—
702C23—2122no—
703C23—2122no—
704C23#1313320214yes—
705C23C2×D4×D5312yes—
706C23C2×D4×D5311yescharacteristic
707Q8—1062no—
708Q8—1062no—
709Q8—2122no—
710D4—1062no—
711D4—1062no—
712D4—2128no—
713D4—2128no—
714D4—2128no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—1068no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1068no—
730C2×C4—1068no—
731C2×C4—1064no—
732C2×C4—1064no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—2128no—
741C2×C4—2128no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2128no—
746C2×C4#1313320214yes—
747C2×C4#1313320218yes—
748C2×C4C2×D4×D5312yes—
749C2×C4C2×D4×D5311yescharacteristic
750C2×C4C2×#1171994512yes—
751C2×C4C2×#1171994514yes—
752C2×C4C2×#1171994912yes—
753C2×C4C2×#1171994914yes—
754C2×C4C24×D5311yescharacteristic
755C8—22no—
756C8—22no—
757C8—1062no—
758C8—1062no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—534no—
763C22—1062no—
764C22—1062no—
765C22—1068no—
766C22—1062no—
767C22—1062no—
768C22—1062no—
769C22—4244no—
770C22—21216no—
771C22—2122no—
772C22—2122no—
773C22—2122no—
774C22—2124no—
775C22C2×#1313320214yes—
776C22C2×#1313320212yes—
777C22#135×D5312yes—
778C22#1681142012yes—
779C22C22×D4×D5311yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—1062no—
785C4—1062no—
786C4—2122no—
787C4—2122no—
788C4—2122no—
789C4C2×#1313320214yes—
790C4C2×#1313320212yes—
791C4C22×#1171994511yescharacteristic
792C4C22×#1171994911yescharacteristic
793C2—24no—
794C2—1064no—
795C2—4242no—
796C2—2122no—
797C2#2028463214yesdirect product factor
798C2C22×#1313320211yescharacteristic
799C2C2×#135×D5311yescharacteristic
800C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#427C2
socleC23×C53C22×D4
prime radicalC2×#16811135C2
hypercenterC2×#427D53
hypocenterC53C2×#3091
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#117×D53C2semidirect
3. #20284632C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810967C2semidirect
7. C2×#16810966C2semidirect
8. C2×#16810950C2semidirect
9. C2×#16810949C2semidirect
10. C2×#16810955C2semidirect
11. C2×#16810938C2semidirect
12. C2×#16810659C2semidirect
13. C2×#16810620C2semidirect
14. C2×#16810617C2semidirect
15. C22×#13133129C2semidirect
16. C2×C53×#427C2semidirect
36. #117×D53C22semidirect
41. #16810967C22semidirect
42. #16810966C22semidirect
43. #16810960C22semidirect
44. #16810955C22semidirect
45. #16810950C22semidirect
46. #16810949C22semidirect
47. #16810943C22semidirect
48. #16810938C22semidirect
49. #16810659C22semidirect
50. C2×#13133150C22semidirect
51. C2×#13133150C22semidirect
52. C2×#13133148C22semidirect
53. C2×#13133148C22semidirect
54. #16810620C22semidirect
55. #16810617C22semidirect
56. C2×#13133142C22semidirect
57. C2×#13133142C22semidirect
58. C2×#13133140C22semidirect
59. C2×#13133140C22semidirect
60. C2×#13133139C22semidirect
61. C2×#13133139C22semidirect
62. C2×#13133137C22semidirect
63. C2×#13133137C22semidirect
68. C2×#13133129C22semidirect
72. C53×#427C22semidirect
73. C2×#107×C53C22semidirect
74. C2×#107×C53C22semidirect
75. C2×#106×C53C22semidirect
76. C2×#106×C53C22semidirect
145. #13133150C23semidirect
146. #13133150C23semidirect
147. #13133148C23semidirect
148. #13133148C23semidirect
149. #13133142C23semidirect
150. #13133142C23semidirect
151. #13133140C23semidirect
152. #13133140C23semidirect
153. #13133139C23semidirect
154. #13133139C23semidirect
155. #13133137C23semidirect
156. #13133137C23semidirect
178. #107×C53C23semidirect
179. #107×C53C23semidirect
180. #106×C53C23semidirect
181. #106×C53C23semidirect
405. C2×#427D53semidirect
410. C2×C53#3091semidirect
453. #427C2×D53semidirect
456. C2×#107C2×D53semidirect
457. C2×#107C2×D53semidirect
460. C2×#106C2×D53semidirect
461. C2×#106C2×D53semidirect
477. C53C2×#3091semidirect
565. #107C22×D53semidirect
566. #107C22×D53semidirect
569. #106C22×D53semidirect
570. #106C22×D53semidirect
797. C2#20284632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111352
C2×#117×D532
#202846322
C2×#168109602
C2×#168109432
C2×#168109672
C2×#168109662
C2×#168109502
C2×#168109492
C2×#168109552
C2×#168109382
C2×#168106592
C2×#168106202
C2×#168106172
C22×#131331292
C2×C53×#4272
C2×#309153