Finite Group Databasebeta

← C2×#20284677 #28251924

Subgroups — C2×#20284677 #28251924

Order 13568.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811196C211yesmaximal, characteristic
2C2×#16811104C211yesmaximal, characteristic
3#20284677C2116yesmaximal, direct product factor
4C2×#16810958C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810967C211yesmaximal, characteristic, complemented
7C2×#16810965C211yesmaximal, characteristic, complemented
8C2×#16810962C211yesmaximal, characteristic, complemented
9C2×#16810961C211yesmaximal, characteristic, complemented
10C2×#16810955C211yesmaximal, characteristic, complemented
11C2×#16810662C211yesmaximal, characteristic, complemented
12C2×#16810658C211yesmaximal, characteristic, complemented
13C2×#16810630C211yesmaximal, characteristic, complemented
14C2×#103×D53C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811196—24no—
22#16811196C2218yes—
23C2×#13133216—21no—
24C2×#13133203—21no—
25C2×#13133202—21no—
26C2×#13133199—21no—
27C2×#13133197C2211yescharacteristic
28C2×#13133196C2211yescharacteristic
29C2×#13133193C2211yescharacteristic
30#16811104—24no—
31#16811104C2218yes—
32C2×#13133182—21no—
33C2×#13133179—21no—
34C2×C4×C22⋊D53—21no—
35C2×C4×C22⋊D53—21no—
36C2×#13133176C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810967C2218yescomplemented
43#16810965C2218yescomplemented
44#16810962C2218yescomplemented
45#16810961C2218yescomplemented
46#16810958C2218yescomplemented
47#16810957C2218yescomplemented
48#16810955C2218yescomplemented
49#16810662C2218yescomplemented
50#16810658C2218yescomplemented
51C2×#13133151C2211yescharacteristic
52C2×#13133150C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57#16810630C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64#103×D53C2218yescomplemented
65#16810588C2218yes—
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#483C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—24no—
78C2×#11719945—24no—
79C2×#11719945D414yes—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106D411yescharacteristic
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—24no—
86C2×Q8×D53—24no—
87C2×Q8×D53C2314yes—
88C22×D212D411yescharacteristic
89C22×C22⋊D53D411yescharacteristic
90C22×C22⋊D53D411yescharacteristic
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×#11719912—24no—
97C2×#11719912C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C2×C8×D53—24no—
101C2×C8×D53C2314yes—
102#13133216—28no—
103#13133203—28no—
104#13133202—28no—
105#13133199—28no—
106#13133197—22no—
107#13133197C2314yes—
108#13133196—22no—
109#13133196C2314yes—
110#13133193—22no—
111#13133193C2314yes—
112#13133182—28no—
113#13133179—28no—
114C4×C22⋊D53—28no—
115C4×C22⋊D53—28no—
116#13133176—22no—
117#13133176C2314yes—
118#13133175—22no—
119#13133175—22no—
120#13133175—22no—
121#13133175C2314yes—
122#13133175C2314yes—
123#13133175C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C4⋊C4×D53C2314yes—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147#13133151C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133150C2314yes—
151#13133149C2314yes—
152#13133148C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—22no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53C2×D411yescharacteristic
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—82no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53C2×D414yes—
204C2×C22⋊D53C2×D414yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211Q8×D53—28no—
212Q8×D53—28no—
213Q8×D53—48no—
214#11719945—216no—
215#11719945—28no—
216#11719945—28no—
217C2×D212—24no—
218C2×D212C2×D414yes—
219C2×C4×D53—22no—
220C2×C4×D53—22no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×C4×D53—82no—
226C2×C4×D53—82no—
227C2×C4×D53C2×D412yes—
228C2×C4×D53C2×D412yes—
229C2×C4×D53#4114yes—
230C2×C4×D53#4114yes—
231C2×C4×D53C2412yes—
232C2×C4×D53C2412yes—
233C2×Dic106—24no—
234C2×Dic106—22no—
235C2×Dic106—22no—
236C2×Dic106—21no—
237C2×Dic106—24no—
238C2×Dic106—44no—
239C2×Dic106C2×D414yes—
240C2×Dic106C2412yes—
241C2×C8×C53—22no—
242C2×C8×C53—22no—
243C2×C8×C53C2412yes—
244C2×C8×C53C2412yes—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—24no—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C22⋊C4×C53—24no—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53C2412yes—
266C4⋊Dic53C2412yes—
267C4⋊Dic53C2412yes—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272C4×Dic53—24no—
273C4×Dic53—24no—
274C4×Dic53—24no—
275C4×Dic53—24no—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280#11719912—28no—
281C8×D53—28no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53C22×D412yes—
286C23×C53C22×D411yescharacteristic
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53#12314yes—
293C22×D53C22×D412yes—
294C22×D53C22×D412yes—
295Q8×C53—22no—
296Q8×C53—22no—
297Q8×C53—42no—
298C2×C4×C53—22no—
299C2×C4×C53—24no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—84no—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4112yes—
314C2×C4×C53C2×#4112yes—
315C2×C4×C53C2511yescharacteristic
316C22⋊D53—28no—
317C22⋊D53—28no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53#12314yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330D212—28no—
331C4×D53—24no—
332C4×D53—22no—
333C4×D53—22no—
334C4×D53—48no—
335C4×D53—84no—
336C4×D53—84no—
337C4×D53#12318yes—
338C4×D53C2×#4114yes—
339C4×D53C2×#4114yes—
340Dic106—28no—
341Dic106—22no—
342Dic106—22no—
343Dic106—42no—
344Dic106—48no—
345C8×C53—22no—
346C8×C53—22no—
347#88322—22no—
348#88322—22no—
349C2×#3097—531nomaximal, Sylow
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—44no—
354C22×C53C2×#12312yes—
355C22×C53#57712yes—
356C22×C53#57812yes—
357C22×C53C23×D411yescharacteristic
358C2×D53—28no—
359C2×D53—22no—
360C2×D53—22no—
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—22no—
364C2×D53—44no—
365C2×D53C2×#12314yes—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53C2×#12312yes—
372C4×C53C22×#4111yescharacteristic
373C4×C53C22×#4111yescharacteristic
374Dic53—22no—
375Dic53—42no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379Dic53C2×#12314yes—
380C2×#536—531no—
381C2×#520—531no—
382#3097—5316no—
383C2×#484—531no—
384C2×#484—531no—
385C2×#485—531no—
386C2×#485—531no—
387C2×#485—531no—
388C2×#485—531no—
389C2×#483—531no—
390C2×#483D5311yescharacteristic, complemented
391C2×#428—531no—
392C2×#427—531no—
393C2×#419—531no—
394C22×#103—531no—
395C2×#408—531no—
396C2×C53—42no—
397C2×C53#309714yescomplemented
398C2×C53C22×#12311yescharacteristic
399C2×C53C2×#57711yescharacteristic
400C2×C53C2×#57811yescharacteristic
401D53—24no—
402D53—42no—
403C22×#41—531no—
404C23×Q8—531no—
405C22×M16—531no—
406C23×C8—531no—
407#536—538no—
408#536—1064no—
409C2×C4⋊Q8—1061no—
410C2×#124—1061no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—531no—
414C2×C22⋊Q8—531no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8C2×D5311yescharacteristic
417#520—538no—
418#520—1064no—
419C2×C4×Q8—1061no—
420C2×C4×D4—1061no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×#117—531no—
424C2×#117—531no—
425C2×#117—531no—
426C2×#117—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4C2×D5311yescharacteristic
430#485—538no—
431#485—538no—
432#485—538no—
433#485—538no—
434#484—538no—
435#484—538no—
436#483—538no—
437#483C2×D5318yescomplemented
438#428—538no—
439#427—538no—
440C2×#107—531no—
441C2×#107—531no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×#106C2×D5311yescharacteristic
447C2×#106C2×D5311yescharacteristic
448#419—538no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—538no—
456C2×#103C2×D5311yescharacteristic
457C2×#103C2×D5311yescharacteristic
458#408—538no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×C22⋊C8—531no—
462C2×C22⋊C8C2×D5311yescharacteristic
463C53C2×#309711yescharacteristic, complemented, Sylow
464C2×#41—534no—
465C2×#41—534no—
466C2×#41—1064no—
467C2×#41—1064no—
468C22×Q8—531no—
469C22×Q8—534no—
470C22×Q8—531no—
471C22×Q8—1061no—
472C22×Q8—1062no—
473C22×Q8—1064no—
474C22×Q8—1064no—
475C22×Q8C22×D5311yescharacteristic
476C22×D4—531no—
477C22×D4—531no—
478C22×D4—531no—
479C23×C4—21no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—1061no—
483C23×C4—1061no—
484C23×C4—1061no—
485C23×C4C22×D5311yescharacteristic
486C2×M16—534no—
487C2×M16—1064no—
488C22×C8—531no—
489C22×C8—531no—
490C22×C8—534no—
491C22×C8—1064no—
492C22×C8C22×D5311yescharacteristic
493C22×C8C22×D5311yescharacteristic
494C4⋊Q8—1068no—
495#124—1068no—
496#123—1068no—
497#123—1068no—
498C22⋊Q8—22no—
499C22⋊Q8—534no—
500C22⋊Q8—534no—
501C22⋊Q8—534no—
502C22⋊Q8—1062no—
503C22⋊Q8—1062no—
504C22⋊Q8—1062no—
505C22⋊Q8C22×D5314yes—
506C4×Q8—1068no—
507C4×D4—1068no—
508C4×D4—1068no—
509C4×D4—1068no—
510#117—534no—
511#117—534no—
512#117—534no—
513#117—534no—
514#117—1062no—
515#117—1062no—
516#117—1062no—
517#117—1062no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—1062no—
527C2×C4⋊C4—1062no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C4⋊C4C22×D5311yescharacteristic
535C2×C4⋊C4C22×D5314yes—
536C2×C4⋊C4C22×D5311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42—1061no—
548C2×C42—1061no—
549#107—534no—
550#107—534no—
551#107—534no—
552#107—534no—
553#106—534no—
554#106—534no—
555#106C22×D5314yes—
556#106C22×D5314yes—
557#103—534no—
558#103—534no—
559#103—534no—
560#103—534no—
561#103—534no—
562#103—534no—
563#103C22×D5314yes—
564#103C22×D5314yes—
565C22⋊C8—534no—
566C22⋊C8—534no—
567C22⋊C8—534no—
568C22⋊C8C22×D5314yes—
569C24—531no—
570C24—531no—
571C24D4×D5311yescharacteristic
572#41—10616no—
573#41—1068no—
574#41—1068no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—534no—
579C2×Q8—532no—
580C2×Q8—1064no—
581C2×Q8—1064no—
582C2×Q8—1068no—
583C2×Q8—1068no—
584C2×Q8—1061no—
585C2×Q8—1062no—
586C2×Q8—1062no—
587C2×Q8—2124no—
588C2×Q8—2128no—
589C2×Q8C23×D5312yes—
590C2×D4—534no—
591C2×D4—534no—
592C2×D4—534no—
593C2×D4—1064no—
594C2×D4—1064no—
595C2×D4—1064no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—531no—
605C22×C4—532no—
606C22×C4—534no—
607C22×C4—534no—
608C22×C4—532no—
609C22×C4—531no—
610C22×C4—532no—
611C22×C4—532no—
612C22×C4—1064no—
613C22×C4—1064no—
614C22×C4—1064no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—4242no—
622C22×C4—4242no—
623C22×C4—2124no—
624C22×C4D4×D5312yes—
625C22×C4D4×D5311yescharacteristic
626C22×C4C23×D5312yes—
627C22×C4C23×D5311yescharacteristic
628M16—1068no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—532no—
632C2×C8—532no—
633C2×C8—1068no—
634C2×C8—1062no—
635C2×C8—1062no—
636C2×C8C23×D5312yes—
637C2×C8C23×D5312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—532no—
644C4⋊C4—532no—
645C4⋊C4—532no—
646C4⋊C4—1064no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1064no—
654C4⋊C4C23×D5312yes—
655C4⋊C4C23×D5312yes—
656C4⋊C4C23×D5312yes—
657C22⋊C4—24no—
658C22⋊C4—1064no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C42—1064no—
666C42—1064no—
667C42—1064no—
668C42—1064no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—534no—
673C23—532no—
674C23—532no—
675C23—1062no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23C2×D4×D5312yes—
681C23C2×D4×D5311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—1068no—
686Q8—1062no—
687Q8—1062no—
688Q8—2128no—
689Q8—2122no—
690D4—1068no—
691D4—1068no—
692D4—1068no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—84no—
706C2×C4—534no—
707C2×C4—532no—
708C2×C4—538no—
709C2×C4—534no—
710C2×C4—534no—
711C2×C4—532no—
712C2×C4—1062no—
713C2×C4—1064no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—4244no—
721C2×C4—4244no—
722C2×C4—2128no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4C2×D4×D5312yes—
728C2×C4C2×D4×D5311yescharacteristic
729C2×C4#41×D5312yes—
730C2×C4#41×D5312yes—
731C2×C4C24×D5311yescharacteristic
732C8—22no—
733C8—22no—
734C8—1062no—
735C8—1062no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—534no—
741C22—1068no—
742C22—1062no—
743C22—1062no—
744C22—1062no—
745C22—1062no—
746C22—1062no—
747C22—2124no—
748C22#123×D5312yes—
749C22#1681142912yes—
750C22#1681143912yes—
751C22C22×D4×D5311yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—534no—
758C4—1062no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4—2122no—
763C4#123×D5312yes—
764C4C2×#41×D5311yescharacteristic
765C4C2×#41×D5311yescharacteristic
766C2—42no—
767C2—1064no—
768C2—2122no—
769C2#2028467714yesdirect product factor
770C2C2×#123×D5311yescharacteristic
771C2C2×#1681142911yescharacteristic
772C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#483D53
hypocenterC53C2×#3097
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #20284677C2direct (N × H)
4. C2×#16810958C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810967C2semidirect
7. C2×#16810965C2semidirect
8. C2×#16810962C2semidirect
9. C2×#16810961C2semidirect
10. C2×#16810955C2semidirect
11. C2×#16810662C2semidirect
12. C2×#16810658C2semidirect
13. C2×#16810630C2semidirect
14. C2×#103×D53C2semidirect
16. C2×C53×#483C2semidirect
42. #16810967C22semidirect
43. #16810965C22semidirect
44. #16810962C22semidirect
45. #16810961C22semidirect
46. #16810958C22semidirect
47. #16810957C22semidirect
48. #16810955C22semidirect
49. #16810662C22semidirect
50. #16810658C22semidirect
57. #16810630C22semidirect
64. #103×D53C22semidirect
71. C53×#483C22semidirect
390. C2×#483D53semidirect
397. C2×C53#3097semidirect
437. #483C2×D53semidirect
463. C53C2×#3097semidirect
769. C2#20284677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111962
C2×#168111042
#202846772
C2×#168109582
C2×#168109572
C2×#168109672
C2×#168109652
C2×#168109622
C2×#168109612
C2×#168109552
C2×#168106622
C2×#168106582
C2×#168106302
C2×#103×D532
C2×#168105882
C2×C53×#4832
C2×#309753