Finite Group Databasebeta

← #27555573

Subgroups — #27555573

Order 13568.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811154C211yesmaximal, characteristic, complemented
2C2×#41×Dic53C211yesmaximal, characteristic, complemented
3#20280320C214yesmaximal, complemented
4#20280308C214yesmaximal, complemented
5#20279918C211yesmaximal, characteristic, complemented
6#20279908C211yesmaximal, characteristic, complemented
7#20279694C211yesmaximal, characteristic, complemented
8#20279683C211yesmaximal, characteristic, complemented
9#20279178C211yesmaximal, characteristic, complemented
10#20279168C211yesmaximal, characteristic, complemented
11#20278339C211yesmaximal, characteristic, complemented
12#20277950C214yesmaximal, complemented
13#20277284C211yesmaximal, characteristic, complemented
14#127×Dic53C211yesmaximal, characteristic, complemented
15#20277262C211yesmaximal, characteristic, complemented
16#124×Dic53C211yesmaximal, characteristic, complemented
17#20277155C214yesmaximal, complemented
18C4×#13133173C211yesmaximal, characteristic, complemented
19C53×#2431C211yesmaximal, characteristic
20C2×#13133215C2211yescharacteristic
21#16811154—28no—
22C2×#13133210C2212yes—
23C2×#13133208C2211yescharacteristic
24C2×#13133204C2211yescharacteristic
25C2×#13133204C2211yescharacteristic
26C2×#13133198C2212yes—
27C2×#13133196C2211yescharacteristic
28#41×Dic53—28no—
29C2×Q8×Dic53C2211yescharacteristic
30C2×Q8×Dic53C2211yescharacteristic
31C2×#13133182C2211yescharacteristic
32C2×D4×Dic53C2212yes—
33C2×D4×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×D4×Dic53C2214yes—
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2212yes—
38C2×D4×Dic53C2212yes—
39C2×#13133176C2211yescharacteristic
40C2×#13133176C2212yes—
41C2×#13133173C2212yes—
42C2×#13133173C2212yes—
43C22×C4×Dic53C2212yes—
44C22×C4×Dic53C2211yescharacteristic
45#16810555C2214yes—
46#16810548C2214yes—
47#16810546C2214yes—
48#16810546C2214yes—
49#16810537C2214yes—
50#16810537C2214yes—
51#16810537C2214yes—
52#16810530C2211yescharacteristic
53#16810529C2211yescharacteristic
54#16810529C2211yescharacteristic
55#16810526C2214yes—
56#16810526C2211yescharacteristic
57#16810526C2211yescharacteristic
58#16810526C2211yescharacteristic
59#16810520C2214yes—
60#16810517C2214yes—
61#16810516C2214yes—
62#16810511C2214yes—
63#16810511C2214yes—
64#16810508C2214yes—
65#16810506C2214yes—
66#16810503C2214yes—
67#16810496C2214yes—
68#16810495C2214yes—
69#16810493C2211yescharacteristic
70#16810492C2211yescharacteristic
71#16810489C2211yescharacteristic
72#16810488C2211yescharacteristic
73C4×#11719919C2211yescharacteristic
74C4×#11719919C2211yescharacteristic
75#16810474C2214yes—
76#16810474C2212yes—
77C22⋊C4×Dic53C2212yes—
78C22⋊C4×Dic53C2214yes—
79C22⋊C4×Dic53C2214yes—
80C4×C22⋊Dic53C2211yescharacteristic
81#16810468C2212yes—
82C42×Dic53C2211yescharacteristic
83C42×Dic53C2211yescharacteristic
84C22×#41×C53C2211yescharacteristic
85C2×#127×C53C2211yescharacteristic
86C2×#124×C53C2211yescharacteristic
87C2×#121×C53C2211yescharacteristic
88C53×#392C2214yes—
89C53×#391C2211yescharacteristic
90C53×#390C2211yescharacteristic
91C53×#386C2214yes—
92C4×C22⋊C4×C53C2211yescharacteristic
93C22×Dic106C2311yescharacteristic
94C23×Dic53C2312yes—
95C23×Dic53C2312yes—
96C23×Dic53C2311yescharacteristic
97C23×Dic53C2312yes—
98C23×Dic53C2311yescharacteristic
99#13133215—24no—
100#13133210—28no—
101#13133208—24no—
102#13133204—24no—
103#13133204—24no—
104#13133198—28no—
105#13133196—24no—
106Q8×Dic53—24no—
107Q8×Dic53—24no—
108#13133182—24no—
109D4×Dic53—24no—
110D4×Dic53—24no—
111D4×Dic53—24no—
112D4×Dic53—216no—
113D4×Dic53—28no—
114D4×Dic53—28no—
115D4×Dic53—28no—
116#13133176—28no—
117#13133176—24no—
118#13133173—28no—
119#13133173—28no—
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2312yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2312yes—
126C2×C4⋊Dic53C2312yes—
127C2×#11719919C2312yes—
128C2×#11719919C2314yes—
129C2×#11719919C2312yes—
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2314yes—
134C2×C22⋊Dic53C2314yes—
135C2×C22⋊Dic53C2314yes—
136C2×C22⋊Dic53C2312yes—
137C2×C22⋊Dic53C2312yes—
138C2×C22⋊Dic53C2314yes—
139C2×C22⋊Dic53C2312yes—
140C2×C22⋊Dic53C2312yes—
141C2×C22⋊Dic53C2312yes—
142C2×C22⋊Dic53C2312yes—
143C2×C22⋊Dic53C2312yes—
144C2×C22⋊Dic53C2312yes—
145C2×C22⋊Dic53C2314yes—
146C2×C4×Dic53—28no—
147C2×C4×Dic53D418yescomplemented
148C2×C4×Dic53C2312yes—
149C2×C4×Dic53C2312yes—
150C2×C4×Dic53C2311yescharacteristic
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2311yescharacteristic
158C2×C4×Dic53C2311yescharacteristic
159C2×C4×Dic53C2311yescharacteristic
160C2×C4×Dic53C2311yescharacteristic
161C2×C4×Dic53C2312yes—
162#13133124C2312yes—
163#13133124C2314yes—
164#13133124C2312yes—
165#13133124C2314yes—
166#13133124C2314yes—
167#13133124C2314yes—
168#13133124C2314yes—
169#13133124C2312yes—
170C2×#41×C53—24no—
171C2×#41×C53—24no—
172C2×#41×C53—24no—
173C22×Q8×C53C2311yescharacteristic
174C22×D4×C53C2311yescharacteristic
175C22×D4×C53C2312yes—
176C22×D4×C53C2314yes—
177C22×D4×C53C2311yescharacteristic
178C22×D4×C53C2312yes—
179C23×C4×C53C2312yes—
180C23×C4×C53C2311yescharacteristic
181#127×C53—24no—
182#124×C53—24no—
183#121×C53—24no—
184C2×C4⋊C4×C53C2311yescharacteristic
185C2×C22⋊C4×C53C2312yes—
186C2×C22⋊C4×C53C2314yes—
187C2×C22⋊C4×C53C2312yes—
188C2×C22⋊C4×C53C2314yes—
189C2×C42×C53C2311yescharacteristic
190C2×C42×C53C2311yescharacteristic
191#95×C53C2314yes—
192#95×C53C2312yes—
193C24×C53C2412yes—
194C24×C53C2411yescharacteristic
195C24×C53C2412yes—
196#41×C53—232no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53#4114yes—
200C2×D4×C53—24no—
201C2×D4×C53—24no—
202C2×D4×C53—24no—
203C2×D4×C53—28no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—24no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—28no—
211C2×D4×C53—44no—
212C2×D4×C53—44no—
213C2×D4×C53#4114yes—
214C22×C4×C53—24no—
215C22×C4×C53—24no—
216C22×C4×C53—24no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53C2×D414yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2411yescharacteristic
223C22×C4×C53C2412yes—
224C22×C4×C53C2412yes—
225C22×C4×C53C2411yescharacteristic
226C22×Dic53—24no—
227C22×Dic53—24no—
228C22×Dic53—24no—
229C22×Dic53—24no—
230C22×Dic53—28no—
231C22×Dic53—28no—
232C22×Dic53—42no—
233C22×Dic53—44no—
234C22×Dic53C2×D414yes—
235C22×Dic53C2×D414yes—
236C22×Dic53C2412yes—
237C22×Dic53C2412yes—
238C22×Dic53C2412yes—
239C22×Dic53C2412yes—
240C22×Dic53C2412yes—
241C22×Dic53C2411yescharacteristic
242C22×Dic53C2411yescharacteristic
243C22×Dic53C2411yescharacteristic
244C22×Dic53C2412yes—
245C22×Dic53C2411yescharacteristic
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—22no—
249C4⋊C4×C53—22no—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—28no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53—44no—
254C42×C53—22no—
255C42×C53—22no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—28no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53—28no—
266C22⋊Dic53—28no—
267C22⋊Dic53—44no—
268C4⋊Dic53—22no—
269C4⋊Dic53—22no—
270C4⋊Dic53—22no—
271C4⋊Dic53—28no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—28no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919—44no—
282C4×Dic53—24no—
283C4×Dic53—22no—
284C4×Dic53—22no—
285C4×Dic53—24no—
286C4×Dic53—24no—
287C4×Dic53—24no—
288C4×Dic53—24no—
289C4×Dic53—42no—
290C4×Dic53—42no—
291C4×Dic53C2×D414yes—
292C4×Dic53C2×D414yes—
293C4×Dic53C2×D414yes—
294C4×Dic53C2×D414yes—
295C4×Dic53#4118yescomplemented
296C23×C53—22no—
297C23×C53—24no—
298C23×C53—22no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—24no—
304C23×C53—22no—
305C23×C53—24no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—24no—
309C23×C53C22×D412yes—
310C23×C53C2×#4114yes—
311C23×C53C2511yescharacteristic
312Q8×C53—28no—
313D4×C53—216no—
314D4×C53—28no—
315D4×C53—416no—
316D4×C53—48no—
317D4×C53—44no—
318C2×C4×C53—216no—
319C2×C4×C53—22no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—28no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—24no—
330C2×C4×C53—22no—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C2×#4114yes—
334C2×C4×C53C2×#4114yes—
335C2×C4×C53C2×#4112yes—
336C2×C4×C53C2×#4112yes—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—28no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—24no—
350C2×Dic53—24no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—24no—
354C2×Dic53—22no—
355C2×Dic53—44no—
356C2×Dic53—48no—
357C2×Dic53—48no—
358C2×Dic53—48no—
359C2×Dic53C22×D412yes—
360C2×Dic53C22×D412yes—
361C2×Dic53C22×D412yes—
362C2×Dic53C22×D412yes—
363C2×Dic53C2×#4114yes—
364C2×Dic53C2×#4114yes—
365Dic106—44no—
366#34910—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—24no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—28no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—44no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—44no—
381C22×C53—44no—
382C22×C53C23×D411yescharacteristic
383C22×C53C22×#4112yes—
384C22×C53C22×#4111yescharacteristic
385C22×C53C22×#4111yescharacteristic
386C22×C53#58512yes—
387C4×C53—22no—
388C4×C53—24no—
389C4×C53—24no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#52514yes—
393Dic53—22no—
394Dic53—22no—
395Dic53—22no—
396Dic53—24no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401Dic53—42no—
402Dic53#53214yes—
403C2×#529—531no—
404C2×C4×#41—531no—
405#2602—534no—
406#2601—534no—
407#2566—531no—
408#2565—531no—
409#2545—531no—
410#2544—531no—
411#2500—531no—
412#2499—531no—
413#2432—531no—
414#2431D5311yescharacteristic
415#2392—534no—
416C4×C4⋊Q8—531no—
417C4×#127—531no—
418C4×#124—531no—
419C4×#124—531no—
420#2290—534no—
421C4×#117—531no—
422C2×C53—42no—
423C2×C53—44no—
424C2×C53—82no—
425C2×C53C2×#52511yescharacteristic
426C2×C53C2×#53211yescharacteristic
427C2×C53#344911yescharacteristic
428C2×C53#347512yes—
429C2×C53#348012yes—
430C22×#41C2×D5311yescharacteristic
431C2×C4⋊Q8—531no—
432C2×#127C2×D5311yescharacteristic
433#529—1068no—
434C2×#126—532no—
435C2×#125—531no—
436C2×#124—531no—
437C2×#124—531no—
438C2×#124C2×D5311yescharacteristic
439C2×#123—532no—
440C2×C22⋊Q8—531no—
441C2×#121C2×D5311yescharacteristic
442C4×#41—1068no—
443C2×C4×Q8—531no—
444C2×C4×Q8—531no—
445C2×C4×Q8—531no—
446C2×C4×D4—534no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—531no—
450C2×C4×D4—532no—
451C2×C4×D4—532no—
452C2×C4×D4—532no—
453C2×#117—532no—
454C2×#117—531no—
455C2×#117—532no—
456C2×#117—532no—
457C22×C42—531no—
458C22×C42—532no—
459#398—534no—
460#397—534no—
461#396—534no—
462#396—534no—
463#394—534no—
464#394—534no—
465#394—534no—
466#392C2×D5314yes—
467#391—531no—
468#391—531no—
469#391—531no—
470#391C2×D5311yescharacteristic
471#390—531no—
472#390—534no—
473#390—531no—
474#390—531no—
475#390C2×D5311yescharacteristic
476#389—534no—
477#388—534no—
478#388—534no—
479#388—534no—
480#388—534no—
481#387—534no—
482#387—534no—
483#386—534no—
484#386C2×D5314yes—
485#385—534no—
486#385—534no—
487#384—531no—
488#384—531no—
489#382—531no—
490#382—531no—
491C4×C4⋊C4—531no—
492C4×C4⋊C4—531no—
493C4×C4⋊C4—534no—
494C4×C4⋊C4—532no—
495C4×C22⋊C4—531no—
496C4×C22⋊C4—532no—
497C4×C22⋊C4—534no—
498C4×C22⋊C4—534no—
499C4×C22⋊C4C2×D5311yescharacteristic
500#376—532no—
501C43—531no—
502C43—531no—
503C53#3491011yescharacteristic, complemented, Sylow
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C22×Q8—531no—
508C22×Q8C22×D5311yescharacteristic
509C22×D4C22×D5312yes—
510C22×D4C22×D5311yescharacteristic
511C22×D4C22×D5314yes—
512C22×D4C22×D5311yescharacteristic
513C22×D4C22×D5312yes—
514C23×C4—531no—
515C23×C4—531no—
516C23×C4—532no—
517C23×C4—532no—
518C23×C4—532no—
519C23×C4C22×D5312yes—
520C23×C4C22×D5311yescharacteristic
521C4⋊Q8—1064no—
522#127—24no—
523#126—1068no—
524#125—1064no—
525#124—24no—
526#124—1064no—
527#124—1064no—
528#123—1068no—
529C22⋊Q8—1064no—
530#121—24no—
531C4×Q8—1064no—
532C4×Q8—1064no—
533C4×Q8—1064no—
534C4×D4—1064no—
535C4×D4—1064no—
536C4×D4—1064no—
537C4×D4—10616no—
538C4×D4—1068no—
539C4×D4—1068no—
540C4×D4—1068no—
541#117—1068no—
542#117—1068no—
543#117—1068no—
544#117—1064no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—531no—
547C2×C4⋊C4—532no—
548C2×C4⋊C4—532no—
549C2×C4⋊C4—532no—
550C2×C4⋊C4—532no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4—532no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4—534no—
556C2×C4⋊C4—532no—
557C2×C4⋊C4—534no—
558C2×C4⋊C4—534no—
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C22⋊C4—532no—
561C2×C22⋊C4—532no—
562C2×C22⋊C4—532no—
563C2×C22⋊C4—532no—
564C2×C22⋊C4—532no—
565C2×C22⋊C4—532no—
566C2×C22⋊C4—532no—
567C2×C22⋊C4—532no—
568C2×C22⋊C4—534no—
569C2×C22⋊C4—534no—
570C2×C22⋊C4—534no—
571C2×C22⋊C4—534no—
572C2×C22⋊C4C22×D5312yes—
573C2×C22⋊C4C22×D5312yes—
574C2×C22⋊C4C22×D5314yes—
575C2×C22⋊C4C22×D5314yes—
576C2×C42—538no—
577C2×C42—531no—
578C2×C42—531no—
579C2×C42—532no—
580C2×C42—531no—
581C2×C42—531no—
582C2×C42—532no—
583C2×C42—532no—
584C2×C42—532no—
585C2×C42—532no—
586C2×C42—532no—
587C2×C42—531no—
588C2×C42—531no—
589C2×C42—532no—
590C2×C42—532no—
591C2×C42—1068no—
592C2×C42C22×D5311yescharacteristic
593C2×C42C22×D5311yescharacteristic
594#95—532no—
595#95—532no—
596#95—532no—
597#95—534no—
598#95—534no—
599#95—534no—
600#95—534no—
601#95—534no—
602#95C22×D5312yes—
603#95C22×D5314yes—
604C24C23×D5312yes—
605C24C23×D5311yescharacteristic
606C24C23×D5312yes—
607#41—232no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8#1171994714yes—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—28no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4#1171994714yes—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—531no—
634C22×C4—534no—
635C22×C4—531no—
636C22×C4—532no—
637C22×C4—531no—
638C22×C4—531no—
639C22×C4—534no—
640C22×C4—532no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—532no—
645C22×C4—1064no—
646C22×C4—1064no—
647C22×C4—1064no—
648C22×C4—1064no—
649C22×C4—1068no—
650C22×C4—1068no—
651C22×C4—2122no—
652C22×C4—2124no—
653C22×C4D4×D5314yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5312yes—
656C22×C4C23×D5311yescharacteristic
657C22×C4C23×D5312yes—
658C22×C4C23×D5312yes—
659C22×C4C23×D5311yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4—1064no—
667C4⋊C4—1062no—
668C4⋊C4—1062no—
669C4⋊C4—1064no—
670C4⋊C4—1062no—
671C4⋊C4—1064no—
672C4⋊C4—1068no—
673C4⋊C4—1068no—
674C4⋊C4—2124no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—28no—
678C22⋊C4—44no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C22⋊C4—1064no—
685C22⋊C4—1068no—
686C22⋊C4—1068no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1068no—
690C22⋊C4—2124no—
691C42—22no—
692C42—22no—
693C42—534no—
694C42—534no—
695C42—534no—
696C42—534no—
697C42—538no—
698C42—1064no—
699C42—1064no—
700C42—1064no—
701C42—1064no—
702C42—1064no—
703C42—1062no—
704C42—1062no—
705C42—2122no—
706C42—2122no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23C2×D4×D5312yes—
721C23C2×#1171994714yes—
722C23C24×D5311yescharacteristic
723Q8—28no—
724Q8—2124no—
725D4—216no—
726D4—28no—
727D4—416no—
728D4—48no—
729D4—44no—
730C2×C4—216no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—532no—
744C2×C4—534no—
745C2×C4—532no—
746C2×C4—532no—
747C2×C4—532no—
748C2×C4—534no—
749C2×C4—1068no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1064no—
761C2×C4—1064no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1064no—
767C2×C4—2128no—
768C2×C4—2128no—
769C2×C4—2124no—
770C2×C4—2128no—
771C2×C4C2×D4×D5312yes—
772C2×C4C2×D4×D5312yes—
773C2×C4#41×D5314yes—
774C2×C4C2×#1171994714yes—
775C2×C4C2×#1171994712yes—
776C2×C4C2×#1171994712yes—
777C22—28no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—22no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—42no—
787C22—44no—
788C22—42no—
789C22—44no—
790C22—42no—
791C22—42no—
792C22C22×D4×D5311yescharacteristic
793C22C2×#41×D5312yes—
794C22C22×#1171994711yescharacteristic
795C22C22×#1171994711yescharacteristic
796C22#1681145812yes—
797C4—24no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—534no—
803C4—1062no—
804C4—1062no—
805C4—1064no—
806C4—1062no—
807C4—2122no—
808C4—2122no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681112914yes—
813C2—44no—
814C2—42no—
815C2—82no—
816C2C2×#1681112911yescharacteristic
817C2#532×D5311yescharacteristic
818C2#2028804611yescharacteristic
819C2#2028826612yes—
820C2#2028831412yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
Fitting, prime radicalC53×#2431C2
hypercenter#2431D53
hypocenterC53#34910
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C2×#16811154C2semidirect
2. C2×#41×Dic53C2semidirect
3. #20280320C2semidirect
4. #20280308C2semidirect
5. #20279918C2semidirect
6. #20279908C2semidirect
7. #20279694C2semidirect
8. #20279683C2semidirect
9. #20279178C2semidirect
10. #20279168C2semidirect
11. #20278339C2semidirect
12. #20277950C2semidirect
13. #20277284C2semidirect
14. #127×Dic53C2semidirect
15. #20277262C2semidirect
16. #124×Dic53C2semidirect
17. #20277155C2semidirect
18. C4×#13133173C2semidirect
147. C2×C4×Dic53D4semidirect
295. C4×Dic53#41semidirect
503. C53#34910semidirect

Maximal subgroups

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

subgroupindex
C2×#168111542
C2×#41×Dic532
#202803202
#202803082
#202799182
#202799082
#202796942
#202796832
#202791782
#202791682
#202783392
#202779502
#202772842
#127×Dic532
#202772622
#124×Dic532
#202771552
C4×#131331732
C53×#24312
#3491053