Finite Group Databasebeta

← #27290805

Subgroups — #27290805

Order 13568.

1558 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133206C211yesmaximal, characteristic
2C22×#13133141C211yesmaximal, characteristic, complemented
3C22×#13133139C211yesmaximal, characteristic
4C22×#13133137C211yesmaximal, characteristic
5C2×#16810377C211yesmaximal, characteristic, complemented
6#20272944C211yesmaximal, characteristic, complemented
7C22×#103×C53C211yesmaximal, characteristic, complemented
8C23×D212C2211yescharacteristic
9C23×#88322C2211yescharacteristic
10C2×#13133206—22no—
11C2×#13133206—22no—
12C2×#13133206—22no—
13C2×#13133206—22no—
14C2×#13133206—22no—
15C2×#13133206C414yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719921—22no—
18C22×C4×Dic53C2211yescharacteristic
19C2×#13133141—22no—
20C2×#13133141—22no—
21C2×#13133141—22no—
22C2×#13133139—22no—
23C2×#13133139—22no—
24C2×#13133139—22no—
25C2×#13133137—22no—
26C2×#13133137—22no—
27C2×#13133137—22no—
28C2×#13133124—22no—
29#16810377—22no—
30C23×Q8×C53C2211yescharacteristic
31C23×C8×C53C2211yescharacteristic
32C22×C4⋊C4×C53C2211yescharacteristic
33C2×#103×C53—22no—
34C2×#103×C53—22no—
35C2×#103×C53—22no—
36C24×D53—21no—
37C22×D212—21no—
38C22×D212—21no—
39C22×D212—21no—
40C22×D212—21no—
41C22×D212—21no—
42C22×D212—21no—
43C22×D212—21no—
44C22×D212—21no—
45C22×D212—21no—
46C22×D212—21no—
47C22×D212—21no—
48C22×D212C2×C412yes—
49C22×D212D412yes—
50C22×D212D412yes—
51C23×Dic53—21no—
52C23×Dic53D412yes—
53C22×#88322—21no—
54C22×#88322—21no—
55C22×#88322—21no—
56C22×#88322—21no—
57C22×#88322—21no—
58C22×#88322—21no—
59C22×#88322D412yes—
60#13133206—28no—
61#13133206—28no—
62#13133206—28no—
63#13133206—28no—
64C2×C4⋊Dic53—21no—
65C2×C4⋊Dic53—21no—
66C2×C4⋊Dic53—21no—
67C2×C4⋊Dic53—21no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53D412yes—
70C2×#11719921—28no—
71C2×#11719921—28no—
72C2×#11719921—28no—
73C2×C4×Dic53—21no—
74C2×C4×Dic53—21no—
75C2×C4×Dic53—21no—
76C2×C4×Dic53—21no—
77C2×C4×Dic53C2×C412yes—
78C2×C4×Dic53D412yes—
79#13133141—28no—
80#13133139—28no—
81#13133137—28no—
82#13133124—44no—
83C22×Q8×C53—21no—
84C22×Q8×C53—21no—
85C22×Q8×C53—21no—
86C22×Q8×C53—21no—
87C22×Q8×C53—21no—
88C22×Q8×C53—21no—
89C22×Q8×C53—21no—
90C22×Q8×C53—21no—
91C22×Q8×C53—21no—
92C22×Q8×C53—21no—
93C22×Q8×C53—21no—
94C22×Q8×C53C2×C412yes—
95C22×Q8×C53D412yes—
96C22×Q8×C53D412yes—
97C23×C4×C53—21no—
98C23×C4×C53—21no—
99C23×C4×C53C2311yescharacteristic
100C22×C8×C53—21no—
101C22×C8×C53—21no—
102C22×C8×C53—21no—
103C22×C8×C53—21no—
104C22×C8×C53—21no—
105C22×C8×C53—21no—
106C22×C8×C53D412yes—
107C2×C4⋊C4×C53—21no—
108C2×C4⋊C4×C53—21no—
109C2×C4⋊C4×C53—21no—
110C2×C4⋊C4×C53—21no—
111C2×C4⋊C4×C53—21no—
112C2×C4⋊C4×C53D412yes—
113#103×C53—28no—
114C24×C53C2×D411yescharacteristic
115C23×D53—22no—
116C23×D53—22no—
117C23×D53—22no—
118C23×D53—41no—
119C23×D53—41no—
120C23×D53—41no—
121C23×D53—41no—
122C23×D53—42no—
123C23×D53—42no—
124C23×D53—42no—
125C23×D53—42no—
126C2×Q8×C53—22no—
127C2×Q8×C53—22no—
128C2×Q8×C53—22no—
129C2×Q8×C53—22no—
130C2×Q8×C53—22no—
131C2×Q8×C53—22no—
132C2×Q8×C53—22no—
133C2×Q8×C53—22no—
134C2×Q8×C53—22no—
135C2×Q8×C53—22no—
136C2×Q8×C53—22no—
137C2×Q8×C53—22no—
138C2×Q8×C53—22no—
139C2×Q8×C53—22no—
140C2×Q8×C53—22no—
141C2×Q8×C53—41no—
142C2×Q8×C53—41no—
143C2×Q8×C53—41no—
144C2×Q8×C53—41no—
145C2×Q8×C53—41no—
146C2×Q8×C53—41no—
147C2×Q8×C53—41no—
148C2×Q8×C53—41no—
149C2×Q8×C53—41no—
150C2×Q8×C53—41no—
151C2×Q8×C53—41no—
152C2×Q8×C53—41no—
153C2×Q8×C53C22⋊C414yes—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—41no—
159C22×C4×C53—41no—
160C22×C4×C53—41no—
161C22×C4×C53—41no—
162C22×C4×C53—41no—
163C22×C4×C53—41no—
164C22×C4×C53—42no—
165C22×C4×C53—42no—
166C22×C4×C53C22×C411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53#4111yescharacteristic
177C22×C4×C53#4111yescharacteristic
178C22×C4×C53#4111yescharacteristic
179C22×C4×C53#4111yescharacteristic
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—41no—
188C22×Dic53—41no—
189C22×Dic53—42no—
190C22×Dic53—42no—
191C22×Dic53C22⋊C414yes—
192C2×D212—22no—
193C2×D212—22no—
194C2×D212—22no—
195C2×D212—22no—
196C2×D212—22no—
197C2×D212—22no—
198C2×D212—22no—
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—41no—
208C2×D212—41no—
209C2×D212—41no—
210C2×D212—41no—
211C2×D212—41no—
212C2×D212—41no—
213C2×D212—41no—
214C2×D212—41no—
215C2×D212—41no—
216C2×D212—41no—
217C2×D212—41no—
218C2×D212—41no—
219C2×D212C22⋊C414yes—
220C2×C8×C53—22no—
221C2×C8×C53—22no—
222C2×C8×C53—22no—
223C2×C8×C53—41no—
224C2×C8×C53—41no—
225C2×C8×C53—41no—
226C2×C8×C53—41no—
227C4⋊C4×C53—22no—
228C4⋊C4×C53—22no—
229C4⋊C4×C53—41no—
230C4⋊C4×C53—41no—
231#11719921—232no—
232C4⋊Dic53—22no—
233C4⋊Dic53—22no—
234C4⋊Dic53—41no—
235C4⋊Dic53—41no—
236C4×Dic53—22no—
237C4×Dic53—22no—
238C4×Dic53—22no—
239C4×Dic53—22no—
240C2×#88322—22no—
241C2×#88322—22no—
242C2×#88322—22no—
243C2×#88322—41no—
244C2×#88322—41no—
245C2×#88322—41no—
246C2×#88322—41no—
247C23×C53C2×C22⋊C411yescharacteristic
248C23×C53#12011yescharacteristic
249C23×C53#12011yescharacteristic
250C23×C53#12111yescharacteristic
251C23×C53#12111yescharacteristic
252C23×C53#12411yescharacteristic
253C23×C53#12711yescharacteristic
254C23×C53#13512yes—
255C23×C53#13512yes—
256C23×C53AGL(1,ℤ/8)12yes—
257C23×C53#13712yes—
258C22×D53—24no—
259C22×D53—42no—
260C22×D53—42no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—44no—
266C22×D53—44no—
267C22×D53—44no—
268C22×D53—44no—
269C22×D53—44no—
270C22×D53—44no—
271C22×D53—82no—
272C22×D53—82no—
273C22×D53—82no—
274C22×D53—82no—
275C22×D53—82no—
276C22×D53—82no—
277C22×D53—81no—
278C22×D53—81no—
279C22×D53—81no—
280C22×D53—81no—
281Q8×C53—24no—
282Q8×C53—24no—
283Q8×C53—42no—
284Q8×C53—42no—
285Q8×C53—42no—
286Q8×C53—42no—
287Q8×C53—42no—
288Q8×C53—42no—
289C2×C4×C53—24no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—44no—
298C2×C4×C53—82no—
299C2×C4×C53—81no—
300C2×C4×C53—81no—
301C2×C4×C53C2×C22⋊C411yescharacteristic
302C2×C4×C53C2×C22⋊C411yescharacteristic
303C2×C4×C53C4×D411yescharacteristic
304C2×C4×C53C4×D411yescharacteristic
305C2×C4×C53C4×D411yescharacteristic
306C2×C4×C53C4×D411yescharacteristic
307C2×C4×C53#12011yescharacteristic
308C2×C4×C53#12011yescharacteristic
309C2×C4×C53#12011yescharacteristic
310C2×C4×C53#12011yescharacteristic
311C2×C4×C53#12011yescharacteristic
312C2×C4×C53#12011yescharacteristic
313C2×C4×C53#12111yescharacteristic
314C2×C4×C53#12111yescharacteristic
315C2×C4×C53#12111yescharacteristic
316C2×C4×C53#12111yescharacteristic
317C2×C4×C53#12111yescharacteristic
318C2×C4×C53#12111yescharacteristic
319C2×C4×C53#12111yescharacteristic
320C2×C4×C53#12111yescharacteristic
321C2×C4×C53#12111yescharacteristic
322C2×C4×C53#12111yescharacteristic
323C2×C4×C53#12311yescharacteristic
324C2×C4×C53#12311yescharacteristic
325C2×C4×C53#12311yescharacteristic
326C2×C4×C53#12311yescharacteristic
327C2×C4×C53#12411yescharacteristic
328C2×C4×C53#12711yescharacteristic
329C2×Dic53—24no—
330C2×Dic53—24no—
331C2×Dic53—24no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—44no—
338C2×Dic53—82no—
339C2×Dic53—81no—
340C2×Dic53—81no—
341D212—24no—
342D212—24no—
343D212—42no—
344D212—42no—
345D212—42no—
346D212—42no—
347D212—42no—
348D212—42no—
349C8×C53—42no—
350#88322—42no—
351#11009—531nomaximal, Sylow
352C22×C53#37911yescharacteristic
353C22×C53#39011yescharacteristic
354C22×C53#39011yescharacteristic
355C22×C53#39211yescharacteristic
356C22×C53#39211yescharacteristic
357C22×C53#39411yescharacteristic
358C22×C53#39411yescharacteristic
359C22×C53#41612yes—
360C22×C53#41712yes—
361C22×C53#44912yes—
362C22×C53#44912yes—
363C22×C53#45212yes—
364C22×C53#45212yes—
365C22×C53#46312yes—
366C22×C53#46312yes—
367C22×C53#46412yes—
368C22×C53#46412yes—
369C22×C53#48812yes—
370C22×C53#48912yes—
371C22×C53#49511yescharacteristic
372C22×C53#49511yescharacteristic
373C22×C53#49611yescharacteristic
374C22×C53#49711yescharacteristic
375C2×D53—44no—
376C2×D53—48no—
377C2×D53—82no—
378C2×D53—82no—
379C2×D53—84no—
380C2×D53—82no—
381C2×D53—82no—
382C2×D53—82no—
383C2×D53—82no—
384C2×D53—84no—
385C2×D53—84no—
386C4×C53—44no—
387C4×C53—82no—
388C4×C53#38611yescharacteristic
389C4×C53#38611yescharacteristic
390C4×C53#38611yescharacteristic
391C4×C53#38611yescharacteristic
392C4×C53#39211yescharacteristic
393C4×C53#39211yescharacteristic
394C4×C53#39411yescharacteristic
395C4×C53#39411yescharacteristic
396Dic53—44no—
397Dic53—82no—
398C22×#124—531no—
399C22×#103—531no—
400C22×#103D5311yescharacteristic, complemented
401C22×#102—531no—
402C22×#102—531no—
403C2×#336—531no—
404C4⋊#95—531no—
405C2×C53#143811yescharacteristic
406C2×C53#178812yes—
407C2×C53#195811yescharacteristic
408C2×C53#195911yescharacteristic
409C2×C53#198312yes—
410C2×C53#201211yescharacteristic
411C2×C53#201211yescharacteristic
412C2×C53#201511yescharacteristic
413C2×C53#201511yescharacteristic
414C2×C53#204212yes—
415C2×C53#204212yes—
416D53—84no—
417C23×Q8C2×D5311yescharacteristic
418C23×D4—531no—
419C23×C8—531no—
420C23×C8C2×D5311yescharacteristic
421C2×#124—534no—
422C2×#124—1062no—
423C2×#124—1062no—
424C2×#124—1062no—
425C2×#124—1062no—
426C2×#124—1062no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4C2×D5311yescharacteristic
429C22×C22⋊C4—1062no—
430C22×C42—531no—
431C2×#103—22no—
432C2×#103—22no—
433C2×#103—22no—
434C2×#103—1062no—
435C2×#103—1062no—
436C2×#103—1062no—
437C2×#102—1062no—
438C2×#102—1062no—
439C2×#102—1062no—
440C2×#102—1062no—
441C2×#102—1062no—
442C2×#102—1062no—
443C2×#95—1062no—
444#336—1062no—
445C53#1100911yescharacteristic, complemented, Sylow
446C25—1061no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8—21no—
458C22×Q8C4×D5312yes—
459C22×Q8D21212yes—
460C22×Q8C22⋊D5312yes—
461C22×D4—532no—
462C22×D4—532no—
463C22×D4—532no—
464C22×D4—1061no—
465C22×D4—1061no—
466C22×D4—1061no—
467C22×D4—1061no—
468C22×D4—1061no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4—1061no—
474C22×D4—1061no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—532no—
478C23×C4—1061no—
479C23×C4C22×D5311yescharacteristic
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—532no—
487C22×C8—1061no—
488C22×C8—1061no—
489C22×C8—1061no—
490C22×C8—1061no—
491C22×C8—1061no—
492C22×C8—1061no—
493C22×C8C22⋊D5312yes—
494#124—1068no—
495#124—1068no—
496#124—1068no—
497#124—1068no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—532no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4C22⋊D5312yes—
510C2×C22⋊C4—1068no—
511C2×C22⋊C4—1068no—
512C2×C22⋊C4—1068no—
513C2×C42—532no—
514C2×C42—532no—
515C2×C42—1061no—
516C2×C42—1061no—
517C2×C42—1061no—
518C2×C42—1061no—
519#103—28no—
520#103—1068no—
521#102—1068no—
522#102—1068no—
523#95—2124no—
524C24—1062no—
525C24—1062no—
526C24—1062no—
527C24—2121no—
528C24—2121no—
529C24—2121no—
530C24—2121no—
531C24—2122no—
532C24—2122no—
533C24—2122no—
534C24—2122no—
535C24D4×D5311yescharacteristic
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8#1171992114yes—
564C2×D4—534no—
565C2×D4—1062no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4—1062no—
579C2×D4—1062no—
580C2×D4—2121no—
581C2×D4—2121no—
582C2×D4—2121no—
583C2×D4—2121no—
584C2×D4—2121no—
585C2×D4—2121no—
586C2×D4—2121no—
587C2×D4—2121no—
588C2×D4—2121no—
589C2×D4—2121no—
590C2×D4—2121no—
591C2×D4—2121no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—534no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—2121no—
613C22×C4—2121no—
614C22×C4—2122no—
615C22×C4—2122no—
616C22×C4C2×C4×D5311yescharacteristic
617C22×C4C2×D21211yescharacteristic
618C22×C4#1171994511yescharacteristic
619C22×C4#1171994511yescharacteristic
620C22×C4D4×D5311yescharacteristic
621C22×C4D4×D5311yescharacteristic
622C22×C4D4×D5311yescharacteristic
623C22×C4D4×D5311yescharacteristic
624C22×C4D4×D5311yescharacteristic
625C22×C4#1171994711yescharacteristic
626C22×C4#1171994711yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C2×C22⋊D5311yescharacteristic
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—1062no—
638C2×C8—1062no—
639C2×C8—1062no—
640C2×C8—2121no—
641C2×C8—2121no—
642C2×C8—2121no—
643C2×C8—2121no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—1062no—
649C4⋊C4—1062no—
650C4⋊C4—2121no—
651C4⋊C4—2121no—
652C22⋊C4—10632no—
653C42—1062no—
654C42—1062no—
655C42—1062no—
656C42—1062no—
657C23—1064no—
658C23—4241no—
659C23—4241no—
660C23—4241no—
661C23—4242no—
662C23—4242no—
663C23—4242no—
664C23—4242no—
665C23—4242no—
666C23—4242no—
667C23—4241no—
668C23—2124no—
669C23—2124no—
670C23—2122no—
671C23—2122no—
672C23—2124no—
673C23—2122no—
674C23—2122no—
675C23—2124no—
676C23—2122no—
677C23—2122no—
678C23—2124no—
679C23—2124no—
680C23C22⋊C4×D5311yescharacteristic
681C23#1313318511yescharacteristic
682C23#1313318711yescharacteristic
683C23#1313318911yescharacteristic
684C23#1313319011yescharacteristic
685C23#1313320311yescharacteristic
686C23#1313321311yescharacteristic
687C23#1313323812yes—
688C23#1313324012yes—
689C23#1313324412yes—
690C23#1313324912yes—
691Q8—24no—
692Q8—24no—
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699D4—1064no—
700D4—1064no—
701D4—2122no—
702D4—2122no—
703D4—2122no—
704D4—2122no—
705D4—2122no—
706D4—2122no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4—81no—
719C2×C4—1064no—
720C2×C4—1064no—
721C2×C4—1064no—
722C2×C4—4241no—
723C2×C4—4241no—
724C2×C4—4242no—
725C2×C4—2122no—
726C2×C4—2124no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4C22⋊C4×D5311yescharacteristic
732C2×C4C2×#1171992111yescharacteristic
733C2×C4#1313317711yescharacteristic
734C2×C4#1313317711yescharacteristic
735C2×C4C4×C22⋊D5311yescharacteristic
736C2×C4C4×C22⋊D5311yescharacteristic
737C2×C4#1313318511yescharacteristic
738C2×C4#1313318511yescharacteristic
739C2×C4#1313318511yescharacteristic
740C2×C4#1313318611yescharacteristic
741C2×C4#1313318711yescharacteristic
742C2×C4#1313318711yescharacteristic
743C2×C4#1313318811yescharacteristic
744C2×C4#1313318811yescharacteristic
745C2×C4#1313318911yescharacteristic
746C2×C4#1313318911yescharacteristic
747C2×C4#1313318911yescharacteristic
748C2×C4#1313319011yescharacteristic
749C2×C4#1313319011yescharacteristic
750C2×C4#1313319011yescharacteristic
751C2×C4#1313319111yescharacteristic
752C2×C4#1313319111yescharacteristic
753C2×C4#1313319911yescharacteristic
754C2×C4#1313319911yescharacteristic
755C2×C4#1313320011yescharacteristic
756C2×C4#1313320111yescharacteristic
757C2×C4#1313320311yescharacteristic
758C2×C4#1313321311yescharacteristic
759C8—42no—
760C8—2122no—
761C22—4242no—
762C22—4242no—
763C22—4242no—
764C22—4242no—
765C22—4242no—
766C22—4242no—
767C22—4244no—
768C22—4244no—
769C22—4244no—
770C22—2124no—
771C22—2128no—
772C22#1681047811yescharacteristic
773C22#1681052311yescharacteristic
774C22#1681052311yescharacteristic
775C22#1681053111yescharacteristic
776C22#1681053211yescharacteristic
777C22#1681053811yescharacteristic
778C22#1681053911yescharacteristic
779C22#1681061812yes—
780C22#1681062312yes—
781C22#1681076712yes—
782C22#1681077112yes—
783C22#1681078412yes—
784C22#1681078812yes—
785C22#1681084012yes—
786C22#1681084112yes—
787C22#1681084712yes—
788C22#1681084812yes—
789C22#1681097912yes—
790C22#1681098412yes—
791C22#1681100411yescharacteristic
792C22#1681100811yescharacteristic
793C22#1681100911yescharacteristic
794C22#1681101611yescharacteristic
795C4—44no—
796C4—82no—
797C4—4242no—
798C4—2124no—
799C4#1681049911yescharacteristic
800C4#1681049911yescharacteristic
801C4#1681050011yescharacteristic
802C4#1681050211yescharacteristic
803C4#1681053111yescharacteristic
804C4#1681053211yescharacteristic
805C4#1681053811yescharacteristic
806C4#1681053911yescharacteristic
807C2—4244no—
808C2#2027295411yescharacteristic
809C2#2027465412yes—
810C2#2027552311yescharacteristic
811C2#2027552811yescharacteristic
812C2#2027564412yes—
813C2#2027578911yescharacteristic
814C2#2027579311yescharacteristic
815C2#2027580611yescharacteristic
816C2#2027581011yescharacteristic
817C2#2027595212yes—
818C2#2027595312yes—
subgroupG/H
centerC24D4×D53
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
FittingC22×#103×C53C2
socleC24×C53C2×D4
prime radicalC23×D212C22
cosocleC23×C4×C53C23
hypercenterC22×#103D53
hypocenterC53#11009
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#13133141C2semidirect
5. C2×#16810377C2semidirect
6. #20272944C2semidirect
7. C22×#103×C53C2semidirect
15. C2×#13133206C4semidirect
400. C22×#103D53semidirect
445. C53#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#131332062
C22×#131331412
C22×#131331392
C22×#131331372
C2×#168103772
#202729442
C22×#103×C532
#1100953