Finite Group Databasebeta

← #27290604

Subgroups — #27290604

Order 13568.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133197C211yesmaximal, characteristic
2C22×#13133142C211yesmaximal, characteristic, complemented
3C22×#13133140C211yesmaximal, characteristic, complemented
4C22×#13133129C211yesmaximal, characteristic
5C2×#16810480C211yesmaximal, characteristic
6C2×#16810385C211yesmaximal, characteristic, complemented
7C2×C53×#340C211yesmaximal, characteristic, complemented
8C23×Dic106C2211yescharacteristic
9C23×C4×D53C2211yescharacteristic
10C23×#88322C2211yescharacteristic
11C2×#13133197—22no—
12C2×#13133197—22no—
13C2×#13133197—22no—
14C2×#13133197—22no—
15C2×#13133197—22no—
16C2×#13133197C414yescomplemented
17C22×C4⋊Dic53—21no—
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719921—21no—
20C22×#11719921—21no—
21C2×#13133142—22no—
22C2×#13133142—22no—
23C2×#13133142—22no—
24C2×#13133140—22no—
25C2×#13133140—22no—
26C2×#13133140—22no—
27C2×#13133129—22no—
28C2×#13133129—22no—
29C2×#13133129—22no—
30#16810480—22no—
31#16810480—22no—
32C2×#13133124—21no—
33#16810385—22no—
34C23×C8×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C53×#340—22no—
38C24×D53D411yescharacteristic
39C22×Dic106—21no—
40C22×Dic106—21no—
41C22×Dic106—21no—
42C22×Dic106—21no—
43C22×Dic106—21no—
44C22×Dic106—21no—
45C22×Dic106—21no—
46C22×Dic106—21no—
47C22×Dic106—21no—
48C22×Dic106—21no—
49C22×Dic106—21no—
50C22×Dic106C2×C412yes—
51C22×Dic106D412yes—
52C22×Dic106D412yes—
53C23×Dic53—21no—
54C23×Dic53—21no—
55C23×Dic53D411yescharacteristic
56C22×C4×D53—21no—
57C22×C4×D53—21no—
58C22×C4×D53—21no—
59C22×C4×D53—21no—
60C22×C4×D53—21no—
61C22×C4×D53—21no—
62C22×C4×D53—21no—
63C22×C4×D53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C22×C4×D53—21no—
67C22×C4×D53—21no—
68C22×C4×D53C2×C412yes—
69C22×C4×D53D412yes—
70C22×#88322—21no—
71C22×#88322—21no—
72C22×#88322—21no—
73C22×#88322—21no—
74C22×#88322—21no—
75C22×#88322—21no—
76C22×#88322D412yes—
77#13133197—28no—
78#13133197—28no—
79#13133197—28no—
80#13133197—28no—
81C2×C4⋊Dic53—24no—
82C2×C4⋊Dic53—24no—
83C2×C4⋊Dic53—21no—
84C2×C4⋊Dic53—24no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53D412yes—
90C2×#11719921—24no—
91C2×#11719921—24no—
92C2×#11719921—24no—
93C2×#11719921—24no—
94C2×#11719921—42no—
95C2×#11719921—42no—
96#13133142—28no—
97#13133140—28no—
98#13133129—28no—
99#13133124—24no—
100C23×C4×C53—21no—
101C23×C4×C53—21no—
102C23×C4×C53C2311yescharacteristic
103C22×C8×C53—21no—
104C22×C8×C53—21no—
105C22×C8×C53—21no—
106C22×C8×C53—21no—
107C22×C8×C53—21no—
108C22×C8×C53—21no—
109C22×C8×C53D412yes—
110C2×C4⋊C4×C53—21no—
111C2×C4⋊C4×C53—21no—
112C2×C4⋊C4×C53—21no—
113C2×C4⋊C4×C53—21no—
114C2×C4⋊C4×C53—21no—
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53C2×C412yes—
119C2×C4⋊C4×C53D412yes—
120C2×C4⋊C4×C53D412yes—
121C2×C4⋊C4×C53D412yes—
122C24×C53C2×D411yescharacteristic
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—21no—
128C23×D53—21no—
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—21no—
134C23×D53—21no—
135C23×D53C22⋊C412yes—
136C23×D53SD1612yes—
137C23×D53Q1612yes—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—41no—
143C22×C4×C53—41no—
144C22×C4×C53—41no—
145C22×C4×C53—41no—
146C22×C4×C53—41no—
147C22×C4×C53—41no—
148C22×C4×C53—41no—
149C22×C4×C53—41no—
150C22×C4×C53—41no—
151C22×C4×C53—41no—
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C2×D411yescharacteristic
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53#4111yescharacteristic
163C22×C4×C53#4111yescharacteristic
164C22×C4×C53#4111yescharacteristic
165C22×C4×C53#4111yescharacteristic
166C22×Dic53—22no—
167C22×Dic53—21no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—22no—
176C22×Dic53—41no—
177C22×Dic53—41no—
178C22×Dic53—41no—
179C22×Dic53—41no—
180C22×Dic53—41no—
181C22×Dic53—41no—
182C22×Dic53—41no—
183C22×Dic53—41no—
184C22×Dic53—41no—
185C22×Dic53—41no—
186C22×Dic53C22⋊C412yes—
187C2×C4×D53—22no—
188C2×C4×D53—22no—
189C2×C4×D53—22no—
190C2×C4×D53—22no—
191C2×C4×D53—22no—
192C2×C4×D53—22no—
193C2×C4×D53—22no—
194C2×C4×D53—22no—
195C2×C4×D53—22no—
196C2×C4×D53—22no—
197C2×C4×D53—22no—
198C2×C4×D53—22no—
199C2×C4×D53—41no—
200C2×C4×D53—41no—
201C2×C4×D53—41no—
202C2×C4×D53—41no—
203C2×C4×D53—41no—
204C2×C4×D53—41no—
205C2×C4×D53—41no—
206C2×C4×D53—41no—
207C2×C4×D53—41no—
208C2×C4×D53—41no—
209C2×C4×D53—41no—
210C2×C4×D53—41no—
211C2×C4×D53—41no—
212C2×C4×D53—41no—
213C2×C4×D53—41no—
214C2×C4×D53—41no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—41no—
231C2×Dic106—41no—
232C2×Dic106—41no—
233C2×Dic106—41no—
234C2×Dic106—41no—
235C2×Dic106—41no—
236C2×Dic106—41no—
237C2×Dic106—41no—
238C2×Dic106—41no—
239C2×Dic106—41no—
240C2×Dic106—41no—
241C2×Dic106—41no—
242C2×Dic106C22⋊C414yescomplemented
243C2×C8×C53—22no—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53—41no—
247C2×C8×C53—41no—
248C2×C8×C53—41no—
249C2×C8×C53—41no—
250C4⋊C4×C53—22no—
251C4⋊C4×C53—22no—
252C4⋊C4×C53—22no—
253C4⋊C4×C53—22no—
254C4⋊C4×C53—22no—
255C4⋊C4×C53—41no—
256C4⋊C4×C53—41no—
257C4⋊C4×C53C22⋊C414yescomplemented
258#11719921—216no—
259#11719921—48no—
260C4⋊Dic53—216no—
261C4⋊Dic53—22no—
262C4⋊Dic53—22no—
263C4⋊Dic53—41no—
264C4⋊Dic53—41no—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322—41no—
269C2×#88322—41no—
270C2×#88322—41no—
271C2×#88322—41no—
272C23×C53C2×C22⋊C411yescharacteristic
273C23×C53#12011yescharacteristic
274C23×C53#12011yescharacteristic
275C23×C53#12011yescharacteristic
276C23×C53#12111yescharacteristic
277C23×C53#12111yescharacteristic
278C23×C53#12311yescharacteristic
279C23×C53C2×SD1611yescharacteristic
280C23×C53C2×Q1611yescharacteristic
281C23×C53#13511yescharacteristic
282C23×C53#13511yescharacteristic
283C23×C53AGL(1,ℤ/8)11yescharacteristic
284C23×C53#13711yescharacteristic
285C23×C53#13711yescharacteristic
286C23×C53#13711yescharacteristic
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—41no—
317C22×D53—41no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—41no—
321C22×D53#10314yescomplemented
322C2×C4×C53—24no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—81no—
333C2×C4×C53—81no—
334C2×C4×C53—81no—
335C2×C4×C53—81no—
336C2×C4×C53C2×C22⋊C411yescharacteristic
337C2×C4×C53C2×C22⋊C411yescharacteristic
338C2×C4×C53C4×D411yescharacteristic
339C2×C4×C53C4×D411yescharacteristic
340C2×C4×C53C4×D411yescharacteristic
341C2×C4×C53C4×D411yescharacteristic
342C2×C4×C53#12011yescharacteristic
343C2×C4×C53#12011yescharacteristic
344C2×C4×C53#12011yescharacteristic
345C2×C4×C53#12011yescharacteristic
346C2×C4×C53#12011yescharacteristic
347C2×C4×C53#12111yescharacteristic
348C2×C4×C53#12111yescharacteristic
349C2×C4×C53#12111yescharacteristic
350C2×C4×C53#12111yescharacteristic
351C2×C4×C53#12111yescharacteristic
352C2×C4×C53#12111yescharacteristic
353C2×C4×C53#12111yescharacteristic
354C2×C4×C53#12111yescharacteristic
355C2×C4×C53#12111yescharacteristic
356C2×C4×C53#12111yescharacteristic
357C2×C4×C53#12311yescharacteristic
358C2×C4×C53#12311yescharacteristic
359C2×C4×C53#12311yescharacteristic
360C2×C4×C53#12411yescharacteristic
361C2×C4×C53#12411yescharacteristic
362C2×C4×C53#12711yescharacteristic
363C2×C4×C53#12711yescharacteristic
364C2×Dic53—24no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—42no—
369C2×Dic53—42no—
370C2×Dic53—42no—
371C2×Dic53—42no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374C2×Dic53—42no—
375C2×Dic53—42no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—42no—
379C2×Dic53—42no—
380C2×Dic53—42no—
381C2×Dic53—81no—
382C2×Dic53—81no—
383C2×Dic53—81no—
384C2×Dic53—81no—
385C4×D53—42no—
386C4×D53—42no—
387C4×D53—42no—
388C4×D53—42no—
389C4×D53—42no—
390C4×D53—42no—
391C4×D53—42no—
392C4×D53—42no—
393Dic106—24no—
394Dic106—24no—
395Dic106—42no—
396Dic106—42no—
397Dic106—42no—
398Dic106—42no—
399Dic106—42no—
400Dic106—42no—
401C8×C53—42no—
402#88322—42no—
403#10970—531nomaximal, Sylow
404C22×C53#37911yescharacteristic
405C22×C53#38611yescharacteristic
406C22×C53#38611yescharacteristic
407C22×C53#39211yescharacteristic
408C22×C53#39211yescharacteristic
409C22×C53#39411yescharacteristic
410C22×C53#39411yescharacteristic
411C22×C53C2×#10311yescharacteristic
412C22×C53#41611yescharacteristic
413C22×C53#41711yescharacteristic
414C22×C53#41911yescharacteristic
415C22×C53#44811yescharacteristic
416C22×C53#44811yescharacteristic
417C22×C53#44911yescharacteristic
418C22×C53#44911yescharacteristic
419C22×C53#45011yescharacteristic
420C22×C53#45111yescharacteristic
421C22×C53#45111yescharacteristic
422C22×C53#45111yescharacteristic
423C22×C53#45211yescharacteristic
424C22×C53#45211yescharacteristic
425C22×C53#45211yescharacteristic
426C22×C53#45211yescharacteristic
427C22×C53#46511yescharacteristic
428C22×C53#46511yescharacteristic
429C22×C53#46711yescharacteristic
430C22×C53#46711yescharacteristic
431C22×C53#46811yescharacteristic
432C22×C53#46811yescharacteristic
433C22×C53#47011yescharacteristic
434C22×C53#47011yescharacteristic
435C22×C53#48311yescharacteristic
436C22×C53#48411yescharacteristic
437C22×C53#48511yescharacteristic
438C22×C53#48511yescharacteristic
439C2×D53—24no—
440C2×D53—24no—
441C2×D53—24no—
442C2×D53—42no—
443C2×D53—42no—
444C2×D53—42no—
445C2×D53—42no—
446C2×D53—42no—
447C2×D53—42no—
448C2×D53—42no—
449C2×D53—42no—
450C2×D53—42no—
451C2×D53—42no—
452C2×D53—42no—
453C2×D53—42no—
454C4×C53—44no—
455C4×C53—82no—
456C4×C53#38611yescharacteristic
457C4×C53#38611yescharacteristic
458C4×C53#39011yescharacteristic
459C4×C53#39011yescharacteristic
460C4×C53#39211yescharacteristic
461C4×C53#39211yescharacteristic
462C4×C53#39411yescharacteristic
463C4×C53#39411yescharacteristic
464Dic53—44no—
465Dic53—42no—
466Dic53—82no—
467C22×C22⋊Q8—531no—
468C22×#103—531no—
469C22×#103—531no—
470C22×C22⋊C8—531no—
471C2×#380—531no—
472C2×#340—531no—
473C2×#340D5311yescharacteristic, complemented
474C2×C53#143811yescharacteristic
475C2×C53#178711yescharacteristic
476C2×C53#178811yescharacteristic
477C2×C53#187211yescharacteristic
478C2×C53#187311yescharacteristic
479C2×C53#189211yescharacteristic
480C2×C53#189411yescharacteristic
481C2×C53#200011yescharacteristic
482C2×C53#200011yescharacteristic
483C2×C53#200111yescharacteristic
484C2×C53#200111yescharacteristic
485C2×C53#203511yescharacteristic
486C2×C53#203511yescharacteristic
487C2×C53#203611yescharacteristic
488C2×C53#203611yescharacteristic
489D53—44no—
490C23×Q8—531no—
491C24×C4—531no—
492C23×C8—531no—
493C23×C8C2×D5311yescharacteristic
494C2×C22⋊Q8—534no—
495C2×C22⋊Q8—1062no—
496C2×C22⋊Q8—1062no—
497C2×C22⋊Q8—1062no—
498C2×C22⋊Q8—1062no—
499C2×C22⋊Q8—1062no—
500C22×C4⋊C4—531no—
501C22×C4⋊C4—1061no—
502C22×C4⋊C4C2×D5311yescharacteristic
503C22×C4⋊C4C2×D5311yescharacteristic
504C22×C22⋊C4—1061no—
505C22×C22⋊C4—1061no—
506C2×#103—1062no—
507C2×#103—1062no—
508C2×#103—1062no—
509C2×#103—1062no—
510C2×#103—1062no—
511C2×#103—1062no—
512C2×C22⋊C8—1062no—
513C2×C22⋊C8—1062no—
514C2×C22⋊C8—1062no—
515#380—1062no—
516#380—1062no—
517C2×#95—1061no—
518#340—22no—
519#340—1062no—
520C53#1097011yescharacteristic, complemented, Sylow
521C25—531no—
522C22×Q8—532no—
523C22×Q8—532no—
524C22×Q8—532no—
525C22×Q8—1061no—
526C22×Q8—1061no—
527C22×Q8—1061no—
528C22×Q8—1061no—
529C22×Q8—1061no—
530C22×Q8—1061no—
531C22×Q8—1061no—
532C22×Q8—1061no—
533C22×Q8—1061no—
534C22×Q8—1061no—
535C22×Q8—1061no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—531no—
539C23×C4—532no—
540C23×C4—532no—
541C23×C4—1061no—
542C23×C4—1061no—
543C23×C4—1061no—
544C23×C4—1061no—
545C23×C4—1061no—
546C23×C4—1061no—
547C23×C4—1061no—
548C23×C4—1061no—
549C23×C4—1061no—
550C23×C4—1061no—
551C23×C4—1061no—
552C23×C4—1061no—
553C23×C4—1061no—
554C23×C4—1061no—
555C23×C4C22×D5311yescharacteristic
556C22×C8—21no—
557C22×C8—21no—
558C22×C8—21no—
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8—532no—
563C22×C8—1061no—
564C22×C8—1061no—
565C22×C8—1061no—
566C22×C8—1061no—
567C22×C8—1061no—
568C22×C8—1061no—
569C22×C8D21212yes—
570C22⋊Q8—1068no—
571C22⋊Q8—1068no—
572C22⋊Q8—1068no—
573C22⋊Q8—1068no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—532no—
583C2×C4⋊C4—1064no—
584C2×C4⋊C4—1064no—
585C2×C4⋊C4—1064no—
586C2×C4⋊C4—1061no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C4⋊C4C4×D5312yes—
592C2×C4⋊C4D21212yes—
593C2×C4⋊C4D21212yes—
594C2×C4⋊C4C22⋊D5312yes—
595C2×C22⋊C4—1064no—
596C2×C22⋊C4—1064no—
597C2×C22⋊C4—1064no—
598C2×C22⋊C4—1064no—
599C2×C22⋊C4—2122no—
600C2×C22⋊C4—2122no—
601#103—1068no—
602#103—1068no—
603C22⋊C8—1068no—
604#95—1064no—
605C24—532no—
606C24—532no—
607C24—532no—
608C24—1061no—
609C24—1061no—
610C24—1061no—
611C24—1061no—
612C24—1061no—
613C24—1061no—
614C24—1061no—
615C24—1061no—
616C24—1061no—
617C24—1061no—
618C24—1061no—
619C24—1061no—
620C24D4×D5311yescharacteristic
621C2×Q8—534no—
622C2×Q8—1062no—
623C2×Q8—1062no—
624C2×Q8—1062no—
625C2×Q8—1062no—
626C2×Q8—1062no—
627C2×Q8—1062no—
628C2×Q8—1062no—
629C2×Q8—1062no—
630C2×Q8—1062no—
631C2×Q8—1062no—
632C2×Q8—1062no—
633C2×Q8—1062no—
634C2×Q8—1062no—
635C2×Q8—1062no—
636C2×Q8—1062no—
637C2×Q8—2121no—
638C2×Q8—2121no—
639C2×Q8—2121no—
640C2×Q8—2121no—
641C2×Q8—2121no—
642C2×Q8—2121no—
643C2×Q8—2121no—
644C2×Q8—2121no—
645C2×Q8—2121no—
646C2×Q8—2121no—
647C2×Q8—2121no—
648C2×Q8—2121no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—532no—
664C22×C4—1062no—
665C22×C4—1062no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—1062no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4—1062no—
678C22×C4—1062no—
679C22×C4—1062no—
680C22×C4—1062no—
681C22×C4—1062no—
682C22×C4—1062no—
683C22×C4—1062no—
684C22×C4—1062no—
685C22×C4—1062no—
686C22×C4—2121no—
687C22×C4—2121no—
688C22×C4—2121no—
689C22×C4—2121no—
690C22×C4—2121no—
691C22×C4—2121no—
692C22×C4—2121no—
693C22×C4—2121no—
694C22×C4—2121no—
695C22×C4—2121no—
696C22×C4—2121no—
697C22×C4—2121no—
698C22×C4—2121no—
699C22×C4—2121no—
700C22×C4—2121no—
701C22×C4—2121no—
702C22×C4—2121no—
703C22×C4—2121no—
704C22×C4—2121no—
705C22×C4—2121no—
706C22×C4—2121no—
707C22×C4—2121no—
708C22×C4—2121no—
709C22×C4—2121no—
710C22×C4—2121no—
711C22×C4—2121no—
712C22×C4C2×C4×D5311yescharacteristic
713C22×C4C2×D21211yescharacteristic
714C22×C4C2×D21211yescharacteristic
715C22×C4C2×D21211yescharacteristic
716C22×C4#1171994511yescharacteristic
717C22×C4#1171994511yescharacteristic
718C22×C4D4×D5311yescharacteristic
719C22×C4D4×D5311yescharacteristic
720C22×C4D4×D5311yescharacteristic
721C22×C4D4×D5311yescharacteristic
722C22×C4D4×D5311yescharacteristic
723C22×C4#1171994911yescharacteristic
724C22×C4#1171994911yescharacteristic
725C22×C4C2×C22⋊D5311yescharacteristic
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—1062no—
734C2×C8—1062no—
735C2×C8—1062no—
736C2×C8—2121no—
737C2×C8—2121no—
738C2×C8—2121no—
739C2×C8—2121no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—10616no—
748C4⋊C4—1062no—
749C4⋊C4—1062no—
750C4⋊C4—2121no—
751C4⋊C4—2121no—
752C4⋊C4#1171992114yescomplemented
753C22⋊C4—10616no—
754C22⋊C4—2128no—
755C23—534no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—1062no—
771C23—1062no—
772C23—1062no—
773C23—1062no—
774C23—2121no—
775C23—2121no—
776C23—2121no—
777C23—2121no—
778C23—2121no—
779C23—2121no—
780C23—2121no—
781C23—2121no—
782C23—2121no—
783C23—2121no—
784C23—2121no—
785C23—2121no—
786C23—2121no—
787C23—2121no—
788C23—2121no—
789C23—2121no—
790C23C22⋊C4×D5311yescharacteristic
791C23#1313318511yescharacteristic
792C23#1313318711yescharacteristic
793C23#1313318711yescharacteristic
794C23#1313319011yescharacteristic
795C23#1313319211yescharacteristic
796C23#1313320211yescharacteristic
797C23SD16×D5311yescharacteristic
798C23Q16×D5311yescharacteristic
799C23#1313323611yescharacteristic
800C23#1313323811yescharacteristic
801C23#1313324111yescharacteristic
802C23#1313324611yescharacteristic
803C23#1313324611yescharacteristic
804C23#1313324911yescharacteristic
805Q8—1064no—
806Q8—1064no—
807Q8—2122no—
808Q8—2122no—
809Q8—2122no—
810Q8—2122no—
811Q8—2122no—
812Q8—2122no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—1062no—
828C2×C4—1062no—
829C2×C4—1064no—
830C2×C4—1062no—
831C2×C4—4241no—
832C2×C4—4241no—
833C2×C4—4241no—
834C2×C4—4241no—
835C2×C4—2122no—
836C2×C4—2122no—
837C2×C4—2122no—
838C2×C4—2122no—
839C2×C4—2122no—
840C2×C4—2121no—
841C2×C4—2122no—
842C2×C4—2121no—
843C2×C4—2122no—
844C2×C4—2121no—
845C2×C4—2122no—
846C2×C4—2121no—
847C2×C4—2122no—
848C2×C4—2122no—
849C2×C4—2122no—
850C2×C4—2122no—
851C2×C4—2122no—
852C2×C4—2122no—
853C2×C4—2122no—
854C2×C4—2122no—
855C2×C4—2122no—
856C2×C4C22⋊C4×D5311yescharacteristic
857C2×C4C2×#1171992111yescharacteristic
858C2×C4#1313317911yescharacteristic
859C2×C4#1313317911yescharacteristic
860C2×C4C4×D21211yescharacteristic
861C2×C4C4×D21211yescharacteristic
862C2×C4#1313318511yescharacteristic
863C2×C4#1313318711yescharacteristic
864C2×C4#1313318711yescharacteristic
865C2×C4#1313318711yescharacteristic
866C2×C4#1313318711yescharacteristic
867C2×C4#1313319011yescharacteristic
868C2×C4#1313319011yescharacteristic
869C2×C4#1313319011yescharacteristic
870C2×C4#1313319111yescharacteristic
871C2×C4#1313319111yescharacteristic
872C2×C4#1313319211yescharacteristic
873C2×C4#1313319211yescharacteristic
874C2×C4#1313319211yescharacteristic
875C2×C4#1313319211yescharacteristic
876C2×C4#1313319211yescharacteristic
877C2×C4#1313320211yescharacteristic
878C2×C4#1313320211yescharacteristic
879C2×C4#1313320211yescharacteristic
880C2×C4#1313320511yescharacteristic
881C2×C4#1313320611yescharacteristic
882C2×C4#1313321311yescharacteristic
883C2×C4#1313321411yescharacteristic
884C8—42no—
885C8—2122no—
886C22—1064no—
887C22—1064no—
888C22—1064no—
889C22—2122no—
890C22—2122no—
891C22—2122no—
892C22—2122no—
893C22—2122no—
894C22—2122no—
895C22—2122no—
896C22—2122no—
897C22—2122no—
898C22—2122no—
899C22—2122no—
900C22—2122no—
901C22#1681047811yescharacteristic
902C22#1681050111yescharacteristic
903C22#1681050111yescharacteristic
904C22#1681053211yescharacteristic
905C22#1681053311yescharacteristic
906C22#1681054011yescharacteristic
907C22#1681054111yescharacteristic
908C22#103×D5311yescharacteristic
909C22#1681061611yescharacteristic
910C22#1681062111yescharacteristic
911C22#1681063011yescharacteristic
912C22#1681076011yescharacteristic
913C22#1681076311yescharacteristic
914C22#1681076511yescharacteristic
915C22#1681076911yescharacteristic
916C22#1681077511yescharacteristic
917C22#1681077711yescharacteristic
918C22#1681078011yescharacteristic
919C22#1681078011yescharacteristic
920C22#1681078211yescharacteristic
921C22#1681078611yescharacteristic
922C22#1681078611yescharacteristic
923C22#1681078811yescharacteristic
924C22#1681085111yescharacteristic
925C22#1681085311yescharacteristic
926C22#1681086311yescharacteristic
927C22#1681086511yescharacteristic
928C22#1681086811yescharacteristic
929C22#1681087011yescharacteristic
930C22#1681088011yescharacteristic
931C22#1681088211yescharacteristic
932C22#1681095511yescharacteristic
933C22#1681096011yescharacteristic
934C22#1681096611yescharacteristic
935C22#1681096711yescharacteristic
936C4—44no—
937C4—82no—
938C4—4242no—
939C4—2122no—
940C4—2124no—
941C4#1681050111yescharacteristic
942C4#1681050111yescharacteristic
943C4#1681052411yescharacteristic
944C4#1681052511yescharacteristic
945C4#1681053211yescharacteristic
946C4#1681053311yescharacteristic
947C4#1681054011yescharacteristic
948C4#1681054111yescharacteristic
949C2—2124no—
950C2#2027295511yescharacteristic
951C2#2027464811yescharacteristic
952C2#2027465211yescharacteristic
953C2#2027502111yescharacteristic
954C2#2027502611yescharacteristic
955C2#2027513711yescharacteristic
956C2#2027514711yescharacteristic
957C2#2027571911yescharacteristic
958C2#2027572111yescharacteristic
959C2#2027572411yescharacteristic
960C2#2027572611yescharacteristic
961C2#2027591311yescharacteristic
962C2#2027591411yescharacteristic
963C2#2027592011yescharacteristic
964C2#2027592111yescharacteristic
subgroupG/H
centerC24D4×D53
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
FittingC2×C53×#340C2
socleC24×C53C2×D4
prime radicalC24×D53D4
cosocleC23×C4×C53C23
hypercenterC2×#340D53
hypocenterC53#10970
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#13133142C2semidirect
3. C22×#13133140C2semidirect
6. C2×#16810385C2semidirect
7. C2×C53×#340C2semidirect
16. C2×#13133197C4semidirect
242. C2×Dic106C22⋊C4semidirect
257. C4⋊C4×C53C22⋊C4semidirect
321. C22×D53#103semidirect
473. C2×#340D53semidirect
520. C53#10970semidirect
752. C4⋊C4#11719921semidirect

Maximal subgroups

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

subgroupindex
C22×#131331972
C22×#131331422
C22×#131331402
C22×#131331292
C2×#168104802
C2×#168103852
C2×C53×#3402
#1097053