Finite Group Databasebeta

← #27308580

Subgroups — #27308580

Order 13568.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133204C211yesmaximal, characteristic
2C2×#16810527C211yesmaximal, characteristic, complemented
3C2×#16810517C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20272985C211yesmaximal, characteristic, complemented
6#20272962C211yesmaximal, characteristic, complemented
7#20272958C211yesmaximal, characteristic, complemented
8#20272956C211yesmaximal, characteristic
9#20272952C211yesmaximal, characteristic, complemented
10#20272952C211yesmaximal, characteristic, complemented
11#20272952C211yesmaximal, characteristic, complemented
12#20272941C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C2×C53×#386C211yesmaximal, characteristic
16C23×Dic106C2211yescharacteristic
17C2×#13133204—24no—
18C2×#13133204—24no—
19C2×#13133204C418yescomplemented
20C22×#11719919C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810527—24no—
34#16810517—24no—
35C4×C22⋊Dic53—24no—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C23×D4×C53C2211yescharacteristic
51C24×C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C53×#386—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C22×Dic106—22no—
59C22×Dic106—22no—
60C22×Dic106—22no—
61C22×Dic106—22no—
62C22×Dic106—41no—
63C22×Dic106—41no—
64C22×Dic106C2×C414yescomplemented
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73#13133204—232no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—41no—
77C2×C22⋊Dic53—22no—
78C2×C22⋊Dic53—22no—
79C2×C22⋊Dic53—22no—
80C2×C22⋊Dic53—22no—
81C2×C22⋊Dic53—22no—
82C2×C22⋊Dic53—22no—
83C2×C22⋊Dic53—22no—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53—22no—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—41no—
92C2×C22⋊Dic53—41no—
93C2×C22⋊Dic53—41no—
94C2×C22⋊Dic53—41no—
95C2×C22⋊Dic53C2×C414yes—
96C2×C22⋊Dic53C2×C414yes—
97C2×C22⋊Dic53C2×C414yescomplemented
98C2×C22⋊Dic53C2×C414yescomplemented
99C2×C22⋊Dic53D414yes—
100C2×C22⋊Dic53D414yes—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53—41no—
110C2×C4×Dic53—41no—
111C2×C4×Dic53—41no—
112C2×C4×Dic53C2×C414yescomplemented
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—41no—
126#13133124—41no—
127C25×C53C2311yescharacteristic
128C25×C53C2311yescharacteristic
129C22×D4×C53—22no—
130C22×D4×C53—22no—
131C22×D4×C53—22no—
132C22×D4×C53—22no—
133C22×D4×C53—41no—
134C22×D4×C53—41no—
135C22×D4×C53C2×C414yes—
136C23×C4×C53—22no—
137C23×C4×C53—22no—
138C23×C4×C53—22no—
139C23×C4×C53—22no—
140C23×C4×C53—22no—
141C23×C4×C53—41no—
142C23×C4×C53—41no—
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C2×C22⋊C4×C53—22no—
149C2×C22⋊C4×C53—22no—
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—41no—
156C2×C22⋊C4×C53—41no—
157#95×C53—22no—
158#95×C53D414yes—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53C22×C412yes—
186C24×C53C22×C412yes—
187C24×C53C2×D412yes—
188C24×C53C2×D412yes—
189C24×C53C2411yescharacteristic
190C2×D4×C53—28no—
191C2×D4×C53—28no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—44no—
196C2×D4×C53—44no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—28no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—44no—
226C22×C4×C53—44no—
227C22×C4×C53—44no—
228C22×C4×C53—44no—
229C22×C4×C53—44no—
230C22×C4×C53—44no—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53#4112yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
238C22×C4×C53#4112yes—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53C22×C412yes—
285C22×Dic53C22×C412yes—
286C22×Dic53C22×C412yes—
287C22×Dic53C22×C412yes—
288C22×Dic53C2×D412yes—
289C22×Dic53C2×D412yes—
290C22×Dic53C2×D412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53#4112yes—
293C22×Dic53#4112yes—
294C22×Dic53#4112yes—
295C2×Dic106—28no—
296C2×Dic106—28no—
297C2×Dic106—44no—
298C2×Dic106—44no—
299C2×Dic106—44no—
300C2×Dic106—44no—
301C2×Dic106—44no—
302C22⋊C4×C53—44no—
303C22⋊C4×C53—44no—
304C22⋊C4×C53—44no—
305C22⋊Dic53—28no—
306C22⋊Dic53—28no—
307C22⋊Dic53—28no—
308C22⋊Dic53—28no—
309C22⋊Dic53—44no—
310C22⋊Dic53—44no—
311C22⋊Dic53—44no—
312C22⋊Dic53C22⋊C4116yescomplemented
313#11719919—44no—
314C4×Dic53—28no—
315C4×Dic53—44no—
316C4×Dic53—44no—
317C4×Dic53—44no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53C2×C22⋊C414yes—
388C23×C53C23×C411yescharacteristic
389C23×C53C22×D411yescharacteristic
390C23×C53C22×D411yescharacteristic
391C23×C53C22×D411yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53C2×#4111yescharacteristic
396C23×C53C2×#4111yescharacteristic
397C23×C53C2×#4111yescharacteristic
398C23×C53C2×#4111yescharacteristic
399C23×C53H(5,𝔽2)11yescharacteristic
400C23×C53H(5,𝔽2)11yescharacteristic
401C23×C53H(5,𝔽2)11yescharacteristic
402C23×C532−1+411yescharacteristic
403D4×C53—416no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—416no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53C4×D414yes—
439C2×C4×C53#12414yescomplemented
440C2×Dic53—22no—
441C2×Dic53—22no—
442C2×Dic53—22no—
443C2×Dic53—22no—
444C2×Dic53—22no—
445C2×Dic53—22no—
446C2×Dic53—22no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53C2×C22⋊C414yes—
495C2×Dic53C2×C22⋊C414yes—
496Dic106—416no—
497#14098—531nomaximal, Sylow
498C22×C53—24no—
499C22×C53—24no—
500C22×C53—24no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—42no—
518C22×C53—42no—
519C22×C53—42no—
520C22×C53—81no—
521C22×C53—81no—
522C22×C53—81no—
523C22×C53—81no—
524C22×C53—81no—
525C22×C53—81no—
526C22×C53—81no—
527C22×C53—81no—
528C22×C53C22×C22⋊C411yescharacteristic
529C22×C53C2×C4×D411yescharacteristic
530C22×C53C4×#4111yescharacteristic
531C22×C53C4×#4111yescharacteristic
532C22×C53C4×#4111yescharacteristic
533C22×C53#51811yescharacteristic
534C22×C53#52011yescharacteristic
535C22×C53#52511yescharacteristic
536C22×C53#52511yescharacteristic
537C22×C53C2×#12411yescharacteristic
538C22×C53#52911yescharacteristic
539C22×C53#52911yescharacteristic
540C22×C53#53211yescharacteristic
541C22×C53#53211yescharacteristic
542C22×C53#53211yescharacteristic
543C22×C53#53811yescharacteristic
544C22×C53#53811yescharacteristic
545C22×C53#54211yescharacteristic
546C22×C53#54211yescharacteristic
547C22×C53D4211yescharacteristic
548C22×C53D4211yescharacteristic
549C22×C53#54611yescharacteristic
550C22×C53#54611yescharacteristic
551C22×C53#54611yescharacteristic
552C22×C53#54611yescharacteristic
553C22×C53#54611yescharacteristic
554C22×C53#54711yescharacteristic
555C22×C53#54711yescharacteristic
556C22×C53#54811yescharacteristic
557C22×C53#55111yescharacteristic
558C22×C53#55111yescharacteristic
559C22×C53#55511yescharacteristic
560C22×C53#55511yescharacteristic
561C22×C53#55611yescharacteristic
562C22×C53#55911yescharacteristic
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—42no—
566C4×C53—42no—
567C4×C53—81no—
568Dic53—24no—
569Dic53—24no—
570Dic53—42no—
571Dic53—42no—
572Dic53—42no—
573Dic53—42no—
574Dic53—42no—
575Dic53—81no—
576C22×#124—531no—
577C2×#391—531no—
578C2×#388—531no—
579C2×#386D5311yescharacteristic
580C2×C4×C22⋊C4—531no—
581#1446—531no—
582#1440—531no—
583#1439—531no—
584#1438—531no—
585#1437—531no—
586#1437—531no—
587#1437—531no—
588#1434—531no—
589C22⋊#95—531no—
590C4×#95—531no—
591C2×C53—44no—
592C2×C53—82no—
593C2×C53#229711yescharacteristic
594C2×C53C4×#12411yescharacteristic
595C2×C53#233711yescharacteristic
596C2×C53D4×C22⋊C411yescharacteristic
597C2×C53#233911yescharacteristic
598C2×C53#236711yescharacteristic
599C2×C53#237211yescharacteristic
600C2×C53#245911yescharacteristic
601C2×C53#246111yescharacteristic
602C2×C53#247211yescharacteristic
603C2×C53#247411yescharacteristic
604C2×C53#249111yescharacteristic
605C2×C53#252111yescharacteristic
606C2×C53#255511yescharacteristic
607C2×C53#255711yescharacteristic
608C23×Q8—531no—
609C23×D4C2×D5311yescharacteristic
610C24×C4C2×D5311yescharacteristic
611C2×#124—538no—
612C2×#124—1064no—
613C2×#124—1064no—
614C22×C4⋊C4—531no—
615C22×C22⋊C4—531no—
616C22×C22⋊C4—531no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—531no—
619C22×C22⋊C4—531no—
620C22×C22⋊C4—531no—
621C22×C22⋊C4—531no—
622C22×C22⋊C4—531no—
623C22×C22⋊C4C2×D5311yescharacteristic
624C22×C22⋊C4C2×D5311yescharacteristic
625C22×C22⋊C4C2×D5311yescharacteristic
626C22×C42—531no—
627C22×C42—531no—
628C22×C42—531no—
629C22×C42—531no—
630#391—1064no—
631#388—1064no—
632#386—24no—
633C4×C22⋊C4—1064no—
634C2×#95—531no—
635C2×#95—531no—
636C2×#95—531no—
637C2×#95—531no—
638C2×#95—531no—
639C2×#95—531no—
640C2×#95—531no—
641C2×#95—531no—
642C2×#95—531no—
643C2×#95—531no—
644C2×#95—531no—
645C2×#95—531no—
646C2×#95—531no—
647C2×#95—531no—
648C2×#95C2×D5311yescharacteristic
649C2×#95C2×D5311yescharacteristic
650C53#1409811yescharacteristic, complemented, Sylow
651C25C22×D5311yescharacteristic
652C25C22×D5311yescharacteristic
653C22×Q8—534no—
654C22×Q8—1062no—
655C22×Q8—1062no—
656C22×Q8—1062no—
657C22×Q8—1062no—
658C22×Q8—2121no—
659C22×Q8—2121no—
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C4×D5314yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—531no—
675C23×C4—531no—
676C23×C4—531no—
677C23×C4—531no—
678C23×C4—531no—
679C23×C4—531no—
680C23×C4—531no—
681C23×C4—531no—
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686C23×C4C22×D5311yescharacteristic
687#124—10632no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—2121no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—534no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—534no—
703C2×C22⋊C4—534no—
704C2×C22⋊C4—534no—
705C2×C22⋊C4—534no—
706C2×C22⋊C4—1062no—
707C2×C22⋊C4—1062no—
708C2×C22⋊C4—1062no—
709C2×C22⋊C4—1062no—
710C2×C22⋊C4—1062no—
711C2×C22⋊C4—1062no—
712C2×C22⋊C4—1062no—
713C2×C22⋊C4—1062no—
714C2×C22⋊C4—1062no—
715C2×C22⋊C4—1062no—
716C2×C22⋊C4—1062no—
717C2×C22⋊C4—1062no—
718C2×C22⋊C4—1062no—
719C2×C22⋊C4—1062no—
720C2×C22⋊C4—2121no—
721C2×C22⋊C4—2121no—
722C2×C22⋊C4—2121no—
723C2×C22⋊C4—2121no—
724C2×C42—534no—
725C2×C42—1062no—
726C2×C42—1062no—
727C2×C42—1062no—
728C2×C42—1062no—
729C2×C42—1062no—
730C2×C42—1062no—
731C2×C42—1062no—
732C2×C42—1062no—
733C2×C42—2121no—
734C2×C42—2121no—
735C2×C42—2121no—
736#95—22no—
737#95—1062no—
738#95—1062no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—1062no—
744#95—1062no—
745#95—1062no—
746#95—1062no—
747#95—1062no—
748#95—1062no—
749#95—2121no—
750#95—2121no—
751#95C22⋊D5314yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C2×C4×D5312yes—
779C24C2×C4×D5312yes—
780C24D4×D5312yes—
781C24D4×D5312yes—
782C24C23×D5311yescharacteristic
783C2×Q8—1068no—
784C2×Q8—1068no—
785C2×Q8—2124no—
786C2×Q8—2124no—
787C2×Q8—2124no—
788C2×Q8—2124no—
789C2×Q8—2124no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—28no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—532no—
832C22×C4—532no—
833C22×C4—532no—
834C22×C4—532no—
835C22×C4—532no—
836C22×C4—532no—
837C22×C4—532no—
838C22×C4—532no—
839C22×C4—532no—
840C22×C4—532no—
841C22×C4—532no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1061no—
846C22×C4—1061no—
847C22×C4—1061no—
848C22×C4—1061no—
849C22×C4—1061no—
850C22×C4—1061no—
851C22×C4—1061no—
852C22×C4—1061no—
853C22×C4—1061no—
854C22×C4—1061no—
855C22×C4—1061no—
856C22×C4—1061no—
857C22×C4—1061no—
858C22×C4—1061no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4C2×C4×D5312yes—
888C22×C4#1171994512yes—
889C22×C4#1171994712yes—
890C22×C4#1171994712yes—
891C22×C4#1171994712yes—
892C22×C4C2×C22⋊D5312yes—
893C22×C4C2×C22⋊D5312yes—
894C22×C4C2×C22⋊D5312yes—
895C4⋊C4—2124no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—5316no—
900C22⋊C4—1068no—
901C22⋊C4—1068no—
902C22⋊C4—1068no—
903C22⋊C4—1068no—
904C22⋊C4—2124no—
905C22⋊C4—2124no—
906C22⋊C4—2124no—
907C42—1068no—
908C42—2124no—
909C42—2124no—
910C42—2124no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C22⋊C4×D5314yes—
981C23C22×C4×D5311yescharacteristic
982C23C2×D4×D5311yescharacteristic
983C23C2×D4×D5311yescharacteristic
984C23C22×C22⋊D5311yescharacteristic
985C23#41×D5311yescharacteristic
986C23#41×D5311yescharacteristic
987C23#41×D5311yescharacteristic
988C23C2×#1171994711yescharacteristic
989C23C2×#1171994711yescharacteristic
990C23C2×#1171994711yescharacteristic
991C23C2×#1171994511yescharacteristic
992C23#1313326211yescharacteristic
993C23#1313326211yescharacteristic
994C23#1313326211yescharacteristic
995C23#1313326411yescharacteristic
996Q8—21216no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—416no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—534no—
1033C2×C4—534no—
1034C2×C4—1062no—
1035C2×C4—1062no—
1036C2×C4—1062no—
1037C2×C4—1062no—
1038C2×C4—1062no—
1039C2×C4—1062no—
1040C2×C4—1062no—
1041C2×C4—1062no—
1042C2×C4—1062no—
1043C2×C4—1062no—
1044C2×C4—1062no—
1045C2×C4—1062no—
1046C2×C4—1062no—
1047C2×C4—1062no—
1048C2×C4—1062no—
1049C2×C4—1062no—
1050C2×C4—1062no—
1051C2×C4—1062no—
1052C2×C4—1062no—
1053C2×C4—1062no—
1054C2×C4—1062no—
1055C2×C4—1062no—
1056C2×C4—1062no—
1057C2×C4—1062no—
1058C2×C4—1062no—
1059C2×C4—1062no—
1060C2×C4—1062no—
1061C2×C4—2121no—
1062C2×C4—2121no—
1063C2×C4—2121no—
1064C2×C4—2121no—
1065C2×C4—2121no—
1066C2×C4—2121no—
1067C2×C4—2121no—
1068C2×C4—2121no—
1069C2×C4—2121no—
1070C2×C4—2121no—
1071C2×C4—2121no—
1072C2×C4—2121no—
1073C2×C4—2121no—
1074C2×C4—2121no—
1075C2×C4—2121no—
1076C2×C4—2121no—
1077C2×C4—2121no—
1078C2×C4—2121no—
1079C2×C4—2121no—
1080C2×C4—2121no—
1081C2×C4—2121no—
1082C2×C4—2121no—
1083C2×C4—2121no—
1084C2×C4—2121no—
1085C2×C4—2121no—
1086C2×C4—2121no—
1087C2×C4—2121no—
1088C2×C4C4×C22⋊D5314yes—
1089C2×C4#1313320414yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C2×C22⋊C4×D5311yescharacteristic
1121C22C2×C4×C22⋊D5311yescharacteristic
1122C22C4×#1171994711yescharacteristic
1123C22C4×#1171994711yescharacteristic
1124C22C4×#1171994711yescharacteristic
1125C22#1681109611yescharacteristic
1126C22#1681110211yescharacteristic
1127C22#1681112911yescharacteristic
1128C22#1681113111yescharacteristic
1129C22C2×#1313320411yescharacteristic
1130C22#1681115511yescharacteristic
1131C22#1681115511yescharacteristic
1132C22#1681116811yescharacteristic
1133C22#1681116811yescharacteristic
1134C22#1681116911yescharacteristic
1135C22#1681120511yescharacteristic
1136C22#1681120811yescharacteristic
1137C22#1681124011yescharacteristic
1138C22#1681124111yescharacteristic
1139C22D4×C22⋊D5311yescharacteristic
1140C22D4×C22⋊D5311yescharacteristic
1141C22#1681126011yescharacteristic
1142C22#1681126211yescharacteristic
1143C22#1681126311yescharacteristic
1144C22#1681126311yescharacteristic
1145C22#1681126711yescharacteristic
1146C22#1681127111yescharacteristic
1147C22#1681127311yescharacteristic
1148C22#1681128011yescharacteristic
1149C22#1681130111yescharacteristic
1150C22#1681130411yescharacteristic
1151C22#1681133711yescharacteristic
1152C22#1681133711yescharacteristic
1153C22#1681134311yescharacteristic
1154C22#1681135611yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—1064no—
1161C4—1064no—
1162C4—4241no—
1163C4—2122no—
1164C4—2122no—
1165C4—2122no—
1166C4—2122no—
1167C4—2122no—
1168C2—44no—
1169C2—82no—
1170C2#2027720011yescharacteristic
1171C2C4×#1313320411yescharacteristic
1172C2#2027752411yescharacteristic
1173C2C22⋊C4×C22⋊D5311yescharacteristic
1174C2#2027754111yescharacteristic
1175C2#2027778811yescharacteristic
1176C2#2027782411yescharacteristic
1177C2#2027865111yescharacteristic
1178C2#2027868111yescharacteristic
1179C2#2027884011yescharacteristic
1180C2#2027887011yescharacteristic
1181C2#2027908011yescharacteristic
1182C2#2027942211yescharacteristic
1183C2#2027978811yescharacteristic
1184C2#2027981311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#14098
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16810527C2semidirect
3. C2×#16810517C2semidirect
4. C2×C4×C22⋊Dic53C2semidirect
5. #20272985C2semidirect
6. #20272962C2semidirect
7. #20272958C2semidirect
9. #20272952C2semidirect
10. #20272952C2semidirect
11. #20272952C2semidirect
12. #20272941C2semidirect
13. #20272938C2semidirect
14. #95×Dic53C2semidirect
19. C2×#13133204C4semidirect
64. C22×Dic106C2×C4semidirect
97. C2×C22⋊Dic53C2×C4semidirect
98. C2×C22⋊Dic53C2×C4semidirect
112. C2×C4×Dic53C2×C4semidirect
312. C22⋊Dic53C22⋊C4semidirect
439. C2×C4×C53#124semidirect
650. C53#14098semidirect
1089. C2×C4#13133204semidirect

Maximal subgroups

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

subgroupindex
C22×#131332042
C2×#168105272
C2×#168105172
C2×C4×C22⋊Dic532
#202729852
#202729622
#202729582
#202729562
#202729522
#202729412
#202729382
#95×Dic532
C2×C53×#3862
#1409853