Finite Group Databasebeta

← #27308525

Subgroups — #27308525

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133198C211yesmaximal, characteristic
2C2×#16810504C211yesmaximal, characteristic, complemented
3C2×C4×#11719919C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5#20272965C211yesmaximal, characteristic, complemented
6#20272958C211yesmaximal, characteristic, complemented
7#20272958C211yesmaximal, characteristic, complemented
8#20272956C211yesmaximal, characteristic
9#20272952C211yesmaximal, characteristic, complemented
10#20272952C211yesmaximal, characteristic, complemented
11#20272952C211yesmaximal, characteristic, complemented
12#20272952C211yesmaximal, characteristic, complemented
13#20272948C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C2×C53×#390C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C2×#13133198—24no—
18C2×#13133198—24no—
19C2×#13133198C418yescomplemented
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810504—24no—
34C4×#11719919—24no—
35C22⋊C4×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
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C53×#390—24no—
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—41no—
63C23×Dic53—41no—
64C23×Dic53C2×C414yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73#13133198—232no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919C2×C414yes—
80C2×#11719919C2×C414yes—
81C2×#11719919D414yes—
82C2×#11719919D414yes—
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—22no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—41no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C22⋊Dic53C2×C414yes—
102C2×C22⋊Dic53C2×C414yes—
103C2×C22⋊Dic53C2×C414yes—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53—22no—
110C2×C4×Dic53—22no—
111C2×C4×Dic53—41no—
112C2×C4×Dic53—41no—
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—41no—
124#13133124—41no—
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×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53—22no—
142C2×C4⋊C4×C53—22no—
143C2×C4⋊C4×C53—41no—
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
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—41no—
154C2×C22⋊C4×C53—41no—
155C2×C22⋊C4×C53D414yes—
156C2×C42×C53—22no—
157C2×C42×C53—22no—
158C2×C42×C53—41no—
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×C53#4112yes—
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—21no—
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×C53C22×C412yes—
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2×D412yes—
229C22×C4×C53#4112yes—
230C22×C4×C53#4112yes—
231C22×C4×C53#4112yes—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—28no—
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—28no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—44no—
280C22×Dic53—44no—
281C22×Dic53—44no—
282C22×Dic53—44no—
283C22×Dic53—44no—
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—
295C4⋊C4×C53—44no—
296C22⋊C4×C53—28no—
297C22⋊C4×C53—44no—
298C22⋊C4×C53—44no—
299C22⋊C4×C53—44no—
300C42×C53—44no—
301C22⋊Dic53—28no—
302C22⋊Dic53—28no—
303C22⋊Dic53—28no—
304C22⋊Dic53—28no—
305C22⋊Dic53—44no—
306C22⋊Dic53—44no—
307C22⋊Dic53—44no—
308#11719919—28no—
309#11719919—28no—
310#11719919C22⋊C4116yescomplemented
311C4×Dic53—28no—
312C4×Dic53—44no—
313C4×Dic53—44no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
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—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
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×C53C4×D414yes—
384C23×C53C23×C411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C2×#4111yescharacteristic
389C23×C53C2×#4111yescharacteristic
390C23×C53C2×#4111yescharacteristic
391C23×C53C2×#4111yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53H(5,𝔽2)11yescharacteristic
396C23×C53H(5,𝔽2)11yescharacteristic
397C23×C53H(5,𝔽2)11yescharacteristic
398C23×C532−1+411yescharacteristic
399D4×C53—416no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
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—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
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×C53C2×C22⋊C414yes—
434C2×C4×C53#12314yescomplemented
435C2×Dic53—22no—
436C2×Dic53—22no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
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—416no—
463C2×Dic53—41no—
464C2×Dic53—41no—
465C2×Dic53—41no—
466C2×Dic53—41no—
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×Dic53C2×C22⋊C414yes—
491C2×Dic53C2×C22⋊C414yes—
492#14095—531nomaximal, Sylow
493C22×C53—24no—
494C22×C53—24no—
495C22×C53—24no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—42no—
499C22×C53—42no—
500C22×C53—42no—
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—81no—
516C22×C53—81no—
517C22×C53—81no—
518C22×C53—81no—
519C22×C53—81no—
520C22×C53—81no—
521C22×C53—81no—
522C22×C53—81no—
523C22×C53C22×C22⋊C411yescharacteristic
524C22×C53C2×C4×D411yescharacteristic
525C22×C53C4×#4111yescharacteristic
526C22×C53C4×#4111yescharacteristic
527C22×C53C4×#4111yescharacteristic
528C22×C53#51811yescharacteristic
529C22×C53#52011yescharacteristic
530C22×C53C2×#12311yescharacteristic
531C22×C53#52511yescharacteristic
532C22×C53#52511yescharacteristic
533C22×C53#52511yescharacteristic
534C22×C53#52911yescharacteristic
535C22×C53#52911yescharacteristic
536C22×C53#53211yescharacteristic
537C22×C53#53211yescharacteristic
538C22×C53#53811yescharacteristic
539C22×C53#53911yescharacteristic
540C22×C53#54011yescharacteristic
541C22×C53#54211yescharacteristic
542C22×C53D4211yescharacteristic
543C22×C53D4211yescharacteristic
544C22×C53#54611yescharacteristic
545C22×C53#54611yescharacteristic
546C22×C53#54611yescharacteristic
547C22×C53#54711yescharacteristic
548C22×C53#54811yescharacteristic
549C22×C53#54811yescharacteristic
550C22×C53#55011yescharacteristic
551C22×C53#55011yescharacteristic
552C22×C53#55111yescharacteristic
553C22×C53#55111yescharacteristic
554C22×C53#55211yescharacteristic
555C22×C53#55311yescharacteristic
556C22×C53#55311yescharacteristic
557C22×C53#55911yescharacteristic
558C4×C53—24no—
559C4×C53—24no—
560C4×C53—42no—
561C4×C53—42no—
562C4×C53—81no—
563Dic53—24no—
564Dic53—24no—
565Dic53—42no—
566Dic53—42no—
567Dic53—42no—
568Dic53—42no—
569Dic53—42no—
570Dic53—81no—
571C22×#123—531no—
572C2×#390D5311yescharacteristic
573C2×#387—531no—
574C2×C4×C4⋊C4—531no—
575C2×C4×C22⋊C4—531no—
576#1441—531no—
577#1439—531no—
578#1439—531no—
579#1438—531no—
580#1437—531no—
581#1437—531no—
582#1437—531no—
583#1437—531no—
584#1436—531no—
585C22⋊#95—531no—
586C2×C53—44no—
587C2×C53—82no—
588C2×C53#229711yescharacteristic
589C2×C53C4×#12311yescharacteristic
590C2×C53#233511yescharacteristic
591C2×C53D4×C22⋊C411yescharacteristic
592C2×C53#234111yescharacteristic
593C2×C53#235911yescharacteristic
594C2×C53#237411yescharacteristic
595C2×C53#244311yescharacteristic
596C2×C53#244511yescharacteristic
597C2×C53#245611yescharacteristic
598C2×C53#245811yescharacteristic
599C2×C53#246111yescharacteristic
600C2×C53#247111yescharacteristic
601C2×C53#255411yescharacteristic
602C2×C53#255811yescharacteristic
603C23×D4C2×D5311yescharacteristic
604C24×C4—531no—
605C2×#123—538no—
606C2×#123—1064no—
607C2×#123—1064no—
608C22×C4⋊C4—531no—
609C22×C4⋊C4—531no—
610C22×C4⋊C4—531no—
611C22×C4⋊C4C2×D5311yescharacteristic
612C22×C22⋊C4—531no—
613C22×C22⋊C4—531no—
614C22×C22⋊C4—531no—
615C22×C22⋊C4—531no—
616C22×C22⋊C4—531no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—531no—
619C22×C22⋊C4C2×D5311yescharacteristic
620C22×C22⋊C4C2×D5311yescharacteristic
621C22×C22⋊C4C2×D5311yescharacteristic
622C22×C22⋊C4C2×D5311yescharacteristic
623C22×C42—531no—
624C22×C42—531no—
625C22×C42—531no—
626C22×C42C2×D5311yescharacteristic
627#390—24no—
628#387—1064no—
629C4×C4⋊C4—1064no—
630C4×C22⋊C4—1064no—
631C2×#95—531no—
632C2×#95—531no—
633C2×#95—531no—
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—
645C53#1409511yescharacteristic, complemented, Sylow
646C25C22×D5311yescharacteristic
647C25C22×D5311yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C4×D5314yes—
655C23×C4—531no—
656C23×C4—531no—
657C23×C4—531no—
658C23×C4—531no—
659C23×C4—531no—
660C23×C4—531no—
661C23×C4—531no—
662C23×C4—534no—
663C23×C4—531no—
664C23×C4—1062no—
665C23×C4—1062no—
666C23×C4—1062no—
667C23×C4—1062no—
668C23×C4—2121no—
669C23×C4—2121no—
670C23×C4C22×D5311yescharacteristic
671C23×C4C22×D5311yescharacteristic
672C23×C4C22×D5311yescharacteristic
673C23×C4C22×D5311yescharacteristic
674C23×C4C22×D5311yescharacteristic
675#123—10632no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—534no—
680C2×C4⋊C4—534no—
681C2×C4⋊C4—534no—
682C2×C4⋊C4—534no—
683C2×C4⋊C4—1062no—
684C2×C4⋊C4—1062no—
685C2×C4⋊C4—1062no—
686C2×C4⋊C4—1062no—
687C2×C4⋊C4—1062no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
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—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—534no—
700C2×C22⋊C4—534no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—1062no—
703C2×C22⋊C4—1062no—
704C2×C22⋊C4—1062no—
705C2×C22⋊C4—1062no—
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—2121no—
717C2×C22⋊C4—2121no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4C22⋊D5314yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—41no—
724C2×C42—1062no—
725C2×C42—1062no—
726C2×C42—1062no—
727C2×C42—1062no—
728C2×C42—1062no—
729C2×C42—1062no—
730C2×C42—1062no—
731C2×C42—2121no—
732C2×C42—2121no—
733#95—1062no—
734#95—1062no—
735#95—1062no—
736#95—1062no—
737#95—1062no—
738#95—1062no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—2121no—
744#95—2121no—
745#95—2121no—
746#95—2121no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
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—
773C24C2×C4×D5312yes—
774C24C2×C4×D5312yes—
775C24#1171994512yes—
776C24C2×C22⋊D5312yes—
777C24C23×D5311yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—532no—
813C22×C4—532no—
814C22×C4—532no—
815C22×C4—532no—
816C22×C4—532no—
817C22×C4—532no—
818C22×C4—532no—
819C22×C4—532no—
820C22×C4—532no—
821C22×C4—532no—
822C22×C4—532no—
823C22×C4—1068no—
824C22×C4—1061no—
825C22×C4—1061no—
826C22×C4—1061no—
827C22×C4—1061no—
828C22×C4—1061no—
829C22×C4—1061no—
830C22×C4—1061no—
831C22×C4—1061no—
832C22×C4—1068no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
841C22×C4—1061no—
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—2124no—
871C22×C4—2124no—
872C22×C4—2124no—
873C22×C4—2124no—
874C22×C4—2124no—
875C22×C4C2×C4×D5312yes—
876C22×C4D4×D5312yes—
877C22×C4D4×D5312yes—
878C22×C4#1171994712yes—
879C22×C4#1171994712yes—
880C22×C4#1171994712yes—
881C22×C4C2×C22⋊D5312yes—
882C22×C4C2×C22⋊D5312yes—
883C4⋊C4—44no—
884C4⋊C4—5316no—
885C4⋊C4—1068no—
886C4⋊C4—1068no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—1068no—
892C22⋊C4—1068no—
893C22⋊C4—1068no—
894C22⋊C4—1068no—
895C22⋊C4—2124no—
896C22⋊C4—2124no—
897C22⋊C4—2124no—
898C42—44no—
899C42—1068no—
900C42—2124no—
901C42—2124no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
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—
971C23C4×C22⋊D5314yes—
972C23C22×C4×D5311yescharacteristic
973C23C2×D4×D5311yescharacteristic
974C23C2×D4×D5311yescharacteristic
975C23C22×C22⋊D5311yescharacteristic
976C23#41×D5311yescharacteristic
977C23#41×D5311yescharacteristic
978C23#41×D5311yescharacteristic
979C23C2×#1171994711yescharacteristic
980C23C2×#1171994711yescharacteristic
981C23C2×#1171994711yescharacteristic
982C23C2×#1171994511yescharacteristic
983C23#1313326211yescharacteristic
984C23#1313326211yescharacteristic
985C23#1313326211yescharacteristic
986C23#1313326411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
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—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—534no—
1022C2×C4—534no—
1023C2×C4—1062no—
1024C2×C4—1062no—
1025C2×C4—1062no—
1026C2×C4—1062no—
1027C2×C4—1062no—
1028C2×C4—1062no—
1029C2×C4—1062no—
1030C2×C4—1062no—
1031C2×C4—1062no—
1032C2×C4—1062no—
1033C2×C4—1062no—
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—21216no—
1051C2×C4—2121no—
1052C2×C4—2121no—
1053C2×C4—2121no—
1054C2×C4—2121no—
1055C2×C4—2121no—
1056C2×C4—2121no—
1057C2×C4—2121no—
1058C2×C4—2121no—
1059C2×C4—2121no—
1060C2×C4—2121no—
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×C4C22⋊C4×D5314yes—
1079C2×C4#1313319814yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C22⋊C4×D5311yescharacteristic
1111C22C2×C4×C22⋊D5311yescharacteristic
1112C22C4×#1171994711yescharacteristic
1113C22C4×#1171994711yescharacteristic
1114C22C4×#1171994711yescharacteristic
1115C22#1681109611yescharacteristic
1116C22#1681110211yescharacteristic
1117C22C2×#1313319811yescharacteristic
1118C22#1681113011yescharacteristic
1119C22#1681113311yescharacteristic
1120C22#1681113311yescharacteristic
1121C22#1681115311yescharacteristic
1122C22#1681115311yescharacteristic
1123C22#1681117111yescharacteristic
1124C22#1681117211yescharacteristic
1125C22#1681120511yescharacteristic
1126C22#1681121811yescharacteristic
1127C22#1681122711yescharacteristic
1128C22#1681123711yescharacteristic
1129C22D4×C22⋊D5311yescharacteristic
1130C22D4×C22⋊D5311yescharacteristic
1131C22#1681126311yescharacteristic
1132C22#1681126311yescharacteristic
1133C22#1681126711yescharacteristic
1134C22#1681127211yescharacteristic
1135C22#1681127911yescharacteristic
1136C22#1681128111yescharacteristic
1137C22#1681129111yescharacteristic
1138C22#1681129311yescharacteristic
1139C22#1681130211yescharacteristic
1140C22#1681130311yescharacteristic
1141C22#1681131311yescharacteristic
1142C22#1681131611yescharacteristic
1143C22#1681131611yescharacteristic
1144C22#1681135911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—1064no—
1151C4—1064no—
1152C4—4241no—
1153C4—2122no—
1154C4—2122no—
1155C4—2122no—
1156C4—2122no—
1157C4—2122no—
1158C2—44no—
1159C2—82no—
1160C2#2027720211yescharacteristic
1161C2C4×#1313319811yescharacteristic
1162C2#2027750211yescharacteristic
1163C2C22⋊C4×C22⋊D5311yescharacteristic
1164C2#2027755411yescharacteristic
1165C2#2027770111yescharacteristic
1166C2#2027785011yescharacteristic
1167C2#2027844611yescharacteristic
1168C2#2027847611yescharacteristic
1169C2#2027861211yescharacteristic
1170C2#2027864211yescharacteristic
1171C2#2027867811yescharacteristic
1172C2#2027883111yescharacteristic
1173C2#2027978011yescharacteristic
1174C2#2027983411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#390C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#390D53
hypocenterC53#14095
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16810504C2semidirect
3. C2×C4×#11719919C2semidirect
4. C2×C22⋊C4×Dic53C2semidirect
5. #20272965C2semidirect
6. #20272958C2semidirect
7. #20272958C2semidirect
9. #20272952C2semidirect
10. #20272952C2semidirect
11. #20272952C2semidirect
12. #20272952C2semidirect
13. #20272948C2semidirect
14. #20272937C2semidirect
19. C2×#13133198C4semidirect
310. #11719919C22⋊C4semidirect
434. C2×C4×C53#123semidirect
645. C53#14095semidirect
1079. C2×C4#13133198semidirect

Maximal subgroups

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

subgroupindex
C22×#131331982
C2×#168105042
C2×C4×#117199192
C2×C22⋊C4×Dic532
#202729652
#202729582
#202729562
#202729522
#202729482
#202729372
C2×C53×#3902
#1409553