Finite Group Databasebeta

← #27306299

Subgroups — #27306299

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810490C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic53C211yesmaximal, characteristic
3C22×#13133124C211yesmaximal, characteristic
4#20272976C211yesmaximal, characteristic, complemented
5#20272976C211yesmaximal, characteristic, complemented
6#20272975C211yesmaximal, characteristic, complemented
7#20272975C211yesmaximal, characteristic, complemented
8#20272941C211yesmaximal, characteristic, complemented
9#20272940C211yesmaximal, characteristic, complemented
10#20272939C211yesmaximal, characteristic, complemented
11#20272938C211yesmaximal, characteristic
12#20272937C211yesmaximal, characteristic
13#20272937C211yesmaximal, characteristic
14#20272937C211yesmaximal, characteristic
15C53×C22⋊#95C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C4×Dic53C2211yescharacteristic
21C22×C4×Dic53C2211yescharacteristic
22#16810490—24no—
23C22⋊C4×Dic53C418yescomplemented
24C2×#13133124—24no—
25C2×#13133124C2211yescharacteristic
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C24×C4×C53C2211yescharacteristic
48C22×C22⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C23×Dic53—22no—
55C23×Dic53—22no—
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—41no—
64C23×Dic53—41no—
65C23×Dic53—41no—
66C23×Dic53—41no—
67C23×Dic53C2×C414yes—
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—22no—
78C2×C22⋊Dic53—22no—
79C2×C22⋊Dic53—22no—
80C2×C22⋊Dic53—22no—
81C2×C22⋊Dic53C2×C414yes—
82C2×C4×Dic53—22no—
83C2×C4×Dic53—22no—
84C2×C4×Dic53—41no—
85C2×C4×Dic53—41no—
86C2×C4×Dic53C2×C414yescomplemented
87C2×C4×Dic53C2×C414yescomplemented
88#13133124—22no—
89#13133124—22no—
90#13133124—22no—
91#13133124—22no—
92#13133124—22no—
93#13133124—22no—
94#13133124—22no—
95#13133124—22no—
96#13133124—22no—
97#13133124—22no—
98#13133124—22no—
99#13133124—41no—
100#13133124—41no—
101#13133124—41no—
102#13133124—41no—
103#13133124—41no—
104#13133124—41no—
105#13133124—41no—
106#13133124—41no—
107#13133124C2×C414yescomplemented
108#13133124C2×C414yescomplemented
109#13133124D414yes—
110C25×C53C2311yescharacteristic
111C23×C4×C53—22no—
112C23×C4×C53—22no—
113C23×C4×C53—22no—
114C23×C4×C53—22no—
115C23×C4×C53—22no—
116C23×C4×C53—41no—
117C23×C4×C53—41no—
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—22no—
125C2×C22⋊C4×C53—22no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53C2×C414yes—
130#95×C53—22no—
131#95×C53—22no—
132#95×C53—41no—
133#95×C53—41no—
134C24×C53—21no—
135C24×C53—21no—
136C24×C53—21no—
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53C22×C412yes—
143C24×C53#4112yes—
144C24×C53#4112yes—
145C24×C53#4112yes—
146C24×C53#4112yes—
147C24×C53#4112yes—
148C24×C53#4112yes—
149C24×C53C2411yescharacteristic
150C22×C4×C53—28no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—44no—
190C22×C4×C53—44no—
191C22×C4×C53—44no—
192C22×C4×C53—44no—
193C22×C4×C53—44no—
194C22×C4×C53—44no—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C22×C412yes—
197C22×C4×C53C2×D412yes—
198C22×C4×C53#4112yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—28no—
204C22×Dic53—28no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—28no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
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—44no—
251C22×Dic53—44no—
252C22×Dic53—44no—
253C22×Dic53—44no—
254C22×Dic53—44no—
255C22×Dic53—44no—
256C22×Dic53—44no—
257C22×Dic53—44no—
258C22×Dic53—44no—
259C22×Dic53—44no—
260C22×Dic53—44no—
261C22×Dic53C22×C412yes—
262C22×Dic53C22×C412yes—
263C22×Dic53C22×C412yes—
264C22×Dic53C22×C412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×D412yes—
267C22×Dic53#4112yes—
268C22×Dic53#4112yes—
269C22⋊C4×C53—28no—
270C22⋊C4×C53—44no—
271C22⋊Dic53—28no—
272C22⋊Dic53—44no—
273C4×Dic53—28no—
274C4×Dic53—44no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53#11714yes—
304C23×C53#11714yes—
305C23×C53#11714yes—
306C23×C53#12614yes—
307C23×C53#12614yes—
308C23×C53#12614yes—
309C23×C53#12614yes—
310C23×C53C23×C411yescharacteristic
311C23×C53C22×D411yescharacteristic
312C23×C53C2×#4111yescharacteristic
313C23×C53C2×#4111yescharacteristic
314C23×C53C2×#4111yescharacteristic
315C23×C53C2×#4111yescharacteristic
316C23×C53C2×#4111yescharacteristic
317C23×C53C2×#4111yescharacteristic
318C23×C53C2×#4111yescharacteristic
319C23×C53C2×#4111yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53H(5,𝔽2)11yescharacteristic
322C23×C53H(5,𝔽2)11yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C532−1+411yescharacteristic
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—416no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—416no—
390C2×Dic53—416no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53C4×D414yes—
426#13901—531nomaximal, Sylow
427C22×C53—24no—
428C22×C53—24no—
429C22×C53—24no—
430C22×C53—24no—
431C22×C53—24no—
432C22×C53—24no—
433C22×C53—24no—
434C22×C53—24no—
435C22×C53—24no—
436C22×C53—24no—
437C22×C53—24no—
438C22×C53—24no—
439C22×C53—24no—
440C22×C53—24no—
441C22×C53#38318yescomplemented
442C22×C53C2×#11711yescharacteristic
443C22×C53C2×#11711yescharacteristic
444C22×C53C2×#11711yescharacteristic
445C22×C53C2×C4×D411yescharacteristic
446C22×C53C4×#4111yescharacteristic
447C22×C53#51811yescharacteristic
448C22×C53#52011yescharacteristic
449C22×C53#52511yescharacteristic
450C22×C53#52511yescharacteristic
451C22×C53C2×#12611yescharacteristic
452C22×C53C2×#12611yescharacteristic
453C22×C53C2×#12611yescharacteristic
454C22×C53C2×#12611yescharacteristic
455C22×C53#52911yescharacteristic
456C22×C53#52911yescharacteristic
457C22×C53#53811yescharacteristic
458C22×C53#53811yescharacteristic
459C22×C53#53911yescharacteristic
460C22×C53#53911yescharacteristic
461C22×C53#54611yescharacteristic
462C22×C53#54611yescharacteristic
463C22×C53#54611yescharacteristic
464C22×C53#54811yescharacteristic
465C22×C53#55111yescharacteristic
466C22×C53#55111yescharacteristic
467C22×C53#55111yescharacteristic
468C22×C53#55111yescharacteristic
469C22×C53#55111yescharacteristic
470C22×C53#55111yescharacteristic
471C22×C53#55211yescharacteristic
472C22×C53#55211yescharacteristic
473C22×C53#55211yescharacteristic
474C22×C53#55311yescharacteristic
475C22×C53#55311yescharacteristic
476C22×C53#55311yescharacteristic
477C4×C53—42no—
478C4×C53—42no—
479C4×C53—42no—
480C4×C53—42no—
481C4×C53—81no—
482C4×C53—81no—
483Dic53—24no—
484Dic53—42no—
485Dic53—42no—
486Dic53—42no—
487Dic53—42no—
488Dic53—42no—
489Dic53—81no—
490Dic53—81no—
491C2×#383—531no—
492C2×C4×C22⋊C4—531no—
493C22×#95—531no—
494#1443—531no—
495#1443—531no—
496#1443—531no—
497#1443—531no—
498#1434—531no—
499#1434—531no—
500#1434—531no—
501C22⋊#95—531no—
502C22⋊#95—531no—
503C22⋊#95—531no—
504C22⋊#95—531no—
505C22⋊#95D5311yescharacteristic
506C2×C53—28no—
507C2×C53C2×#38311yescharacteristic
508C2×C53#229011yescharacteristic
509C2×C53#231811yescharacteristic
510C2×C53#234211yescharacteristic
511C2×C53#234311yescharacteristic
512C2×C53#235211yescharacteristic
513C2×C53#235311yescharacteristic
514C2×C53#248011yescharacteristic
515C2×C53#248011yescharacteristic
516C2×C53#248111yescharacteristic
517C2×C53#248111yescharacteristic
518C2×C53#249311yescharacteristic
519C2×C53#249311yescharacteristic
520C2×C53#251011yescharacteristic
521C2×C53#251011yescharacteristic
522C24×C4—531no—
523C24×C4—531no—
524C24×C4C2×D5311yescharacteristic
525C22×C22⋊C4—531no—
526C22×C22⋊C4—531no—
527C22×C22⋊C4C2×D5311yescharacteristic
528C22×C22⋊C4C2×D5311yescharacteristic
529C22×C42—531no—
530C22×C42—531no—
531#383—1064no—
532C4×C22⋊C4—538no—
533C2×#95—531no—
534C2×#95—531no—
535C2×#95—531no—
536C2×#95—531no—
537C2×#95—531no—
538C2×#95—531no—
539C2×#95—531no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—1064no—
556C2×#95C2×D5311yescharacteristic
557C2×#95C2×D5311yescharacteristic
558C2×#95C2×D5311yescharacteristic
559C2×#95C2×D5311yescharacteristic
560C53#1390111yescharacteristic, complemented, Sylow
561C25C22×D5311yescharacteristic
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—41no—
568C23×C4—41no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4—531no—
574C23×C4—531no—
575C23×C4—534no—
576C23×C4—531no—
577C23×C4—531no—
578C23×C4—1062no—
579C23×C4—1062no—
580C23×C4—1062no—
581C23×C4—1062no—
582C23×C4—1062no—
583C23×C4—1062no—
584C23×C4—1062no—
585C23×C4—1062no—
586C23×C4—1062no—
587C23×C4—2121no—
588C23×C4—2121no—
589C23×C4—2121no—
590C23×C4—2121no—
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C23×C4C22×D5311yescharacteristic
594C23×C4C22×D5311yescharacteristic
595C23×C4C22×D5311yescharacteristic
596C23×C4C22×D5311yescharacteristic
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—534no—
603C2×C22⋊C4—1062no—
604C2×C22⋊C4—1062no—
605C2×C22⋊C4—1062no—
606C2×C22⋊C4—1062no—
607C2×C22⋊C4—1062no—
608C2×C22⋊C4C4×D5314yes—
609C2×C42—534no—
610C2×C42—534no—
611C2×C42—1062no—
612C2×C42—1062no—
613C2×C42—2121no—
614C2×C42—2121no—
615#95—22no—
616#95—22no—
617#95—41no—
618#95—41no—
619#95—534no—
620#95—534no—
621#95—534no—
622#95—1062no—
623#95—1062no—
624#95—1062no—
625#95—1062no—
626#95—1062no—
627#95—1062no—
628#95—1062no—
629#95—1062no—
630#95—1062no—
631#95—1062no—
632#95—1062no—
633#95—2121no—
634#95—2121no—
635#95—2121no—
636#95—2121no—
637#95—2121no—
638#95—2121no—
639#95—2121no—
640#95—2121no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×C4×D5312yes—
650C24#1171994512yes—
651C24#1171994512yes—
652C24#1171994712yes—
653C24#1171994712yes—
654C24#1171994712yes—
655C24#1171994912yes—
656C24C23×D5311yescharacteristic
657C22×C4—28no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—1068no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1068no—
716C22×C4—1068no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—2124no—
762C22×C4—2124no—
763C22×C4—2124no—
764C22×C4—2124no—
765C22×C4—2124no—
766C22×C4—2124no—
767C22×C4—2124no—
768C22×C4—2124no—
769C22×C4—2124no—
770C22×C4—2124no—
771C22×C4—2124no—
772C22×C4C2×C4×D5312yes—
773C22×C4C2×C4×D5312yes—
774C22×C4D4×D5312yes—
775C22×C4#1171994712yes—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—1068no—
779C22⋊C4—2124no—
780C42—1068no—
781C42—2124no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23#1313317314yes—
811C23#1313317414yes—
812C23#1313317514yes—
813C23#1313321014yes—
814C23#1313321014yes—
815C23#1313321214yes—
816C23#1313321214yes—
817C23C22×C4×D5311yescharacteristic
818C23C2×D4×D5311yescharacteristic
819C23#41×D5311yescharacteristic
820C23#41×D5311yescharacteristic
821C23C2×#1171994711yescharacteristic
822C23C2×#1171994711yescharacteristic
823C23C2×#1171994711yescharacteristic
824C23C2×#1171994711yescharacteristic
825C23C2×#1171994511yescharacteristic
826C23C2×#1171994511yescharacteristic
827C23C2×#1171994911yescharacteristic
828C23#1313326211yescharacteristic
829C23#1313326211yescharacteristic
830C23#1313326311yescharacteristic
831C23#1313326411yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—416no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—534no—
876C2×C4—1062no—
877C2×C4—1062no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—1062no—
881C2×C4—1062no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—21216no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4—2121no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—21216no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22#1681049018yescomplemented
948C22C2×#1313317311yescharacteristic
949C22C2×#1313317411yescharacteristic
950C22C2×#1313317511yescharacteristic
951C22C4×D4×D5311yescharacteristic
952C22C4×#1171994711yescharacteristic
953C22#1681109511yescharacteristic
954C22#1681110211yescharacteristic
955C22#1681112911yescharacteristic
956C22#1681113311yescharacteristic
957C22C2×#1313321011yescharacteristic
958C22C2×#1313321011yescharacteristic
959C22C2×#1313321211yescharacteristic
960C22C2×#1313321211yescharacteristic
961C22#1681115011yescharacteristic
962C22#1681115411yescharacteristic
963C22#1681120811yescharacteristic
964C22#1681121011yescharacteristic
965C22#1681121711yescharacteristic
966C22#1681121811yescharacteristic
967C22#1681126011yescharacteristic
968C22#1681126311yescharacteristic
969C22#1681126411yescharacteristic
970C22#1681128211yescharacteristic
971C22#1681129611yescharacteristic
972C22#1681129711yescharacteristic
973C22#1681129911yescharacteristic
974C22#1681130011yescharacteristic
975C22#1681130011yescharacteristic
976C22#1681130411yescharacteristic
977C22#1681130611yescharacteristic
978C22#1681131011yescharacteristic
979C22#1681131511yescharacteristic
980C22#1681131911yescharacteristic
981C22#1681132211yescharacteristic
982C22#1681132211yescharacteristic
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C4—1064no—
990C4—4241no—
991C4—4241no—
992C4—2122no—
993C4—2122no—
994C4—2122no—
995C4—2122no—
996C4—2122no—
997C2—28no—
998C2C2×#1681049011yescharacteristic
999C2#2027715511yescharacteristic
1000C2#2027734111yescharacteristic
1001C2#2027756211yescharacteristic
1002C2#2027757311yescharacteristic
1003C2#2027763811yescharacteristic
1004C2#2027764911yescharacteristic
1005C2#2027895811yescharacteristic
1006C2#2027896611yescharacteristic
1007C2#2027897311yescharacteristic
1008C2#2027898111yescharacteristic
1009C2#2027910411yescharacteristic
1010C2#2027910611yescharacteristic
1011C2#2027927911yescharacteristic
1012C2#2027928111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22⋊#95D53
hypocenterC53#13901
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#16810490C2semidirect
4. #20272976C2semidirect
5. #20272976C2semidirect
6. #20272975C2semidirect
7. #20272975C2semidirect
8. #20272941C2semidirect
9. #20272940C2semidirect
10. #20272939C2semidirect
23. C22⋊C4×Dic53C4semidirect
86. C2×C4×Dic53C2×C4semidirect
87. C2×C4×Dic53C2×C4semidirect
107. #13133124C2×C4semidirect
108. #13133124C2×C4semidirect
441. C22×C53#383semidirect
560. C53#13901semidirect
947. C22#16810490semidirect

Maximal subgroups

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

subgroupindex
C2×#168104902
C2×C22⋊C4×Dic532
C22×#131331242
#202729762
#202729752
#202729412
#202729402
#202729392
#202729382
#202729372
C53×C22⋊#952
#1390153