Finite Group Databasebeta

← #27312265

Subgroups — #27312265

Order 13568.

2126 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
1C2×#16810530C211yesmaximal, characteristic, complemented
2C2×#16810516C211yesmaximal, characteristic, complemented
3C2×#16810503C211yesmaximal, characteristic
4C2×#16810498C211yesmaximal, characteristic, complemented
5#20272986C211yesmaximal, characteristic, complemented
6#20272964C211yesmaximal, characteristic, complemented
7#20272960C211yesmaximal, characteristic, complemented
8#20272960C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic, complemented
10#20272956C211yesmaximal, characteristic
11#20272952C211yesmaximal, characteristic, complemented
12#20272945C211yesmaximal, characteristic, complemented
13#20272942C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C22×#124×C53C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810530—24no—
29#16810516—24no—
30#16810503—24no—
31#16810498—24no—
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
47C2×#13133124C2211yescharacteristic
48C23×Q8×C53C2211yescharacteristic
49C23×D4×C53C2211yescharacteristic
50C2×#124×C53—24no—
51C2×#124×C53—24no—
52C2×#124×C53C418yescomplemented
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C22×C42×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—41no—
62C23×Dic53—41no—
63C23×Dic53—41no—
64C23×Dic53—41no—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53—41no—
81C2×C4⋊Dic53—41no—
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⋊Dic53—41no—
96C2×C22⋊Dic53—41no—
97C2×C22⋊Dic53—41no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C22⋊Dic53—41no—
102C2×C22⋊Dic53—41no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—41no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—41no—
116#13133124—41no—
117#13133124—41no—
118#13133124—41no—
119#13133124—41no—
120#13133124—41no—
121#13133124D414yes—
122C25×C53C2311yescharacteristic
123C25×C53C2311yescharacteristic
124C22×Q8×C53—22no—
125C22×Q8×C53—22no—
126C22×Q8×C53—22no—
127C22×Q8×C53—22no—
128C22×Q8×C53—41no—
129C22×Q8×C53—41no—
130C22×Q8×C53C2×C414yescomplemented
131C22×D4×C53—22no—
132C22×D4×C53—22no—
133C22×D4×C53—22no—
134C22×D4×C53—22no—
135C22×D4×C53—41no—
136C22×D4×C53—41no—
137C22×D4×C53C2×C414yes—
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143#124×C53—232no—
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×C53C2×C414yes—
151C2×C22⋊C4×C53C2×C414yes—
152C2×C22⋊C4×C53C2×C414yescomplemented
153C2×C22⋊C4×C53C2×C414yescomplemented
154C2×C22⋊C4×C53D414yes—
155C2×C22⋊C4×C53D414yes—
156C2×C42×C53—22no—
157C2×C42×C53—22no—
158C2×C42×C53C2×C414yescomplemented
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×Q8×C53—28no—
191C2×Q8×C53—28no—
192C2×Q8×C53—44no—
193C2×Q8×C53—44no—
194C2×Q8×C53—44no—
195C2×Q8×C53—44no—
196C2×Q8×C53—44no—
197C2×D4×C53—28no—
198C2×D4×C53—28no—
199C2×D4×C53—44no—
200C2×D4×C53—44no—
201C2×D4×C53—44no—
202C2×D4×C53—44no—
203C2×D4×C53—44no—
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×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53C22×C412yes—
229C22×C4×C53C22×C412yes—
230C22×C4×C53C22×C412yes—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C22×C412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53C2×D412yes—
237C22×C4×C53C2×D412yes—
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×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—44no—
292C22×Dic53—44no—
293C22×Dic53—44no—
294C22×Dic53—44no—
295C22×Dic53—44no—
296C22×Dic53—44no—
297C22×Dic53—44no—
298C22×Dic53C2×D412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53#4112yes—
301C22×Dic53#4112yes—
302C22⋊C4×C53—28no—
303C22⋊C4×C53—28no—
304C22⋊C4×C53—28no—
305C22⋊C4×C53C22⋊C4116yescomplemented
306C42×C53—28no—
307C22⋊Dic53—44no—
308C22⋊Dic53—44no—
309C22⋊Dic53—44no—
310C22⋊Dic53—44no—
311C22⋊Dic53—44no—
312C22⋊Dic53—44no—
313C22⋊Dic53—44no—
314C4⋊Dic53—44no—
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×C53H(5,𝔽2)11yescharacteristic
396C23×C53H(5,𝔽2)11yescharacteristic
397C23×C53H(5,𝔽2)11yescharacteristic
398C23×C53H(5,𝔽2)11yescharacteristic
399C23×C53H(5,𝔽2)11yescharacteristic
400C23×C532−1+411yescharacteristic
401C23×C532−1+411yescharacteristic
402C23×C532−1+411yescharacteristic
403Q8×C53—416no—
404D4×C53—416no—
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—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
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×C53C2×C22⋊C414yes—
438C2×C4×C53C2×C22⋊C414yes—
439C2×C4×C53C4×D414yes—
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—416no—
453C2×Dic53—41no—
454C2×Dic53—41no—
455C2×Dic53—41no—
456C2×Dic53—41no—
457C2×Dic53—41no—
458C2×Dic53—41no—
459C2×Dic53—41no—
460C2×Dic53—41no—
461C2×Dic53—41no—
462C2×Dic53—41no—
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×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C2×Dic53—41no—
496C2×Dic53—41no—
497#14421—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×C53#51811yescharacteristic
532C22×C53#52011yescharacteristic
533C22×C53#52011yescharacteristic
534C22×C53#52011yescharacteristic
535C22×C53#53511yescharacteristic
536C22×C53#53511yescharacteristic
537C22×C53#53611yescharacteristic
538C22×C53#53611yescharacteristic
539C22×C53#53711yescharacteristic
540C22×C53#53711yescharacteristic
541C22×C53#53811yescharacteristic
542C22×C53#53811yescharacteristic
543C22×C53#54211yescharacteristic
544C22×C53#54211yescharacteristic
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#55611yescharacteristic
558C22×C53#55911yescharacteristic
559C22×C53H(3,𝔽4)11yescharacteristic
560C22×C53#56211yescharacteristic
561C22×C53#56211yescharacteristic
562C22×C53#56311yescharacteristic
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—24no—
566C4×C53—42no—
567C4×C53—42no—
568Dic53—42no—
569Dic53—42no—
570Dic53—42no—
571Dic53—42no—
572Dic53—81no—
573Dic53—81no—
574Dic53—81no—
575Dic53—81no—
576C22×#124D5311yescharacteristic
577C2×#391—531no—
578C2×#388—531no—
579C2×#386—531no—
580C2×#385—531no—
581#1446—531no—
582#1440—531no—
583#1439—531no—
584#1439—531no—
585#1439—531no—
586#1438—531no—
587#1437—531no—
588C4⋊#95—531no—
589#1434—531no—
590C22⋊#95—531no—
591C2×C53—44no—
592C2×C53—82no—
593C2×C53#231111yescharacteristic
594C2×C53#232611yescharacteristic
595C2×C53#233711yescharacteristic
596C2×C53D4×C22⋊C411yescharacteristic
597C2×C53#233911yescharacteristic
598C2×C53#236711yescharacteristic
599C2×C53#237911yescharacteristic
600C2×C53#267011yescharacteristic
601C2×C53#267211yescharacteristic
602C2×C53#267411yescharacteristic
603C2×C53#267611yescharacteristic
604C2×C53#270011yescharacteristic
605C2×C53#271011yescharacteristic
606C2×C53#271211yescharacteristic
607C2×C53#271511yescharacteristic
608C23×Q8C2×D5311yescharacteristic
609C23×D4C2×D5311yescharacteristic
610C24×C4—531no—
611C2×#124—24no—
612C2×#124—24no—
613C2×#124Dic5318yescomplemented
614C22×C4⋊C4—531no—
615C22×C4⋊C4—531no—
616C22×C4⋊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⋊C4—531no—
624C22×C22⋊C4C2×D5311yescharacteristic
625C22×C22⋊C4C2×D5311yescharacteristic
626C22×C22⋊C4C2×D5311yescharacteristic
627C22×C22⋊C4C2×D5311yescharacteristic
628C22×C42—531no—
629C22×C42C2×D5311yescharacteristic
630#391—1064no—
631#388—1064no—
632#386—1064no—
633#385—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×#95—531no—
649C2×#95—531no—
650C53#1442111yescharacteristic, complemented, Sylow
651C25C22×D5311yescharacteristic
652C25C22×D5311yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×Dic5314yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×Dic5314yes—
667C23×C4—531no—
668C23×C4—531no—
669C23×C4—531no—
670C23×C4—531no—
671C23×C4—531no—
672C23×C4—531no—
673C23×C4—531no—
674C23×C4—531no—
675C23×C4—1062no—
676C23×C4—1062no—
677C23×C4—1062no—
678C23×C4—2121no—
679C23×C4—2121no—
680C23×C4—2121no—
681C23×C4—2121no—
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686C23×C4C22×D5311yescharacteristic
687#124—232no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—1062no—
691C2×C4⋊C4—1062no—
692C2×C4⋊C4—1062no—
693C2×C4⋊C4—1062no—
694C2×C4⋊C4—2121no—
695C2×C4⋊C4—2121no—
696C2×C4⋊C4—2121no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
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—2121no—
713C2×C22⋊C4—2121no—
714C2×C22⋊C4—2121no—
715C2×C22⋊C4—2121no—
716C2×C22⋊C4—2121no—
717C2×C22⋊C4—2121no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4—2121no—
721C2×C22⋊C4—2121no—
722C2×C22⋊C4—2121no—
723C2×C22⋊C4—2121no—
724C2×C22⋊C4C2×Dic5314yes—
725C2×C22⋊C4C2×Dic5314yes—
726C2×C22⋊C4C2×Dic5314yescomplemented
727C2×C22⋊C4C2×Dic5314yescomplemented
728C2×C22⋊C4C22⋊D5314yes—
729C2×C22⋊C4C22⋊D5314yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—1062no—
733C2×C42—1062no—
734C2×C42—2121no—
735C2×C42C2×Dic5314yescomplemented
736#95—534no—
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—2121no—
747#95—2121no—
748#95—2121no—
749#95—2121no—
750#95—2121no—
751#95—2121no—
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—
778C24C22×Dic5312yes—
779C24C22×Dic5312yes—
780C24C2×C22⋊D5312yes—
781C24C2×C22⋊D5312yes—
782C24C23×D5311yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
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—21no—
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—532no—
822C22×C4—532no—
823C22×C4—532no—
824C22×C4—532no—
825C22×C4—1061no—
826C22×C4—1061no—
827C22×C4—1061no—
828C22×C4—1061no—
829C22×C4—1061no—
830C22×C4—1061no—
831C22×C4—1061no—
832C22×C4—1061no—
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—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—2124no—
878C22×C4—2124no—
879C22×C4—2124no—
880C22×C4—2124no—
881C22×C4—2124no—
882C22×C4—2124no—
883C22×C4—2124no—
884C22×C4D4×D5312yes—
885C22×C4#1171994712yes—
886C22×C4C22×Dic5312yes—
887C22×C4C22×Dic5312yes—
888C22×C4C22×Dic5312yes—
889C22×C4C22×Dic5312yes—
890C22×C4C22×Dic5312yes—
891C22×C4C2×C22⋊D5312yes—
892C22×C4C2×C22⋊D5312yes—
893C22×C4C2×C22⋊D5312yes—
894C22×C4C2×C22⋊D5312yes—
895C4⋊C4—2124no—
896C4⋊C4—2124no—
897C4⋊C4—2124no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—2124no—
902C22⋊C4—2124no—
903C22⋊C4—2124no—
904C22⋊C4—2124no—
905C22⋊C4—2124no—
906C22⋊C4—2124no—
907C22⋊C4—2124no—
908C22⋊C4C22⋊Dic53116yescomplemented
909C42—28no—
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—
980C23C2×C22⋊Dic5314yes—
981C23C23×Dic5311yescharacteristic
982C23C2×D4×D5311yescharacteristic
983C23C22×C22⋊D5311yescharacteristic
984C23C22×C22⋊D5311yescharacteristic
985C23#41×D5311yescharacteristic
986C23#41×D5311yescharacteristic
987C23C2×#1171994711yescharacteristic
988C23#1313326211yescharacteristic
989C23#1313326211yescharacteristic
990C23#1313326311yescharacteristic
991C23#1313326311yescharacteristic
992C23#1313326311yescharacteristic
993C23#1313326411yescharacteristic
994C23#1313326411yescharacteristic
995C23#1313326411yescharacteristic
996Q8—416no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
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—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—2121no—
1043C2×C4—2121no—
1044C2×C4—2121no—
1045C2×C4—2121no—
1046C2×C4—2121no—
1047C2×C4—2121no—
1048C2×C4—2121no—
1049C2×C4—2121no—
1050C2×C4—2121no—
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—21216no—
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×C4C2×C22⋊Dic5314yes—
1088C2×C4C2×C22⋊Dic5314yes—
1089C2×C4D4×Dic5314yes—
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—
1120C22C22×C22⋊Dic5311yescharacteristic
1121C22C2×D4×Dic5311yescharacteristic
1122C22#41×Dic5311yescharacteristic
1123C22#1681109811yescharacteristic
1124C22#1681110611yescharacteristic
1125C22#1681110611yescharacteristic
1126C22#1681110611yescharacteristic
1127C22#1681118711yescharacteristic
1128C22#1681119111yescharacteristic
1129C22#1681119311yescharacteristic
1130C22#1681119411yescharacteristic
1131C22#1681120111yescharacteristic
1132C22#1681120111yescharacteristic
1133C22#1681120711yescharacteristic
1134C22#1681120711yescharacteristic
1135C22#1681123711yescharacteristic
1136C22#1681123711yescharacteristic
1137C22#1681124211yescharacteristic
1138C22#1681124211yescharacteristic
1139C22D4×C22⋊D5311yescharacteristic
1140C22D4×C22⋊D5311yescharacteristic
1141C22#1681126111yescharacteristic
1142C22#1681126111yescharacteristic
1143C22#1681126611yescharacteristic
1144C22#1681126711yescharacteristic
1145C22#1681126711yescharacteristic
1146C22#1681127211yescharacteristic
1147C22#1681127211yescharacteristic
1148C22#1681128111yescharacteristic
1149C22#1681134211yescharacteristic
1150C22#1681135511yescharacteristic
1151C22#1681136511yescharacteristic
1152C22#1681136711yescharacteristic
1153C22#1681136711yescharacteristic
1154C22#1681137311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—4241no—
1161C4—4241no—
1162C4—4241no—
1163C4—4241no—
1164C4—2122no—
1165C4—2122no—
1166C4—2122no—
1167C4—2122no—
1168C2—44no—
1169C2—82no—
1170C2#2027730711yescharacteristic
1171C2#2027742811yescharacteristic
1172C2#2027753011yescharacteristic
1173C2D4×C22⋊Dic5311yescharacteristic
1174C2#2027754511yescharacteristic
1175C2#2027779011yescharacteristic
1176C2#2027788911yescharacteristic
1177C2#2028093611yescharacteristic
1178C2#2028096111yescharacteristic
1179C2#2028099011yescharacteristic
1180C2#2028101111yescharacteristic
1181C2#2028130711yescharacteristic
1182C2#2028145111yescharacteristic
1183C2#2028148111yescharacteristic
1184C2#2028152011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#124×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×#124D53
hypocenterC53#14421
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16810530C2semidirect
2. C2×#16810516C2semidirect
4. C2×#16810498C2semidirect
5. #20272986C2semidirect
6. #20272964C2semidirect
7. #20272960C2semidirect
8. #20272960C2semidirect
9. #20272960C2semidirect
11. #20272952C2semidirect
12. #20272945C2semidirect
13. #20272942C2semidirect
14. #20272937C2semidirect
52. C2×#124×C53C4semidirect
130. C22×Q8×C53C2×C4semidirect
152. C2×C22⋊C4×C53C2×C4semidirect
153. C2×C22⋊C4×C53C2×C4semidirect
158. C2×C42×C53C2×C4semidirect
305. C22⋊C4×C53C22⋊C4semidirect
613. C2×#124Dic53semidirect
650. C53#14421semidirect
659. C22×Q8C2×Dic53semidirect
726. C2×C22⋊C4C2×Dic53semidirect
727. C2×C22⋊C4C2×Dic53semidirect
735. C2×C42C2×Dic53semidirect
908. C22⋊C4C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105302
C2×#168105162
C2×#168105032
C2×#168104982
#202729862
#202729642
#202729602
#202729562
#202729522
#202729452
#202729422
#202729372
C22×#124×C532
#1442153