Finite Group Databasebeta

← #27308547

Subgroups — #27308547

Order 13568.

2266 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×#16810516C211yesmaximal, characteristic, complemented
2C2×#16810503C211yesmaximal, characteristic
3C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20272983C211yesmaximal, characteristic, complemented
6#20272964C211yesmaximal, characteristic, complemented
7#20272960C211yesmaximal, characteristic, complemented
8#20272956C211yesmaximal, characteristic
9#20272952C211yesmaximal, characteristic, complemented
10#20272947C211yesmaximal, characteristic, complemented
11#20272947C211yesmaximal, characteristic, complemented
12#20272944C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C22×#123×C53C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810516—24no—
29#16810503—24no—
30C22⋊C4×Dic53—24no—
31C4×C22⋊Dic53—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×D4×C53C2211yescharacteristic
49C24×C4×C53C2211yescharacteristic
50C2×#123×C53—24no—
51C2×#123×C53—24no—
52C2×#123×C53C418yescomplemented
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C4⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C22×C22⋊C4×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
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—41no—
76C2×C22⋊Dic53—22no—
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—22no—
92C2×C22⋊Dic53—41no—
93C2×C22⋊Dic53—41no—
94C2×C22⋊Dic53—41no—
95C2×C22⋊Dic53—41no—
96C2×C22⋊Dic53D414yes—
97C2×C4×Dic53—22no—
98C2×C4×Dic53—22no—
99C2×C4×Dic53—22no—
100C2×C4×Dic53—22no—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—41no—
104C2×C4×Dic53—41no—
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—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—41no—
119#13133124—41no—
120#13133124—41no—
121#13133124—41no—
122C25×C53C2311yescharacteristic
123C25×C53C2311yescharacteristic
124C22×D4×C53—22no—
125C22×D4×C53—22no—
126C22×D4×C53—22no—
127C22×D4×C53—22no—
128C22×D4×C53—41no—
129C22×D4×C53—41no—
130C22×D4×C53C2×C414yes—
131C23×C4×C53—22no—
132C23×C4×C53—22no—
133C23×C4×C53—22no—
134C23×C4×C53—22no—
135C23×C4×C53—41no—
136C23×C4×C53—41no—
137C23×C4×C53C2×C414yescomplemented
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143#123×C53—232no—
144C2×C4⋊C4×C53—22no—
145C2×C4⋊C4×C53—22no—
146C2×C4⋊C4×C53—22no—
147C2×C4⋊C4×C53—22no—
148C2×C4⋊C4×C53C2×C414yescomplemented
149C2×C4⋊C4×C53C2×C414yescomplemented
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53C2×C414yes—
155C2×C22⋊C4×C53C2×C414yes—
156C2×C22⋊C4×C53C2×C414yescomplemented
157C2×C22⋊C4×C53D414yes—
158C2×C22⋊C4×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×C53C22×C412yes—
184C24×C53C22×C412yes—
185C24×C53C2×D412yes—
186C24×C53C2×D412yes—
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—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—28no—
225C22×C4×C53—44no—
226C22×C4×C53—44no—
227C22×C4×C53—44no—
228C22×C4×C53—44no—
229C22×C4×C53—44no—
230C22×C4×C53C22×C412yes—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C22×C412yes—
233C22×C4×C53C22×C412yes—
234C22×C4×C53C22×C412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53C2×D412yes—
237C22×C4×C53C2×D412yes—
238C22×C4×C53C2×D412yes—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—28no—
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—44no—
289C22×Dic53—44no—
290C22×Dic53—44no—
291C22×Dic53—44no—
292C22×Dic53—44no—
293C22×Dic53—44no—
294C22×Dic53C2×D412yes—
295C22×Dic53C2×D412yes—
296C22×Dic53#4112yes—
297C22×Dic53#4112yes—
298C22×Dic53#4112yes—
299C22×Dic53#4112yes—
300C22×Dic53#4112yes—
301C22×Dic53#4112yes—
302C4⋊C4×C53—28no—
303C4⋊C4×C53—28no—
304C22⋊C4×C53—28no—
305C22⋊C4×C53—28no—
306C22⋊C4×C53C22⋊C4116yescomplemented
307C22⋊Dic53—28no—
308C22⋊Dic53—28no—
309C22⋊Dic53—28no—
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—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
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×C53C2×C22⋊C414yes—
387C23×C53C4×D414yes—
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—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—416no—
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×C53C2×C22⋊C414yes—
439C2×C4×C53C2×C22⋊C414yes—
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—416no—
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#12314yescomplemented
497#14096—531nomaximal, Sylow
498C22×C53—24no—
499C22×C53—24no—
500C22×C53—24no—
501C22×C53—24no—
502C22×C53—24no—
503C22×C53—24no—
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—42no—
521C22×C53—42no—
522C22×C53—42no—
523C22×C53—42no—
524C22×C53—42no—
525C22×C53—42no—
526C22×C53—42no—
527C22×C53—42no—
528C22×C53C22×C22⋊C411yescharacteristic
529C22×C53C2×C4×D411yescharacteristic
530C22×C53C4×#4111yescharacteristic
531C22×C53C4×#4111yescharacteristic
532C22×C53C4×#4111yescharacteristic
533C22×C53#51811yescharacteristic
534C22×C53#52011yescharacteristic
535C22×C53C2×#12311yescharacteristic
536C22×C53#52511yescharacteristic
537C22×C53#52511yescharacteristic
538C22×C53#52511yescharacteristic
539C22×C53#52911yescharacteristic
540C22×C53#52911yescharacteristic
541C22×C53#53211yescharacteristic
542C22×C53#53211yescharacteristic
543C22×C53#53811yescharacteristic
544C22×C53#53911yescharacteristic
545C22×C53#54011yescharacteristic
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#54711yescharacteristic
557C22×C53#55111yescharacteristic
558C22×C53#55111yescharacteristic
559C22×C53#55211yescharacteristic
560C22×C53#55311yescharacteristic
561C22×C53#55311yescharacteristic
562C22×C53#55911yescharacteristic
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—42no—
566C4×C53—42no—
567C4×C53—42no—
568Dic53—24no—
569Dic53—42no—
570Dic53—42no—
571Dic53—42no—
572Dic53—42no—
573Dic53—42no—
574Dic53—81no—
575Dic53—81no—
576C22×#123D5311yescharacteristic
577C2×#388—531no—
578C2×#386—531no—
579C2×C4×C22⋊C4—531no—
580C2×C4×C22⋊C4—531no—
581#1445—531no—
582#1440—531no—
583#1439—531no—
584#1438—531no—
585#1437—531no—
586#1436—531no—
587#1436—531no—
588C4⋊#95—531no—
589C22⋊#95—531no—
590C22⋊#95—531no—
591C2×C53—44no—
592C2×C53—44no—
593C2×C53#229711yescharacteristic
594C2×C53C4×#12311yescharacteristic
595C2×C53#233511yescharacteristic
596C2×C53D4×C22⋊C411yescharacteristic
597C2×C53#233911yescharacteristic
598C2×C53#235911yescharacteristic
599C2×C53#237411yescharacteristic
600C2×C53#241811yescharacteristic
601C2×C53#242211yescharacteristic
602C2×C53#245511yescharacteristic
603C2×C53#245711yescharacteristic
604C2×C53#246411yescharacteristic
605C2×C53#247011yescharacteristic
606C2×C53#255311yescharacteristic
607C2×C53#255711yescharacteristic
608C23×D4C2×D5311yescharacteristic
609C24×C4—531no—
610C24×C4C2×D5311yescharacteristic
611C2×#123—24no—
612C2×#123—24no—
613C2×#123Dic5318yescomplemented
614C22×C4⋊C4—531no—
615C22×C4⋊C4C2×D5311yescharacteristic
616C22×C4⋊C4C2×D5311yescharacteristic
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×C42—531no—
628C22×C42—531no—
629C22×C42—531no—
630#388—1064no—
631#386—1064no—
632C4×C22⋊C4—1064no—
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×#95—531no—
649C2×#95—531no—
650C53#1409611yescharacteristic, complemented, Sylow
651C25C22×D5311yescharacteristic
652C25C22×D5311yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×Dic5314yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4—531no—
667C23×C4—531no—
668C23×C4—531no—
669C23×C4—531no—
670C23×C4—531no—
671C23×C4—531no—
672C23×C4—531no—
673C23×C4—531no—
674C23×C4—1062no—
675C23×C4—1062no—
676C23×C4—1062no—
677C23×C4—1062no—
678C23×C4—1062no—
679C23×C4—2121no—
680C23×C4—2121no—
681C23×C4C2×Dic5314yescomplemented
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686C23×C4C22×D5311yescharacteristic
687#123—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—1062no—
693C2×C4⋊C4—1062no—
694C2×C4⋊C4—2121no—
695C2×C4⋊C4C2×Dic5314yescomplemented
696C2×C4⋊C4C2×Dic5314yescomplemented
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
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—1062no—
717C2×C22⋊C4—1062no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4—2121no—
721C2×C22⋊C4—2121no—
722C2×C22⋊C4C2×Dic5314yes—
723C2×C22⋊C4C2×Dic5314yes—
724C2×C22⋊C4C2×Dic5314yescomplemented
725C2×C22⋊C4C22⋊D5314yes—
726C2×C22⋊C4C22⋊D5314yes—
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—1062no—
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—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—
776C24D4×D5312yes—
777C24#1171994712yes—
778C24C22×Dic5312yes—
779C24C22×Dic5312yes—
780C24C2×C22⋊D5312yes—
781C24C2×C22⋊D5312yes—
782C24C23×D5311yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
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—28no—
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—28no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—532no—
824C22×C4—532no—
825C22×C4—532no—
826C22×C4—532no—
827C22×C4—532no—
828C22×C4—532no—
829C22×C4—532no—
830C22×C4—532no—
831C22×C4—1061no—
832C22×C4—1061no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1068no—
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—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—2124no—
881C22×C4—2124no—
882C22×C4—2124no—
883C22×C4—2124no—
884C22×C4—2124no—
885C22×C4—2124no—
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—28no—
896C4⋊C4—28no—
897C4⋊C4—2124no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—1068no—
901C22⋊C4—1068no—
902C22⋊C4—1068no—
903C22⋊C4—2124no—
904C22⋊C4—2124no—
905C22⋊C4—2124no—
906C22⋊C4—2124no—
907C22⋊C4C22⋊Dic53116yescomplemented
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—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
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—
979C23C2×C22⋊Dic5314yes—
980C23D4×Dic5314yes—
981C23C23×Dic5311yescharacteristic
982C23C2×D4×D5311yescharacteristic
983C23C22×C22⋊D5311yescharacteristic
984C23C22×C22⋊D5311yescharacteristic
985C23#41×D5311yescharacteristic
986C23#41×D5311yescharacteristic
987C23#41×D5311yescharacteristic
988C23#41×D5311yescharacteristic
989C23#41×D5311yescharacteristic
990C23#41×D5311yescharacteristic
991C23C2×#1171994711yescharacteristic
992C23#1313326211yescharacteristic
993C23#1313326211yescharacteristic
994C23#1313326311yescharacteristic
995C23#1313326411yescharacteristic
996D4—416no—
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—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—416no—
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—534no—
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—1062no—
1051C2×C4—1062no—
1052C2×C4—1062no—
1053C2×C4—21216no—
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×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×C4C2×C22⋊Dic5314yes—
1089C2×C4C2×C22⋊Dic5314yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
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—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊Dic5311yescharacteristic
1121C22C2×D4×Dic5311yescharacteristic
1122C22#41×Dic5311yescharacteristic
1123C22#41×Dic5311yescharacteristic
1124C22#41×Dic5311yescharacteristic
1125C22#1681109811yescharacteristic
1126C22#1681110611yescharacteristic
1127C22#123×D5311yescharacteristic
1128C22#1681113011yescharacteristic
1129C22#1681113011yescharacteristic
1130C22#1681113111yescharacteristic
1131C22#1681115011yescharacteristic
1132C22#1681115011yescharacteristic
1133C22#1681116911yescharacteristic
1134C22#1681116911yescharacteristic
1135C22#1681120911yescharacteristic
1136C22#1681121611yescharacteristic
1137C22#1681122511yescharacteristic
1138C22#1681124111yescharacteristic
1139C22D4×C22⋊D5311yescharacteristic
1140C22D4×C22⋊D5311yescharacteristic
1141C22#1681126111yescharacteristic
1142C22#1681126111yescharacteristic
1143C22#1681126511yescharacteristic
1144C22#1681126711yescharacteristic
1145C22#1681126711yescharacteristic
1146C22#1681127111yescharacteristic
1147C22#1681127211yescharacteristic
1148C22#1681127211yescharacteristic
1149C22#1681129611yescharacteristic
1150C22#1681130111yescharacteristic
1151C22#1681131011yescharacteristic
1152C22#1681131811yescharacteristic
1153C22#1681131811yescharacteristic
1154C22#1681135711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—1064no—
1161C4—4241no—
1162C4—4241no—
1163C4—2122no—
1164C4—2122no—
1165C4—2122no—
1166C4—2122no—
1167C4—2122no—
1168C2—44no—
1169C2—44no—
1170C2#2027720611yescharacteristic
1171C2#123×Dic5311yescharacteristic
1172C2#2027750911yescharacteristic
1173C2D4×C22⋊Dic5311yescharacteristic
1174C2#2027754511yescharacteristic
1175C2#2027771111yescharacteristic
1176C2#2027785111yescharacteristic
1177C2#2027817411yescharacteristic
1178C2#2027822611yescharacteristic
1179C2#2027859411yescharacteristic
1180C2#2027861811yescharacteristic
1181C2#2027871811yescharacteristic
1182C2#2027880711yescharacteristic
1183C2#2027975611yescharacteristic
1184C2#2027981011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#123×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×#123D53
hypocenterC53#14096
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#16810516C2semidirect
3. C2×C22⋊C4×Dic53C2semidirect
4. C2×C4×C22⋊Dic53C2semidirect
5. #20272983C2semidirect
6. #20272964C2semidirect
7. #20272960C2semidirect
9. #20272952C2semidirect
10. #20272947C2semidirect
11. #20272947C2semidirect
12. #20272944C2semidirect
13. #20272938C2semidirect
14. #20272937C2semidirect
52. C2×#123×C53C4semidirect
137. C23×C4×C53C2×C4semidirect
148. C2×C4⋊C4×C53C2×C4semidirect
149. C2×C4⋊C4×C53C2×C4semidirect
156. C2×C22⋊C4×C53C2×C4semidirect
306. C22⋊C4×C53C22⋊C4semidirect
496. C2×Dic53#123semidirect
613. C2×#123Dic53semidirect
650. C53#14096semidirect
681. C23×C4C2×Dic53semidirect
695. C2×C4⋊C4C2×Dic53semidirect
696. C2×C4⋊C4C2×Dic53semidirect
724. C2×C22⋊C4C2×Dic53semidirect
907. C22⋊C4C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105162
C2×#168105032
C2×C22⋊C4×Dic532
C2×C4×C22⋊Dic532
#202729832
#202729642
#202729602
#202729562
#202729522
#202729472
#202729442
#202729382
#202729372
C22×#123×C532
#1409653