Finite Group Databasebeta

← #15785710

Subgroups — #15785710

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718603C211yesmaximal, characteristic
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6#13113090C211yesmaximal, characteristic, complemented
7#13113088C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113069C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113064C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88132—24no—
36C2×#88132—24no—
37C2×#88132C418yescomplemented
38C2×C4×Dic26—24no—
39C2×C4×Dic26—24no—
40C2×C4×Dic26—24no—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718603—24no—
58C22⋊C4×Dic13—24no—
59#11718307—24no—
60C25×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—22no—
70C23×Dic13—22no—
71C23×Dic13—22no—
72C23×Dic13—22no—
73C23×Dic13C2×C414yes—
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—22no—
85C22×Dic26—22no—
86C22×Dic26C2×C414yes—
87C22×Dic26D414yes—
88C22×Dic26D414yes—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—41no—
96C2×C13×C22⋊C4C2×C414yes—
97C2×C13×C22⋊C4Q814yescomplemented
98C2×C42×C13—22no—
99C2×C42×C13—22no—
100C2×C42×C13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—22no—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—22no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—22no—
108C2×C22⋊Dic13—41no—
109C2×C22⋊Dic13C2×C414yes—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13C2×C414yes—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—22no—
123C2×#6101—22no—
124C2×#6101—22no—
125C2×#6101—22no—
126C2×#6101—22no—
127C2×#6101—22no—
128C2×#6101C2×C414yes—
129C2×#6101C2×C414yes—
130C2×#6101D414yes—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—22no—
134C2×C4×Dic13—22no—
135C2×C4×Dic13—22no—
136C2×C4×Dic13—22no—
137C2×C4×Dic13—22no—
138C2×C4×Dic13—22no—
139C2×C4×Dic13D414yes—
140#88132—232no—
141C4×Dic26—232no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—41no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—41no—
156#88071—41no—
157#88071—41no—
158#13969—131nomaximal, Sylow
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13C22×C412yes—
172C24×C13C2×Q812yes—
173C24×C13#4112yes—
174C24×C13C2411yescharacteristic
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13C22×C412yes—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×Q812yes—
215C22×C4×C13C2×Q812yes—
216C22×C4×C13#4112yes—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—28no—
252C22×Dic13—28no—
253C22×Dic13—28no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—44no—
262C22×Dic13—44no—
263C22×Dic13—44no—
264C22×Dic13—44no—
265C22×Dic13C22×C412yes—
266C22×Dic13C22×C412yes—
267C22×Dic13C22×C412yes—
268C22×Dic13C22×C412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×D412yes—
271C22×Dic13C2×D412yes—
272C22×Dic13C2×D412yes—
273C22×Dic13C2×D412yes—
274C22×Dic13C2×D412yes—
275C22×Dic13C2×D412yes—
276C22×Dic13C2×D412yes—
277C22×Dic13#4112yes—
278C22×Dic13#4112yes—
279C22×Dic13#4112yes—
280C2×Dic26—28no—
281C2×Dic26—28no—
282C2×Dic26—28no—
283C2×Dic26—28no—
284C2×Dic26—28no—
285C2×Dic26—28no—
286C2×Dic26C22⋊C4116yescomplemented
287C13×C22⋊C4—28no—
288C13×C22⋊C4—28no—
289C13×C22⋊C4—44no—
290C42×C13—28no—
291C22⋊Dic13—28no—
292C22⋊Dic13—28no—
293C22⋊Dic13—44no—
294C4⋊Dic13—28no—
295C4⋊Dic13—28no—
296#6101—28no—
297#6101—28no—
298#6101—28no—
299#6101—28no—
300#6101—44no—
301C4×Dic13—28no—
302C4×Dic13—28no—
303C4×Dic13—44no—
304C22×C22⋊Q8—131no—
305C22×C4×Q8—131no—
306C2×#391—131no—
307C2×#380—131no—
308C2×C4×C22⋊C4—131no—
309#1441—131no—
310#1441—131no—
311#1439—131no—
312#1439—131no—
313#1437—131no—
314#1437D1311yescharacteristic
315#1436—131no—
316#1436—131no—
317C4⋊#95—131no—
318C4⋊#95—131no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—41no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13—41no—
353C23×C13C4×Q814yescomplemented
354C23×C13C23×C411yescharacteristic
355C23×C13C22×D411yescharacteristic
356C23×C13C22×D411yescharacteristic
357C23×C13C22×D411yescharacteristic
358C23×C13C22×D411yescharacteristic
359C23×C13C22×Q811yescharacteristic
360C23×C13C2×#4111yescharacteristic
361C23×C13C2×#4111yescharacteristic
362C23×C13C2×#4111yescharacteristic
363C23×C13C2×#4111yescharacteristic
364C23×C13C2×#4111yescharacteristic
365C23×C13H(5,𝔽2)11yescharacteristic
366C23×C132−1+411yescharacteristic
367C23×C132−1+411yescharacteristic
368C23×C132−1+411yescharacteristic
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13C2×C22⋊C414yes—
410C2×C4×C13C22⋊Q814yescomplemented
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—416no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13C2×C22⋊C414yes—
461C2×Dic13C2×C22⋊C414yes—
462C2×Dic13C4×D414yes—
463C2×Dic13C4×D414yes—
464C2×Dic13#12014yes—
465C2×Dic13#12114yes—
466C2×Dic13#12114yes—
467C2×Dic13#12314yes—
468Dic26—232no—
469C23×Q8—131no—
470C24×C4—131no—
471C2×C22⋊Q8—138no—
472C2×C22⋊Q8—264no—
473C2×C22⋊Q8—264no—
474C2×C4×Q8—264no—
475C2×C4×Q8—264no—
476C2×C4×Q8—264no—
477C22×C4⋊C4—131no—
478C22×C4⋊C4—131no—
479C22×C4⋊C4—131no—
480C22×C4⋊C4—131no—
481C22×C4⋊C4—131no—
482C22×C4⋊C4—131no—
483C22×C4⋊C4—131no—
484C22×C22⋊C4—131no—
485C22×C22⋊C4—131no—
486C22×C22⋊C4—131no—
487C22×C22⋊C4C2×D1311yescharacteristic
488C22×C22⋊C4C2×D1311yescharacteristic
489C22×C22⋊C4C2×D1311yescharacteristic
490C22×C42—131no—
491C22×C42—131no—
492C22×C42—131no—
493C22×C42C2×D1311yescharacteristic
494#391—264no—
495#380—264no—
496C4×C22⋊C4—264no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
502C2×#95—131no—
503C2×#95—131no—
504C2×#95—131no—
505C2×#95—131no—
506C2×#95—131no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95—131no—
510C2×#95C2×D1311yescharacteristic
511C2×#95C2×D1311yescharacteristic
512C2×#95C2×D1311yescharacteristic
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—24no—
516C22×C13—42no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13—42no—
520C22×C13—42no—
521C22×C13—42no—
522C22×C13—42no—
523C22×C13—42no—
524C22×C13—42no—
525C22×C13—42no—
526C22×C13—42no—
527C22×C13—42no—
528C22×C13C22×C22⋊C411yescharacteristic
529C22×C13C2×C4×D411yescharacteristic
530C22×C13C2×C4×D411yescharacteristic
531C22×C13C2×C4×Q811yescharacteristic
532C22×C13C4×#4111yescharacteristic
533C22×C13#51911yescharacteristic
534C22×C13#52011yescharacteristic
535C22×C13C2×#12011yescharacteristic
536C22×C13C2×#12111yescharacteristic
537C22×C13C2×#12111yescharacteristic
538C22×C13C2×C22⋊Q811yescharacteristic
539C22×C13C2×#12311yescharacteristic
540C22×C13#52511yescharacteristic
541C22×C13#52911yescharacteristic
542C22×C13#53311yescharacteristic
543C22×C13#53611yescharacteristic
544C22×C13#53711yescharacteristic
545C22×C13#54111yescharacteristic
546C22×C13#54211yescharacteristic
547C22×C13#54611yescharacteristic
548C22×C13#54711yescharacteristic
549C22×C13#54811yescharacteristic
550C22×C13#54811yescharacteristic
551C22×C13#54811yescharacteristic
552C22×C13#54811yescharacteristic
553C22×C13#54811yescharacteristic
554C22×C13D4×Q811yescharacteristic
555C22×C13D4×Q811yescharacteristic
556C22×C13D4×Q811yescharacteristic
557C22×C13#55011yescharacteristic
558C22×C13#55011yescharacteristic
559C22×C13#55211yescharacteristic
560C22×C13#55211yescharacteristic
561C22×C13#55411yescharacteristic
562C22×C13#55611yescharacteristic
563C4×C13—24no—
564C4×C13—24no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—42no—
568C4×C13—81no—
569Dic13—24no—
570Dic13—42no—
571Dic13—42no—
572Dic13—42no—
573Dic13—42no—
574Dic13—42no—
575Dic13—81no—
576Dic13#38618yes—
577C25C22×D1311yescharacteristic
578C22×Q8—134no—
579C22×Q8—134no—
580C22×Q8—134no—
581C22×Q8—262no—
582C22×Q8—262no—
583C22×Q8—262no—
584C22×Q8—262no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—134no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—131no—
591C23×C4—131no—
592C23×C4—131no—
593C23×C4—131no—
594C23×C4—262no—
595C23×C4—262no—
596C23×C4—262no—
597C23×C4—262no—
598C23×C4—262no—
599C23×C4—262no—
600C23×C4C22×D1311yescharacteristic
601C23×C4C22×D1311yescharacteristic
602C23×C4C22×D1311yescharacteristic
603C23×C4C22×D1311yescharacteristic
604C23×C4C22×D1311yescharacteristic
605C23×C4C22×D1311yescharacteristic
606C22⋊Q8—2632no—
607C4×Q8—2632no—
608C2×C4⋊C4—134no—
609C2×C4⋊C4—134no—
610C2×C4⋊C4—134no—
611C2×C4⋊C4—134no—
612C2×C4⋊C4—262no—
613C2×C4⋊C4—262no—
614C2×C4⋊C4—262no—
615C2×C4⋊C4—262no—
616C2×C4⋊C4—262no—
617C2×C4⋊C4—262no—
618C2×C4⋊C4—262no—
619C2×C4⋊C4—262no—
620C2×C4⋊C4—262no—
621C2×C4⋊C4—262no—
622C2×C4⋊C4—262no—
623C2×C4⋊C4—262no—
624C2×C4⋊C4—262no—
625C2×C4⋊C4—262no—
626C2×C4⋊C4—262no—
627C2×C4⋊C4—262no—
628C2×C4⋊C4—262no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4—134no—
637C2×C22⋊C4—262no—
638C2×C22⋊C4—262no—
639C2×C22⋊C4—262no—
640C2×C22⋊C4—262no—
641C2×C22⋊C4—262no—
642C2×C22⋊C4—262no—
643C2×C22⋊C4—262no—
644C2×C22⋊C4—521no—
645C2×C22⋊C4Dic2614yescomplemented
646C2×C22⋊C4C4×D1314yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—134no—
651C2×C42—262no—
652C2×C42—262no—
653C2×C42—262no—
654C2×C42—262no—
655C2×C42—262no—
656C2×C42—262no—
657C2×C42—262no—
658C2×C42—262no—
659#95—22no—
660#95—22no—
661#95—41no—
662#95—262no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—262no—
670#95—262no—
671#95—262no—
672#95—521no—
673#95—521no—
674#95—521no—
675C2×C13—44no—
676C2×C13C2×#38611yescharacteristic
677C2×C13C4×C22⋊Q811yescharacteristic
678C2×C13#232311yescharacteristic
679C2×C13Q8×C22⋊C411yescharacteristic
680C2×C13#234111yescharacteristic
681C2×C13#236011yescharacteristic
682C2×C13#236211yescharacteristic
683C2×C13#240711yescharacteristic
684C2×C13#240911yescharacteristic
685C2×C13#242111yescharacteristic
686C2×C13#242311yescharacteristic
687C2×C13#242611yescharacteristic
688C2×C13#242911yescharacteristic
689C2×C13#253611yescharacteristic
690C2×C13#253811yescharacteristic
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×Dic2612yes—
704C24C2×C4×D1312yes—
705C24#612712yes—
706C24C23×D1311yescharacteristic
707C2×Q8—1316no—
708C2×Q8—268no—
709C2×Q8—268no—
710C2×Q8—268no—
711C2×Q8—268no—
712C2×Q8—268no—
713C2×Q8—268no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—132no—
748C22×C4—132no—
749C22×C4—132no—
750C22×C4—132no—
751C22×C4—132no—
752C22×C4—132no—
753C22×C4—132no—
754C22×C4—132no—
755C22×C4—132no—
756C22×C4—132no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—132no—
762C22×C4—268no—
763C22×C4—268no—
764C22×C4—268no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—524no—
807C22×C4—524no—
808C22×C4—524no—
809C22×C4—524no—
810C22×C4C2×Dic2612yes—
811C22×C4C2×Dic2612yes—
812C22×C4C2×C4×D1312yes—
813C22×C4C2×C4×D1312yes—
814C22×C4D4×D1312yes—
815C22×C4D4×D1312yes—
816C22×C4D4×D1312yes—
817C22×C4D4×D1312yes—
818C22×C4#612912yes—
819C4⋊C4—268no—
820C4⋊C4—268no—
821C4⋊C4—268no—
822C4⋊C4—268no—
823C4⋊C4—268no—
824C4⋊C4—268no—
825C4⋊C4—524no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—44no—
829C22⋊C4—268no—
830C22⋊C4—268no—
831C22⋊C4—524no—
832C42—28no—
833C42—268no—
834C42—268no—
835C42—524no—
836C13#1396911yescharacteristic, complemented, Sylow
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23C4×Dic2614yescomplemented
872C23C22×Dic2611yescharacteristic
873C23C22×C4×D1311yescharacteristic
874C23C2×#612711yescharacteristic
875C23C2×D4×D1311yescharacteristic
876C23C2×D4×D1311yescharacteristic
877C23C2×D4×D1311yescharacteristic
878C23C2×D4×D1311yescharacteristic
879C23C2×#612911yescharacteristic
880C23#8825111yescharacteristic
881C23#41×D1311yescharacteristic
882C23#41×D1311yescharacteristic
883C23#41×D1311yescharacteristic
884C23#8825711yescharacteristic
885C23#8825711yescharacteristic
886C23#8825711yescharacteristic
887Q8—2632no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—134no—
929C2×C4—134no—
930C2×C4—134no—
931C2×C4—134no—
932C2×C4—134no—
933C2×C4—134no—
934C2×C4—134no—
935C2×C4—134no—
936C2×C4—262no—
937C2×C4—262no—
938C2×C4—262no—
939C2×C4—262no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—262no—
943C2×C4—262no—
944C2×C4—262no—
945C2×C4—262no—
946C2×C4—262no—
947C2×C4—262no—
948C2×C4—262no—
949C2×C4—262no—
950C2×C4—262no—
951C2×C4—262no—
952C2×C4—262no—
953C2×C4—262no—
954C2×C4—262no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—5216no—
958C2×C4—521no—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—521no—
970C2×C4—521no—
971C2×C4—521no—
972C2×C4—521no—
973C2×C4—521no—
974C2×C4—521no—
975C2×C4—521no—
976C2×C4—521no—
977C2×C4—521no—
978C2×C4—521no—
979C2×C4—521no—
980C2×C4—521no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4—521no—
985C2×C4#8813214yescomplemented
986C2×C4C22⋊C4×D1314yes—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22C2×C4×Dic2611yescharacteristic
1003C22C2×#8813211yescharacteristic
1004C22C2×C22⋊C4×D1311yescharacteristic
1005C22#1171919511yescharacteristic
1006C22#1171922111yescharacteristic
1007C22#1171922211yescharacteristic
1008C22#1171923611yescharacteristic
1009C22C4×#612911yescharacteristic
1010C22D4×Dic2611yescharacteristic
1011C22D4×Dic2611yescharacteristic
1012C22D4×Dic2611yescharacteristic
1013C22#1171924311yescharacteristic
1014C22#1171924411yescharacteristic
1015C22C4×D4×D1311yescharacteristic
1016C22C4×D4×D1311yescharacteristic
1017C22#1171925111yescharacteristic
1018C22#1171925211yescharacteristic
1019C22#1171925711yescharacteristic
1020C22#1171925711yescharacteristic
1021C22D13×#12011yescharacteristic
1022C22#1171930311yescharacteristic
1023C22#1171930311yescharacteristic
1024C22#1171930411yescharacteristic
1025C22D13×#12111yescharacteristic
1026C22D13×#12111yescharacteristic
1027C22#1171931311yescharacteristic
1028C22#1171935311yescharacteristic
1029C22D13×#12311yescharacteristic
1030C22#1171936011yescharacteristic
1031C22#1171937411yescharacteristic
1032C22#1171937611yescharacteristic
1033C22#1171938211yescharacteristic
1034C22#1171940611yescharacteristic
1035C22#1171941311yescharacteristic
1036C22#1171942311yescharacteristic
1037C4—24no—
1038C4—24no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—81no—
1043C4—138no—
1044C4—264no—
1045C4—522no—
1046C4—522no—
1047C4—522no—
1048C4—522no—
1049C4—522no—
1050C4—1041no—
1051C2—44no—
1052C2D13×#38611yescharacteristic
1053C2C4×#8813211yescharacteristic
1054C2#1311751511yescharacteristic
1055C2C22⋊C4×Dic2611yescharacteristic
1056C2#1311767511yescharacteristic
1057C2#1311784211yescharacteristic
1058C2#1311786611yescharacteristic
1059C2#1311817811yescharacteristic
1060C2#1311819811yescharacteristic
1061C2#1311833611yescharacteristic
1062C2#1311835811yescharacteristic
1063C2#1311839911yescharacteristic
1064C2#1311843211yescharacteristic
1065C2#1311974411yescharacteristic
1066C2#1311975611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#13969
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic26C2semidirect
3. C2×#11718307C2semidirect
6. #13113090C2semidirect
7. #13113088C2semidirect
11. #13113070C2semidirect
12. #13113069C2semidirect
13. #13113064C2semidirect
14. #13113064C2semidirect
37. C2×#88132C4semidirect
97. C2×C13×C22⋊C4Q8semidirect
286. C2×Dic26C22⋊C4semidirect
353. C23×C13C4×Q8semidirect
410. C2×C4×C13C22⋊Q8semidirect
645. C2×C22⋊C4Dic26semidirect
836. C13#13969semidirect
871. C23C4×Dic26semidirect
985. C2×C4#88132semidirect

Maximal subgroups

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

subgroupindex
C22×#881322
C22×C4×Dic262
C2×#117183072
C2×#117186032
C2×C22⋊C4×Dic132
#131130902
#131130882
#131130812
#131130792
#131130732
#131130702
#131130692
#131130642
C13×#14372
#1396913