Finite Group Databasebeta

← #15785240

Subgroups — #15785240

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718331C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718638C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×#11718327C211yesmaximal, characteristic
6#13113101C211yesmaximal, characteristic, complemented
7#13113082C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic, complemented
10#13113068C211yesmaximal, characteristic, complemented
11#13113065C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718651—24no—
52#11718648—24no—
53#11718638—24no—
54#11718331—24no—
55#11718327C418yescomplemented
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—41no—
98C2×#6103—41no—
99C2×#6103—41no—
100C2×#6103—41no—
101C2×#6103C2×C414yes—
102C2×#6103C2×C414yes—
103C2×#6103D414yes—
104C2×#6103Q814yes—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—41no—
111C2×C4⋊Dic13—41no—
112C2×C4⋊Dic13—41no—
113C2×C4⋊Dic13—41no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13C2×C414yes—
125C2×C4×Dic13C2×C414yes—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95C2×C414yes—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071C2×C414yes—
143#88071D414yes—
144#13915—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×D412yes—
160C23×D13C2×Q812yes—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
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×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×Q812yes—
205C22×C4×C13#4112yes—
206C22×C4×C13#4112yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
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×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×Q812yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C13×C4⋊C4—44no—
267C13×C4⋊C4—44no—
268C13×C4⋊C4—44no—
269#6103—28no—
270#6103—44no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274#6103C4⋊C4116yescomplemented
275C4⋊Dic13—44no—
276C4⋊Dic13—44no—
277C4⋊Dic13—44no—
278C4×Dic13—28no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#382—131no—
285C2×#380—131no—
286C2×C4×C22⋊C4—131no—
287#1444—131no—
288#1444D1311yescharacteristic, complemented
289#1439—131no—
290#1439—131no—
291#1436—131no—
292#1436—131no—
293C4⋊#95—131no—
294#1434—131no—
295C22⋊#95—131no—
296C4×#95—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C132−1+411yescharacteristic
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13C2×C4⋊C414yes—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13C2×C4⋊C414yes—
394C2×C4×C13#11714yes—
395C2×C4×C13#11714yes—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
444C2×Dic13C4×D414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4C2×D1311yescharacteristic
451C22×C4⋊C4C2×D1311yescharacteristic
452C22×C4⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463#388—264no—
464#388—264no—
465#382—264no—
466#380—264no—
467C4×C22⋊C4—138no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4⋊C411yescharacteristic
487C22×C13C2×#11711yescharacteristic
488C22×C13C2×#11711yescharacteristic
489C22×C13C2×C4×D411yescharacteristic
490C22×C13C4×#4111yescharacteristic
491C22×C13#51811yescharacteristic
492C22×C13#52011yescharacteristic
493C22×C13#52911yescharacteristic
494C22×C13#52911yescharacteristic
495C22×C13#53211yescharacteristic
496C22×C13#53211yescharacteristic
497C22×C13#53211yescharacteristic
498C22×C13#53211yescharacteristic
499C22×C13#53311yescharacteristic
500C22×C13#53311yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53811yescharacteristic
503C22×C13#53911yescharacteristic
504C22×C13#53911yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54611yescharacteristic
510C22×C13#54711yescharacteristic
511C22×C13D4×Q811yescharacteristic
512C22×C13#55111yescharacteristic
513C22×C13#55111yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55211yescharacteristic
516C22×C13#55411yescharacteristic
517C22×C13#55411yescharacteristic
518C22×C13#55411yescharacteristic
519C22×C13#55511yescharacteristic
520C22×C13#55511yescharacteristic
521C2×D13—24no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—24no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—81no—
542C4×C13—81no—
543Dic13—24no—
544Dic13—24no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—81no—
549Dic13—81no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—134no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—262no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—521no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—134no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—262no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—521no—
605C2×C22⋊C4—521no—
606C2×C22⋊C4—521no—
607C2×C22⋊C4—521no—
608C2×C42—134no—
609C2×C42—134no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—134no—
624#95—134no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—262no—
637#95C4×D1314yes—
638C2×C13#228511yescharacteristic
639C2×C13#229311yescharacteristic
640C2×C13#231811yescharacteristic
641C2×C13#234211yescharacteristic
642C2×C13#234611yescharacteristic
643C2×C13D4×C4⋊C411yescharacteristic
644C2×C13#234911yescharacteristic
645C2×C13#255311yescharacteristic
646C2×C13#255311yescharacteristic
647C2×C13#255511yescharacteristic
648C2×C13#255511yescharacteristic
649C2×C13#255611yescharacteristic
650C2×C13#255611yescharacteristic
651C2×C13#257411yescharacteristic
652C2×C13#257411yescharacteristic
653D13—44no—
654C24—132no—
655C24—132no—
656C24—132no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24—261no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24C23×D1311yescharacteristic
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—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—268no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—268no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—524no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4C2×C4×D1312yes—
765C22×C4C2×C4×D1312yes—
766C22×C4C2×C4×D1312yes—
767C22×C4D4×D1312yes—
768C22×C4D4×D1312yes—
769C22×C4#612912yes—
770C22×C4#612912yes—
771C22×C4Q8×D1312yes—
772C22×C4#613112yes—
773C22×C4#613112yes—
774C22×C4#613112yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—524no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C22⋊C4—1316no—
782C22⋊C4—268no—
783C22⋊C4—524no—
784C22⋊C4—524no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C42—268no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1391511yescharacteristic, complemented, Sylow
792C23—134no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23—521no—
818C23—521no—
819C23—521no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23C22×C4×D1311yescharacteristic
828C23C2×D4×D1311yescharacteristic
829C23C2×D4×D1311yescharacteristic
830C23C2×#612911yescharacteristic
831C23C2×#612911yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23C2×Q8×D1311yescharacteristic
835C23C2×#613111yescharacteristic
836C23C2×#613111yescharacteristic
837C23C2×#613111yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#8825611yescharacteristic
841C23#8825711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—134no—
889C2×C4—134no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—5216no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4C4⋊C4×D1314yes—
939C2×C4#8814614yes—
940C2×C4#8814614yes—
941C22—264no—
942C22—264no—
943C22—264no—
944C22—522no—
945C22—522no—
946C22—522no—
947C22—522no—
948C22—522no—
949C22—522no—
950C22—522no—
951C22—522no—
952C22—522no—
953C22—522no—
954C22—522no—
955C22—522no—
956C22C2×C4⋊C4×D1311yescharacteristic
957C22C2×#8814611yescharacteristic
958C22C2×#8814611yescharacteristic
959C22C4×D4×D1311yescharacteristic
960C22#1171925011yescharacteristic
961C22#1171925111yescharacteristic
962C22C4×#613111yescharacteristic
963C22#1171929511yescharacteristic
964C22#1171929611yescharacteristic
965C22#1171929811yescharacteristic
966C22#1171930111yescharacteristic
967C22#1171931711yescharacteristic
968C22#1171932111yescharacteristic
969C22#1171932911yescharacteristic
970C22#1171933511yescharacteristic
971C22#1171933511yescharacteristic
972C22#1171933711yescharacteristic
973C22#1171934111yescharacteristic
974C22#1171934211yescharacteristic
975C22#1171934711yescharacteristic
976C22#1171934911yescharacteristic
977C22#1171935011yescharacteristic
978C22#1171936011yescharacteristic
979C22#1171936311yescharacteristic
980C22#1171937011yescharacteristic
981C22#1171939511yescharacteristic
982C22#1171939611yescharacteristic
983C22#1171939911yescharacteristic
984C22#1171942111yescharacteristic
985C22#1171943011yescharacteristic
986C22#1171943011yescharacteristic
987C22#1171943311yescharacteristic
988C22#1171943311yescharacteristic
989C22#1171943511yescharacteristic
990C22#1171943911yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—81no—
998C4—264no—
999C4—264no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—1041no—
1004C4—1041no—
1005C2—524no—
1006C2#1311724111yescharacteristic
1007C2#1311729411yescharacteristic
1008C2#1311746411yescharacteristic
1009C2#1311768311yescharacteristic
1010C2#1311772011yescharacteristic
1011C2#1311773411yescharacteristic
1012C2#1311774511yescharacteristic
1013C2#1311988211yescharacteristic
1014C2#1311988411yescharacteristic
1015C2#1311990611yescharacteristic
1016C2#1311991111yescharacteristic
1017C2#1311991511yescharacteristic
1018C2#1311992311yescharacteristic
1019C2#1312010511yescharacteristic
1020C2#1312011311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1444D13
hypocenterC13#13915
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#11718638C2semidirect
6. #13113101C2semidirect
9. #13113070C2semidirect
10. #13113068C2semidirect
11. #13113065C2semidirect
12. #13113062C2semidirect
14. #95×Dic13C2semidirect
15. C13×#1444C2semidirect
55. #11718327C4semidirect
274. #6103C4⋊C4semidirect
288. #1444D13semidirect
791. C13#13915semidirect

Maximal subgroups

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

subgroupindex
C2×#117183312
C2×#117186512
C2×#117186382
C2×#117186482
C2×#117183272
#131131012
#131130822
#131130782
#131130702
#131130682
#131130652
#131130622
#131130572
#95×Dic132
C13×#14442
#1391513