Finite Group Databasebeta

← #15791359

Subgroups — #15791359

Order 3328.

1650 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×#11718646C211yesmaximal, characteristic, complemented
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718330C211yesmaximal, characteristic
4C2×#11718329C211yesmaximal, characteristic
5C2×#11718329C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113092C211yesmaximal, characteristic, complemented
9#13113082C211yesmaximal, characteristic
10#13113078C211yesmaximal, characteristic
11#13113067C211yesmaximal, characteristic, complemented
12#13113065C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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#11718651C418yescomplemented
52#11718646—24no—
53#11718330—24no—
54#11718329—24no—
55#11718329—24no—
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—41no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13—41no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4C2×C414yescomplemented
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103D414yes—
101C2×#6103Q814yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—41no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13—41no—
108C2×C4⋊Dic13—41no—
109C2×C4⋊Dic13—41no—
110C2×C4⋊Dic13D414yes—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—41no—
118C2×#6101—41no—
119C2×#6101—41no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13C2×C414yescomplemented
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—41no—
130C13×#95—41no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yescomplemented
143#88071C2×C414yescomplemented
144#14442—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×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×Q812yes—
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×Dic13—21no—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×Q812yes—
258C22×Dic13#4112yes—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C13×C4⋊C4—28no—
267C13×C4⋊C4—44no—
268#6103—28no—
269#6103—44no—
270#6103—44no—
271#6103—44no—
272#6103—44no—
273#6103C4⋊C4116yescomplemented
274C4⋊Dic13—44no—
275C4⋊Dic13—44no—
276C4⋊Dic13—44no—
277#6101—44no—
278#6101—44no—
279#6101—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#389—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#385—131no—
286C2×#385—131no—
287#1444—131no—
288#1442—131no—
289#1442—131no—
290#1441D1311yescharacteristic, complemented
291#1439—131no—
292#1439—131no—
293#1436—131no—
294C4⋊#95—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13H(5,𝔽2)11yescharacteristic
305C23×C13H(5,𝔽2)11yescharacteristic
306C23×C13H(5,𝔽2)11yescharacteristic
307C23×C13H(5,𝔽2)11yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C132−1+411yescharacteristic
310C23×C132−1+411yescharacteristic
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—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
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×C13—41no—
394C2×C4×C13C2×C4⋊C414yes—
395C2×C4×C13C4×D414yes—
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×Dic13—41no—
444C2×Dic13C2×C4⋊C414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4C2×D1311yescharacteristic
454C22×C4⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C42—131no—
462C22×C42—131no—
463#389—264no—
464#388—138no—
465#388—264no—
466#385—264no—
467#385—264no—
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×#95C2×D1311yescharacteristic
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4⋊C411yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C4×#4111yescharacteristic
489C22×C13#51811yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#52011yescharacteristic
493C22×C13#53411yescharacteristic
494C22×C13#53511yescharacteristic
495C22×C13#53611yescharacteristic
496C22×C13#53711yescharacteristic
497C22×C13#53811yescharacteristic
498C22×C13#53811yescharacteristic
499C22×C13#53911yescharacteristic
500C22×C13#53911yescharacteristic
501C22×C13#54111yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54411yescharacteristic
504C22×C13#54411yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13#54811yescharacteristic
511C22×C13D4×Q811yescharacteristic
512C22×C13#55411yescharacteristic
513C22×C13#55411yescharacteristic
514C22×C13#55411yescharacteristic
515C22×C13#55611yescharacteristic
516C22×C13#55911yescharacteristic
517C22×C13#56011yescharacteristic
518C22×C13#56211yescharacteristic
519C22×C13#56211yescharacteristic
520C22×C13#56311yescharacteristic
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—42no—
539C4×C13—42no—
540C4×C13—81no—
541C4×C13—81no—
542C4×C13—81no—
543Dic13—24no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—42no—
549Dic13—81no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—262no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—521no—
562C23×C4—521no—
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—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—134no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C4⋊C4—521no—
591C2×C4⋊C4—521no—
592C2×C4⋊C4—521no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4—521no—
595C2×C4⋊C4C4×D1314yescomplemented
596C2×C22⋊C4—134no—
597C2×C22⋊C4—134no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—521no—
609C2×C22⋊C4—521no—
610C2×C22⋊C4—521no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4—521no—
614C2×C42—134no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—134no—
626#95—134no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95—521no—
638C2×C13#231711yescharacteristic
639C2×C13#232511yescharacteristic
640C2×C13#233411yescharacteristic
641C2×C13D4×C4⋊C411yescharacteristic
642C2×C13#234911yescharacteristic
643C2×C13#236711yescharacteristic
644C2×C13#237611yescharacteristic
645C2×C13#267811yescharacteristic
646C2×C13#268111yescharacteristic
647C2×C13#268911yescharacteristic
648C2×C13#270411yescharacteristic
649C2×C13#271011yescharacteristic
650C2×C13#272911yescharacteristic
651C2×C13#278811yescharacteristic
652C2×C13#280711yescharacteristic
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—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
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—261no—
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—261no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4—524no—
765C22×C4—524no—
766C22×C4—524no—
767C22×C4C2×C4×D1312yes—
768C22×C4C2×C4×D1312yes—
769C22×C4C2×C4×D1312yes—
770C22×C4D4×D1312yes—
771C22×C4D4×D1312yes—
772C22×C4#612912yes—
773C22×C4Q8×D1312yes—
774C22×C4#613112yes—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C4⋊C4—524no—
782C4⋊C4—524no—
783C22⋊C4—1316no—
784C22⋊C4—268no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C22⋊C4—524no—
788C22⋊C4—524no—
789C42—524no—
790C42—524no—
791C13#1444211yescharacteristic, 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
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23C2×Q8×D1311yescharacteristic
834C23C2×#613111yescharacteristic
835C23#8825411yescharacteristic
836C23#41×D1311yescharacteristic
837C23#8825611yescharacteristic
838C23#8825611yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
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—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—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—41no—
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×C4—521no—
939C2×C4#8813514yes—
940C2×C4C4⋊C4×D1314yes—
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×#8813511yescharacteristic
957C22C2×C4⋊C4×D1311yescharacteristic
958C22#1171922811yescharacteristic
959C22#1171925011yescharacteristic
960C22#1171925111yescharacteristic
961C22C4×#613111yescharacteristic
962C22#1171927911yescharacteristic
963C22#1171929811yescharacteristic
964C22#1171930211yescharacteristic
965C22#1171931011yescharacteristic
966C22#1171931211yescharacteristic
967C22#1171931411yescharacteristic
968C22#1171931611yescharacteristic
969C22#1171931711yescharacteristic
970C22#1171933311yescharacteristic
971C22#1171933511yescharacteristic
972C22#1171933511yescharacteristic
973C22#1171933711yescharacteristic
974C22#1171933811yescharacteristic
975C22#1171934011yescharacteristic
976C22#1171934911yescharacteristic
977C22#1171935211yescharacteristic
978C22#1171936711yescharacteristic
979C22#1171937011yescharacteristic
980C22#1171937211yescharacteristic
981C22#1171938611yescharacteristic
982C22#1171939411yescharacteristic
983C22#1171939511yescharacteristic
984C22#1171940211yescharacteristic
985C22#1171940411yescharacteristic
986C22#1171941211yescharacteristic
987C22#1171941611yescharacteristic
988C22#1171943411yescharacteristic
989C22#1171943511yescharacteristic
990C22#1171943711yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—264no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—522no—
1004C4—1041no—
1005C2—524no—
1006C2#1311745811yescharacteristic
1007C2#1311753711yescharacteristic
1008C2#1311761411yescharacteristic
1009C2#1311773211yescharacteristic
1010C2#1311774511yescharacteristic
1011C2#1311791211yescharacteristic
1012C2#1311798311yescharacteristic
1013C2#1312116611yescharacteristic
1014C2#1312119311yescharacteristic
1015C2#1312129411yescharacteristic
1016C2#1312149311yescharacteristic
1017C2#1312158511yescharacteristic
1018C2#1312181711yescharacteristic
1019C2#1312258811yescharacteristic
1020C2#1312280911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1441D13
hypocenterC13#14442
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
1. C2×#11718646C2semidirect
6. #13113100C2semidirect
7. #13113094C2semidirect
8. #13113092C2semidirect
11. #13113067C2semidirect
12. #13113065C2semidirect
13. #13113064C2semidirect
15. C13×#1441C2semidirect
51. #11718651C4semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
125. C2×C4×Dic13C2×C4semidirect
142. #88071C2×C4semidirect
143. #88071C2×C4semidirect
273. #6103C4⋊C4semidirect
290. #1441D13semidirect
595. C2×C4⋊C4C4×D13semidirect
791. C13#14442semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186512
C2×#117183302
C2×#117183292
#131131002
#131130942
#131130922
#131130822
#131130782
#131130672
#131130652
#131130642
#131130572
C13×#14412
#1444213