Finite Group Databasebeta

← #15791729

Subgroups — #15791729

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718329C211yesmaximal, characteristic
4#13113102C211yesmaximal, characteristic, complemented
5#13113089C211yesmaximal, characteristic, complemented
6#13113088C211yesmaximal, characteristic, complemented
7#13113084C211yesmaximal, characteristic
8#13113084C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113060C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
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×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88152—24no—
32C2×#88152—24no—
33C2×#88152C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718651—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—22no—
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—22no—
92C2×#6103—22no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103D414yes—
101C2×#6103D414yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13C2×C414yescomplemented
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—41no—
113C2×#6101C2×C414yescomplemented
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13C2×C414yescomplemented
120#88152—232no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—41no—
124C13×#95—41no—
125C13×#95—41no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#14475—131nomaximal, Sylow
142C24×C13C2411yescharacteristic
143C23×D13—21no—
144C23×D13—21no—
145C23×D13—21no—
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×D13C22×C412yes—
156C23×D13C2×D412yes—
157C23×D13C2×D412yes—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
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×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13#4112yes—
206C22×C4×C13#4112yes—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
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×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C2×C4×D13—44no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C13×C4⋊C4—28no—
264C13×C4⋊C4—44no—
265#6103—28no—
266#6103—28no—
267#6103—44no—
268#6103—44no—
269#6103—44no—
270#6103C22⋊C4116yes—
271C4⋊Dic13—28no—
272C4⋊Dic13—44no—
273#6101—28no—
274#6101—44no—
275C4×Dic13—28no—
276C4×Dic13—44no—
277C22×#126—131no—
278C2×#388—131no—
279C2×#385—131no—
280#1445—131no—
281#1441—131no—
282#1441—131no—
283#1441D1311yescharacteristic, complemented
284#1440—131no—
285#1440—131no—
286#1436—131no—
287C4⋊#95—131no—
288C4⋊#95—131no—
289#1434—131no—
290C22⋊#95—131no—
291C22⋊#95—131no—
292C23×C13C23×C411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C22×D411yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13C2×#4111yescharacteristic
299C23×C13H(5,𝔽2)11yescharacteristic
300C23×C13H(5,𝔽2)11yescharacteristic
301C23×C13H(5,𝔽2)11yescharacteristic
302C23×C13H(5,𝔽2)11yescharacteristic
303C23×C132−1+411yescharacteristic
304C23×C132−1+411yescharacteristic
305C23×C132−1+411yescharacteristic
306C23×C132−1+411yescharacteristic
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
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—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
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×D13C2×C22⋊C414yes—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
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—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
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×C13C2×C22⋊C414yes—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
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—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
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×Dic13C2×C22⋊C414yes—
440C4×D13—416no—
441C24×C4—131no—
442C2×#126—138no—
443C2×#126—264no—
444C2×#126—264no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4C2×D1311yescharacteristic
450C22×C4⋊C4C2×D1311yescharacteristic
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C42—131no—
458C22×C42—131no—
459#388—264no—
460#385—264no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
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×#95C2×D1311yescharacteristic
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C2×#95C2×D1311yescharacteristic
481C22×C13C22×C22⋊C411yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13#52011yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#53511yescharacteristic
489C22×C13#53611yescharacteristic
490C22×C13#53711yescharacteristic
491C22×C13#53711yescharacteristic
492C22×C13#53811yescharacteristic
493C22×C13#53811yescharacteristic
494C22×C13#53911yescharacteristic
495C22×C13#53911yescharacteristic
496C22×C13#54111yescharacteristic
497C22×C13#54111yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13#54211yescharacteristic
500C22×C13#54611yescharacteristic
501C22×C13#54611yescharacteristic
502C22×C13#54611yescharacteristic
503C22×C13#54611yescharacteristic
504C22×C13#54711yescharacteristic
505C22×C13#54711yescharacteristic
506C22×C13#54711yescharacteristic
507C22×C13#54711yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55211yescharacteristic
510C22×C13#55311yescharacteristic
511C22×C13#55611yescharacteristic
512C22×C13#56011yescharacteristic
513C22×C13#56311yescharacteristic
514C22×C13#56311yescharacteristic
515C22×C13#56311yescharacteristic
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—24no—
519C2×D13—42no—
520C2×D13—42no—
521C2×D13—42no—
522C2×D13—42no—
523C2×D13—42no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C4×C13—24no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—81no—
537C4×C13—81no—
538Dic13—24no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—81no—
544Dic13—81no—
545C25—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—262no—
554C23×C4—262no—
555C23×C4—262no—
556C23×C4—521no—
557C23×C4—521no—
558C23×C4—521no—
559C23×C4—521no—
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567#126—2632no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—521no—
584C2×C4⋊C4—521no—
585C2×C4⋊C4C4×D1314yescomplemented
586C2×C22⋊C4—134no—
587C2×C22⋊C4—134no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
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—521no—
601C2×C22⋊C4—521no—
602C2×C22⋊C4—521no—
603C2×C22⋊C4—521no—
604C2×C42—134no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42—521no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—521no—
622#95—521no—
623#95—521no—
624#95—521no—
625#95—521no—
626#95—521no—
627#95—521no—
628#95—521no—
629#95—521no—
630C2×C13#231111yescharacteristic
631C2×C13#233411yescharacteristic
632C2×C13#233411yescharacteristic
633C2×C13#233911yescharacteristic
634C2×C13#233911yescharacteristic
635C2×C13#237311yescharacteristic
636C2×C13#238311yescharacteristic
637C2×C13#268511yescharacteristic
638C2×C13#268911yescharacteristic
639C2×C13#269111yescharacteristic
640C2×C13#269511yescharacteristic
641C2×C13#269811yescharacteristic
642C2×C13#271511yescharacteristic
643C2×C13#271811yescharacteristic
644C2×C13#272211yescharacteristic
645D13—44no—
646C24—132no—
647C24—132no—
648C24—132no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24—261no—
656C24—261no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24C23×D1311yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
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—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
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—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—524no—
754C22×C4—524no—
755C22×C4—524no—
756C22×C4—524no—
757C22×C4—524no—
758C22×C4—524no—
759C22×C4—524no—
760C22×C4C2×C4×D1312yes—
761C22×C4C2×C4×D1312yes—
762C22×C4C2×C4×D1312yes—
763C22×C4D4×D1312yes—
764C22×C4D4×D1312yes—
765C22×C4#612912yes—
766C22×C4#613112yes—
767C4⋊C4—28no—
768C4⋊C4—44no—
769C4⋊C4—268no—
770C4⋊C4—268no—
771C4⋊C4—524no—
772C4⋊C4—524no—
773C22⋊C4—1316no—
774C22⋊C4—268no—
775C22⋊C4—268no—
776C22⋊C4—524no—
777C22⋊C4—524no—
778C22⋊C4—524no—
779C42—268no—
780C42—524no—
781C13#1447511yescharacteristic, complemented, Sylow
782C23—134no—
783C23—262no—
784C23—262no—
785C23—262no—
786C23—262no—
787C23—262no—
788C23—262no—
789C23—262no—
790C23—262no—
791C23—262no—
792C23—262no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23—521no—
807C23—521no—
808C23—521no—
809C23—521no—
810C23—521no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23C22×C4×D1311yescharacteristic
818C23C2×D4×D1311yescharacteristic
819C23C2×D4×D1311yescharacteristic
820C23C2×#612911yescharacteristic
821C23#8825111yescharacteristic
822C23#8825111yescharacteristic
823C23C2×#613111yescharacteristic
824C23#8825411yescharacteristic
825C23#8825411yescharacteristic
826C23#41×D1311yescharacteristic
827C23#41×D1311yescharacteristic
828C23#8825611yescharacteristic
829C23#8825611yescharacteristic
830C23#8825711yescharacteristic
831C23#8825711yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
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—134no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
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—5216no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
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×C4C22⋊C4×D1314yes—
931C22—264no—
932C22—264no—
933C22—264no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22—522no—
941C22—522no—
942C22—522no—
943C22—522no—
944C22—522no—
945C22—522no—
946C22C2×C22⋊C4×D1311yescharacteristic
947C22#1171920911yescharacteristic
948C22#1171922811yescharacteristic
949C22C4×#612911yescharacteristic
950C22#1171925111yescharacteristic
951C22C4×#613111yescharacteristic
952C22#1171927911yescharacteristic
953C22#1171929611yescharacteristic
954C22#1171930611yescharacteristic
955C22#1171931211yescharacteristic
956C22#1171931311yescharacteristic
957C22#1171931511yescharacteristic
958C22#1171931611yescharacteristic
959C22#1171932511yescharacteristic
960C22#1171933311yescharacteristic
961C22#1171933411yescharacteristic
962C22#1171933511yescharacteristic
963C22#1171933611yescharacteristic
964C22#1171934211yescharacteristic
965C22#1171934811yescharacteristic
966C22#1171934911yescharacteristic
967C22#1171935111yescharacteristic
968C22#1171936011yescharacteristic
969C22#1171936711yescharacteristic
970C22#1171937011yescharacteristic
971C22#1171938111yescharacteristic
972C22#1171939811yescharacteristic
973C22#1171940111yescharacteristic
974C22#1171940211yescharacteristic
975C22#1171940411yescharacteristic
976C22#1171940911yescharacteristic
977C22#1171941211yescharacteristic
978C22#1171943111yescharacteristic
979C22#1171943711yescharacteristic
980C22#1171944011yescharacteristic
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—81no—
987C4—81no—
988C4—264no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4—522no—
993C4—1041no—
994C4—1041no—
995C2—524no—
996C2#1311742511yescharacteristic
997C2#1311761411yescharacteristic
998C2#1311761611yescharacteristic
999C2#1311766211yescharacteristic
1000C2#1311766511yescharacteristic
1001C2#1311795911yescharacteristic
1002C2#1311802711yescharacteristic
1003C2#1312123411yescharacteristic
1004C2#1312129411yescharacteristic
1005C2#1312132211yescharacteristic
1006C2#1312137611yescharacteristic
1007C2#1312141511yescharacteristic
1008C2#1312164911yescharacteristic
1009C2#1312169311yescharacteristic
1010C2#1312174511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1441D13
hypocenterC13#14475
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
4. #13113102C2semidirect
5. #13113089C2semidirect
6. #13113088C2semidirect
9. #13113070C2semidirect
10. #13113065C2semidirect
11. #13113064C2semidirect
12. #13113060C2semidirect
15. C13×#1441C2semidirect
33. C2×#88152C4semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
107. C2×C4⋊Dic13C2×C4semidirect
113. C2×#6101C2×C4semidirect
119. C2×C4×Dic13C2×C4semidirect
283. #1441D13semidirect
585. C2×C4⋊C4C4×D13semidirect
781. C13#14475semidirect

Maximal subgroups

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

subgroupindex
C22×#881522
C2×#117186512
C2×#117183292
#131131022
#131130892
#131130882
#131130842
#131130702
#131130652
#131130642
#131130602
#131130572
C13×#14412
#1447513