Finite Group Databasebeta

← #15790663

Subgroups — #15790663

Order 3328.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718611C211yesmaximal, characteristic
2C2×#11718598C211yesmaximal, characteristic, complemented
3#13113104C211yesmaximal, characteristic, complemented
4#13113093C211yesmaximal, characteristic, complemented
5#13113093C211yesmaximal, characteristic, complemented
6#13113089C211yesmaximal, characteristic, complemented
7#13113085C211yesmaximal, characteristic
8#13113081C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113066C211yesmaximal, characteristic, complemented
12#13113061C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C2×C13×#388C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
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×C4⋊Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C13×#388C418yescomplemented
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
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
51C2×#88071C2211yescharacteristic
52#11718611—24no—
53#11718598—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—22no—
62C23×Dic13—22no—
63C23×Dic13—22no—
64C23×Dic13—41no—
65C23×Dic13—41no—
66C23×Dic13—41no—
67C23×Dic13—41no—
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4C2×C414yescomplemented
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4C2×C414yes—
86C2×C13×C22⋊C4C2×C414yes—
87C2×C13×C22⋊C4C2×C414yes—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C2×C42×C13C2×C414yescomplemented
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13—41no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—22no—
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—22no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C13×#95C2×C414yescomplemented
113C13×#95C2×C414yescomplemented
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071D414yes—
134#14389—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13C22×C412yes—
148C24×C13#4112yes—
149C24×C13#4112yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
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×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C22×C412yes—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13#4112yes—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
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—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C13×C4⋊C4—44no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4—28no—
259C13×C22⋊C4—44no—
260C42×C13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C22⋊Dic13—44no—
264C4⋊Dic13—44no—
265C4⋊Dic13—44no—
266C4⋊Dic13—44no—
267C4×Dic13—44no—
268C2×#388D1311yescharacteristic
269C2×#385—131no—
270C2×#383—131no—
271#1445—131no—
272#1442—131no—
273#1442—131no—
274#1441—131no—
275#1440—131no—
276#1439—131no—
277#1437—131no—
278#1436—131no—
279C4⋊#95—131no—
280#1434—131no—
281C22⋊#95—131no—
282C22⋊#95—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13#11714yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C23×C132−1+411yescharacteristic
332C23×C132−1+411yescharacteristic
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
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—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
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×C13C4×D414yes—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—416no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
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—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42—131no—
444C22×C42C2×D1311yescharacteristic
445#388Dic1318yescomplemented
446#385—264no—
447#383—264no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×#11711yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C4×#4111yescharacteristic
488C22×C13#51811yescharacteristic
489C22×C13#52011yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#53511yescharacteristic
493C22×C13#53711yescharacteristic
494C22×C13#53811yescharacteristic
495C22×C13#53811yescharacteristic
496C22×C13#53811yescharacteristic
497C22×C13#53811yescharacteristic
498C22×C13#53911yescharacteristic
499C22×C13#53911yescharacteristic
500C22×C13#54011yescharacteristic
501C22×C13#54211yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#54611yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54711yescharacteristic
507C22×C13#54811yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55211yescharacteristic
512C22×C13#55211yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#56011yescharacteristic
517C22×C13#56311yescharacteristic
518C22×C13#56311yescharacteristic
519C22×C13#56311yescharacteristic
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—81no—
531Dic13—81no—
532Dic13—81no—
533Dic13—81no—
534C25C22×D1311yescharacteristic
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—262no—
544C23×C4—262no—
545C23×C4—262no—
546C23×C4—521no—
547C23×C4—521no—
548C23×C4—521no—
549C23×C4—521no—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4C2×Dic1314yescomplemented
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—521no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4C2×Dic1314yes—
584C2×C22⋊C4C2×Dic1314yes—
585C2×C22⋊C4C2×Dic1314yes—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—262no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42C2×Dic1314yescomplemented
592#95—134no—
593#95—262no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—521no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95C2×Dic1314yescomplemented
613#95C2×Dic1314yescomplemented
614C2×C13—44no—
615C2×C13#231811yescharacteristic
616C2×C13#232411yescharacteristic
617C2×C13#233711yescharacteristic
618C2×C13#234311yescharacteristic
619C2×C13#235211yescharacteristic
620C2×C13#235911yescharacteristic
621C2×C13#238311yescharacteristic
622C2×C13#268511yescharacteristic
623C2×C13#269511yescharacteristic
624C2×C13#270211yescharacteristic
625C2×C13#272311yescharacteristic
626C2×C13#273811yescharacteristic
627C2×C13#274911yescharacteristic
628C2×C13#276411yescharacteristic
629C2×C13#277011yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24#612712yes—
643C24#612712yes—
644C24C22×Dic1312yes—
645C24C23×D1311yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
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—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
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—524no—
737C22×C4—524no—
738C22×C4—524no—
739C22×C4—524no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4D4×D1312yes—
744C22×C4#612912yes—
745C22×C4C22×Dic1312yes—
746C22×C4C22×Dic1312yes—
747C22×C4C22×Dic1312yes—
748C22×C4C22×Dic1312yes—
749C22×C4C22×Dic1312yes—
750C22×C4C22×Dic1312yes—
751C4⋊C4—44no—
752C4⋊C4—524no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C42—28no—
762C42—524no—
763C13#1438911yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#8818014yes—
799C23C2×#612711yescharacteristic
800C23C2×#612711yescharacteristic
801C23C2×D4×D1311yescharacteristic
802C23C2×#612911yescharacteristic
803C23#8825111yescharacteristic
804C23#8825111yescharacteristic
805C23#41×D1311yescharacteristic
806C23#41×D1311yescharacteristic
807C23#8825611yescharacteristic
808C23#8825611yescharacteristic
809C23#8825611yescharacteristic
810C23#8825711yescharacteristic
811C23#8825711yescharacteristic
812C23#8825711yescharacteristic
813C23C23×Dic1311yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—5216no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
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×C4D4×Dic1314yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#1171923211yescharacteristic
929C22#1171923211yescharacteristic
930C22#1171923611yescharacteristic
931C22#1171923611yescharacteristic
932C22#1171924611yescharacteristic
933C22#1171925511yescharacteristic
934C22#1171925711yescharacteristic
935C22#1171926511yescharacteristic
936C22#1171926511yescharacteristic
937C22#1171926911yescharacteristic
938C22#1171926911yescharacteristic
939C22#1171927011yescharacteristic
940C22#1171930811yescharacteristic
941C22#1171931211yescharacteristic
942C22#1171931311yescharacteristic
943C22#1171932411yescharacteristic
944C22#1171935511yescharacteristic
945C22#1171935911yescharacteristic
946C22#1171936011yescharacteristic
947C22#1171936311yescharacteristic
948C22#1171937411yescharacteristic
949C22#1171937411yescharacteristic
950C22#1171938311yescharacteristic
951C22#1171938311yescharacteristic
952C22#1171941611yescharacteristic
953C22#1171941711yescharacteristic
954C22#1171941711yescharacteristic
955C22#1171941711yescharacteristic
956C22C2×#8818011yescharacteristic
957C22C2×D4×Dic1311yescharacteristic
958C22#1171950311yescharacteristic
959C22#41×Dic1311yescharacteristic
960C22#1171953211yescharacteristic
961C22#1171953211yescharacteristic
962C22#1171953211yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—522no—
970C4—522no—
971C4—522no—
972C4—522no—
973C4—1041no—
974C4—1041no—
975C4—1041no—
976C4—1041no—
977C2—44no—
978C2#1311746911yescharacteristic
979C2#1311753111yescharacteristic
980C2#1311765111yescharacteristic
981C2#1311769611yescharacteristic
982C2#1311776511yescharacteristic
983C2#1311783211yescharacteristic
984C2#1311802811yescharacteristic
985C2#1312123011yescharacteristic
986C2#1312137411yescharacteristic
987C2#1312146511yescharacteristic
988C2#1312175911yescharacteristic
989C2#1312190011yescharacteristic
990C2#1312205411yescharacteristic
991C2#1312226111yescharacteristic
992C2#1312234411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14389
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11718598C2semidirect
3. #13113104C2semidirect
4. #13113093C2semidirect
5. #13113093C2semidirect
6. #13113089C2semidirect
10. #13113070C2semidirect
11. #13113066C2semidirect
12. #13113061C2semidirect
29. C13×#388C4semidirect
78. C2×C13×C4⋊C4C2×C4semidirect
90. C2×C42×C13C2×C4semidirect
112. C13×#95C2×C4semidirect
113. C13×#95C2×C4semidirect
445. #388Dic13semidirect
567. C2×C4⋊C4C2×Dic13semidirect
591. C2×C42C2×Dic13semidirect
612. #95C2×Dic13semidirect
613. #95C2×Dic13semidirect
763. C13#14389semidirect

Maximal subgroups

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

subgroupindex
C2×#117186112
C2×#117185982
#131131042
#131130932
#131130892
#131130852
#131130812
#131130732
#131130702
#131130662
#131130612
#131130582
C2×C13×#3882
#1438913