Finite Group Databasebeta

← #15786469

Subgroups — #15786469

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C211yesmaximal, characteristic
2C2×#11718314C211yesmaximal, characteristic, complemented
3C2×#11718607C211yesmaximal, characteristic
4C2×#11718310C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6#13113094C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C13×#1440C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
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
51#11718612C418yescomplemented
52#11718607—24no—
53C22⋊C4×Dic13—24no—
54#11718314—24no—
55#11718310—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—41no—
69C23×Dic13—41no—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4C2×C414yes—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13C2×C414yes—
95C2×C22⋊Dic13C2×C414yes—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13C2×C414yescomplemented
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—41no—
107C2×#6101D414yes—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13C2×C414yescomplemented
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—41no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071C2×C414yescomplemented
138#88071C2×C414yescomplemented
139#88071D414yes—
140#14032—131nomaximal, Sylow
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13C22×C412yes—
154C24×C13#4112yes—
155C24×C13#4112yes—
156C24×C13C2411yescharacteristic
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×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×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13#4112yes—
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—28no—
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—44no—
244C22×Dic13—44no—
245C22×Dic13—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C22×Dic13#4112yes—
260C22×Dic13#4112yes—
261C22×Dic13#4112yes—
262C13×C22⋊C4—28no—
263C13×C22⋊C4—28no—
264C13×C22⋊C4—44no—
265C22⋊Dic13—28no—
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268C4⋊Dic13—28no—
269#6101—28no—
270#6101—28no—
271#6101—44no—
272C4×Dic13—28no—
273C4×Dic13—44no—
274C4×Dic13—44no—
275C4×Dic13—44no—
276C2×#388—131no—
277C2×#387—131no—
278C2×#385—131no—
279C2×C4×C4⋊C4—131no—
280C2×C4×C22⋊C4—131no—
281#1442—131no—
282#1442—131no—
283#1440D1311yescharacteristic
284#1439—131no—
285#1437—131no—
286#1436—131no—
287#1436—131no—
288#1434—131no—
289#1434—131no—
290C22⋊#95—131no—
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—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
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—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13#11714yes—
326C23×C13C23×C411yescharacteristic
327C23×C13C22×D411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C13H(5,𝔽2)11yescharacteristic
339C23×C132−1+411yescharacteristic
340C23×C132−1+411yescharacteristic
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—22no—
355C2×C4×C13—22no—
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×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×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
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—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—416no—
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×Dic13C4×D414yes—
438C2×Dic13C4×D414yes—
439C2×Dic13#12314yes—
440C24×C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—131no—
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4C2×D1311yescharacteristic
449C22×C22⋊C4C2×D1311yescharacteristic
450C22×C22⋊C4C2×D1311yescharacteristic
451C22×C42—131no—
452C22×C42—131no—
453C22×C42—131no—
454C22×C42—131no—
455#388—138no—
456#387—264no—
457#385—264no—
458C4×C4⋊C4—264no—
459C4×C22⋊C4—264no—
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×#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
480C22×C13—24no—
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13C2×#11711yescharacteristic
496C22×C13C2×C4×D411yescharacteristic
497C22×C13C2×C4×D411yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13C4×#4111yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13C2×#12311yescharacteristic
503C22×C13#52511yescharacteristic
504C22×C13#52511yescharacteristic
505C22×C13#52511yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#52911yescharacteristic
509C22×C13#52911yescharacteristic
510C22×C13#53811yescharacteristic
511C22×C13#53911yescharacteristic
512C22×C13#54111yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13D4211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54811yescharacteristic
519C22×C13#54811yescharacteristic
520C22×C13#54811yescharacteristic
521C22×C13#55111yescharacteristic
522C22×C13#55111yescharacteristic
523C22×C13#55211yescharacteristic
524C22×C13#55211yescharacteristic
525C22×C13#55211yescharacteristic
526C22×C13#55311yescharacteristic
527C22×C13#55311yescharacteristic
528C22×C13#55611yescharacteristic
529C22×C13#55911yescharacteristic
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—81no—
536Dic13—24no—
537Dic13—24no—
538Dic13—24no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—81no—
544C25C22×D1311yescharacteristic
545C23×C4—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—262no—
557C23×C4—262no—
558C23×C4—521no—
559C23×C4—521no—
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—521no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—134no—
587C2×C22⋊C4—134no—
588C2×C22⋊C4—262no—
589C2×C22⋊C4—262no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—521no—
595C2×C22⋊C4C4×D1314yes—
596C2×C42—134no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—521no—
606C2×C42—521no—
607C2×C42—521no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—134no—
613#95—134no—
614#95—134no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—521no—
626#95—521no—
627#95—521no—
628C2×C13—44no—
629C2×C13#229011yescharacteristic
630C2×C13C4×#12311yescharacteristic
631C2×C13#233411yescharacteristic
632C2×C13#234311yescharacteristic
633C2×C13#235211yescharacteristic
634C2×C13#236111yescharacteristic
635C2×C13#236711yescharacteristic
636C2×C13#241811yescharacteristic
637C2×C13#242111yescharacteristic
638C2×C13#245811yescharacteristic
639C2×C13#246311yescharacteristic
640C2×C13#246811yescharacteristic
641C2×C13#247511yescharacteristic
642C2×C13#257311yescharacteristic
643C2×C13#259511yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1312yes—
657C24#612912yes—
658C24#612912yes—
659C24C23×D1311yescharacteristic
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—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—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
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—268no—
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—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×C4D4×D1312yes—
763C22×C4D4×D1312yes—
764C22×C4#612912yes—
765C4⋊C4—268no—
766C4⋊C4—268no—
767C4⋊C4—268no—
768C4⋊C4—524no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—44no—
772C22⋊C4—268no—
773C22⋊C4—268no—
774C22⋊C4—524no—
775C42—268no—
776C42—524no—
777C42—524no—
778C42—524no—
779C13#1403211yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23#8813114yes—
815C23C22×C4×D1311yescharacteristic
816C23C2×D4×D1311yescharacteristic
817C23C2×D4×D1311yescharacteristic
818C23C2×#612911yescharacteristic
819C23C2×#612911yescharacteristic
820C23C2×#612911yescharacteristic
821C23#8825111yescharacteristic
822C23#41×D1311yescharacteristic
823C23#41×D1311yescharacteristic
824C23#41×D1311yescharacteristic
825C23#41×D1311yescharacteristic
826C23#41×D1311yescharacteristic
827C23#8825611yescharacteristic
828C23#8825711yescharacteristic
829C23#8825711yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
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—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—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—134no—
873C2×C4—134no—
874C2×C4—134no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
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—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—5216no—
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—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×#8813111yescharacteristic
945C22#1171922711yescharacteristic
946C22#1171922811yescharacteristic
947C22C4×#612911yescharacteristic
948C22C4×D4×D1311yescharacteristic
949C22C4×D4×D1311yescharacteristic
950C22#1171925111yescharacteristic
951C22#1171929111yescharacteristic
952C22#1171929611yescharacteristic
953C22#1171930311yescharacteristic
954C22#1171930511yescharacteristic
955C22#1171930611yescharacteristic
956C22#1171930811yescharacteristic
957C22#1171931111yescharacteristic
958C22#1171931111yescharacteristic
959C22#1171931411yescharacteristic
960C22#1171931511yescharacteristic
961C22#1171935411yescharacteristic
962C22#1171935511yescharacteristic
963C22#1171935511yescharacteristic
964C22#1171935511yescharacteristic
965C22D13×#12311yescharacteristic
966C22#1171936011yescharacteristic
967C22#1171936311yescharacteristic
968C22#1171936311yescharacteristic
969C22#1171936911yescharacteristic
970C22#1171937011yescharacteristic
971C22#1171938211yescharacteristic
972C22#1171938211yescharacteristic
973C22#1171938311yescharacteristic
974C22#1171938511yescharacteristic
975C22#1171940611yescharacteristic
976C22#1171940711yescharacteristic
977C22#1171941111yescharacteristic
978C22#1171941411yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—264no—
986C4—264no—
987C4—264no—
988C4—522no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4—1041no—
993C2—44no—
994C2#1311727611yescharacteristic
995C2#1311736311yescharacteristic
996C2#1311761811yescharacteristic
997C2#1311769811yescharacteristic
998C2#1311776311yescharacteristic
999C2#1311784911yescharacteristic
1000C2#1311790211yescharacteristic
1001C2#1311829311yescharacteristic
1002C2#1311833211yescharacteristic
1003C2#1311875911yescharacteristic
1004C2#1311882811yescharacteristic
1005C2#1311889711yescharacteristic
1006C2#1311900811yescharacteristic
1007C2#1312009611yescharacteristic
1008C2#1312036011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1440C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1440D13
hypocenterC13#14032
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#11718314C2semidirect
4. C2×#11718310C2semidirect
6. #13113094C2semidirect
7. #13113094C2semidirect
10. #13113070C2semidirect
11. #13113067C2semidirect
12. #13113062C2semidirect
13. #13113060C2semidirect
51. #11718612C4semidirect
98. C2×C4⋊Dic13C2×C4semidirect
119. C2×C4×Dic13C2×C4semidirect
137. #88071C2×C4semidirect
138. #88071C2×C4semidirect
779. C13#14032semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117183142
C2×#117186072
C2×#117183102
C2×C22⋊C4×Dic132
#131130942
#131130792
#131130732
#131130702
#131130672
#131130622
#131130602
#131130582
C13×#14402
#1403213