Finite Group Databasebeta

← #15786476

Subgroups — #15786476

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×#11718651C211yesmaximal, characteristic
2C2×#11718642C211yesmaximal, characteristic, complemented
3C2×#11718329C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic
6#13113094C211yesmaximal, characteristic, complemented
7#13113092C211yesmaximal, characteristic, complemented
8#13113084C211yesmaximal, characteristic
9#13113080C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113071C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
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#11718651C418yescomplemented
52#11718642—24no—
53C4×#6103—24no—
54C4×#6101—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—22no—
75C22×C4×D13—22no—
76C22×C4×D13—41no—
77C22×C4×D13—41no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4C2×C414yescomplemented
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—41no—
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—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—41no—
98C2×#6103—41no—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103C2×C414yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—41no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101D414yes—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13C2×C414yescomplemented
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—41no—
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×C13C2411yescharacteristic
142C23×D13—21no—
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×D13C22×C412yes—
155C23×D13#4112yes—
156C23×D13#4112yes—
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×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13#4112yes—
203C22×C4×C13#4112yes—
204C22×C4×C13#4112yes—
205C22×C4×C13#4112yes—
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—21no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13C2×D412yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C2×C4×D13—28no—
256C2×C4×D13—44no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C13×C4⋊C4—28no—
263C42×C13—44no—
264#6103—28no—
265#6103—28no—
266#6103—28no—
267#6103—28no—
268#6103—44no—
269#6103—44no—
270C4⋊Dic13—44no—
271#6101—28no—
272#6101—28no—
273C4×Dic13—28no—
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#1440—131no—
284#1439—131no—
285#1437—131no—
286#1436—131no—
287#1436D1311yescharacteristic, complemented
288#1434—131no—
289#1434—131no—
290C22⋊#95—131no—
291C23×C13C23×C411yescharacteristic
292C23×C13C22×D411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13C2×#4111yescharacteristic
299C23×C13C2×#4111yescharacteristic
300C23×C13C2×#4111yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13H(5,𝔽2)11yescharacteristic
303C23×C13H(5,𝔽2)11yescharacteristic
304C23×C132−1+411yescharacteristic
305C23×C132−1+411yescharacteristic
306C22×D13—22no—
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—41no—
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#11714yes—
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—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
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×C13C4×D414yes—
389C2×C4×C13#12314yes—
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—22no—
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×Dic13C4×D414yes—
439C4×D13—416no—
440C24×C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4C2×D1311yescharacteristic
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C42—131no—
452C22×C42—131no—
453C22×C42—131no—
454C22×C42C2×D1311yescharacteristic
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×#95C2×D1311yescharacteristic
476C2×#95C2×D1311yescharacteristic
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C22×C13C2×#11711yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C2×C4×D411yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13C4×#4111yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13C2×#12311yescharacteristic
488C22×C13#52511yescharacteristic
489C22×C13#52511yescharacteristic
490C22×C13#52511yescharacteristic
491C22×C13#52911yescharacteristic
492C22×C13#52911yescharacteristic
493C22×C13#52911yescharacteristic
494C22×C13#52911yescharacteristic
495C22×C13#53811yescharacteristic
496C22×C13#53911yescharacteristic
497C22×C13#54111yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13D4211yescharacteristic
500C22×C13#54611yescharacteristic
501C22×C13#54611yescharacteristic
502C22×C13#54711yescharacteristic
503C22×C13#54811yescharacteristic
504C22×C13#54811yescharacteristic
505C22×C13#54811yescharacteristic
506C22×C13#55111yescharacteristic
507C22×C13#55111yescharacteristic
508C22×C13#55211yescharacteristic
509C22×C13#55211yescharacteristic
510C22×C13#55211yescharacteristic
511C22×C13#55311yescharacteristic
512C22×C13#55311yescharacteristic
513C22×C13#55611yescharacteristic
514C22×C13#55911yescharacteristic
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—42no—
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—
530C4×C13—24no—
531C4×C13—24no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—81no—
536C4×C13—81no—
537Dic13—24no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—42no—
544C25—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—262no—
553C23×C4—262no—
554C23×C4—262no—
555C23×C4—262no—
556C23×C4—262no—
557C23×C4—521no—
558C23×C4—521no—
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—134no—
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—521no—
577C2×C4⋊C4C4×D1314yescomplemented
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
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⋊C4—521no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—41no—
599C2×C42—134no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—262no—
606C2×C42—521no—
607C2×C42—521no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—134no—
614#95—134no—
615#95—134no—
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#229011yescharacteristic
629C2×C13C4×#12311yescharacteristic
630C2×C13#233411yescharacteristic
631C2×C13#234311yescharacteristic
632C2×C13#235211yescharacteristic
633C2×C13#236111yescharacteristic
634C2×C13#236711yescharacteristic
635C2×C13#241811yescharacteristic
636C2×C13#242111yescharacteristic
637C2×C13#245811yescharacteristic
638C2×C13#246311yescharacteristic
639C2×C13#246811yescharacteristic
640C2×C13#247511yescharacteristic
641C2×C13#257311yescharacteristic
642C2×C13#259511yescharacteristic
643D13—44no—
644C24—132no—
645C24—132no—
646C24—132no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24—261no—
656C24—261no—
657C24—261no—
658C24—261no—
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—21no—
698C22×C4—21no—
699C22×C4—21no—
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—268no—
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—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—524no—
751C22×C4—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4—524no—
755C22×C4—524no—
756C22×C4C2×C4×D1312yes—
757C22×C4C2×C4×D1312yes—
758C22×C4C2×C4×D1312yes—
759C22×C4#612712yes—
760C22×C4#612712yes—
761C22×C4D4×D1312yes—
762C22×C4D4×D1312yes—
763C22×C4#612912yes—
764C22×C4#613112yes—
765C4⋊C4—28no—
766C4⋊C4—268no—
767C4⋊C4—268no—
768C4⋊C4—524no—
769C22⋊C4—268no—
770C22⋊C4—268no—
771C22⋊C4—268no—
772C22⋊C4—268no—
773C22⋊C4—524no—
774C22⋊C4—524no—
775C42—44no—
776C42—268no—
777C42—524no—
778C42—524no—
779C13#1403211yescharacteristic, complemented, Sylow
780C23—134no—
781C23—262no—
782C23—262no—
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—521no—
800C23—521no—
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—
815C23C22×C4×D1311yescharacteristic
816C23C2×#612711yescharacteristic
817C23C2×#612711yescharacteristic
818C23C2×D4×D1311yescharacteristic
819C23C2×D4×D1311yescharacteristic
820C23C2×#612911yescharacteristic
821C23#8825111yescharacteristic
822C23C2×#613111yescharacteristic
823C23#8825411yescharacteristic
824C23#41×D1311yescharacteristic
825C23#41×D1311yescharacteristic
826C23#41×D1311yescharacteristic
827C23#41×D1311yescharacteristic
828C23#8825611yescharacteristic
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—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
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—134no—
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—5216no—
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#8813514yes—
928C2×C4#8814814yes—
929C22—264no—
930C22—264no—
931C22—264no—
932C22—522no—
933C22—522no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22—522no—
941C22—522no—
942C22—522no—
943C22—522no—
944C22C4×#612711yescharacteristic
945C22C2×#8813511yescharacteristic
946C22C2×#8814811yescharacteristic
947C22#1171922011yescharacteristic
948C22D13×#11711yescharacteristic
949C22#1171923311yescharacteristic
950C22#1171923911yescharacteristic
951C22C4×D4×D1311yescharacteristic
952C22#1171925111yescharacteristic
953C22#1171925211yescharacteristic
954C22#1171925211yescharacteristic
955C22#1171925211yescharacteristic
956C22#1171926211yescharacteristic
957C22#1171926211yescharacteristic
958C22#1171926511yescharacteristic
959C22C4×#613111yescharacteristic
960C22#1171927911yescharacteristic
961C22#1171928511yescharacteristic
962C22#1171928811yescharacteristic
963C22#1171929511yescharacteristic
964C22#1171930311yescharacteristic
965C22#1171930611yescharacteristic
966C22#1171933511yescharacteristic
967C22#1171933811yescharacteristic
968C22#1171933811yescharacteristic
969C22#1171934211yescharacteristic
970C22#1171935911yescharacteristic
971C22#1171936011yescharacteristic
972C22#1171936411yescharacteristic
973C22#1171938611yescharacteristic
974C22#1171939811yescharacteristic
975C22#1171939911yescharacteristic
976C22#1171941311yescharacteristic
977C22#1171941411yescharacteristic
978C22#1171943711yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4—264no—
987C4—522no—
988C4—522no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4—522no—
993C2—524no—
994C2#1311728211yescharacteristic
995C2C4×#8814811yescharacteristic
996C2#1311760511yescharacteristic
997C2#1311769511yescharacteristic
998C2#1311776011yescharacteristic
999C2#1311784711yescharacteristic
1000C2#1311791211yescharacteristic
1001C2#1311830011yescharacteristic
1002C2#1311834011yescharacteristic
1003C2#1311876011yescharacteristic
1004C2#1311883211yescharacteristic
1005C2#1311890411yescharacteristic
1006C2#1311900911yescharacteristic
1007C2#1312009711yescharacteristic
1008C2#1312035911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#14032
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#11718642C2semidirect
4. C2×C4×#6101C2semidirect
6. #13113094C2semidirect
7. #13113092C2semidirect
11. #13113071C2semidirect
12. #13113062C2semidirect
13. #13113061C2semidirect
15. C13×#1436C2semidirect
51. #11718651C4semidirect
80. C2×C13×C4⋊C4C2×C4semidirect
119. C2×C4×Dic13C2×C4semidirect
137. #88071C2×C4semidirect
138. #88071C2×C4semidirect
287. #1436D13semidirect
577. C2×C4⋊C4C4×D13semidirect
779. C13#14032semidirect

Maximal subgroups

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

subgroupindex
C2×#117186512
C2×#117186422
C2×#117183292
C2×C4×#61012
C2×C4×#61032
#131130942
#131130922
#131130842
#131130802
#131130722
#131130712
#131130622
#131130612
#131130572
C13×#14362
#1403213