Finite Group Databasebeta

← #15788280

Subgroups — #15788280

Order 3328.

1694 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×#11718611C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic
5#13113104C211yesmaximal, characteristic, complemented
6#13113093C211yesmaximal, characteristic, complemented
7#13113085C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113070C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C2×C13×#397C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#397C418yescomplemented
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
51C2×#88071C2211yescharacteristic
52C4⋊C4×Dic13—24no—
53#11718612—24no—
54#11718611—24no—
55C22⋊C4×Dic13—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×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4C2×C414yescomplemented
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4C2×C414yes—
88C2×C13×C22⋊C4C2×C414yes—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C22⋊Dic13—22no—
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⋊Dic13D414yes—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13D414yes—
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—22no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C13×#95C2×C414yescomplemented
121C13×#95C2×C414yescomplemented
122C13×#95C2×C414yescomplemented
123#88071—22no—
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—22no—
135#88071—22no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#14177—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×C13C2×D412yes—
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×C13C22×C412yes—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
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—28no—
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—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13#4112yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C22×Dic13#4112yes—
260C22×Dic13#4112yes—
261C22×Dic13#4112yes—
262C13×C4⋊C4—28no—
263C13×C22⋊C4—28no—
264C13×C22⋊C4—28no—
265C13×C22⋊C4—28no—
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268C22⋊Dic13—44no—
269C4⋊Dic13—28no—
270C4⋊Dic13—44no—
271C4⋊Dic13—44no—
272C4×Dic13—28no—
273C4×Dic13—44no—
274C4×Dic13—44no—
275C4×Dic13—44no—
276C2×#397D1311yescharacteristic
277C2×#388—131no—
278C2×#385—131no—
279C2×C4×C4⋊C4—131no—
280C2×C4×C22⋊C4—131no—
281#1445—131no—
282#1442—131no—
283#1440—131no—
284#1437—131no—
285#1436—131no—
286#1436—131no—
287#1436—131no—
288#1436—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×C13C4×D414yes—
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—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×C13C4×D414yes—
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—416no—
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—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13#12314yes—
439C2×Dic13#12314yes—
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⋊C4C2×D1311yescharacteristic
449C22×C22⋊C4C2×D1311yescharacteristic
450C22×C22⋊C4C2×D1311yescharacteristic
451C22×C42—131no—
452C22×C42—131no—
453C22×C42—131no—
454C22×C42—131no—
455#397Dic1318yescomplemented
456#388—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×#95—131no—
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×C4×D411yescharacteristic
496C22×C13C2×C4×D411yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13C4×#4111yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13C2×#12311yescharacteristic
503C22×C13C2×#12311yescharacteristic
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#54711yescharacteristic
519C22×C13#54811yescharacteristic
520C22×C13#54811yescharacteristic
521C22×C13#55111yescharacteristic
522C22×C13#55111yescharacteristic
523C22×C13#55211yescharacteristic
524C22×C13#55211yescharacteristic
525C22×C13#55311yescharacteristic
526C22×C13#55311yescharacteristic
527C22×C13#55611yescharacteristic
528C22×C13#55611yescharacteristic
529C22×C13#55911yescharacteristic
530C4×C13—24no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536Dic13—24no—
537Dic13—24no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—81no—
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—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⋊C4C2×Dic1314yescomplemented
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—134no—
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—521no—
592C2×C22⋊C4—521no—
593C2×C22⋊C4C2×Dic1314yes—
594C2×C22⋊C4C2×Dic1314yes—
595C2×C22⋊C4C2×Dic1314yes—
596C2×C42—262no—
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—262no—
609#95—262no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
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#95C2×Dic1314yescomplemented
626#95C2×Dic1314yescomplemented
627#95C2×Dic1314yescomplemented
628C2×C13—44no—
629C2×C13C4×#12311yescharacteristic
630C2×C13C4×#12311yescharacteristic
631C2×C13#233411yescharacteristic
632C2×C13#235911yescharacteristic
633C2×C13#236111yescharacteristic
634C2×C13#236711yescharacteristic
635C2×C13#237311yescharacteristic
636C2×C13#241811yescharacteristic
637C2×C13#242111yescharacteristic
638C2×C13#244311yescharacteristic
639C2×C13#244711yescharacteristic
640C2×C13#247711yescharacteristic
641C2×C13#247811yescharacteristic
642C2×C13#257711yescharacteristic
643C2×C13#259711yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24D4×D1312yes—
657C24#612912yes—
658C24C22×Dic1312yes—
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—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
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—268no—
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—524no—
752C22×C4—524no—
753C22×C4—524no—
754C22×C4—524no—
755C22×C4—524no—
756C22×C4—524no—
757C22×C4D4×D1312yes—
758C22×C4#612912yes—
759C22×C4C22×Dic1312yes—
760C22×C4C22×Dic1312yes—
761C22×C4C22×Dic1312yes—
762C22×C4C22×Dic1312yes—
763C22×C4C22×Dic1312yes—
764C22×C4C22×Dic1312yes—
765C4⋊C4—28no—
766C4⋊C4—268no—
767C4⋊C4—524no—
768C4⋊C4—524no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—268no—
773C22⋊C4—524no—
774C22⋊C4—524no—
775C42—268no—
776C42—524no—
777C42—524no—
778C42—524no—
779C13#1417711yescharacteristic, 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—
814C23D4×Dic1314yes—
815C23C2×D4×D1311yescharacteristic
816C23C2×D4×D1311yescharacteristic
817C23C2×#612911yescharacteristic
818C23C2×#612911yescharacteristic
819C23#41×D1311yescharacteristic
820C23#41×D1311yescharacteristic
821C23#41×D1311yescharacteristic
822C23#41×D1311yescharacteristic
823C23#41×D1311yescharacteristic
824C23#41×D1311yescharacteristic
825C23#8825611yescharacteristic
826C23#8825611yescharacteristic
827C23#8825711yescharacteristic
828C23#8825711yescharacteristic
829C23C23×Dic1311yescharacteristic
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—134no—
872C2×C4—134no—
873C2×C4—262no—
874C2×C4—262no—
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—5216no—
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×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×C4D4×Dic1314yes—
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—
944C22#1171930311yescharacteristic
945C22#1171931411yescharacteristic
946C22#1171931611yescharacteristic
947C22#1171932311yescharacteristic
948C22#1171935411yescharacteristic
949C22#1171935411yescharacteristic
950C22#1171935411yescharacteristic
951C22#1171935411yescharacteristic
952C22#1171935511yescharacteristic
953C22D13×#12311yescharacteristic
954C22D13×#12311yescharacteristic
955C22#1171935911yescharacteristic
956C22#1171936011yescharacteristic
957C22#1171936111yescharacteristic
958C22#1171936111yescharacteristic
959C22#1171936311yescharacteristic
960C22#1171937611yescharacteristic
961C22#1171938111yescharacteristic
962C22#1171938211yescharacteristic
963C22#1171938611yescharacteristic
964C22#1171940611yescharacteristic
965C22#1171940711yescharacteristic
966C22#1171940911yescharacteristic
967C22#1171941011yescharacteristic
968C22#1171941211yescharacteristic
969C22#1171941311yescharacteristic
970C22#1171941411yescharacteristic
971C22#1171941511yescharacteristic
972C22C2×D4×Dic1311yescharacteristic
973C22C2×D4×Dic1311yescharacteristic
974C22#41×Dic1311yescharacteristic
975C22#41×Dic1311yescharacteristic
976C22#41×Dic1311yescharacteristic
977C22#1171953211yescharacteristic
978C22#1171953211yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—264no—
986C4—264no—
987C4—522no—
988C4—522no—
989C4—522no—
990C4—522no—
991C4—1041no—
992C4—1041no—
993C2—44no—
994C2#123×Dic1311yescharacteristic
995C2#123×Dic1311yescharacteristic
996C2#1311761511yescharacteristic
997C2#1311783211yescharacteristic
998C2#1311785611yescharacteristic
999C2#1311791111yescharacteristic
1000C2#1311796011yescharacteristic
1001C2#1311829911yescharacteristic
1002C2#1311833211yescharacteristic
1003C2#1311856611yescharacteristic
1004C2#1311861811yescharacteristic
1005C2#1311903011yescharacteristic
1006C2#1311904711yescharacteristic
1007C2#1312015611yescharacteristic
1008C2#1312038811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#397C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#397D13
hypocenterC13#14177
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic13C2semidirect
5. #13113104C2semidirect
6. #13113093C2semidirect
9. #13113070C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113070C2semidirect
13. #13113061C2semidirect
31. C13×#397C4semidirect
80. C2×C13×C4⋊C4C2×C4semidirect
120. C13×#95C2×C4semidirect
121. C13×#95C2×C4semidirect
122. C13×#95C2×C4semidirect
455. #397Dic13semidirect
577. C2×C4⋊C4C2×Dic13semidirect
625. #95C2×Dic13semidirect
626. #95C2×Dic13semidirect
627. #95C2×Dic13semidirect
779. C13#14177semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117186112
C2×C4⋊C4×Dic132
C2×C22⋊C4×Dic132
#131131042
#131130932
#131130852
#131130732
#131130702
#131130612
#131130582
C2×C13×#3972
#1417713