Finite Group Databasebeta

← #15784444

Subgroups — #15784444

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718331C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×C4×#6103C211yesmaximal, characteristic
4C2×#11718327C211yesmaximal, characteristic
5C2×#11718309C211yesmaximal, characteristic, complemented
6#13113072C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113070C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113062C211yesmaximal, characteristic, complemented
11#13113057C211yesmaximal, characteristic
12C4×#88071C211yesmaximal, characteristic, complemented
13#95×Dic13C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
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×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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
52C4×#6103—24no—
53#11718331C418yescomplemented
54#11718327C418yescomplemented
55#11718309—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—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4—41no—
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—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103C2×C414yes—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103C2×C414yes—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×C4⋊Dic13C2×C414yescomplemented
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
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—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13C2×C414yes—
123C2×C4×Dic13C2×C414yes—
124C2×C4×Dic13C2×C414yescomplemented
125C2×C4×Dic13C2×C414yescomplemented
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—41no—
129C13×#95C2×C414yes—
130C13×#95C2×C414yescomplemented
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—41no—
139#88071C2×C414yes—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071D414yes—
144#13816—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
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×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C22×C412yes—
160C23×D13C22×C412yes—
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×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13#4112yes—
256C22×Dic13#4112yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C13×C4⋊C4—44no—
267C42×C13—44no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—44no—
272#6103—44no—
273#6103C42116yescomplemented
274C4⋊Dic13—44no—
275C4×Dic13—28no—
276C4×Dic13—28no—
277C4×Dic13—28no—
278C4×Dic13—44no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×C4×C22⋊C4—131no—
285C2×C4×C22⋊C4—131no—
286C2×#376—131no—
287#1437—131no—
288#1437—131no—
289#1436—131no—
290#1436D1311yescharacteristic, complemented
291C4⋊#95—131no—
292#1434—131no—
293C22⋊#95—131no—
294C4×#95—131no—
295C4×#95—131no—
296C4×#95—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C23×C411yescharacteristic
299C23×C13C23×C411yescharacteristic
300C23×C13C22×D411yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C132−1+411yescharacteristic
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—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
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×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13C2×C4214yes—
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—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
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×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13C2×C4214yes—
394C2×C4×C13#11714yes—
395C2×C4×C13C4×D414yes—
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—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
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×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13C2×C4214yes—
442C2×Dic13#11714yes—
443C2×Dic13C4×D414yes—
444C2×Dic13C4×D414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4C2×D1311yescharacteristic
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C42—131no—
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42C2×D1311yescharacteristic
463#388—138no—
464#388—138no—
465C4×C22⋊C4—138no—
466C4×C22⋊C4—264no—
467#376—264no—
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×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95C2×D1311yescharacteristic
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4211yescharacteristic
487C22×C13C2×#11711yescharacteristic
488C22×C13C2×#11711yescharacteristic
489C22×C13C2×C4×D411yescharacteristic
490C22×C13C2×C4×D411yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C4×#4111yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13C4×#4111yescharacteristic
496C22×C13C4×#4111yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13#51811yescharacteristic
500C22×C13#51811yescharacteristic
501C22×C13#51811yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#52011yescharacteristic
504C22×C13#52011yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54711yescharacteristic
508C22×C13#55011yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55111yescharacteristic
512C22×C13#55111yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55511yescharacteristic
518C22×C13#55511yescharacteristic
519C22×C13#55511yescharacteristic
520C22×C13#55611yescharacteristic
521C2×D13—24no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—24no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543Dic13—24no—
544Dic13—24no—
545Dic13—24no—
546Dic13—24no—
547Dic13—42no—
548Dic13—42no—
549Dic13—42no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—134no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—262no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—521no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4C4×D1314yescomplemented
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
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—521no—
593C2×C22⋊C4—521no—
594C2×C22⋊C4—521no—
595C2×C22⋊C4—521no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—41no—
599C2×C42—134no—
600C2×C42—134no—
601C2×C42—134no—
602C2×C42—134no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42—262no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—521no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—41no—
623#95—134no—
624#95—134no—
625#95—134no—
626#95—134no—
627#95—134no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—521no—
636#95C4×D1314yes—
637#95C4×D1314yescomplemented
638C2×C13C4×#11711yescharacteristic
639C2×C13C42×D411yescharacteristic
640C2×C13#227511yescharacteristic
641C2×C13#234211yescharacteristic
642C2×C13#234611yescharacteristic
643C2×C13#235311yescharacteristic
644C2×C13#235411yescharacteristic
645C2×C13#235911yescharacteristic
646C2×C13#235911yescharacteristic
647C2×C13#236311yescharacteristic
648C2×C13#236311yescharacteristic
649C2×C13#237211yescharacteristic
650C2×C13#237211yescharacteristic
651C2×C13#237311yescharacteristic
652C2×C13#237311yescharacteristic
653D13—44no—
654C24—132no—
655C24—132no—
656C24—132no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24—261no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24C23×D1311yescharacteristic
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—21no—
705C22×C4—21no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—268no—
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—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—268no—
757C22×C4—524no—
758C22×C4—524no—
759C22×C4—524no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4C2×C4×D1312yes—
763C22×C4C2×C4×D1312yes—
764C22×C4C2×C4×D1312yes—
765C22×C4C2×C4×D1312yes—
766C22×C4C2×C4×D1312yes—
767C22×C4C2×C4×D1312yes—
768C22×C4C2×C4×D1312yes—
769C22×C4C2×C4×D1312yes—
770C22×C4C2×C4×D1312yes—
771C22×C4D4×D1312yes—
772C22×C4#612912yes—
773C22×C4#613112yes—
774C22×C4#613112yes—
775C4⋊C4—44no—
776C4⋊C4—524no—
777C22⋊C4—1316no—
778C22⋊C4—268no—
779C22⋊C4—268no—
780C22⋊C4—268no—
781C22⋊C4—524no—
782C22⋊C4—524no—
783C42—44no—
784C42—268no—
785C42—268no—
786C42—268no—
787C42—524no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1381611yescharacteristic, complemented, Sylow
792C23—134no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23—521no—
818C23—521no—
819C23—521no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23C22×C4×D1311yescharacteristic
828C23C22×C4×D1311yescharacteristic
829C23C22×C4×D1311yescharacteristic
830C23C2×D4×D1311yescharacteristic
831C23C2×#612911yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23C2×#613111yescharacteristic
835C23C2×#613111yescharacteristic
836C23#41×D1311yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#8825611yescharacteristic
841C23#8825711yescharacteristic
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—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
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—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—134no—
889C2×C4—134no—
890C2×C4—134no—
891C2×C4—134no—
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—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—5216no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4C42×D1314yes—
939C2×C4#8814614yes—
940C2×C4#8814714yes—
941C22—264no—
942C22—264no—
943C22—264no—
944C22—522no—
945C22—522no—
946C22—522no—
947C22—522no—
948C22—522no—
949C22—522no—
950C22—522no—
951C22—522no—
952C22—522no—
953C22—522no—
954C22—522no—
955C22—522no—
956C22C2×C42×D1311yescharacteristic
957C22#1171919111yescharacteristic
958C22C2×#8814611yescharacteristic
959C22C2×#8814711yescharacteristic
960C22D13×#11711yescharacteristic
961C22#1171922711yescharacteristic
962C22#1171922811yescharacteristic
963C22C4×#612911yescharacteristic
964C22C4×#612911yescharacteristic
965C22C4×D4×D1311yescharacteristic
966C22C4×D4×D1311yescharacteristic
967C22#1171925011yescharacteristic
968C22#1171925011yescharacteristic
969C22#1171925111yescharacteristic
970C22#1171925111yescharacteristic
971C22C4×#613111yescharacteristic
972C22C4×#613111yescharacteristic
973C22C4×#613111yescharacteristic
974C22C4×#613111yescharacteristic
975C22#1171929611yescharacteristic
976C22#1171930411yescharacteristic
977C22#1171932111yescharacteristic
978C22#1171933511yescharacteristic
979C22#1171934211yescharacteristic
980C22#1171934211yescharacteristic
981C22#1171934711yescharacteristic
982C22#1171936011yescharacteristic
983C22#1171936311yescharacteristic
984C22#1171936611yescharacteristic
985C22#1171937511yescharacteristic
986C22#1171939911yescharacteristic
987C22#1171940011yescharacteristic
988C22#1171940711yescharacteristic
989C22#1171941011yescharacteristic
990C22#1171943911yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—264no—
999C4—264no—
1000C4—264no—
1001C4—264no—
1002C4—522no—
1003C4—522no—
1004C4—522no—
1005C2—524no—
1006C2C4×#8814611yescharacteristic
1007C2C4×#8814711yescharacteristic
1008C2#1311719511yescharacteristic
1009C2#1311768311yescharacteristic
1010C2#1311772011yescharacteristic
1011C2#1311777511yescharacteristic
1012C2#1311778211yescharacteristic
1013C2#1311782611yescharacteristic
1014C2#1311783511yescharacteristic
1015C2#1311787311yescharacteristic
1016C2#1311787711yescharacteristic
1017C2#1311794311yescharacteristic
1018C2#1311794711yescharacteristic
1019C2#1311795511yescharacteristic
1020C2#1311796211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#13816
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
5. C2×#11718309C2semidirect
8. #13113070C2semidirect
9. #13113065C2semidirect
10. #13113062C2semidirect
12. C4×#88071C2semidirect
13. #95×Dic13C2semidirect
14. #95×Dic13C2semidirect
15. C13×#1436C2semidirect
51. #11718651C4semidirect
53. #11718331C4semidirect
54. #11718327C4semidirect
80. C2×C13×C4⋊C4C2×C4semidirect
104. C2×C4⋊Dic13C2×C4semidirect
124. C2×C4×Dic13C2×C4semidirect
125. C2×C4×Dic13C2×C4semidirect
130. C13×#95C2×C4semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
273. #6103C42semidirect
290. #1436D13semidirect
577. C2×C4⋊C4C4×D13semidirect
637. #95C4×D13semidirect
791. C13#13816semidirect

Maximal subgroups

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

subgroupindex
C2×#117183312
C2×#117186512
C2×C4×#61032
C2×#117183272
C2×#117183092
#131130722
#131130702
#131130652
#131130622
#131130572
C4×#880712
#95×Dic132
C13×#14362
#1381613