Finite Group Databasebeta

← #15784267

Subgroups — #15784267

Order 3328.

1826 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×#11718601C211yesmaximal, characteristic
3C2×#11718329C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic
6#13113074C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113071C211yesmaximal, characteristic, complemented
9#13113070C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113066C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
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#11718601C418yescomplemented
52C4×#6103—24no—
53C4×#6101—24no—
54#11718331C418yescomplemented
55#11718329C418yescomplemented
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—41no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C42×C13—22no—
79C2×C42×C13—41no—
80C2×C42×C13—41no—
81C2×C42×C13—41no—
82C2×C42×C13—41no—
83C2×C42×C13—41no—
84C2×C42×C13—41no—
85C2×C42×C13C2×C414yescomplemented
86C2×C42×C13D414yes—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103C2×C414yes—
102C2×#6103C2×C414yes—
103C2×#6103C2×C414yes—
104C2×#6103C2×C414yes—
105C2×C4⋊Dic13—41no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13—41no—
108C2×C4⋊Dic13—41no—
109C2×C4⋊Dic13C2×C414yes—
110C2×C4⋊Dic13C2×C414yescomplemented
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101C2×C414yes—
116C2×#6101C2×C414yescomplemented
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13C2×C414yescomplemented
126C13×#95—22no—
127C13×#95—22no—
128C13×#95C2×C414yes—
129C13×#95C2×C414yescomplemented
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071C2×C414yes—
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071C2×C414yescomplemented
144#13789—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×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
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×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
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×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C2×C4×D13—28no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C42×C13—44no—
267C42×C13—44no—
268C42×C13—44no—
269#6103—28no—
270#6103—28no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274#6103C42116yescomplemented
275C4⋊Dic13—44no—
276C4⋊Dic13—44no—
277#6101—28no—
278#6101—28no—
279C4×Dic13—28no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#385—131no—
285C2×C4×C4⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1437—131no—
288#1437—131no—
289#1436—131no—
290#1436—131no—
291#1436—131no—
292#1436—131no—
293C4⋊#95—131no—
294#1434—131no—
295C22⋊#95—131no—
296C4×#95D1311yescharacteristic, complemented
297C23×C13C23×C411yescharacteristic
298C23×C13C23×C411yescharacteristic
299C23×C13C23×C411yescharacteristic
300C23×C13C22×D411yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13H(5,𝔽2)11yescharacteristic
305C23×C13H(5,𝔽2)11yescharacteristic
306C23×C13H(5,𝔽2)11yescharacteristic
307C23×C13H(5,𝔽2)11yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C132−1+411yescharacteristic
310C23×C132−1+411yescharacteristic
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—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
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×C13C2×C4214yes—
393C2×C4×C13C4×D414yes—
394C2×C4×C13C4×D414yes—
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—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—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13C2×C4214yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460C22×C42C2×D1311yescharacteristic
461C22×C42C2×D1311yescharacteristic
462C22×C42C2×D1311yescharacteristic
463#388—138no—
464#388—138no—
465#385—138no—
466C4×C4⋊C4—264no—
467C4×C22⋊C4—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×#95—131no—
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4211yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C2×C4×D411yescharacteristic
489C22×C13C2×C4×D411yescharacteristic
490C22×C13C4×#4111yescharacteristic
491C22×C13C4×#4111yescharacteristic
492C22×C13C4×#4111yescharacteristic
493C22×C13#51811yescharacteristic
494C22×C13#51811yescharacteristic
495C22×C13#51811yescharacteristic
496C22×C13#51811yescharacteristic
497C22×C13#51911yescharacteristic
498C22×C13#52011yescharacteristic
499C22×C13#52011yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#52011yescharacteristic
504C22×C13#52011yescharacteristic
505C22×C13#53411yescharacteristic
506C22×C13#53511yescharacteristic
507C22×C13#53611yescharacteristic
508C22×C13#53711yescharacteristic
509C22×C13#53811yescharacteristic
510C22×C13#53811yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53911yescharacteristic
513C22×C13#53911yescharacteristic
514C22×C13#53911yescharacteristic
515C22×C13#54011yescharacteristic
516C22×C13#54111yescharacteristic
517C22×C13#54211yescharacteristic
518C22×C13#54211yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13#54211yescharacteristic
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—24no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543Dic13—24no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
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—521no—
562C23×C4—521no—
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—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4—521no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
586C2×C22⋊C4—134no—
587C2×C22⋊C4—134no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4—521no—
598C2×C22⋊C4—521no—
599C2×C22⋊C4—521no—
600C2×C22⋊C4—521no—
601C2×C22⋊C4—521no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42—134no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—521no—
615C2×C42—521no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42C4×D1314yescomplemented
619C2×C42D5214yes—
620#95—22no—
621#95—22no—
622#95—134no—
623#95—134no—
624#95—134no—
625#95—134no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—521no—
631#95—521no—
632#95—521no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95C4×D1314yes—
637#95C4×D1314yescomplemented
638C2×C13C42×D411yescharacteristic
639C2×C13#227411yescharacteristic
640C2×C13#227511yescharacteristic
641C2×C13#232111yescharacteristic
642C2×C13#232211yescharacteristic
643C2×C13#232311yescharacteristic
644C2×C13#232411yescharacteristic
645C2×C13#232511yescharacteristic
646C2×C13#232611yescharacteristic
647C2×C13#233211yescharacteristic
648C2×C13#233411yescharacteristic
649C2×C13#233411yescharacteristic
650C2×C13#233511yescharacteristic
651C2×C13#233511yescharacteristic
652C2×C13#233711yescharacteristic
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—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
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—261no—
752C22×C4—261no—
753C22×C4—268no—
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×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×D5212yes—
770C22×C4C2×D5212yes—
771C22×C4C2×D5212yes—
772C22×C4#612712yes—
773C22×C4#612712yes—
774C22×C4#612712yes—
775C4⋊C4—268no—
776C4⋊C4—268no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C22⋊C4—1316no—
780C22⋊C4—268no—
781C22⋊C4—268no—
782C22⋊C4—524no—
783C22⋊C4—524no—
784C22⋊C4—524no—
785C42—44no—
786C42—44no—
787C42—44no—
788C42—268no—
789C42—524no—
790C42—524no—
791C13#1378911yescharacteristic, 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
830C23C22×D5211yescharacteristic
831C23C2×#612711yescharacteristic
832C23C2×#612711yescharacteristic
833C23C2×#612711yescharacteristic
834C23#8825111yescharacteristic
835C23#8825111yescharacteristic
836C23#8825111yescharacteristic
837C23#8825411yescharacteristic
838C23#8825611yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
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—22no—
873C2×C4—22no—
874C2×C4—22no—
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—134no—
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—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—5216no—
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—
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×C4C42×D1314yes—
938C2×C4C4×D5214yes—
939C2×C4C4×D5214yes—
940C2×C4C4×D5214yes—
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
957C22C2×C4×D5211yescharacteristic
958C22C2×C4×D5211yescharacteristic
959C22C2×C4×D5211yescharacteristic
960C22C4×#612711yescharacteristic
961C22C4×#612711yescharacteristic
962C22C4×#612711yescharacteristic
963C22#1171919111yescharacteristic
964C22#1171919811yescharacteristic
965C22#1171919911yescharacteristic
966C22#1171920911yescharacteristic
967C22#1171921511yescharacteristic
968C22#1171922011yescharacteristic
969C22#1171922811yescharacteristic
970C22#1171922811yescharacteristic
971C22#1171923011yescharacteristic
972C22#1171923111yescharacteristic
973C22#1171923911yescharacteristic
974C22#1171923911yescharacteristic
975C22#1171925011yescharacteristic
976C22#1171925011yescharacteristic
977C22#1171925011yescharacteristic
978C22#1171925111yescharacteristic
979C22#1171925111yescharacteristic
980C22#1171925111yescharacteristic
981C22#1171926511yescharacteristic
982C22#1171926511yescharacteristic
983C22#1171926611yescharacteristic
984C22#1171926711yescharacteristic
985C22#1171926911yescharacteristic
986C22#1171926911yescharacteristic
987C22#1171927711yescharacteristic
988C22#1171927911yescharacteristic
989C22#1171928711yescharacteristic
990C22#1171928811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—264no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—522no—
1004C4—522no—
1005C2—524no—
1006C2C42×D5211yescharacteristic
1007C2#1311719011yescharacteristic
1008C2#1311719511yescharacteristic
1009C2#1311749611yescharacteristic
1010C2#1311750711yescharacteristic
1011C2#1311751911yescharacteristic
1012C2#1311753011yescharacteristic
1013C2#1311753911yescharacteristic
1014C2#1311754711yescharacteristic
1015C2#1311758711yescharacteristic
1016C2#1311760511yescharacteristic
1017C2#1311761111yescharacteristic
1018C2#1311762611yescharacteristic
1019C2#1311762811yescharacteristic
1020C2#1311764411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#13789
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. C2×C4×#6101C2semidirect
8. #13113071C2semidirect
9. #13113070C2semidirect
10. #13113070C2semidirect
11. #13113069C2semidirect
12. #13113066C2semidirect
13. #13113060C2semidirect
15. C4×C13×#95C2semidirect
51. #11718601C4semidirect
54. #11718331C4semidirect
55. #11718329C4semidirect
85. C2×C42×C13C2×C4semidirect
110. C2×C4⋊Dic13C2×C4semidirect
116. C2×#6101C2×C4semidirect
125. C2×C4×Dic13C2×C4semidirect
129. C13×#95C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
143. #88071C2×C4semidirect
274. #6103C42semidirect
296. C4×#95D13semidirect
618. C2×C42C4×D13semidirect
637. #95C4×D13semidirect
791. C13#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#117183312
C2×#117186012
C2×#117183292
C2×C4×#61012
C2×C4×#61032
#131130742
#131130722
#131130712
#131130702
#131130692
#131130662
#131130602
#131130572
C4×C13×#952
#1378913