Finite Group Databasebeta

← #15788289

Subgroups — #15788289

Order 3328.

1738 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×#11718653C211yesmaximal, characteristic
2C2×#11718639C211yesmaximal, characteristic, complemented
3C2×#11718650C211yesmaximal, characteristic
4C2×#11718310C211yesmaximal, characteristic, complemented
5C2×#11718327C211yesmaximal, characteristic
6#13113102C211yesmaximal, characteristic, complemented
7#13113080C211yesmaximal, characteristic
8#13113072C211yesmaximal, characteristic
9#13113072C211yesmaximal, characteristic
10#13113071C211yesmaximal, characteristic, complemented
11#13113068C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
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#11718653C418yescomplemented
52#11718650—24no—
53#11718639—24no—
54#11718327—24no—
55#11718310—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⋊C4—41no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4C2×C414yescomplemented
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—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103—41no—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103Q814yes—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—41no—
111C2×#6101C2×C414yescomplemented
112C2×#6101C2×C414yescomplemented
113C2×#6101D414yes—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13—41no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—41no—
129C13×#95—41no—
130C13×#95—41no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yescomplemented
143#88071D414yes—
144#14178—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×D13C2×Q812yes—
160C23×D13#4112yes—
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×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2×Q812yes—
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×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13C2×D412yes—
253C22×Dic13C2×Q812yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C22×Dic13#4112yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
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—
266C13×C4⋊C4—44no—
267C13×C4⋊C4—44no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274#6101—28no—
275#6101—28no—
276#6101—28no—
277#6101—44no—
278C4×Dic13—28no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#399—131no—
283C2×#387—131no—
284C2×#385—131no—
285C2×C4×C4⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1445—131no—
288#1441D1311yescharacteristic, complemented
289#1439—131no—
290#1437—131no—
291#1437—131no—
292#1436—131no—
293#1436—131no—
294#1436—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
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×D13C4×Q814yes—
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—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×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
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—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×Dic13C4×D414yes—
442C2×Dic13C4×D414yes—
443C2×Dic13C22⋊Q814yes—
444C2×Dic13#12314yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4C2×D1311yescharacteristic
452C22×C4⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463#399—138no—
464#387—264no—
465#385—264no—
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×#95C2×D1311yescharacteristic
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C2×C4×Q811yescharacteristic
489C22×C13C4×#4111yescharacteristic
490C22×C13C4×#4111yescharacteristic
491C22×C13#51811yescharacteristic
492C22×C13#52011yescharacteristic
493C22×C13C2×C22⋊Q811yescharacteristic
494C22×C13C2×#12311yescharacteristic
495C22×C13#52511yescharacteristic
496C22×C13#52511yescharacteristic
497C22×C13#52911yescharacteristic
498C22×C13#52911yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#53311yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53911yescharacteristic
503C22×C13#54011yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54711yescharacteristic
509C22×C13D4×Q811yescharacteristic
510C22×C13#55011yescharacteristic
511C22×C13#55011yescharacteristic
512C22×C13#55111yescharacteristic
513C22×C13#55111yescharacteristic
514C22×C13#55111yescharacteristic
515C22×C13#55211yescharacteristic
516C22×C13#55211yescharacteristic
517C22×C13#55411yescharacteristic
518C22×C13#55411yescharacteristic
519C22×C13#55411yescharacteristic
520C22×C13#55911yescharacteristic
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—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543Dic13—24no—
544Dic13—24no—
545Dic13—24no—
546Dic13—24no—
547Dic13—42no—
548Dic13—81no—
549Dic13—81no—
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—262no—
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—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—134no—
578C2×C4⋊C4—134no—
579C2×C4⋊C4—134no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4C4×D1314yescomplemented
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—134no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—262no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—521no—
605C2×C22⋊C4—521no—
606C2×C22⋊C4—521no—
607C2×C22⋊C4—521no—
608C2×C42—262no—
609C2×C42—262no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—134no—
626#95—134no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—521no—
637#95—521no—
638C2×C13C4×#12311yescharacteristic
639C2×C13C4×C22⋊Q811yescharacteristic
640C2×C13#233511yescharacteristic
641C2×C13#235911yescharacteristic
642C2×C13#236011yescharacteristic
643C2×C13#236611yescharacteristic
644C2×C13#236811yescharacteristic
645C2×C13#241811yescharacteristic
646C2×C13#242311yescharacteristic
647C2×C13#244911yescharacteristic
648C2×C13#245411yescharacteristic
649C2×C13#247111yescharacteristic
650C2×C13#247911yescharacteristic
651C2×C13#257511yescharacteristic
652C2×C13#258911yescharacteristic
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—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
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—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—268no—
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—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4—524no—
765C22×C4—524no—
766C22×C4—524no—
767C22×C4—524no—
768C22×C4C2×C4×D1312yes—
769C22×C4C2×C4×D1312yes—
770C22×C4C2×C4×D1312yes—
771C22×C4D4×D1312yes—
772C22×C4D4×D1312yes—
773C22×C4Q8×D1312yes—
774C22×C4#613112yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—268no—
778C4⋊C4—268no—
779C4⋊C4—268no—
780C4⋊C4—524no—
781C22⋊C4—268no—
782C22⋊C4—268no—
783C22⋊C4—268no—
784C22⋊C4—524no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C42—268no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1417811yescharacteristic, 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
828C23C2×D4×D1311yescharacteristic
829C23C2×D4×D1311yescharacteristic
830C23#8825111yescharacteristic
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23C2×Q8×D1311yescharacteristic
834C23C2×#613111yescharacteristic
835C23#8825411yescharacteristic
836C23#41×D1311yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#41×D1311yescharacteristic
841C23#41×D1311yescharacteristic
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—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—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—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—134no—
892C2×C4—134no—
893C2×C4—134no—
894C2×C4—134no—
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—5216no—
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×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
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—
956C22#1171919111yescharacteristic
957C22#1171920911yescharacteristic
958C22#1171922711yescharacteristic
959C22C4×D4×D1311yescharacteristic
960C22C4×D4×D1311yescharacteristic
961C22C4×Q8×D1311yescharacteristic
962C22C4×#613111yescharacteristic
963C22#1171929511yescharacteristic
964C22#1171930411yescharacteristic
965C22#1171930411yescharacteristic
966C22#1171931511yescharacteristic
967C22#1171931511yescharacteristic
968C22#1171931811yescharacteristic
969C22#1171932011yescharacteristic
970C22D13×C22⋊Q811yescharacteristic
971C22#1171933211yescharacteristic
972C22#1171934111yescharacteristic
973C22#1171934111yescharacteristic
974C22#1171934211yescharacteristic
975C22#1171934211yescharacteristic
976C22#1171934311yescharacteristic
977C22#1171934511yescharacteristic
978C22D13×#12311yescharacteristic
979C22#1171936111yescharacteristic
980C22#1171936911yescharacteristic
981C22#1171938411yescharacteristic
982C22#1171939311yescharacteristic
983C22#1171939611yescharacteristic
984C22#1171939811yescharacteristic
985C22#1171939811yescharacteristic
986C22#1171941111yescharacteristic
987C22#1171941111yescharacteristic
988C22#1171943111yescharacteristic
989C22#1171943211yescharacteristic
990C22#1171943511yescharacteristic
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—264no—
999C4—264no—
1000C4—264no—
1001C4—264no—
1002C4—522no—
1003C4—1041no—
1004C4—1041no—
1005C2—524no—
1006C2#1311735711yescharacteristic
1007C2#1311737011yescharacteristic
1008C2#1311762211yescharacteristic
1009C2#1311782311yescharacteristic
1010C2#1311783811yescharacteristic
1011C2#1311789911yescharacteristic
1012C2#1311791511yescharacteristic
1013C2#1311829111yescharacteristic
1014C2#1311835611yescharacteristic
1015C2#1311863811yescharacteristic
1016C2#1311870111yescharacteristic
1017C2#1311895011yescharacteristic
1018C2#1311906011yescharacteristic
1019C2#1312012011yescharacteristic
1020C2#1312029011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1441D13
hypocenterC13#14178
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#11718639C2semidirect
4. C2×#11718310C2semidirect
6. #13113102C2semidirect
10. #13113071C2semidirect
11. #13113068C2semidirect
12. #13113067C2semidirect
13. #13113064C2semidirect
15. C13×#1441C2semidirect
51. #11718653C4semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
111. C2×#6101C2×C4semidirect
112. C2×#6101C2×C4semidirect
142. #88071C2×C4semidirect
288. #1441D13semidirect
589. C2×C4⋊C4C4×D13semidirect
791. C13#14178semidirect

Maximal subgroups

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

subgroupindex
C2×#117186532
C2×#117186392
C2×#117186502
C2×#117183102
C2×#117183272
#131131022
#131130802
#131130722
#131130712
#131130682
#131130672
#131130642
#131130572
C13×#14412
#1417813