Finite Group Databasebeta

← #15787079

Subgroups — #15787079

Order 3328.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718589C211yesmaximal, characteristic, complemented
2C2×#11718331C211yesmaximal, characteristic
3C2×#11718601C211yesmaximal, characteristic
4C2×#11718601C211yesmaximal, characteristic
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6#13113096C211yesmaximal, characteristic, complemented
7#13113088C211yesmaximal, characteristic, complemented
8#13113082C211yesmaximal, characteristic
9#13113080C211yesmaximal, characteristic
10#13113074C211yesmaximal, characteristic
11#13113072C211yesmaximal, characteristic
12#13113070C211yesmaximal, characteristic, complemented
13#13113069C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C22×C42×C13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
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#11718601—24no—
52#11718601—24no—
53C4×#6101—24no—
54#11718589—24no—
55#11718331C418yescomplemented
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
71C2×C42×C13—22no—
72C2×C42×C13—22no—
73C2×C42×C13—22no—
74C2×C42×C13—22no—
75C2×C42×C13—41no—
76C2×C42×C13—41no—
77C2×C42×C13—41no—
78C2×C42×C13—41no—
79C2×C42×C13D414yes—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
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×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—41no—
106C2×C4⋊Dic13C2×C414yes—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101D414yes—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—41no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13C2×C414yes—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95C2×C414yes—
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—22no—
137#88071—22no—
138#88071—41no—
139#88071C2×C414yes—
140#14077—131nomaximal, Sylow
141C24×C13C2411yescharacteristic
142C23×D13—21no—
143C23×D13—21no—
144C23×D13—21no—
145C23×D13—21no—
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13C22×C412yes—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13#4112yes—
201C22×C4×C13#4112yes—
202C22×C4×C13#4112yes—
203C22×C4×C13#4112yes—
204C22×C4×C13#4112yes—
205C22×C4×C13#4112yes—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13C2×D412yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C42×C13—44no—
256C42×C13—44no—
257C42×C13—44no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265C4⋊Dic13—28no—
266C4⋊Dic13—44no—
267#6101—28no—
268#6101—28no—
269#6101—44no—
270C4×Dic13—28no—
271C4×Dic13—44no—
272C2×#389—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×#388—131no—
276C2×C4×C4⋊C4—131no—
277#1443—131no—
278#1441—131no—
279#1439—131no—
280#1439—131no—
281#1437—131no—
282#1437—131no—
283#1436—131no—
284#1436—131no—
285#1434—131no—
286C4×#95D1311yescharacteristic, complemented
287C23×C13C23×C411yescharacteristic
288C23×C13C22×D411yescharacteristic
289C23×C13C22×D411yescharacteristic
290C23×C13C2×#4111yescharacteristic
291C23×C13C2×#4111yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4111yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13H(5,𝔽2)11yescharacteristic
299C23×C13H(5,𝔽2)11yescharacteristic
300C23×C132−1+411yescharacteristic
301C23×C132−1+411yescharacteristic
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—41no—
310C22×D13—41no—
311C22×D13—41no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
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—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13#11714yes—
384C2×C4×C13C4×D414yes—
385C2×C4×C13#12114yes—
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—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
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×Dic13C4×D414yes—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C4⋊C4—131no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4—131no—
443C22×C22⋊C4—131no—
444C22×C22⋊C4—131no—
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C42—131no—
448C22×C42—131no—
449C22×C42C2×D1311yescharacteristic
450C22×C42C2×D1311yescharacteristic
451C22×C42C2×D1311yescharacteristic
452#389—264no—
453#388—138no—
454#388—264no—
455#388—264no—
456C4×C4⋊C4—264no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
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×#95C2×D1311yescharacteristic
472C2×#95C2×D1311yescharacteristic
473C2×#95C2×D1311yescharacteristic
474C2×#95C2×D1311yescharacteristic
475C22×C13C2×#11711yescharacteristic
476C22×C13C2×C4×D411yescharacteristic
477C22×C13C2×C4×D411yescharacteristic
478C22×C13C4×#4111yescharacteristic
479C22×C13C4×#4111yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13C2×#12111yescharacteristic
483C22×C13#52511yescharacteristic
484C22×C13#52911yescharacteristic
485C22×C13#52911yescharacteristic
486C22×C13#52911yescharacteristic
487C22×C13#53211yescharacteristic
488C22×C13#53211yescharacteristic
489C22×C13#53211yescharacteristic
490C22×C13#53411yescharacteristic
491C22×C13#53611yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#54611yescharacteristic
495C22×C13#54611yescharacteristic
496C22×C13#54811yescharacteristic
497C22×C13#54811yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55211yescharacteristic
500C22×C13#55211yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55611yescharacteristic
506C22×C13#55611yescharacteristic
507C22×C13#55611yescharacteristic
508C22×C13#55611yescharacteristic
509C22×C13#55911yescharacteristic
510C2×D13—42no—
511C2×D13—42no—
512C2×D13—42no—
513C2×D13—42no—
514C2×D13—42no—
515C2×D13—42no—
516C2×D13—42no—
517C2×D13—81no—
518C2×D13—81no—
519C2×D13—81no—
520C2×D13—81no—
521C2×D13—81no—
522C2×D13—81no—
523C2×D13—81no—
524C2×D13—81no—
525C4×C13—24no—
526C4×C13—24no—
527C4×C13—24no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532Dic13—24no—
533Dic13—42no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—81no—
538Dic13—81no—
539C25—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C2×C4⋊C4—134no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—262no—
564C2×C4⋊C4—262no—
565C2×C4⋊C4—262no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—521no—
569C2×C22⋊C4—134no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—521no—
587C2×C22⋊C4—521no—
588C2×C22⋊C4—521no—
589C2×C22⋊C4—521no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—41no—
595C2×C42—41no—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42—134no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—521no—
603C2×C42—521no—
604C2×C42D5214yes—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—134no—
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#95C4×D1314yes—
623C2×C13#229311yescharacteristic
624C2×C13C4×#12111yescharacteristic
625C2×C13#232211yescharacteristic
626C2×C13#234711yescharacteristic
627C2×C13#235211yescharacteristic
628C2×C13#236711yescharacteristic
629C2×C13#237311yescharacteristic
630C2×C13#254311yescharacteristic
631C2×C13#254511yescharacteristic
632C2×C13#255811yescharacteristic
633C2×C13#256011yescharacteristic
634C2×C13#259411yescharacteristic
635C2×C13#259611yescharacteristic
636C2×C13#260211yescharacteristic
637C2×C13#260411yescharacteristic
638D13—82no—
639C24—132no—
640C24—261no—
641C24—261no—
642C24—261no—
643C24—261no—
644C24—261no—
645C24—261no—
646C24—261no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24C23×D1311yescharacteristic
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
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—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
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—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4C2×C4×D1312yes—
741C22×C4C2×C4×D1312yes—
742C22×C4C2×C4×D1312yes—
743C22×C4C2×D5212yes—
744C22×C4C2×D5212yes—
745C22×C4C2×D5212yes—
746C22×C4#612712yes—
747C22×C4#612712yes—
748C22×C4#612712yes—
749C22×C4#612712yes—
750C22×C4#612712yes—
751C22×C4D4×D1312yes—
752C22×C4#613112yes—
753C4⋊C4—268no—
754C4⋊C4—268no—
755C4⋊C4—268no—
756C4⋊C4—524no—
757C4⋊C4—524no—
758C22⋊C4—268no—
759C22⋊C4—268no—
760C22⋊C4—268no—
761C22⋊C4—524no—
762C22⋊C4—524no—
763C22⋊C4—524no—
764C22⋊C4—524no—
765C42—44no—
766C42—44no—
767C42—44no—
768C42—268no—
769C42—524no—
770C13#1407711yescharacteristic, complemented, Sylow
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—262no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23—521no—
791C23—521no—
792C23—521no—
793C23—521no—
794C23—521no—
795C23—521no—
796C23—521no—
797C23—521no—
798C23—521no—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23C22×C4×D1311yescharacteristic
807C23C22×D5211yescharacteristic
808C23C2×#612711yescharacteristic
809C23C2×#612711yescharacteristic
810C23C2×#612711yescharacteristic
811C23C2×#612711yescharacteristic
812C23C2×#612711yescharacteristic
813C23C2×D4×D1311yescharacteristic
814C23#8825111yescharacteristic
815C23#8825111yescharacteristic
816C23C2×#613111yescharacteristic
817C23#41×D1311yescharacteristic
818C23#41×D1311yescharacteristic
819C23#8825711yescharacteristic
820C23#8825711yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
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—134no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
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—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
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#8812614yes—
917C2×C4C4×D5214yes—
918C2×C4#8814914yes—
919C22—522no—
920C22—522no—
921C22—522no—
922C22—522no—
923C22—522no—
924C22—522no—
925C22—522no—
926C22—1041no—
927C22—1041no—
928C22—1041no—
929C22—1041no—
930C22—1041no—
931C22—1041no—
932C22—1041no—
933C22—1041no—
934C22C2×#8812611yescharacteristic
935C22C2×C4×D5211yescharacteristic
936C22C4×#612711yescharacteristic
937C22#1171918211yescharacteristic
938C22#1171918211yescharacteristic
939C22#1171918411yescharacteristic
940C22#1171918411yescharacteristic
941C22#1171919511yescharacteristic
942C22#1171919511yescharacteristic
943C22#1171919811yescharacteristic
944C22C2×#8814911yescharacteristic
945C22#1171921911yescharacteristic
946C22#1171921911yescharacteristic
947C22#1171922911yescharacteristic
948C22#1171923111yescharacteristic
949C22#1171923611yescharacteristic
950C22#1171923611yescharacteristic
951C22#1171923811yescharacteristic
952C22#1171923811yescharacteristic
953C22#1171924511yescharacteristic
954C22C4×D4×D1311yescharacteristic
955C22#1171925111yescharacteristic
956C22#1171925111yescharacteristic
957C22#1171925311yescharacteristic
958C22#1171925711yescharacteristic
959C22#1171925711yescharacteristic
960C22#1171926111yescharacteristic
961C22#1171926311yescharacteristic
962C22#1171926411yescharacteristic
963C22#1171926911yescharacteristic
964C22#1171926911yescharacteristic
965C22C4×#613111yescharacteristic
966C22#1171928511yescharacteristic
967C22#1171928911yescharacteristic
968C22#1171928911yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—264no—
977C4—522no—
978C4—522no—
979C4—522no—
980C4—522no—
981C4—1041no—
982C4—1041no—
983C2—1042no—
984C2#1311730011yescharacteristic
985C2C4×#8814911yescharacteristic
986C2#1311750711yescharacteristic
987C2#1311772511yescharacteristic
988C2#1311775911yescharacteristic
989C2#1311790811yescharacteristic
990C2#1311795011yescharacteristic
991C2#1311979611yescharacteristic
992C2#1311981611yescharacteristic
993C2#1311995011yescharacteristic
994C2#1311998011yescharacteristic
995C2#1312034211yescharacteristic
996C2#1312037211yescharacteristic
997C2#1312044211yescharacteristic
998C2#1312047411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#14077
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
1. C2×#11718589C2semidirect
5. C2×C4×#6101C2semidirect
6. #13113096C2semidirect
7. #13113088C2semidirect
12. #13113070C2semidirect
13. #13113069C2semidirect
14. #13113060C2semidirect
15. C4×C13×#95C2semidirect
55. #11718331C4semidirect
286. C4×#95D13semidirect
770. C13#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#117185892
C2×#117183312
C2×#117186012
C2×C4×#61012
#131130962
#131130882
#131130822
#131130802
#131130742
#131130722
#131130702
#131130692
#131130602
C4×C13×#952
#1407713