Finite Group Databasebeta

← #15786459

Subgroups — #15786459

Order 3328.

1594 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×#11718601C211yesmaximal, characteristic
2C2×#11718601C211yesmaximal, characteristic
3C2×#11718651C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic, complemented
5#13113099C211yesmaximal, characteristic, complemented
6#13113097C211yesmaximal, characteristic, complemented
7#13113080C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113074C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113063C211yesmaximal, characteristic, complemented
15C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C4×C13×C4⋊C4—24no—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52#11718651—24no—
53#11718601—24no—
54#11718601C418yescomplemented
55C4×#6101—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
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4D414yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—41no—
84C2×C42×C13—41no—
85C2×C42×C13C2×C414yes—
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—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—41no—
101C2×#6103—41no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103C2×C414yes—
105C2×#6103C2×C414yes—
106C2×#6103C2×C414yes—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—41no—
115C2×#6101C2×C414yes—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—41no—
122C13×#95—22no—
123C13×#95—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071C2×C414yes—
138#88071C2×C414yes—
139#88071D414yes—
140#14031—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—
255C13×C4⋊C4—28no—
256C13×C4⋊C4—28no—
257C42×C13—28no—
258C42×C13—44no—
259C42×C13—44no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6101—28no—
268#6101—28no—
269#6101—44no—
270C4×Dic13—28no—
271C4×Dic13—44no—
272C2×#388—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×C4×C4⋊C4—131no—
276C2×C4×C4⋊C4D1311yescharacteristic, complemented
277#1444—131no—
278#1443—131no—
279#1439—131no—
280#1439—131no—
281#1437—131no—
282#1437—131no—
283#1436—131no—
284#1436—131no—
285#1436—131no—
286#1434—131no—
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×C13C4×D414yes—
384C2×C4×C13C4×D414yes—
385C2×C4×C13#12314yes—
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×Dic13#11714yes—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C4⋊C4—131no—
438C22×C4⋊C4C2×D1311yescharacteristic
439C22×C4⋊C4C2×D1311yescharacteristic
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#388—138no—
453#388—264no—
454#388—264no—
455C4×C4⋊C4—24no—
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×#95—131no—
472C2×#95—131no—
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×#12311yescharacteristic
483C22×C13#52511yescharacteristic
484C22×C13#52511yescharacteristic
485C22×C13#52511yescharacteristic
486C22×C13#52911yescharacteristic
487C22×C13#52911yescharacteristic
488C22×C13#52911yescharacteristic
489C22×C13#52911yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#54111yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13D4211yescharacteristic
495C22×C13#54611yescharacteristic
496C22×C13#54711yescharacteristic
497C22×C13#54711yescharacteristic
498C22×C13#54811yescharacteristic
499C22×C13#54811yescharacteristic
500C22×C13#55011yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55511yescharacteristic
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—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—134no—
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—521no—
568C2×C4⋊C4C22⋊D1314yes—
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—22no—
595C2×C42—22no—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—521no—
604C2×C42C4×D1314yes—
605#95—22no—
606#95—22no—
607#95—134no—
608#95—134no—
609#95—134no—
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—521no—
620#95—521no—
621#95—521no—
622#95—521no—
623C2×C13#229011yescharacteristic
624C2×C13C4×#12311yescharacteristic
625C2×C13#233411yescharacteristic
626C2×C13#234711yescharacteristic
627C2×C13#235411yescharacteristic
628C2×C13#236111yescharacteristic
629C2×C13#236711yescharacteristic
630C2×C13#244311yescharacteristic
631C2×C13#244811yescharacteristic
632C2×C13#245611yescharacteristic
633C2×C13#246911yescharacteristic
634C2×C13#246911yescharacteristic
635C2×C13#247411yescharacteristic
636C2×C13#259311yescharacteristic
637C2×C13#259411yescharacteristic
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×C4#612712yes—
744C22×C4#612712yes—
745C22×C4#612712yes—
746C22×C4#612712yes—
747C22×C4#612712yes—
748C22×C4D4×D1312yes—
749C22×C4#613112yes—
750C22×C4C2×C22⋊D1312yes—
751C22×C4C2×C22⋊D1312yes—
752C22×C4C2×C22⋊D1312yes—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—268no—
756C4⋊C4—268no—
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—28no—
766C42—44no—
767C42—44no—
768C42—268no—
769C42—524no—
770C13#1403111yescharacteristic, 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
807C23C2×#612711yescharacteristic
808C23C2×#612711yescharacteristic
809C23C2×#612711yescharacteristic
810C23C2×#612711yescharacteristic
811C23C2×#612711yescharacteristic
812C23C2×D4×D1311yescharacteristic
813C23#8825111yescharacteristic
814C23C2×#613111yescharacteristic
815C23#8825411yescharacteristic
816C23#41×D1311yescharacteristic
817C23#41×D1311yescharacteristic
818C23#8825611yescharacteristic
819C23#8825711yescharacteristic
820C23C22×C22⋊D1311yescharacteristic
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#8814714yes—
917C2×C4C4×C22⋊D1314yes—
918C2×C4#8818314yes—
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—
934C22C4×#612711yescharacteristic
935C22C4×#612711yescharacteristic
936C22#1171918411yescharacteristic
937C22#1171918411yescharacteristic
938C22C2×#8814711yescharacteristic
939C22#1171920911yescharacteristic
940C22#1171921211yescharacteristic
941C22#1171921911yescharacteristic
942C22D13×#11711yescharacteristic
943C22#1171922811yescharacteristic
944C22#1171923711yescharacteristic
945C22#1171923811yescharacteristic
946C22#1171924511yescharacteristic
947C22#1171924511yescharacteristic
948C22#1171925211yescharacteristic
949C22#1171925211yescharacteristic
950C22#1171925511yescharacteristic
951C22#1171925711yescharacteristic
952C22#1171926511yescharacteristic
953C22#1171926911yescharacteristic
954C22#1171927311yescharacteristic
955C22#1171927311yescharacteristic
956C22#1171928511yescharacteristic
957C22#1171928511yescharacteristic
958C22#1171928711yescharacteristic
959C22#1171928811yescharacteristic
960C22#1171928911yescharacteristic
961C22#1171929011yescharacteristic
962C22C2×C4×C22⋊D1311yescharacteristic
963C22C2×#8818311yescharacteristic
964C22#1171949611yescharacteristic
965C22D4×C22⋊D1311yescharacteristic
966C22#1171952211yescharacteristic
967C22#1171952911yescharacteristic
968C22#1171953911yescharacteristic
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#1311727711yescharacteristic
985C2C4×#8818311yescharacteristic
986C2#1311761111yescharacteristic
987C2#1311773011yescharacteristic
988C2#1311778611yescharacteristic
989C2#1311785211yescharacteristic
990C2#1311790511yescharacteristic
991C2#1311856511yescharacteristic
992C2#1311862811yescharacteristic
993C2#1311872211yescharacteristic
994C2#1311891111yescharacteristic
995C2#1311891711yescharacteristic
996C2#1311899211yescharacteristic
997C2#1312032711yescharacteristic
998C2#1312034211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14031
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×#6101C2semidirect
5. #13113099C2semidirect
6. #13113097C2semidirect
11. #13113069C2semidirect
12. #13113068C2semidirect
13. #13113067C2semidirect
14. #13113063C2semidirect
15. C2×C4×C13×C4⋊C4C2semidirect
54. #11718601C4semidirect
276. C2×C4×C4⋊C4D13semidirect
770. C13#14031semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117186512
C2×C4×#61012
#131130992
#131130972
#131130802
#131130782
#131130742
#131130722
#131130692
#131130682
#131130672
#131130632
C2×C4×C13×C4⋊C42
#1403113