Finite Group Databasebeta

← #15786915

Subgroups — #15786915

Order 3328.

1602 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718606C211yesmaximal, characteristic
2C2×C22⋊C4×Dic13C211yesmaximal, characteristic
3C2×#11718309C211yesmaximal, characteristic, complemented
4#13113102C211yesmaximal, characteristic, complemented
5#13113096C211yesmaximal, characteristic, complemented
6#13113083C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113068C211yesmaximal, characteristic, complemented
9#13113068C211yesmaximal, characteristic, complemented
10#13113067C211yesmaximal, characteristic, complemented
11#13113062C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
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
51#11718606C418yescomplemented
52C22⋊C4×Dic13—24no—
53#11718309—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—22no—
62C23×Dic13—22no—
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—22no—
66C23×Dic13—41no—
67C23×Dic13—41no—
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4—41no—
87C2×C13×C22⋊C4C2×C414yes—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13C2×C414yes—
96C2×C22⋊Dic13C2×C414yes—
97C2×#6101—41no—
98C2×#6101—41no—
99C2×#6101C2×C414yescomplemented
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13C2×C414yescomplemented
111C2×C4×Dic13D414yes—
112C13×#95—22no—
113C13×#95—41no—
114C13×#95—41no—
115#88071—22no—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071C2×C414yescomplemented
133#88071C2×C414yescomplemented
134#14066—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13C22×C412yes—
148C24×C13#4112yes—
149C24×C13#4112yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
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×C13C22×C412yes—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—28no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
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—44no—
240C22×Dic13—44no—
241C22×Dic13—44no—
242C22×Dic13—44no—
243C22×Dic13—44no—
244C22×Dic13—44no—
245C22×Dic13C22×C412yes—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C13×C4⋊C4—44no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262C22⋊Dic13—44no—
263#6101—44no—
264C4×Dic13—28no—
265C4×Dic13—28no—
266C4×Dic13—28no—
267C4×Dic13—44no—
268C2×#388—131no—
269C2×C4×C22⋊C4—131no—
270C2×#376—131no—
271#1445—131no—
272#1443—131no—
273#1440—131no—
274#1439D1311yescharacteristic
275#1437—131no—
276#1436—131no—
277#1436—131no—
278#1436—131no—
279#1434—131no—
280#1434—131no—
281C22⋊#95—131no—
282C22⋊#95—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13#11714yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C13H(5,𝔽2)11yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C132−1+411yescharacteristic
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
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—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
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×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
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—416no—
403C2×Dic13—41no—
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×Dic13C4×D414yes—
431C2×Dic13#12314yes—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C42—131no—
442C22×C42—131no—
443C22×C42—131no—
444C22×C42—131no—
445#388—138no—
446C4×C22⋊C4—264no—
447#376—264no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
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×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×#11711yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C4×#4111yescharacteristic
488C22×C13C4×#4111yescharacteristic
489C22×C13C4×#4111yescharacteristic
490C22×C13#51811yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13C2×#12311yescharacteristic
493C22×C13#52511yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13#52511yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13#52911yescharacteristic
498C22×C13#52911yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#53511yescharacteristic
501C22×C13#53711yescharacteristic
502C22×C13#54011yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#55111yescharacteristic
505C22×C13#55111yescharacteristic
506C22×C13#55111yescharacteristic
507C22×C13#55111yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55211yescharacteristic
512C22×C13#55211yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55311yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55511yescharacteristic
518C22×C13#55511yescharacteristic
519C22×C13#55611yescharacteristic
520C4×C13—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—81no—
526Dic13—24no—
527Dic13—24no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—42no—
533Dic13—81no—
534C25C22×D1311yescharacteristic
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—262no—
544C23×C4—262no—
545C23×C4—262no—
546C23×C4—262no—
547C23×C4—262no—
548C23×C4—521no—
549C23×C4—521no—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
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—521no—
579C2×C22⋊C4C4×D1314yes—
580C2×C42—134no—
581C2×C42—134no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—262no—
585C2×C42—262no—
586C2×C42—262no—
587C2×C42—262no—
588C2×C42—262no—
589C2×C42—262no—
590C2×C42—521no—
591C2×C42—521no—
592#95—22no—
593#95—41no—
594#95—41no—
595#95—134no—
596#95—134no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—262no—
606#95—262no—
607#95—262no—
608#95—262no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614C2×C13—44no—
615C2×C13#229011yescharacteristic
616C2×C13C4×#12311yescharacteristic
617C2×C13#232411yescharacteristic
618C2×C13#234311yescharacteristic
619C2×C13#235311yescharacteristic
620C2×C13#237211yescharacteristic
621C2×C13#237311yescharacteristic
622C2×C13#248211yescharacteristic
623C2×C13#248511yescharacteristic
624C2×C13#252611yescharacteristic
625C2×C13#252711yescharacteristic
626C2×C13#253011yescharacteristic
627C2×C13#253111yescharacteristic
628C2×C13#259811yescharacteristic
629C2×C13#260911yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1312yes—
643C24#612912yes—
644C24#613112yes—
645C24C23×D1311yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
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—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—268no—
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×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4—524no—
744C22×C4—524no—
745C22×C4—524no—
746C22×C4C2×C4×D1312yes—
747C22×C4C2×C4×D1312yes—
748C22×C4D4×D1312yes—
749C22×C4#612912yes—
750C22×C4#612912yes—
751C4⋊C4—44no—
752C4⋊C4—524no—
753C22⋊C4—28no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—268no—
757C22⋊C4—268no—
758C22⋊C4—524no—
759C42—268no—
760C42—268no—
761C42—268no—
762C42—524no—
763C13#1406611yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#8814614yes—
799C23C22×C4×D1311yescharacteristic
800C23C2×D4×D1311yescharacteristic
801C23C2×#612911yescharacteristic
802C23C2×#612911yescharacteristic
803C23C2×#612911yescharacteristic
804C23#8825111yescharacteristic
805C23#8825111yescharacteristic
806C23#8825111yescharacteristic
807C23C2×#613111yescharacteristic
808C23#41×D1311yescharacteristic
809C23#41×D1311yescharacteristic
810C23#41×D1311yescharacteristic
811C23#41×D1311yescharacteristic
812C23#41×D1311yescharacteristic
813C23#8825711yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
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—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—134no—
857C2×C4—134no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
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—5216no—
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—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#1171919111yescharacteristic
929C22C2×#8814611yescharacteristic
930C22#1171922711yescharacteristic
931C22C4×#612911yescharacteristic
932C22C4×#612911yescharacteristic
933C22C4×D4×D1311yescharacteristic
934C22#1171925111yescharacteristic
935C22#1171929111yescharacteristic
936C22#1171929211yescharacteristic
937C22#1171929211yescharacteristic
938C22#1171930211yescharacteristic
939C22#1171930611yescharacteristic
940C22#1171930611yescharacteristic
941C22#1171930611yescharacteristic
942C22#1171931111yescharacteristic
943C22#1171932011yescharacteristic
944C22#1171932111yescharacteristic
945C22#1171932111yescharacteristic
946C22#1171932911yescharacteristic
947C22#1171933211yescharacteristic
948C22#1171934211yescharacteristic
949C22#1171934211yescharacteristic
950C22#1171934211yescharacteristic
951C22#1171934711yescharacteristic
952C22#1171935411yescharacteristic
953C22#1171935511yescharacteristic
954C22D13×#12311yescharacteristic
955C22#1171936411yescharacteristic
956C22#1171936411yescharacteristic
957C22#1171937411yescharacteristic
958C22#1171937611yescharacteristic
959C22#1171938511yescharacteristic
960C22#1171941111yescharacteristic
961C22#1171941311yescharacteristic
962C22#1171942011yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—264no—
970C4—264no—
971C4—522no—
972C4—522no—
973C4—522no—
974C4—522no—
975C4—522no—
976C4—1041no—
977C2—44no—
978C2#1311727211yescharacteristic
979C2#1311736311yescharacteristic
980C2#1311752211yescharacteristic
981C2#1311769411yescharacteristic
982C2#1311777811yescharacteristic
983C2#1311794511yescharacteristic
984C2#1311795411yescharacteristic
985C2#1311911111yescharacteristic
986C2#1311912611yescharacteristic
987C2#1311960911yescharacteristic
988C2#1311961611yescharacteristic
989C2#1311966911yescharacteristic
990C2#1311967611yescharacteristic
991C2#1312039511yescharacteristic
992C2#1312050911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14066
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#11718309C2semidirect
4. #13113102C2semidirect
5. #13113096C2semidirect
8. #13113068C2semidirect
9. #13113068C2semidirect
10. #13113067C2semidirect
11. #13113062C2semidirect
12. #13113062C2semidirect
51. #11718606C4semidirect
99. C2×#6101C2×C4semidirect
110. C2×C4×Dic13C2×C4semidirect
132. #88071C2×C4semidirect
133. #88071C2×C4semidirect
763. C13#14066semidirect

Maximal subgroups

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

subgroupindex
C2×#117186062
C2×C22⋊C4×Dic132
C2×#117183092
#131131022
#131130962
#131130832
#131130732
#131130682
#131130672
#131130622
#131130582
C13×#14392
#1406613