Finite Group Databasebeta

← #15792114

Subgroups — #15792114

Order 3328.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718872C211yesmaximal, characteristic
2#13113097C211yesmaximal, characteristic, complemented
3#13113096C211yesmaximal, characteristic, complemented
4#13113094C211yesmaximal, characteristic, complemented
5#13113091C211yesmaximal, characteristic, complemented
6#13113079C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113071C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113062C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31#11718872C418yescomplemented
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
51C2×#88071C2211yescharacteristic
52C25×C13C2311yescharacteristic
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—41no—
56C23×C4×C13—41no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13C2×C414yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—41no—
79C2×C13×C22⋊C4—41no—
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—41no—
85C2×C22⋊Dic13—41no—
86C2×C22⋊Dic13—41no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13C2×C414yes—
91C2×C22⋊Dic13C2×C414yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—41no—
95C2×#6101—41no—
96C2×#6101—41no—
97C2×#6101—41no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—41no—
101C2×C4×Dic13—41no—
102C2×C4×Dic13—41no—
103C2×C4×Dic13—41no—
104C13×#95—41no—
105C13×#95—41no—
106C13×#95—41no—
107C13×#95—41no—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—41no—
113#88071—41no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071C2×C414yes—
125#88071C2×C414yes—
126#88071C2×C414yes—
127#88071C2×C414yes—
128#14508—131nomaximal, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13C22×C412yes—
142C24×C13#4112yes—
143C24×C13#4112yes—
144C24×C13C2411yescharacteristic
145C22×C4×C13—28no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
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—44no—
185C22×C4×C13—44no—
186C22×C4×C13—44no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C22×C412yes—
192C22×C4×C13#4112yes—
193C22×C4×C13#4112yes—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
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—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13#4112yes—
249C22×Dic13#4112yes—
250C13×C22⋊C4—44no—
251C13×C22⋊C4—44no—
252C22⋊Dic13—44no—
253C22⋊Dic13—44no—
254C22⋊Dic13—44no—
255C22⋊Dic13—44no—
256#6101—44no—
257#6101—44no—
258C4×Dic13—44no—
259C4×Dic13—44no—
260C2×#381—131no—
261#1443—131no—
262#1443—131no—
263#1442—131no—
264#1442—131no—
265#1439—131no—
266#1439—131no—
267#1437—131no—
268#1437—131no—
269#1436—131no—
270#1436—131no—
271#1434—131no—
272#1434—131no—
273C22⋊#95—131no—
274C22⋊#95D1311yescharacteristic
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
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—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
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#11714yes—
310C23×C13C23×C411yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13H(5,𝔽2)11yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C132−1+411yescharacteristic
324C23×C132−1+411yescharacteristic
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—416no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
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×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
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—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
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—
424C24×C4C2×D1311yescharacteristic
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4C2×D1311yescharacteristic
433C22×C42—131no—
434C22×C42—131no—
435#381—138no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
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×#95C2×D1311yescharacteristic
457C2×#95C2×D1311yescharacteristic
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C22×C13—24no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13C2×#11711yescharacteristic
476C22×C13C4×#4111yescharacteristic
477C22×C13C4×#4111yescharacteristic
478C22×C13#51811yescharacteristic
479C22×C13#51811yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#53811yescharacteristic
483C22×C13#53811yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53811yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#54011yescharacteristic
491C22×C13#54011yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55211yescharacteristic
500C22×C13#55211yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55211yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55911yescharacteristic
506C22×C13#56011yescharacteristic
507C22×C13#56211yescharacteristic
508C22×C13#56211yescharacteristic
509C22×C13#56311yescharacteristic
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—42no—
514C4×C13—81no—
515C4×C13—81no—
516Dic13—42no—
517Dic13—42no—
518Dic13—42no—
519Dic13—42no—
520Dic13—42no—
521Dic13—42no—
522Dic13—81no—
523Dic13—81no—
524C25C22×D1311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4C4×D1314yes—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C2×C4⋊C4—262no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—521no—
549C2×C4⋊C4—521no—
550C2×C4⋊C4—521no—
551C2×C4⋊C4—521no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—262no—
564C2×C22⋊C4—521no—
565C2×C22⋊C4—521no—
566C2×C22⋊C4—521no—
567C2×C22⋊C4—521no—
568C2×C22⋊C4—521no—
569C2×C22⋊C4—521no—
570C2×C42—262no—
571C2×C42—262no—
572C2×C42—521no—
573C2×C42—521no—
574C2×C42—521no—
575C2×C42—521no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—521no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95—521no—
595#95—521no—
596#95—521no—
597#95—521no—
598#95—521no—
599#95—521no—
600C2×C13—44no—
601C2×C13#231211yescharacteristic
602C2×C13#233511yescharacteristic
603C2×C13#233511yescharacteristic
604C2×C13#234311yescharacteristic
605C2×C13#234311yescharacteristic
606C2×C13#237411yescharacteristic
607C2×C13#237611yescharacteristic
608C2×C13#275011yescharacteristic
609C2×C13#275011yescharacteristic
610C2×C13#275211yescharacteristic
611C2×C13#276011yescharacteristic
612C2×C13#276111yescharacteristic
613C2×C13#276111yescharacteristic
614C2×C13#276411yescharacteristic
615C2×C13#277111yescharacteristic
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C2×C4×D1312yes—
629C24#612912yes—
630C24#612912yes—
631C24C23×D1311yescharacteristic
632C22×C4—28no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
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—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
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—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×C4C2×C4×D1312yes—
734C22×C4C2×C4×D1312yes—
735C22×C4#612712yes—
736C22×C4#612712yes—
737C4⋊C4—524no—
738C4⋊C4—524no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—524no—
742C22⋊C4—524no—
743C22⋊C4—524no—
744C22⋊C4—524no—
745C42—524no—
746C42—524no—
747C13#1450811yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#8813114yes—
783C23C22×C4×D1311yescharacteristic
784C23C2×#612711yescharacteristic
785C23C2×#612711yescharacteristic
786C23C2×#612911yescharacteristic
787C23C2×#612911yescharacteristic
788C23#8825111yescharacteristic
789C23#8825111yescharacteristic
790C23#8825111yescharacteristic
791C23#8825111yescharacteristic
792C23#8825111yescharacteristic
793C23#8825411yescharacteristic
794C23#41×D1311yescharacteristic
795C23#41×D1311yescharacteristic
796C23#8825611yescharacteristic
797C23#8825711yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
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—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C4×#612711yescharacteristic
913C22C2×#8813111yescharacteristic
914C22#1171919111yescharacteristic
915C22#1171919111yescharacteristic
916C22#1171920011yescharacteristic
917C22#1171920011yescharacteristic
918C22#1171920911yescharacteristic
919C22#1171921811yescharacteristic
920C22#1171921811yescharacteristic
921C22#1171922711yescharacteristic
922C22#1171922811yescharacteristic
923C22#1171924511yescharacteristic
924C22#1171926111yescharacteristic
925C22#1171926311yescharacteristic
926C22#1171926411yescharacteristic
927C22#1171926511yescharacteristic
928C22#1171926611yescharacteristic
929C22#1171926711yescharacteristic
930C22#1171926911yescharacteristic
931C22#1171929811yescharacteristic
932C22#1171929811yescharacteristic
933C22#1171929811yescharacteristic
934C22#1171929811yescharacteristic
935C22#1171931811yescharacteristic
936C22#1171932011yescharacteristic
937C22#1171932511yescharacteristic
938C22#1171932611yescharacteristic
939C22#1171934311yescharacteristic
940C22#1171934511yescharacteristic
941C22#1171935111yescharacteristic
942C22#1171935211yescharacteristic
943C22#1171935511yescharacteristic
944C22#1171935511yescharacteristic
945C22#1171936311yescharacteristic
946C22#1171936311yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—522no—
954C4—522no—
955C4—522no—
956C4—522no—
957C4—522no—
958C4—522no—
959C4—1041no—
960C4—1041no—
961C2—44no—
962C2#1311743211yescharacteristic
963C2#1311762211yescharacteristic
964C2#1311762611yescharacteristic
965C2#1311769211yescharacteristic
966C2#1311769811yescharacteristic
967C2#1311796711yescharacteristic
968C2#1311798011yescharacteristic
969C2#1312207411yescharacteristic
970C2#1312207811yescharacteristic
971C2#1312210311yescharacteristic
972C2#1312221211yescharacteristic
973C2#1312222311yescharacteristic
974C2#1312222711yescharacteristic
975C2#1312225711yescharacteristic
976C2#1312235411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14508
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #13113097C2semidirect
3. #13113096C2semidirect
4. #13113094C2semidirect
5. #13113091C2semidirect
10. #13113071C2semidirect
11. #13113067C2semidirect
12. #13113062C2semidirect
13. #13113060C2semidirect
31. #11718872C4semidirect
747. C13#14508semidirect

Maximal subgroups

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

subgroupindex
C2×#117188722
#131130972
#131130962
#131130942
#131130912
#131130792
#131130732
#131130712
#131130672
#131130622
#131130602
#131130592
C13×C22⋊#952
#1450813