Finite Group Databasebeta

← #15785528

Subgroups — #15785528

Order 3328.

1486 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×C22⋊C4×Dic13C211yesmaximal, characteristic
2#13113097C211yesmaximal, characteristic, complemented
3#13113096C211yesmaximal, characteristic, complemented
4#13113083C211yesmaximal, characteristic
5#13113083C211yesmaximal, characteristic
6#13113073C211yesmaximal, characteristic
7#13113063C211yesmaximal, characteristic, complemented
8#13113062C211yesmaximal, characteristic, complemented
9#13113061C211yesmaximal, characteristic, complemented
10#13113061C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
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
51C22⋊C4×Dic13C418yescomplemented
52C25×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—22no—
60C23×Dic13—22no—
61C23×Dic13—41no—
62C23×Dic13—41no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13C2×C414yes—
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—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4C2×C414yes—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—41no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13C2×C414yes—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—41no—
98C2×C4×Dic13—41no—
99C2×C4×Dic13—41no—
100C2×C4×Dic13—41no—
101C2×C4×Dic13—41no—
102C2×C4×Dic13C2×C414yes—
103C2×C4×Dic13C2×C414yes—
104C13×#95—22no—
105C13×#95—22no—
106C13×#95—41no—
107#88071—22no—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071C2×C414yes—
127#88071C2×C414yes—
128#13947—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—21no—
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×C13C22×C412yes—
182C22×C4×C13C22×C412yes—
183C22×C4×C13#4112yes—
184C22×C4×C13#4112yes—
185C22×C4×C13#4112yes—
186C22×C4×C13#4112yes—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
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—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—28no—
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—44no—
237C22×Dic13—44no—
238C22×Dic13—44no—
239C22×Dic13—44no—
240C22×Dic13—44no—
241C22×Dic13—44no—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C22×Dic13#4112yes—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—44no—
252C13×C22⋊C4—44no—
253C42×C13—44no—
254C22⋊Dic13—28no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257C4×Dic13—44no—
258C4×Dic13—44no—
259C4×Dic13—44no—
260C2×C4×C22⋊C4—131no—
261#1443—131no—
262#1443—131no—
263#1440—131no—
264#1440—131no—
265#1437—131no—
266#1437D1311yescharacteristic
267#1434—131no—
268#1434—131no—
269#1434—131no—
270#1434—131no—
271#1434—131no—
272C22⋊#95—131no—
273C22⋊#95—131no—
274C4×#95—131no—
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×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
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—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
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#11714yes—
367C2×Dic13—22no—
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—22no—
387C2×Dic13—22no—
388C2×Dic13—416no—
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#11714yes—
424C24×C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4C2×D1311yescharacteristic
429C22×C22⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4C2×D1311yescharacteristic
431C22×C42—131no—
432C22×C42—131no—
433C22×C42—131no—
434C22×C42C2×D1311yescharacteristic
435C4×C22⋊C4—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×#95—131no—
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×C13C2×#11711yescharacteristic
477C22×C13C2×#11711yescharacteristic
478C22×C13C4×#4111yescharacteristic
479C22×C13C4×#4111yescharacteristic
480C22×C13#51811yescharacteristic
481C22×C13#51811yescharacteristic
482C22×C13#52911yescharacteristic
483C22×C13#52911yescharacteristic
484C22×C13#52911yescharacteristic
485C22×C13#52911yescharacteristic
486C22×C13#52911yescharacteristic
487C22×C13#52911yescharacteristic
488C22×C13#52911yescharacteristic
489C22×C13#52911yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53811yescharacteristic
493C22×C13#53811yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55111yescharacteristic
500C22×C13#55311yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55911yescharacteristic
509C22×C13#55911yescharacteristic
510C4×C13—24no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—42no—
514C4×C13—81no—
515C4×C13—81no—
516Dic13—24no—
517Dic13—42no—
518Dic13—42no—
519Dic13—42no—
520Dic13—42no—
521Dic13—42no—
522Dic13—81no—
523Dic13—81no—
524C25C22×D1311yescharacteristic
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—134no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—262no—
535C23×C4—262no—
536C23×C4—521no—
537C23×C4—521no—
538C23×C4—521no—
539C23×C4—521no—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—262no—
556C2×C22⋊C4—262no—
557C2×C22⋊C4—262no—
558C2×C22⋊C4—262no—
559C2×C22⋊C4—262no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—521no—
562C2×C22⋊C4—521no—
563C2×C22⋊C4C4×D1314yes—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—41no—
567C2×C42—134no—
568C2×C42—134no—
569C2×C42—262no—
570C2×C42—262no—
571C2×C42—521no—
572C2×C42—521no—
573C2×C42—521no—
574C2×C42—521no—
575C2×C42—521no—
576#95—22no—
577#95—22no—
578#95—41no—
579#95—134no—
580#95—134no—
581#95—262no—
582#95—262no—
583#95—262no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—262no—
589#95—262no—
590#95—262no—
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#228311yescharacteristic
602C2×C13#229811yescharacteristic
603C2×C13#231211yescharacteristic
604C2×C13#235311yescharacteristic
605C2×C13#235311yescharacteristic
606C2×C13#235311yescharacteristic
607C2×C13#235711yescharacteristic
608C2×C13#257611yescharacteristic
609C2×C13#257611yescharacteristic
610C2×C13#257811yescharacteristic
611C2×C13#257811yescharacteristic
612C2×C13#259511yescharacteristic
613C2×C13#259511yescharacteristic
614C2×C13#259711yescharacteristic
615C2×C13#259711yescharacteristic
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#612712yes—
630C24#612712yes—
631C24C23×D1311yescharacteristic
632C22×C4—21no—
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—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—268no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
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—524no—
726C22×C4—524no—
727C22×C4—524no—
728C22×C4—524no—
729C22×C4—524no—
730C22×C4—524no—
731C22×C4C2×C4×D1312yes—
732C22×C4C2×C4×D1312yes—
733C22×C4#612912yes—
734C22×C4#612912yes—
735C22×C4#612912yes—
736C22×C4#612912yes—
737C22⋊C4—28no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—268no—
741C22⋊C4—524no—
742C22⋊C4—524no—
743C42—44no—
744C42—524no—
745C42—524no—
746C42—524no—
747C13#1394711yescharacteristic, 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#8812614yes—
783C23C22×C4×D1311yescharacteristic
784C23C2×#612711yescharacteristic
785C23C2×#612711yescharacteristic
786C23C2×#612911yescharacteristic
787C23C2×#612911yescharacteristic
788C23C2×#612911yescharacteristic
789C23C2×#612911yescharacteristic
790C23#8825111yescharacteristic
791C23#8825111yescharacteristic
792C23#41×D1311yescharacteristic
793C23#41×D1311yescharacteristic
794C23#41×D1311yescharacteristic
795C23#41×D1311yescharacteristic
796C23#8825611yescharacteristic
797C23#8825611yescharacteristic
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—22no—
811C2×C4—22no—
812C2×C4—22no—
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—134no—
840C2×C4—262no—
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—262no—
860C2×C4—262no—
861C2×C4—5216no—
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#8813114yes—
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—
912C22C2×#8812611yescharacteristic
913C22C2×#8813111yescharacteristic
914C22#1171920011yescharacteristic
915C22#1171920011yescharacteristic
916C22D13×#11711yescharacteristic
917C22#1171923211yescharacteristic
918C22#1171923211yescharacteristic
919C22C4×#612911yescharacteristic
920C22C4×#612911yescharacteristic
921C22#1171924311yescharacteristic
922C22#1171924311yescharacteristic
923C22#1171924311yescharacteristic
924C22#1171924311yescharacteristic
925C22#1171924511yescharacteristic
926C22#1171924511yescharacteristic
927C22#1171925011yescharacteristic
928C22#1171925011yescharacteristic
929C22#1171927011yescharacteristic
930C22#1171927011yescharacteristic
931C22#1171929211yescharacteristic
932C22#1171930511yescharacteristic
933C22#1171930611yescharacteristic
934C22#1171931811yescharacteristic
935C22#1171931911yescharacteristic
936C22#1171932311yescharacteristic
937C22#1171932311yescharacteristic
938C22#1171935411yescharacteristic
939C22#1171936211yescharacteristic
940C22#1171936311yescharacteristic
941C22#1171938311yescharacteristic
942C22#1171938511yescharacteristic
943C22#1171938611yescharacteristic
944C22#1171940911yescharacteristic
945C22#1171941111yescharacteristic
946C22#1171941811yescharacteristic
947C4—24no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—264no—
954C4—522no—
955C4—522no—
956C4—522no—
957C4—522no—
958C4—522no—
959C4—1041no—
960C4—1041no—
961C2—44no—
962C2#1311723011yescharacteristic
963C2#1311733011yescharacteristic
964C2#1311743011yescharacteristic
965C2#1311777011yescharacteristic
966C2#1311777011yescharacteristic
967C2#1311777411yescharacteristic
968C2#1311780811yescharacteristic
969C2#1312014411yescharacteristic
970C2#1312014611yescharacteristic
971C2#1312017411yescharacteristic
972C2#1312017611yescharacteristic
973C2#1312036111yescharacteristic
974C2#1312036311yescharacteristic
975C2#1312039111yescharacteristic
976C2#1312039311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#13947
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13113097C2semidirect
3. #13113096C2semidirect
7. #13113063C2semidirect
8. #13113062C2semidirect
9. #13113061C2semidirect
10. #13113061C2semidirect
11. #13113060C2semidirect
14. C4×#88071C2semidirect
51. C22⋊C4×Dic13C4semidirect
747. C13#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic132
#131130972
#131130962
#131130832
#131130732
#131130632
#131130622
#131130612
#131130602
#131130582
C4×#880712
C13×#14372
#1394713