Finite Group Databasebeta

← #15883307

Subgroups — #15883307

Order 3328.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718899C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic, complemented
3C2×#11718893C211yesmaximal, characteristic, complemented
4#13117850C211yesmaximal, characteristic, complemented
5#13115701C211yesmaximal, characteristic, complemented
6#13115536C211yesmaximal, characteristic, complemented
7#13115453C211yesmaximal, characteristic, complemented
8#13115272C211yesmaximal, characteristic, complemented
9#13115191C211yesmaximal, characteristic, complemented
10#13115187C211yesmaximal, characteristic, complemented
11#13115090C211yesmaximal, characteristic, complemented
12#13115023C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#2341C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C22×#6104C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C2×#88135—21no—
25C2×C4×D52C2211yescharacteristic
26C13×#390—21no—
27C13×#390—21no—
28C13×#390C2211yescharacteristic
29C13×#390C2211yescharacteristic
30C13×#380—21no—
31C13×#380C2211yescharacteristic
32C4×C13×C22⋊C4—21no—
33C4×C13×C22⋊C4C2211yescharacteristic
34#11718899C418yescomplemented
35#11718893—24no—
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718687—24no—
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718619—21no—
49#11718600C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51#11718589C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718331—21no—
55#11718329—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C2×C13×#41C2×C414yescomplemented
68C22×Q8×C13C2311yescharacteristic
69C22×D4×C13—21no—
70C22×D4×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C22×C22⋊D13—21no—
74C23×Dic13—21no—
75C22×D52C2311yescharacteristic
76C22×C4×D13—21no—
77C4×Q8×C13—22no—
78C4×Q8×C13—22no—
79C4×Q8×C13—41no—
80C4×Q8×C13—41no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C42×C13—21no—
93C2×C42×C13—21no—
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×#6106—22no—
97C2×#6106—22no—
98C2×#6106C2×C414yescomplemented
99C2×#6104—41no—
100C2×#6104—41no—
101C2×#6104C2×C414yescomplemented
102#88184—22no—
103#88184C2×C414yes—
104C2×#6103—21no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103—21no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—21no—
110C2×C4⋊Dic13—41no—
111C2×C4⋊Dic13C2311yescharacteristic
112C2×C4⋊Dic13C2311yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×#6101—21no—
115C2×C4×Dic13—21no—
116C2×#6099—22no—
117C2×#6099—22no—
118C2×#6099—41no—
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123#88135—44no—
124C4×D52—22no—
125C4×D52—41no—
126C13×#95—21no—
127C13×#95D411yescharacteristic
128C13×#95D411yescharacteristic
129#88075—22no—
130#88075C2×C414yescomplemented
131#88075D414yescomplemented
132#88072—22no—
133#88072—22no—
134#88072C2×C414yescomplemented
135#88071—21no—
136#88071—21no—
137C22⋊#1055C2×C414yescomplemented
138#88049—22no—
139#88049—41no—
140#88047—22no—
141#88047—41no—
142#88043—22no—
143C4×#1055—41no—
144#22863—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13C2×D411yescharacteristic
147C23×D13—21no—
148C13×#41—28no—
149C13×#41—44no—
150C13×#41—44no—
151C13×#41—44no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13C22×C412yes—
156C2×Q8×C13C2×D412yes—
157C2×Q8×C13#4112yes—
158C2×D4×C13—24no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—42no—
165C2×D4×C13—42no—
166C2×D4×C13C22×C412yes—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—24no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13#4112yes—
184C22×C4×C13C2411yescharacteristic
185C2×C22⋊D13—24no—
186C2×C22⋊D13—42no—
187C2×C22⋊D13—42no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—42no—
192C22×Dic13—42no—
193C22×Dic13—81no—
194C2×D52—21no—
195C2×D52—21no—
196C2×D52—21no—
197C2×D52—21no—
198C2×D52—21no—
199C2×D52C22×C412yes—
200C2×C4×D13—42no—
201C2×C4×D13—42no—
202C2×C4×D13—81no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4—42no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—41no—
211C13×C22⋊C4—42no—
212C13×C22⋊C4—42no—
213C13×C22⋊C4—81no—
214C13×C22⋊C4—81no—
215C13×C22⋊C4—81no—
216C42×C13—21no—
217C42×C13—21no—
218C42×C13—21no—
219C42×C13—21no—
220C42×C13—42no—
221C42×C13—42no—
222#6106—28no—
223#6104—44no—
224#6103—24no—
225#6103—42no—
226#6103—42no—
227#6103—81no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13—42no—
233C4⋊Dic13C22×C412yes—
234C4⋊Dic13C2×D412yes—
235#6101—42no—
236C4×Dic13—42no—
237#6099—44no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055C22×C412yes—
248C2×#1055C22×C412yes—
249C2×#1055C2×D412yes—
250C2×#449—131no—
251C2×#440—131no—
252C2×#417—131no—
253#2361—131no—
254#2341D1311yescharacteristic, complemented
255#1970—131no—
256#1936—131no—
257#1925—131no—
258#1895—131no—
259#1880—131no—
260#1879—131no—
261#1863—131no—
262#1852—131no—
263C4×#103—131no—
264#1753—131no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—22no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13C4×D412yes—
279C23×C13C22×D411yescharacteristic
280C22×D13—22no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287Q8×C13—22no—
288Q8×C13—22no—
289Q8×C13—22no—
290Q8×C13C4×D414yescomplemented
291D4×C13—22no—
292D4×C13—22no—
293D4×C13—48no—
294D4×C13—41no—
295D4×C13—41no—
296C2×C4×C13—22no—
297C2×C4×C13—21no—
298C2×C4×C13—22no—
299C2×C4×C13—21no—
300C2×C4×C13—22no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—48no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13C4×D412yes—
324C2×C4×C13AGL(1,ℤ/8)12yes—
325C2×C4×C13C23×C411yescharacteristic
326C2×C4×C13C22×D411yescharacteristic
327C2×C4×C13C2×#4111yescharacteristic
328C2×C4×C13C2×#4111yescharacteristic
329C2×C4×C13H(5,𝔽2)11yescharacteristic
330C2×C4×C13H(5,𝔽2)11yescharacteristic
331C22⋊D13—48no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—84no—
342D52—22no—
343D52—22no—
344D52—41no—
345D52—41no—
346C4×D13—84no—
347#1055—22no—
348#1055—22no—
349#1055—22no—
350#1055—41no—
351C22×#41C2×D1311yescharacteristic
352C22×SD16—131no—
353C22×D8—131no—
354C22×M16—131no—
355C2×#121—131no—
356C2×C4×Q8C2×D1311yescharacteristic
357C2×C4×Q8C2×D1311yescharacteristic
358C2×C4×D4—131no—
359C2×C4×D4—261no—
360C22×C4⋊C4—131no—
361#449—138no—
362#440—264no—
363C2×#107—131no—
364C2×#107—131no—
365#417—264no—
366C2×#103—131no—
367C2×#103—131no—
368C2×#103—131no—
369C2×#102—131no—
370C2×#102—131no—
371C2×#102—131no—
372C2×#102—131no—
373C2×#102—131no—
374C2×C22⋊C8—131no—
375C2×#97—131no—
376C2×C4×C8—131no—
377#390—21no—
378#390—21no—
379#390—131no—
380#390C2×D1311yescharacteristic
381#390C2×D1311yescharacteristic
382#389—131no—
383#388—261no—
384#386—261no—
385#385—261no—
386#380—21no—
387#380C2×D1311yescharacteristic
388C4×C4⋊C4—131no—
389C4×C22⋊C4—21no—
390C4×C22⋊C4C2×D1311yescharacteristic
391#340—131no—
392#340—131no—
393#340—131no—
394#340—131no—
395#336—131no—
396#336—131no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13—81no—
411C22×C13C2×C4×D411yescharacteristic
412C22×C13D4211yescharacteristic
413C22×C13#54611yescharacteristic
414C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C13#57511yescharacteristic
416C22×C13#57611yescharacteristic
417C22×C13#57811yescharacteristic
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—81no—
422C2×D13—81no—
423C2×D13—81no—
424C2×D13—81no—
425C4×C13—22no—
426C4×C13—24no—
427C4×C13—22no—
428C4×C13—41no—
429C4×C13—41no—
430C4×C13—41no—
431C4×C13—81no—
432C4×C13—81no—
433C4×C13C2×C4×D411yescharacteristic
434C4×C13#51811yescharacteristic
435C4×C13#54611yescharacteristic
436C4×C13#55111yescharacteristic
437Dic13—42no—
438Dic13—42no—
439Dic13—81no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41C4×D1314yescomplemented
446C22×Q8C22×D1311yescharacteristic
447C22×D4—21no—
448C22×D4—131no—
449C22×D4—261no—
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4C22×D1311yescharacteristic
455C2×SD16—134no—
456C2×SD16—262no—
457C2×SD16—262no—
458C2×D8—134no—
459C2×D8—521no—
460C2×D8—521no—
461C2×M16—262no—
462C2×M16—262no—
463C2×M16—521no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—131no—
468#121—134no—
469#121—262no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—41no—
473C4×Q8—41no—
474C4×D4—262no—
475C4×D4—521no—
476C4×D4—524no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—131no—
480C2×C4⋊C4—131no—
481C2×C4⋊C4—131no—
482C2×C4⋊C4—262no—
483C2×C4⋊C4—261no—
484C2×C4⋊C4—261no—
485C2×C4⋊C4—521no—
486C2×C4⋊C4C22×D1311yescharacteristic
487C2×C4⋊C4C22×D1311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—261no—
494C2×C22⋊C4—261no—
495C2×C22⋊C4—261no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4C22⋊D1311yescharacteristic
498C2×C22⋊C4C22⋊D1311yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—261no—
502C2×C42C22×D1311yescharacteristic
503C2×C42C22×D1311yescharacteristic
504#107—262no—
505#107—521no—
506#103—134no—
507#103—134no—
508#103—262no—
509#102—134no—
510#102—262no—
511#102—262no—
512#102—262no—
513#102—521no—
514C22⋊C8—134no—
515#97—262no—
516C4×C8—521no—
517#95—21no—
518#95—261no—
519#95—261no—
520#95C22⋊D1311yescharacteristic
521#95C22⋊D1311yescharacteristic
522C2×C13—42no—
523C2×C13—82no—
524C2×C13#235811yescharacteristic
525C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
526C2×C13#295111yescharacteristic
527C2×C13#327411yescharacteristic
528C2×C13#327711yescharacteristic
529C2×C13#330811yescharacteristic
530C2×C13#330911yescharacteristic
531D13—82no—
532C24—21no—
533C24—261no—
534C24C2×C22⋊D1311yescharacteristic
535#41—28no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C4×D1312yes—
543C2×Q8D4×D1312yes—
544C2×Q8#612912yes—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—132no—
554C2×D4—264no—
555C2×D4—261no—
556C2×D4—261no—
557C2×D4—261no—
558C2×D4—261no—
559C2×D4—261no—
560C2×D4—522no—
561C2×D4—522no—
562C2×D4C2×C4×D1312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—522no—
577C22×C4—522no—
578C22×C4—522no—
579C22×C4—522no—
580C22×C4—1041no—
581C22×C4—1041no—
582C22×C4C2×C4×D1312yes—
583C22×C4#612712yes—
584C22×C4C2×C22⋊D1311yescharacteristic
585C22×C4C2×C22⋊D1311yescharacteristic
586C22×C4C2×C22⋊D1311yescharacteristic
587C22×C4C2×C22⋊D1311yescharacteristic
588C22×C4C2×C22⋊D1311yescharacteristic
589C22×C4C23×D1311yescharacteristic
590SD16—268no—
591D8—524no—
592M16—524no—
593C2×C8—132no—
594C2×C8—132no—
595C2×C8—132no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—132no—
612C4⋊C4—132no—
613C4⋊C4—261no—
614C4⋊C4—261no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—522no—
618C4⋊C4—522no—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—264no—
627C22⋊C4—522no—
628C22⋊C4—522no—
629C22⋊C4—1041no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—42no—
636C42—522no—
637C13#2286311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—262no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23C4×C22⋊D1312yes—
659C23C22×C22⋊D1311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8#8813514yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—262no—
670D4—262no—
671D4—528no—
672D4—521no—
673D4—521no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—1044no—
711C2×C4—1044no—
712C2×C4C4×C22⋊D1312yes—
713C2×C4#8820312yes—
714C2×C4C22×C4×D1311yescharacteristic
715C2×C4C2×#612711yescharacteristic
716C2×C4C2×D4×D1311yescharacteristic
717C2×C4C2×#612911yescharacteristic
718C2×C4#8825111yescharacteristic
719C2×C4#8825111yescharacteristic
720C8—262no—
721C8—262no—
722C8—262no—
723C8—521no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—522no—
739C22—522no—
740C22—522no—
741C22—1041no—
742C22—1041no—
743C22—1041no—
744C22—1041no—
745C22C2×C4×C22⋊D1311yescharacteristic
746C22D4×C22⋊D1311yescharacteristic
747C22#1171951111yescharacteristic
748C22C2×#8820311yescharacteristic
749C22#1171952711yescharacteristic
750C22#1171954011yescharacteristic
751C22#1171954311yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—522no—
761C4—522no—
762C4—1041no—
763C4C2×#8813511yescharacteristic
764C4#1171919111yescharacteristic
765C4#1171919511yescharacteristic
766C4#1171920011yescharacteristic
767C2—42no—
768C2—82no—
769C2—1042no—
770C2#1311781511yescharacteristic
771C2C4×#8820311yescharacteristic
772C2#1312370911yescharacteristic
773C2#1312645611yescharacteristic
774C2#1312648911yescharacteristic
775C2#1312682711yescharacteristic
776C2#1312684211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2341C2
socleC23×C13C22×D4
prime radicalC2×#11718899C2
cosocleC22×C4×C13C24
hypercenter#2341D13
hypocenterC13#22863
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
3. C2×#11718893C2semidirect
4. #13117850C2semidirect
5. #13115701C2semidirect
6. #13115536C2semidirect
7. #13115453C2semidirect
8. #13115272C2semidirect
9. #13115191C2semidirect
10. #13115187C2semidirect
11. #13115090C2semidirect
12. #13115023C2semidirect
13. C4×#88075C2semidirect
14. #13114620C2semidirect
15. C13×#2341C2semidirect
34. #11718899C4semidirect
67. C2×C13×#41C2×C4semidirect
98. C2×#6106C2×C4semidirect
101. C2×#6104C2×C4semidirect
130. #88075C2×C4semidirect
131. #88075D4semidirect
134. #88072C2×C4semidirect
137. C22⋊#1055C2×C4semidirect
254. #2341D13semidirect
290. Q8×C13C4×D4semidirect
445. C2×#41C4×D13semidirect
637. C13#22863semidirect
663. Q8#88135semidirect

Maximal subgroups

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

subgroupindex
C2×#117188992
C2×#117186872
C2×#117188932
#131178502
#131157012
#131155362
#131154532
#131152722
#131151912
#131151872
#131150902
#131150232
C4×#880752
#131146202
C13×#23412
#2286313