Finite Group Databasebeta

← #15874189

Subgroups — #15874189

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic13C211yesmaximal, characteristic, complemented
2#13117327C211yesmaximal, characteristic, complemented
3#13115719C211yesmaximal, characteristic, complemented
4#13115713C211yesmaximal, characteristic, complemented
5#13115535C211yesmaximal, characteristic, complemented
6#13115528C211yesmaximal, characteristic, complemented
7#13115472C211yesmaximal, characteristic, complemented
8#13115458C211yesmaximal, characteristic, complemented
9#13115186C211yesmaximal, characteristic, complemented
10#13115172C211yesmaximal, characteristic, complemented
11#13115159C211yesmaximal, characteristic, complemented
12#13115037C211yesmaximal, characteristic, complemented
13#13114776C211yesmaximal, characteristic, complemented
14#13114600C211yesmaximal, characteristic, complemented
15C2×C13×#449C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×SD16C2211yescharacteristic
18C22×C13×D8C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×D4×Dic13—21no—
21C2×D4×Dic13C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C13×#449C418yescomplemented
25C2×C13×#103C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28#11718891C2211yescharacteristic
29#11718891C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32#11718882C2211yescharacteristic
33#11718882C2211yescharacteristic
34#11718882C2211yescharacteristic
35#11718881—21no—
36#11718881—21no—
37#11718881—21no—
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42#11718873C2211yescharacteristic
43C4×C22⋊Dic13—21no—
44C4×C22⋊Dic13—21no—
45C2×C22⋊#1055C2211yescharacteristic
46C2×#88058C2211yescharacteristic
47C2×#88057C2211yescharacteristic
48C2×#88055C2211yescharacteristic
49C2×#88055C2211yescharacteristic
50#11718646C2211yescharacteristic
51C4⋊C4×Dic13C2211yescharacteristic
52#11718612—21no—
53C22⋊C4×Dic13—21no—
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C2×C13×#41—22no—
61C2×C13×#41—41no—
62C2×C13×#41—41no—
63C2×C13×#41—41no—
64C2×C13×#41—41no—
65C2×C13×#41C2×C414yescomplemented
66C22×Q8×C13C2311yescharacteristic
67C22×D4×C13—21no—
68C22×D4×C13—21no—
69C22×D4×C13C2311yescharacteristic
70C22×D4×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C23×Dic13—21no—
74C23×Dic13D411yescharacteristic
75C23×Dic13D411yescharacteristic
76C2×C13×SD16—41no—
77C2×C13×SD16—41no—
78C2×C13×SD16C2×C414yescomplemented
79C2×C13×D8—41no—
80C2×C13×D8—41no—
81C2×C13×D8C2×C414yescomplemented
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C13×#121—22no—
85C13×#121C2×C414yes—
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C22⋊C4—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13—21no—
94C2×C22⋊Dic13—21no—
95C2×C22⋊Dic13—21no—
96C2×C22⋊Dic13—21no—
97D4×Dic13—41no—
98D4×Dic13—41no—
99D4×Dic13—44no—
100#88180—41no—
101#88180—41no—
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4⋊Dic13C2311yescharacteristic
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4⋊Dic13C2311yescharacteristic
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13D411yescharacteristic
112C2×C4×Dic13D411yescharacteristic
113C2×C4×Dic13C2311yescharacteristic
114C2×C4×Dic13C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C13×#103C2×C414yescomplemented
118C13×#102C2×C414yescomplemented
119C13×C22⋊C8C2×C414yescomplemented
120#88075—41no—
121#88075—41no—
122#88072—41no—
123#88072—41no—
124#88072—41no—
125#88072—41no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133C22⋊#1055—22no—
134#88058—41no—
135#88057—41no—
136#88055—41no—
137#88055—41no—
138#22051—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13—21no—
141C24×C13C2×D411yescharacteristic
142C13×#41—44no—
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13C22×C412yes—
152C2×D4×C13—24no—
153C2×D4×C13—24no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
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×C13—42no—
167C2×D4×C13—42no—
168C2×D4×C13C22×C412yes—
169C2×D4×C13C22×C412yes—
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—24no—
177C22×C4×C13—42no—
178C22×C4×C13—42no—
179C22×C4×C13C22×C412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13#4112yes—
182C22×C4×C13C2411yescharacteristic
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—41no—
189C22×Dic13—41no—
190C22×Dic13—41no—
191C22×Dic13—41no—
192C22×Dic13—41no—
193C22×Dic13—42no—
194C22×Dic13—42no—
195C22×Dic13—42no—
196C22×Dic13C2×D411yescharacteristic
197C22×Dic13C2×D411yescharacteristic
198C22×Dic13C2×D411yescharacteristic
199C22×Dic13C2×D411yescharacteristic
200C13×SD16—44no—
201C13×D8—44no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13C22×C412yes—
207C2×C8×C13C22×C412yes—
208C13×C4⋊C4—21no—
209C13×C4⋊C4C22×C412yes—
210C13×C22⋊C4—24no—
211C22⋊Dic13—42no—
212C22⋊Dic13—42no—
213C22⋊Dic13—42no—
214C22⋊Dic13—42no—
215C22⋊Dic13—42no—
216C22⋊Dic13—42no—
217C22⋊Dic13—42no—
218C22⋊Dic13—42no—
219C22⋊Dic13—42no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—42no—
229C4×Dic13—21no—
230C4×Dic13—21no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C4×Dic13—41no—
234C4×Dic13—41no—
235C4×Dic13—42no—
236C4×Dic13—42no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#449D1311yescharacteristic
244C4×#121—131no—
245#2297—131no—
246#1973—131no—
247#1972—131no—
248#1936—131no—
249#1935—131no—
250#1927—131no—
251#1925—131no—
252#1879—131no—
253#1877—131no—
254#1875—131no—
255#1854—131no—
256#1788—131no—
257#1749—131no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13C4×D412yes—
279C23×C13C22×D411yescharacteristic
280Q8×C13—22no—
281Q8×C13—22no—
282Q8×C13—41no—
283Q8×C13—41no—
284D4×C13—22no—
285D4×C13—22no—
286D4×C13—22no—
287D4×C13—22no—
288D4×C13—48no—
289D4×C13—48no—
290D4×C13—41no—
291D4×C13—41no—
292D4×C13—41no—
293D4×C13—41no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—48no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13C4×D412yes—
308C2×C4×C13C23×C411yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13H(5,𝔽2)11yescharacteristic
311C2×C4×C13H(5,𝔽2)11yescharacteristic
312C2×C4×C13H(5,𝔽2)11yescharacteristic
313C2×C4×C13H(5,𝔽2)11yescharacteristic
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—84no—
340C2×Dic13AGL(1,ℤ/8)12yes—
341C8×C13—22no—
342C8×C13—22no—
343#1055—41no—
344#1055—41no—
345C22×#41C2×D1311yescharacteristic
346C22×SD16C2×D1311yescharacteristic
347C22×D8C2×D1311yescharacteristic
348C2×#121C2×D1311yescharacteristic
349C2×C4×D4—131no—
350C2×C4×D4—261no—
351C2×#117—131no—
352C22×C42—131no—
353#449Dic1318yescomplemented
354C2×#107—131no—
355C2×#106—131no—
356C2×#103—131no—
357C2×#103—131no—
358C2×#103C2×D1311yescharacteristic
359C2×#102—131no—
360C2×#102—131no—
361C2×#102—131no—
362C2×#102—131no—
363C2×#102C2×D1311yescharacteristic
364C2×C22⋊C8—131no—
365C2×C22⋊C8C2×D1311yescharacteristic
366C2×#97—131no—
367C2×#97—131no—
368#391—131no—
369#391—131no—
370#390—131no—
371#390—131no—
372#390—131no—
373#389—131no—
374#388—261no—
375#386—261no—
376#386—261no—
377#386—261no—
378#380—131no—
379C4×C4⋊C4—131no—
380C4×C22⋊C4—261no—
381C4×C22⋊C4—261no—
382C4×C22⋊C4—261no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13—81no—
405C22×C13—81no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13C2×C4×D411yescharacteristic
411C22×C13#53411yescharacteristic
412C22×C13#53511yescharacteristic
413C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
414C22×C13#57511yescharacteristic
415C22×C13#57511yescharacteristic
416C22×C13#57511yescharacteristic
417C4×C13—22no—
418C4×C13—42no—
419C4×C13—42no—
420C4×C13#51811yescharacteristic
421C4×C13#51811yescharacteristic
422C4×C13#53811yescharacteristic
423C4×C13#53811yescharacteristic
424Dic13—22no—
425Dic13—41no—
426Dic13—41no—
427Dic13—41no—
428Dic13—81no—
429Dic13—81no—
430Dic13—81no—
431Dic13—81no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41—41no—
437C2×#41C2×Dic1314yescomplemented
438C22×Q8C22×D1311yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22×D1311yescharacteristic
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—261no—
447C23×C4C22×D1311yescharacteristic
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic1314yescomplemented
451C2×D8—41no—
452C2×D8—41no—
453C2×D8C2×Dic1314yescomplemented
454C22×C8—131no—
455C22×C8—131no—
456C22×C8C22×D1311yescharacteristic
457C22×C8C22×D1311yescharacteristic
458#121—22no—
459#121C2×Dic1314yes—
460C4×D4—521no—
461C4×D4—521no—
462C4×D4—524no—
463#117—521no—
464#117—521no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4C22×D1311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—261no—
473C2×C22⋊C4—261no—
474C2×C22⋊C4—261no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42—261no—
486C2×C42—261no—
487C2×C42—521no—
488C2×C42—521no—
489#107—521no—
490#106—521no—
491#103—521no—
492#103—521no—
493#103C2×Dic1314yescomplemented
494#102—521no—
495#102—521no—
496#102—521no—
497#102—521no—
498#102C2×Dic1314yescomplemented
499C22⋊C8—262no—
500C22⋊C8C2×Dic1314yescomplemented
501#97—521no—
502#97—521no—
503#95—261no—
504#95—261no—
505#95—261no—
506#95—261no—
507#95—261no—
508#95—261no—
509#95—261no—
510C2×C13—42no—
511C2×C13—82no—
512C2×C13—82no—
513C2×C13#232111yescharacteristic
514C2×C13#294311yescharacteristic
515C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
516C2×C13#319411yescharacteristic
517C2×C13#319711yescharacteristic
518C2×C13#321411yescharacteristic
519C2×C13#321911yescharacteristic
520C24—21no—
521C24—21no—
522C24D4×D1311yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C22×Dic1312yes—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4C22×Dic1312yes—
550C2×D4C22×Dic1312yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—131no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—131no—
564C22×C4—262no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—522no—
570C22×C4—521no—
571C22×C4—521no—
572C22×C4—521no—
573C22×C4—521no—
574C22×C4—521no—
575C22×C4—522no—
576C22×C4—522no—
577C22×C4D4×D1311yescharacteristic
578C22×C4#612912yes—
579C22×C4C22×Dic1312yes—
580C22×C4C23×D1311yescharacteristic
581SD16—44no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8C22×Dic1312yes—
594C2×C8C22×Dic1312yes—
595C4⋊C4—21no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—522no—
605C4⋊C4C22×Dic1312yes—
606C22⋊C4—24no—
607C22⋊C4—522no—
608C22⋊C4—522no—
609C22⋊C4—522no—
610C22⋊C4—522no—
611C22⋊C4—522no—
612C22⋊C4—522no—
613C22⋊C4—522no—
614C22⋊C4—522no—
615C22⋊C4—522no—
616C42—261no—
617C42—261no—
618C42—261no—
619C42—261no—
620C42—521no—
621C42—521no—
622C42—522no—
623C42—522no—
624C13#2205111yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23D4×Dic1312yes—
646C23C2×D4×D1311yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—132no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—524no—
687C2×C4—524no—
688C2×C4—521no—
689C2×C4—521no—
690C2×C4—521no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—1044no—
701C2×C4D4×Dic1312yes—
702C2×C4C2×#612911yescharacteristic
703C2×C4#8825111yescharacteristic
704C2×C4#8825111yescharacteristic
705C2×C4#8825111yescharacteristic
706C2×C4#8825111yescharacteristic
707C2×C4C23×Dic1311yescharacteristic
708C8—22no—
709C8—22no—
710C8—521no—
711C8—521no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#1171929411yescharacteristic
734C22#1171929711yescharacteristic
735C22#1171947311yescharacteristic
736C22#1171947311yescharacteristic
737C22D13×AGL(1,ℤ/8)11yescharacteristic
738C22#1171947811yescharacteristic
739C22C2×D4×Dic1311yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—262no—
744C4—521no—
745C4—521no—
746C4—521no—
747C4—1041no—
748C4—1041no—
749C4—1041no—
750C4—1041no—
751C4#1171929811yescharacteristic
752C4#1171929811yescharacteristic
753C4#1171950311yescharacteristic
754C4#1171950311yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1311749711yescharacteristic
759C2#1312363711yescharacteristic
760C2AGL(1,ℤ/8)×Dic1311yescharacteristic
761C2#1312564811yescharacteristic
762C2#1312567511yescharacteristic
763C2#1312582811yescharacteristic
764C2#1312587111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#449C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#449D13
hypocenterC13#22051
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #121×Dic13C2semidirect
2. #13117327C2semidirect
3. #13115719C2semidirect
4. #13115713C2semidirect
5. #13115535C2semidirect
6. #13115528C2semidirect
7. #13115472C2semidirect
8. #13115458C2semidirect
9. #13115186C2semidirect
10. #13115172C2semidirect
11. #13115159C2semidirect
12. #13115037C2semidirect
13. #13114776C2semidirect
14. #13114600C2semidirect
24. C13×#449C4semidirect
65. C2×C13×#41C2×C4semidirect
78. C2×C13×SD16C2×C4semidirect
81. C2×C13×D8C2×C4semidirect
117. C13×#103C2×C4semidirect
118. C13×#102C2×C4semidirect
119. C13×C22⋊C8C2×C4semidirect
353. #449Dic13semidirect
437. C2×#41C2×Dic13semidirect
450. C2×SD16C2×Dic13semidirect
453. C2×D8C2×Dic13semidirect
493. #103C2×Dic13semidirect
498. #102C2×Dic13semidirect
500. C22⋊C8C2×Dic13semidirect
624. C13#22051semidirect

Maximal subgroups

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

subgroupindex
#121×Dic132
#131173272
#131157192
#131157132
#131155352
#131155282
#131154722
#131154582
#131151862
#131151722
#131151592
#131150372
#131147762
#131146002
C2×C13×#4492
#2205113