Finite Group Databasebeta

← #15873194

Subgroups — #15873194

Order 3328.

1194 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
1C2×D13×C22⋊C8C211yesmaximal, characteristic
2#13117215C211yesmaximal, characteristic
3D13×#380C211yesmaximal, characteristic
4#13115037C211yesmaximal, characteristic, complemented
5#13115035C211yesmaximal, characteristic, complemented
6#13115033C211yesmaximal, characteristic, complemented
7#13115030C211yesmaximal, characteristic, complemented
8#13115027C211yesmaximal, characteristic, complemented
9#13115025C211yesmaximal, characteristic, complemented
10#13115022C211yesmaximal, characteristic, complemented
11#13114864C211yesmaximal, characteristic, complemented
12#13114862C211yesmaximal, characteristic, complemented
13#13114860C211yesmaximal, characteristic, complemented
14#13114858C211yesmaximal, characteristic, complemented
15C13×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C22⋊C4×D13—21no—
24C2×C13×#107C2211yescharacteristic, complemented
25C2×C13×#106C2211yescharacteristic, complemented
26C2×C13×C22⋊C8C2211yescharacteristic
27C13×#380C2211yescharacteristic
28#11718873C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88058C2211yescharacteristic, complemented
33C2×#88057C2211yescharacteristic, complemented
34#11718648C2211yescharacteristic
35#11718648C2211yescharacteristic
36#11718648C2211yescharacteristic
37#11718648C2211yescharacteristic
38#11718648C2211yescharacteristic
39#11718648C2211yescharacteristic
40C2×#88048C2211yescharacteristic, complemented
41C2×#88048C2211yescharacteristic, complemented
42C2×#88047C2211yescharacteristic, complemented
43C2×#88047C2211yescharacteristic, complemented
44#11718616—21no—
45#11718604—21no—
46#11718603—21no—
47C4×#6103—21no—
48C4×#6103—21no—
49D13×C22⋊C8C418yescomplemented
50#11718328—21no—
51D13×#95—21no—
52C13×#340C2211yescharacteristic, complemented
53C13×#340C2211yescharacteristic, complemented
54#11718143C2211yescharacteristic, complemented
55#11718143C2211yescharacteristic, complemented
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718121C2211yescharacteristic, complemented
60C24×D13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13D411yescharacteristic
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13—41no—
66C22×C4×D13—41no—
67C22×C4×D13—41no—
68C22×C4×D13—41no—
69C22×C4×D13C2×C414yes—
70C22×C4×D13D411yescharacteristic
71C22×C4×D13D411yescharacteristic
72C22×C4×D13Q814yes—
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C13×#117—41no—
78C13×#117—41no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C42×C13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94#88180—41no—
95#88180—41no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C2×C8×D13—41no—
106C2×C8×D13—41no—
107C2×C8×D13—41no—
108C2×C8×D13—41no—
109C2×C8×D13C2×C414yescomplemented
110C2×C8×D13C2×C414yescomplemented
111C4⋊C4×D13—41no—
112C4⋊C4×D13—41no—
113C4⋊C4×D13—41no—
114C4⋊C4×D13—41no—
115C22⋊C4×D13—44no—
116C13×#107—41no—
117C13×#106—41no—
118C13×C22⋊C8C2×C414yescomplemented
119C13×#95—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127C22⋊#1055C2×C414yescomplemented
128#88060C2×C414yes—
129#88060C2×C414yes—
130#88058—41no—
131#88057—41no—
132#88048—41no—
133#88048—41no—
134#88047—41no—
135#88047—41no—
136#21941—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C23×D13—22no—
139C23×D13—22no—
140C23×D13—22no—
141C23×D13—22no—
142C23×D13—41no—
143C23×D13—41no—
144C23×D13C4⋊C414yes—
145C23×D13C2×D411yescharacteristic
146C23×D13C2×D411yescharacteristic
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×C13C22×C412yes—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×Q812yes—
158C22×C4×C13C2411yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—41no—
164C22×Dic13—41no—
165C22×Dic13C4⋊C414yes—
166C22×Dic13C2×D411yescharacteristic
167C22×Dic13C2×D411yescharacteristic
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—21no—
175C2×C4×D13—21no—
176C2×C4×D13—44no—
177C2×C4×D13—44no—
178C2×C4×D13—44no—
179C2×C4×D13—44no—
180C2×C4×D13—41no—
181C2×C4×D13—41no—
182C2×C4×D13—41no—
183C2×C4×D13—41no—
184C2×C4×D13—42no—
185C2×C4×D13—42no—
186C2×C4×D13—42no—
187C2×C4×D13—42no—
188C2×C4×D13—42no—
189C2×C4×D13—42no—
190C2×C4×D13C4⋊C414yes—
191C2×C4×D13C4⋊C414yes—
192C2×C4×D13C22×C412yes—
193C2×C4×D13C22×C412yes—
194C2×C4×D13C2×Q812yes—
195C2×C4×D13C2×Q812yes—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13C22×C412yes—
201C2×C8×C13C22×C412yes—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—21no—
210C13×C22⋊C4—42no—
211C13×C22⋊C4—42no—
212C42×C13—42no—
213C22⋊Dic13—42no—
214C22⋊Dic13—42no—
215#6103—42no—
216#6103—42no—
217#6103—42no—
218#6103—42no—
219#6103—42no—
220#6103—42no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229#6101—42no—
230#6101—42no—
231C4×Dic13—42no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055C22×C412yes—
237C2×#1055C22×C412yes—
238C8×D13—44no—
239C8×D13—44no—
240C22×C22⋊C8—131no—
241#2280—131no—
242C2×#380—131no—
243#1854—131no—
244#1854—131no—
245#1854—131no—
246#1854D1311yescharacteristic, complemented
247#1853—131no—
248#1853—131no—
249#1852—131no—
250#1852—131no—
251#1808—131no—
252#1808—131no—
253#1807—131no—
254#1807—131no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13C2×C4⋊C412yes—
262C23×C13C22×D411yescharacteristic
263C22×D13—21no—
264C22×D13—21no—
265C22×D13—21no—
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—28no—
272C22×D13—28no—
273C22×D13—44no—
274C22×D13—44no—
275C22×D13—44no—
276C22×D13—44no—
277C22×D13—44no—
278C22×D13C2×C4⋊C412yes—
279C22×D13C2×C4⋊C412yes—
280C22×D13#13512yes—
281C22×D13#13512yes—
282C22×D13AGL(1,ℤ/8)12yes—
283C22×D13#13712yes—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13C2×C4⋊C412yes—
303C2×C4×C13C23×C411yescharacteristic
304C2×C4×C13C22×Q811yescharacteristic
305C2×C4×C13H(5,𝔽2)11yescharacteristic
306C2×C4×C13H(5,𝔽2)11yescharacteristic
307C2×C4×C13H(5,𝔽2)11yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—44no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13C2×C4⋊C412yes—
327C2×Dic13C2×C4⋊C412yes—
328C4×D13—22no—
329C4×D13—22no—
330C4×D13—22no—
331C4×D13—22no—
332C4×D13—22no—
333C4×D13—22no—
334C4×D13—22no—
335C4×D13—22no—
336C4×D13—44no—
337C4×D13—44no—
338C4×D13—84no—
339C4×D13—84no—
340C8×C13—22no—
341C8×C13—22no—
342#1055—22no—
343#1055—22no—
344C24×C4—131no—
345C23×C8—131no—
346C23×C8—131no—
347C2×#117—131no—
348C2×#117C2×D1311yescharacteristic
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C22⋊C4—261no—
352C2×#107—131no—
353C2×#107—131no—
354C2×#107—131no—
355C2×#107C2×D1311yescharacteristic, complemented
356C2×#106—131no—
357C2×#106—131no—
358C2×#106—131no—
359C2×#106C2×D1311yescharacteristic, complemented
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8—138no—
364C2×C22⋊C8C2×D1311yescharacteristic
365#381—261no—
366#380—131no—
367#380—131no—
368#380—131no—
369#380—131no—
370#380—131no—
371#380—131no—
372#380—131no—
373#380—261no—
374#380—261no—
375#380C2×D1311yescharacteristic
376#379—261no—
377C4×C22⋊C4—261no—
378C4×C22⋊C4—261no—
379C2×#95—261no—
380#340—131no—
381#340—131no—
382#340—131no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340C2×D1311yescharacteristic, complemented
387#340C2×D1311yescharacteristic, complemented
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13C22×C4⋊C411yescharacteristic
396C22×C13#53411yescharacteristic
397C22×C13#53411yescharacteristic
398C22×C13C2×#13511yescharacteristic
399C22×C13C2×#13511yescharacteristic
400C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C13C2×#13711yescharacteristic
402C2×D13—22no—
403C2×D13—22no—
404C2×D13—22no—
405C2×D13—22no—
406C2×D13—22no—
407C2×D13—22no—
408C2×D13—22no—
409C2×D13—22no—
410C2×D13—22no—
411C2×D13—22no—
412C2×D13—22no—
413C2×D13—22no—
414C2×D13—416no—
415C2×D13#42714yes—
416C2×D13#42814yes—
417C4×C13—22no—
418C4×C13—81no—
419C4×C13—81no—
420C4×C13—81no—
421C4×C13—81no—
422C4×C13#51811yescharacteristic
423C4×C13#51811yescharacteristic
424C4×C13#54311yescharacteristic
425C4×C13#54311yescharacteristic
426Dic13—22no—
427Dic13—22no—
428Dic13—81no—
429Dic13—81no—
430Dic13—81no—
431Dic13—81no—
432C25—131no—
433C23×C4—131no—
434C23×C4—131no—
435C23×C4—131no—
436C23×C4—134no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—134no—
440C23×C4—261no—
441C23×C4—261no—
442C23×C4—521no—
443C23×C4—521no—
444C23×C4—521no—
445C23×C4—521no—
446C23×C4C22×D1311yescharacteristic
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—134no—
450C22×C8—134no—
451C22×C8—521no—
452C22×C8—521no—
453C22×C8—521no—
454C22×C8—521no—
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1311yescharacteristic
457#117—41no—
458#117—41no—
459#117—521no—
460#117—521no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—521no—
468C2×C4⋊C4—521no—
469C2×C4⋊C4—521no—
470C2×C4⋊C4—521no—
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C4⋊C4C22×D1311yescharacteristic
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C4⋊C4C22×D1311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4—261no—
483C2×C22⋊C4—261no—
484C2×C22⋊C4—261no—
485C2×C22⋊C4—524no—
486C2×C42—21no—
487C2×C42—261no—
488#107—41no—
489#107—521no—
490#107—521no—
491#107—521no—
492#106—41no—
493#106—521no—
494#106—521no—
495#106—521no—
496C22⋊C8—134no—
497C22⋊C8—134no—
498C22⋊C8—134no—
499C22⋊C8C4×D1314yescomplemented
500#95—21no—
501#95—261no—
502#95—261no—
503#95—261no—
504#95—261no—
505#95—261no—
506#95—261no—
507#95—261no—
508C2×C13—42no—
509C2×C13#231511yescharacteristic
510C2×C13C2×#42711yescharacteristic
511C2×C13C2×#42811yescharacteristic
512C2×C13#318811yescharacteristic
513C2×C13#318811yescharacteristic
514C2×C13#319011yescharacteristic
515C2×C13#319011yescharacteristic
516D13—24no—
517D13—24no—
518C24—131no—
519C24—131no—
520C24—134no—
521C24—262no—
522C24—262no—
523C24—262no—
524C24—262no—
525C24—521no—
526C24—521no—
527C24D4×D1311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—134no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—132no—
543C22×C4—134no—
544C22×C4—134no—
545C22×C4—261no—
546C22×C4—261no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—524no—
558C22×C4—524no—
559C22×C4—524no—
560C22×C4—524no—
561C22×C4—521no—
562C22×C4—521no—
563C22×C4—521no—
564C22×C4—521no—
565C22×C4—522no—
566C22×C4—522no—
567C22×C4—522no—
568C22×C4—522no—
569C22×C4—522no—
570C22×C4—522no—
571C22×C4—521no—
572C22×C4—521no—
573C22×C4C2×C4×D1312yes—
574C22×C4D4×D1311yescharacteristic
575C22×C4Q8×D1312yes—
576C22×C4C23×D1311yescharacteristic
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—132no—
582C2×C8—132no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—524no—
588C2×C8—524no—
589C2×C8C2×C4×D1312yes—
590C2×C8C2×C4×D1312yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—261no—
606C4⋊C4—261no—
607C4⋊C4—522no—
608C4⋊C4—522no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—522no—
612C22⋊C4—522no—
613C22⋊C4—522no—
614C22⋊C4—522no—
615C22⋊C4—522no—
616C22⋊C4—522no—
617C22⋊C4—522no—
618C22⋊C4—522no—
619C42—42no—
620C42—522no—
621C13#2194111yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—132no—
629C23—132no—
630C23—132no—
631C23—132no—
632C23—132no—
633C23—132no—
634C23—268no—
635C23—268no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23—261no—
640C23—261no—
641C23—261no—
642C23—261no—
643C23—261no—
644C23—524no—
645C23—524no—
646C23—524no—
647C23—524no—
648C23—524no—
649C23C4⋊C4×D1312yes—
650C23C2×D4×D1311yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—132no—
670C2×C4—132no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—524no—
684C2×C4—524no—
685C2×C4—524no—
686C2×C4—521no—
687C2×C4—521no—
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—1044no—
699C2×C4—1044no—
700C2×C4C4⋊C4×D1312yes—
701C2×C4C22×C4×D1311yescharacteristic
702C2×C4#8825111yescharacteristic
703C2×C4#8825111yescharacteristic
704C2×C4C2×Q8×D1311yescharacteristic
705C2×C4#8825611yescharacteristic
706C2×C4#8825611yescharacteristic
707C8—22no—
708C8—22no—
709C8—262no—
710C8—262no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—134no—
719C22—134no—
720C22—262no—
721C22—262no—
722C22—262no—
723C22—262no—
724C22—262no—
725C22—262no—
726C22—262no—
727C22—262no—
728C22—262no—
729C22—262no—
730C22—262no—
731C22—262no—
732C22—5216no—
733C22C2×C4⋊C4×D1311yescharacteristic
734C22#1171929411yescharacteristic
735C22#1171935811yescharacteristic
736C22D13×#13511yescharacteristic
737C22D13×#13511yescharacteristic
738C22D13×AGL(1,ℤ/8)11yescharacteristic
739C22D13×#13711yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—262no—
746C4—262no—
747C4—1041no—
748C4—1041no—
749C4—1041no—
750C4—1041no—
751C4#1171925011yescharacteristic
752C4#1171925011yescharacteristic
753C4#1171933911yescharacteristic
754C4#1171933911yescharacteristic
755C2—42no—
756C2—264no—
757C2—264no—
758C2#1311744711yescharacteristic
759C2D13×#42711yescharacteristic
760C2D13×#42811yescharacteristic
761C2#1312559911yescharacteristic
762C2#1312560511yescharacteristic
763C2#1312561511yescharacteristic
764C2#1312562111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1854C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1854D13
hypocenterC13#21941
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13115037C2semidirect
5. #13115035C2semidirect
6. #13115033C2semidirect
7. #13115030C2semidirect
8. #13115027C2semidirect
9. #13115025C2semidirect
10. #13115022C2semidirect
11. #13114864C2semidirect
12. #13114862C2semidirect
13. #13114860C2semidirect
14. #13114858C2semidirect
15. C13×#1854C2semidirect
24. C2×C13×#107C22semidirect
25. C2×C13×#106C22semidirect
32. C2×#88058C22semidirect
33. C2×#88057C22semidirect
40. C2×#88048C22semidirect
41. C2×#88048C22semidirect
42. C2×#88047C22semidirect
43. C2×#88047C22semidirect
49. D13×C22⋊C8C4semidirect
52. C13×#340C22semidirect
53. C13×#340C22semidirect
54. #11718143C22semidirect
55. #11718143C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718121C22semidirect
109. C2×C8×D13C2×C4semidirect
110. C2×C8×D13C2×C4semidirect
118. C13×C22⋊C8C2×C4semidirect
127. C22⋊#1055C2×C4semidirect
246. #1854D13semidirect
355. C2×#107C2×D13semidirect
359. C2×#106C2×D13semidirect
386. #340C2×D13semidirect
387. #340C2×D13semidirect
499. C22⋊C8C4×D13semidirect
621. C13#21941semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊C82
#131172152
D13×#3802
#131150372
#131150352
#131150332
#131150302
#131150272
#131150252
#131150222
#131148642
#131148622
#131148602
#131148582
C13×#18542
#2194113