Finite Group Databasebeta

← #15786299

Subgroups — #15786299

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718891C211yesmaximal, characteristic
2C2×#11718891C211yesmaximal, characteristic
3C2×#11718634C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic
5#13113099C212yesmaximal
6#13113095C212yesmaximal
7#13113069C212yesmaximal
8#13113069C212yesmaximal
9#13113066C211yesmaximal, characteristic
10#13113065C211yesmaximal, characteristic
11C22×C4×Q8×C13C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C2×C4×Q8×C13—24no—
14C2×C4×Q8×C13—24no—
15C2×C4×Q8×C13—24no—
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2212yes—
19C22×C42×C13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2212yes—
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27#11718891—24no—
28#11718891C418yescomplemented
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40#11718634—24no—
41C4×#6101—24no—
42C22×Q8×C13—22no—
43C22×Q8×C13—22no—
44C22×Q8×C13—22no—
45C22×Q8×C13—22no—
46C22×Q8×C13C2×C414yes—
47C22×Q8×C13D414yes—
48C22×Q8×C13Q814yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C4×Q8×C13—232no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4D414yes—
67C2×C42×C13—24no—
68C2×C42×C13—24no—
69C2×C42×C13—24no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×C42×C13D414yes—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—22no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13C2×C414yes—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×#6101—22no—
82C2×#6101—22no—
83C2×#6101—22no—
84C2×#6101—24no—
85C2×#6101—24no—
86C2×#6101—42no—
87C2×#6101Q814yescomplemented
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13C2×C414yes—
94#88071—22no—
95#88071—22no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—42no—
102#88071—42no—
103#88071C2×C418yes—
104#88071C2×C418yes—
105#14017—131nomaximal, Sylow
106C24×C13C2411yescharacteristic
107C2×Q8×C13—28no—
108C2×Q8×C13—28no—
109C2×Q8×C13—28no—
110C2×Q8×C13—28no—
111C2×Q8×C13—28no—
112C2×Q8×C13—28no—
113C2×Q8×C13C4⋊C4116yescomplemented
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C2×D414yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D414yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×Q814yes—
144C22×C4×C13C2×Q812yes—
145C22×C4×C13C2×Q812yes—
146C22×C4×C13#4112yes—
147C22×C4×C13#4112yes—
148C22×C4×C13#4112yes—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—22no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13C22×C412yes—
185C22×Dic13C22×C414yes—
186C22×Dic13C22×C412yes—
187C22×Dic13C2×Q812yes—
188C22×Dic13C2×Q812yes—
189C22×Dic13#4112yes—
190C22×Dic13#4112yes—
191C13×C4⋊C4—216no—
192C13×C4⋊C4—28no—
193C42×C13—216no—
194C42×C13—28no—
195C4⋊Dic13—28no—
196C4⋊Dic13—44no—
197#6101—28no—
198#6101—28no—
199#6101—48no—
200C4×Dic13—28no—
201C4×Dic13—44no—
202C22×C4×Q8D1311yescharacteristic
203C2×#391—131no—
204C2×#391—131no—
205C2×#389—131no—
206C2×C4×C4⋊C4—131no—
207#1444—132no—
208#1442—132no—
209#1436—132no—
210#1436—132no—
211C4⋊#95—131no—
212C4⋊#95—131no—
213C23×C13C23×C411yescharacteristic
214C23×C13C22×D411yescharacteristic
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D411yescharacteristic
217C23×C13C22×Q811yescharacteristic
218C23×C13C22×Q811yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C13C2×#4111yescharacteristic
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C132−1+411yescharacteristic
226C23×C132−1+411yescharacteristic
227C23×C132−1+411yescharacteristic
228Q8×C13—232no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—41no—
255C2×C4×C13C2×C4⋊C418yes—
256C2×C4×C13C2×C4⋊C414yes—
257C2×C4×C13C4×D414yes—
258C2×C4×C13C4×D414yes—
259C2×C4×C13#12014yes—
260C2×C4×C13C22⋊Q814yes—
261C2×C4×C13C22⋊Q814yes—
262C2×C4×C13C22⋊Q814yes—
263C2×C4×C13#12314yes—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—42no—
291C2×Dic13—41no—
292C2×Dic13—42no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13C4×Q814yescomplemented
306C23×Q8C2×D1311yescharacteristic
307C2×C4×Q8—24no—
308C2×C4×Q8—24no—
309C2×C4×Q8—24no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—131no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4—132no—
315C22×C4⋊C4C2×D1312yes—
316C22×C4⋊C4C2×D1311yescharacteristic
317C22×C42—131no—
318C22×C42—131no—
319C22×C42C2×D1312yes—
320C22×C42C2×D1311yescharacteristic
321#391—138no—
322#391—264no—
323#389—264no—
324C4×C4⋊C4—264no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95—132no—
329C2×#95—131no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—131no—
334C2×#95—132no—
335C2×#95—132no—
336C22×C13C22×C4⋊C411yescharacteristic
337C22×C13C2×C4×D411yescharacteristic
338C22×C13C2×C4×D411yescharacteristic
339C22×C13C2×C4×Q811yescharacteristic
340C22×C13C4×#4111yescharacteristic
341C22×C13#51911yescharacteristic
342C22×C13#52011yescharacteristic
343C22×C13C2×#12011yescharacteristic
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13C2×C22⋊Q811yescharacteristic
346C22×C13C2×C22⋊Q811yescharacteristic
347C22×C13C2×#12311yescharacteristic
348C22×C13#52511yescharacteristic
349C22×C13#52911yescharacteristic
350C22×C13#53311yescharacteristic
351C22×C13#53611yescharacteristic
352C22×C13#53711yescharacteristic
353C22×C13#54111yescharacteristic
354C22×C13#54211yescharacteristic
355C22×C13#54611yescharacteristic
356C22×C13#54711yescharacteristic
357C22×C13#54811yescharacteristic
358C22×C13#54811yescharacteristic
359C22×C13#54811yescharacteristic
360C22×C13D4×Q811yescharacteristic
361C22×C13D4×Q811yescharacteristic
362C22×C13#55011yescharacteristic
363C22×C13#55611yescharacteristic
364C22×C13#55611yescharacteristic
365C22×C13#55711yescharacteristic
366C22×C13#55711yescharacteristic
367C22×C13#55711yescharacteristic
368C22×C13#55711yescharacteristic
369C22×C13Q8211yescharacteristic
370C22×C13#55911yescharacteristic
371C4×C13—24no—
372C4×C13—28no—
373C4×C13—42no—
374C4×C13—44no—
375C4×C13#38518yes—
376Dic13—24no—
377Dic13—42no—
378Dic13—44no—
379Dic13—42no—
380Dic13—42no—
381Dic13—82no—
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8Dic2614yes—
387C22×Q8C4×D1314yes—
388C22×Q8C22⋊D1314yes—
389C23×C4—131no—
390C23×C4—131no—
391C23×C4—132no—
392C23×C4—131no—
393C23×C4—131no—
394C23×C4—132no—
395C23×C4C22×D1312yes—
396C23×C4C22×D1311yescharacteristic
397C23×C4C22×D1312yes—
398C23×C4C22×D1311yescharacteristic
399C23×C4C22×D1311yescharacteristic
400C4×Q8—232no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—134no—
407C2×C4⋊C4—134no—
408C2×C4⋊C4—262no—
409C2×C4⋊C4—262no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—262no—
414C2×C4⋊C4—262no—
415C2×C4⋊C4—264no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—262no—
418C2×C4⋊C4—264no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—522no—
421C2×C4⋊C4C22⋊D1314yes—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—134no—
428C2×C42—262no—
429C2×C42—262no—
430C2×C42—262no—
431C2×C42—262no—
432C2×C42—262no—
433C2×C42C22⋊D1314yes—
434#95—138no—
435#95—138no—
436#95—264no—
437#95—264no—
438#95—262no—
439#95—262no—
440#95—264no—
441#95—264no—
442#95—264no—
443#95—522no—
444#95—522no—
445C2×C13C2×#38511yescharacteristic
446C2×C13C4×C22⋊Q811yescharacteristic
447C2×C13#232311yescharacteristic
448C2×C13Q8×C4⋊C411yescharacteristic
449C2×C13#235111yescharacteristic
450C2×C13#236511yescharacteristic
451C2×C13#236711yescharacteristic
452C2×C13#240711yescharacteristic
453C2×C13#240911yescharacteristic
454C2×C13#244611yescharacteristic
455C2×C13#244811yescharacteristic
456C2×C13#245111yescharacteristic
457C2×C13#245311yescharacteristic
458C2×C13#258111yescharacteristic
459C2×C13#258211yescharacteristic
460C24C23×D1311yescharacteristic
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8#6101116yescomplemented
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—132no—
489C22×C4—132no—
490C22×C4—132no—
491C22×C4—132no—
492C22×C4—134no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4—262no—
508C22×C4—261no—
509C22×C4—262no—
510C22×C4—261no—
511C22×C4—262no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—262no—
522C22×C4—261no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4C2×Dic2614yes—
531C22×C4C2×Dic2612yes—
532C22×C4C2×C4×D1314yes—
533C22×C4C2×C4×D1312yes—
534C22×C4#612712yes—
535C22×C4#612712yes—
536C22×C4Q8×D1312yes—
537C22×C4#613112yes—
538C22×C4C2×C22⋊D1314yes—
539C22×C4C2×C22⋊D1312yes—
540C22×C4C2×C22⋊D1314yes—
541C22×C4C2×C22⋊D1312yes—
542C22×C4C2×C22⋊D1312yes—
543C22×C4C2×C22⋊D1312yes—
544C22×C4C2×C22⋊D1312yes—
545C4⋊C4—216no—
546C4⋊C4—28no—
547C4⋊C4—268no—
548C4⋊C4—268no—
549C4⋊C4—268no—
550C4⋊C4—528no—
551C4⋊C4—524no—
552C42—216no—
553C42—28no—
554C42—268no—
555C42—524no—
556C13#1401711yescharacteristic, complemented, Sylow
557C23C22×Dic2611yescharacteristic
558C23C22×C4×D1311yescharacteristic
559C23C2×#612711yescharacteristic
560C23C2×#612711yescharacteristic
561C23C2×Q8×D1311yescharacteristic
562C23C2×#613111yescharacteristic
563C23#8825411yescharacteristic
564C23#8825411yescharacteristic
565C23#41×D1311yescharacteristic
566C23#41×D1311yescharacteristic
567C23#8825611yescharacteristic
568C23#8825711yescharacteristic
569C23C22×C22⋊D1311yescharacteristic
570C23C22×C22⋊D1311yescharacteristic
571C23C22×C22⋊D1311yescharacteristic
572Q8—232no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—134no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—264no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—264no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—264no—
617C2×C4—262no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—522no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—522no—
624C2×C4—521no—
625C2×C4—522no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4—522no—
641C2×C4C2×#610118yes—
642C2×C4C2×#610114yes—
643C2×C4#8817814yes—
644C2×C4#8817814yes—
645C2×C4C4×C22⋊D1314yes—
646C2×C4C4×C22⋊D1314yes—
647C2×C4#8818314yes—
648C2×C4#8820014yes—
649C2×C4#8820714yes—
650C22Q8×Dic2611yescharacteristic
651C22#1171927211yescharacteristic
652C22#1171927311yescharacteristic
653C22#1171927311yescharacteristic
654C22#1171927411yescharacteristic
655C22#1171927411yescharacteristic
656C22#1171927511yescharacteristic
657C22C4×Q8×D1311yescharacteristic
658C22#1171927711yescharacteristic
659C22C4×#613111yescharacteristic
660C22#1171927911yescharacteristic
661C22#1171928311yescharacteristic
662C22#1171928511yescharacteristic
663C22#1171928711yescharacteristic
664C22#1171928811yescharacteristic
665C22#1171929011yescharacteristic
666C22C22×#610111yescharacteristic
667C22C2×#8817811yescharacteristic
668C22C2×#8817811yescharacteristic
669C22C2×C4×C22⋊D1311yescharacteristic
670C22C2×C4×C22⋊D1311yescharacteristic
671C22C2×#8818311yescharacteristic
672C22C2×#8820011yescharacteristic
673C22Q8×C22⋊D1311yescharacteristic
674C22Q8×C22⋊D1311yescharacteristic
675C22#1171952111yescharacteristic
676C22#1171952211yescharacteristic
677C22#1171952211yescharacteristic
678C22#1171952911yescharacteristic
679C22#1171953311yescharacteristic
680C22#1171953411yescharacteristic
681C22#1171953611yescharacteristic
682C22#1171953811yescharacteristic
683C22#1171953911yescharacteristic
684C22C2×#8820711yescharacteristic
685C4—28no—
686C4—24no—
687C4—44no—
688C4—42no—
689C4—264no—
690C4—522no—
691C4—524no—
692C4—522no—
693C4—522no—
694C4—1042no—
695C4#1171887118yes—
696C2C2×#1171887111yescharacteristic
697C2C4×#8820011yescharacteristic
698C2#1311751211yescharacteristic
699C2Q8×#610111yescharacteristic
700C2#1311775411yescharacteristic
701C2#1311789011yescharacteristic
702C2#1311790311yescharacteristic
703C2#1311817511yescharacteristic
704C2#1311819511yescharacteristic
705C2#1311860611yescharacteristic
706C2#1311862811yescharacteristic
707C2#1311866911yescharacteristic
708C2#1311869111yescharacteristic
709C2#1312019811yescharacteristic
710C2#1312020611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×Q8×C13C2
socle, prime radical, cosocleC24×C13C24
hypercenterC22×C4×Q8D13
hypocenterC13#14017
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
28. #11718891C4semidirect
87. C2×#6101Q8semidirect
113. C2×Q8×C13C4⋊C4semidirect
305. C2×Dic13C4×Q8semidirect
467. C2×Q8#6101semidirect
556. C13#14017semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
C2×#117186342
C2×C4×#61012
#131130992
#131130952
#131130692
#131130662
#131130652
C22×C4×Q8×C132
#1401713