Finite Group Databasebeta

← #15768908

Subgroups — #15768908

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×Dic13C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic
3C2×#11718143C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic
5C2×#11718121C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7C2×C13×#340C211yesmaximal, characteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13—21no—
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C2×#88071—21no—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×C8×Dic13—22no—
20C2×C8×Dic13—22no—
21C2×C8×Dic13—22no—
22#11718646—22no—
23#11718646C414yescomplemented
24C13×#340C414yescomplemented
25#11718143—22no—
26#11718121—22no—
27#11718121C414yescomplemented
28C23×C4×C13—21no—
29C23×C4×C13—21no—
30C23×C4×C13C2311yescharacteristic
31C23×Dic13—21no—
32C23×Dic13—21no—
33C23×Dic13D411yescharacteristic
34C23×Dic13D411yescharacteristic
35C22×C8×C13—21no—
36C22×C8×C13—21no—
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C22×C8×C13C2×C412yes—
40C22×C8×C13D412yes—
41C22×C8×C13Q812yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2×C412yes—
51C2×C13×C4⋊C4C2×C412yes—
52C2×C13×C4⋊C4C2×C412yes—
53C2×C13×C4⋊C4C2×C412yes—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13—21no—
64C2×C4⋊Dic13—24no—
65C2×C4⋊Dic13—42no—
66C2×C4⋊Dic13—42no—
67C2×C4⋊Dic13C2×C412yes—
68C2×C4⋊Dic13C2×C412yes—
69C2×C4×Dic13—21no—
70C2×C4×Dic13—21no—
71C2×C4×Dic13—21no—
72C2×C4×Dic13—21no—
73C2×C4×Dic13C2×C412yes—
74C2×C4×Dic13D412yes—
75C22×#1055—21no—
76C22×#1055—21no—
77C22×#1055—21no—
78C22×#1055—21no—
79C22×#1055C2×C412yes—
80C22×#1055D412yes—
81C22×#1055Q812yes—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85C8×Dic13—28no—
86#10880—131nomaximal, Sylow
87C24×C13C2×D411yescharacteristic
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C22×C411yescharacteristic
104C22×C4×C13C22×C411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×Q811yescharacteristic
109C22×C4×C13C2×Q811yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×Dic13—21no—
117C22×Dic13—21no—
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—41no—
127C22×Dic13—41no—
128C22×Dic13—41no—
129C22×Dic13—41no—
130C22×Dic13—41no—
131C22×Dic13—41no—
132C22×Dic13—41no—
133C22×Dic13—41no—
134C22×Dic13—41no—
135C22×Dic13—41no—
136C22×Dic13—41no—
137C22×Dic13—41no—
138C22×Dic13C22⋊C412yes—
139C22×Dic13C22⋊C412yes—
140C22×Dic13D812yes—
141C22×Dic13SD1612yes—
142C22×Dic13SD1612yes—
143C22×Dic13Q1612yes—
144C2×C8×C13—22no—
145C2×C8×C13—22no—
146C2×C8×C13—22no—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13—22no—
150C2×C8×C13C4⋊C414yescomplemented
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4C4214yes—
159C4⋊Dic13—22no—
160C4⋊Dic13—22no—
161C4⋊Dic13—22no—
162C4⋊Dic13—22no—
163C4⋊Dic13—41no—
164C4⋊Dic13—41no—
165C4⋊Dic13—41no—
166C4⋊Dic13—41no—
167C4⋊Dic13—48no—
168C4×Dic13—22no—
169C4×Dic13—22no—
170C4×Dic13—22no—
171C4×Dic13—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055C4⋊C414yescomplemented
179C22×C4×C8—131no—
180C2×#389—131no—
181C2×#340—131no—
182C2×#340—131no—
183C2×#340—131no—
184C2×#340D1311yescharacteristic
185C4⋊#95—131no—
186C23×C13C2×C22⋊C411yescharacteristic
187C23×C13C4×D411yescharacteristic
188C23×C13C4×D411yescharacteristic
189C23×C13#12111yescharacteristic
190C23×C13#12111yescharacteristic
191C23×C13#12411yescharacteristic
192C23×C13C4⋊Q811yescharacteristic
193C23×C13C2×D811yescharacteristic
194C23×C13C2×SD1611yescharacteristic
195C23×C13C2×SD1611yescharacteristic
196C23×C13C2×Q1611yescharacteristic
197C23×C13#13511yescharacteristic
198C23×C13#13511yescharacteristic
199C23×C13#13511yescharacteristic
200C23×C13#13511yescharacteristic
201C2×C4×C13—24no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—81no—
212C2×C4×C13—81no—
213C2×C4×C13—81no—
214C2×C4×C13—81no—
215C2×C4×C13C2×C4211yescharacteristic
216C2×C4×C13C2×C4⋊C411yescharacteristic
217C2×C4×C13C2×C4⋊C411yescharacteristic
218C2×C4×C13#11711yescharacteristic
219C2×C4×C13#11711yescharacteristic
220C2×C4×C13#11711yescharacteristic
221C2×C4×C13C4×D411yescharacteristic
222C2×C4×C13C4×D411yescharacteristic
223C2×C4×C13C4×D411yescharacteristic
224C2×C4×C13C4×D411yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13C4×Q811yescharacteristic
228C2×C4×C13C4×Q811yescharacteristic
229C2×C4×C13C4×Q811yescharacteristic
230C2×C4×C13C4×Q811yescharacteristic
231C2×C4×C13#12011yescharacteristic
232C2×C4×C13C22⋊Q811yescharacteristic
233C2×C4×C13C22⋊Q811yescharacteristic
234C2×C4×C13C22⋊Q811yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12311yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12511yescharacteristic
240C2×C4×C13#12511yescharacteristic
241C2×C4×C13#12611yescharacteristic
242C2×C4×C13#12611yescharacteristic
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—81no—
262C2×Dic13—81no—
263C2×Dic13—81no—
264C2×Dic13—81no—
265C2×Dic13—81no—
266C2×Dic13—81no—
267C2×Dic13—81no—
268C2×Dic13—81no—
269C2×Dic13#10214yes—
270C2×Dic13#10314yes—
271C8×C13—24no—
272#1055—24no—
273C23×C8—131no—
274C23×C8C2×D1311yescharacteristic
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—261no—
278C22×C4⋊C4C2×D1311yescharacteristic
279C22×C4⋊C4C2×D1311yescharacteristic
280C22×C42—131no—
281C2×C4×C8—262no—
282C2×C4×C8—262no—
283C2×C4×C8—262no—
284#389—134no—
285#389—262no—
286C2×#95—261no—
287C2×#95—261no—
288C2×#95—261no—
289#340—134no—
290#340—262no—
291#340—262no—
292#340Dic1314yescomplemented
293C22×C13C4×C22⋊C411yescharacteristic
294C22×C13#38611yescharacteristic
295C22×C13#38811yescharacteristic
296C22×C13#38811yescharacteristic
297C22×C13#38911yescharacteristic
298C22×C13#38911yescharacteristic
299C22×C13#39111yescharacteristic
300C22×C13C2×#10211yescharacteristic
301C22×C13C2×#10311yescharacteristic
302C22×C13#41611yescharacteristic
303C22×C13#41611yescharacteristic
304C22×C13C4×D811yescharacteristic
305C22×C13C4×D811yescharacteristic
306C22×C13C4×SD1611yescharacteristic
307C22×C13C4×SD1611yescharacteristic
308C22×C13C4×SD1611yescharacteristic
309C22×C13C4×SD1611yescharacteristic
310C22×C13C4×Q1611yescharacteristic
311C22×C13C4×Q1611yescharacteristic
312C22×C13#46511yescharacteristic
313C22×C13#46511yescharacteristic
314C22×C13#46511yescharacteristic
315C22×C13#46511yescharacteristic
316C22×C13#46611yescharacteristic
317C22×C13#46611yescharacteristic
318C22×C13#46711yescharacteristic
319C22×C13#46711yescharacteristic
320C22×C13#48611yescharacteristic
321C22×C13#48711yescharacteristic
322C22×C13#48811yescharacteristic
323C22×C13#48811yescharacteristic
324C22×C13#49811yescharacteristic
325C22×C13#49911yescharacteristic
326C22×C13#49911yescharacteristic
327C22×C13#50011yescharacteristic
328C4×C13—44no—
329C4×C13—82no—
330C4×C13C4×C4⋊C411yescharacteristic
331C4×C13C4×C4⋊C411yescharacteristic
332C4×C13#38511yescharacteristic
333C4×C13#38511yescharacteristic
334C4×C13#38711yescharacteristic
335C4×C13#38711yescharacteristic
336C4×C13#38711yescharacteristic
337C4×C13#38711yescharacteristic
338Dic13—24no—
339Dic13—24no—
340Dic13—82no—
341Dic13—82no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—261no—
347C23×C4—261no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C22×C8—132no—
354C22×C8—132no—
355C22×C8—132no—
356C22×C8—261no—
357C22×C8—261no—
358C22×C8—261no—
359C22×C8—261no—
360C22×C8Dic2612yes—
361C22×C8D5212yes—
362C22×C8C2×Dic1312yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—132no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—522no—
385C2×C4⋊C4—522no—
386C2×C4⋊C4C4×D1312yes—
387C2×C4⋊C4C4×D1312yes—
388C2×C4⋊C4C2×Dic1312yes—
389C2×C4⋊C4C2×Dic1312yes—
390C2×C42—132no—
391C2×C42—132no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42—261no—
396C4×C8—268no—
397#95—264no—
398#95—522no—
399#95—522no—
400C2×C13#143611yescharacteristic
401C2×C13C4×#10211yescharacteristic
402C2×C13C4×#10311yescharacteristic
403C2×C13#189211yescharacteristic
404C2×C13#189311yescharacteristic
405C2×C13#193311yescharacteristic
406C2×C13#193311yescharacteristic
407C2×C13#193411yescharacteristic
408C2×C13#193411yescharacteristic
409C2×C13#194111yescharacteristic
410C2×C13#194111yescharacteristic
411C2×C13#194211yescharacteristic
412C2×C13#194211yescharacteristic
413C2×C13#199011yescharacteristic
414C2×C13#199111yescharacteristic
415C24D4×D1311yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—132no—
431C22×C4—132no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—521no—
447C22×C4—521no—
448C22×C4—521no—
449C22×C4—521no—
450C22×C4—521no—
451C22×C4—521no—
452C22×C4—521no—
453C22×C4—521no—
454C22×C4—521no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4C2×Dic2611yescharacteristic
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4C2×C4×D1311yescharacteristic
461C22×C4C2×D5211yescharacteristic
462C22×C4#612711yescharacteristic
463C22×C4#612711yescharacteristic
464C22×C4D4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4#612911yescharacteristic
467C22×C4#612911yescharacteristic
468C22×C4#612911yescharacteristic
469C22×C4Q8×D1311yescharacteristic
470C22×C4#613111yescharacteristic
471C22×C4C22×Dic1311yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—134no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—262no—
484C2×C8—262no—
485C2×C8C4⋊Dic1314yescomplemented
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—262no—
494C4⋊C4—262no—
495C4⋊C4—262no—
496C4⋊C4—262no—
497C4⋊C4—528no—
498C4⋊C4—521no—
499C4⋊C4—521no—
500C4⋊C4—521no—
501C4⋊C4—521no—
502C4⋊C4C4×Dic1314yes—
503C42—262no—
504C42—262no—
505C42—262no—
506C42—262no—
507C13#1088011yescharacteristic, complemented, Sylow
508C23C22⋊C4×D1311yescharacteristic
509C23#8813511yescharacteristic
510C23#8813811yescharacteristic
511C23#8813911yescharacteristic
512C23#8814211yescharacteristic
513C23#8814911yescharacteristic
514C23D8×D1311yescharacteristic
515C23#8816611yescharacteristic
516C23SD16×D1311yescharacteristic
517C23SD16×D1311yescharacteristic
518C23#8817011yescharacteristic
519C23#8817011yescharacteristic
520C23Q16×D1311yescharacteristic
521C23#8817311yescharacteristic
522C23D4×Dic1311yescharacteristic
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—134no—
538C2×C4—134no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—1041no—
558C2×C4—1041no—
559C2×C4—1041no—
560C2×C4—1041no—
561C2×C4—1041no—
562C2×C4—1041no—
563C2×C4—1041no—
564C2×C4—1041no—
565C2×C4C4×Dic2611yescharacteristic
566C2×C4C4×Dic2611yescharacteristic
567C2×C4C4×D5211yescharacteristic
568C2×C4C4×D5211yescharacteristic
569C2×C4#8813111yescharacteristic
570C2×C4#8813211yescharacteristic
571C2×C4#8813211yescharacteristic
572C2×C4#8813311yescharacteristic
573C2×C4#8813511yescharacteristic
574C2×C4#8813611yescharacteristic
575C2×C4#8813711yescharacteristic
576C2×C4#8814011yescharacteristic
577C2×C4#8814111yescharacteristic
578C2×C4#8814311yescharacteristic
579C2×C4#8814411yescharacteristic
580C2×C4C4⋊C4×D1311yescharacteristic
581C2×C4#8814611yescharacteristic
582C2×C4#8814711yescharacteristic
583C2×C4#8814811yescharacteristic
584C2×C4#8815011yescharacteristic
585C2×C4#8815111yescharacteristic
586C2×C4#8815211yescharacteristic
587C2×C4C2×C4×Dic1311yescharacteristic
588C2×C4C2×C4⋊Dic1311yescharacteristic
589C2×C4#8818011yescharacteristic
590C2×C4D4×Dic1311yescharacteristic
591C2×C4D4×Dic1311yescharacteristic
592C2×C4Q8×Dic1311yescharacteristic
593C8—24no—
594C8—264no—
595C22#1171830711yescharacteristic
596C22#1171830811yescharacteristic
597C22#1171832611yescharacteristic
598C22#1171833111yescharacteristic
599C22#1171841711yescharacteristic
600C22#1171841911yescharacteristic
601C22#1171842111yescharacteristic
602C22#1171842911yescharacteristic
603C22D13×#10211yescharacteristic
604C22#1171843311yescharacteristic
605C22#1171843611yescharacteristic
606C22#1171843911yescharacteristic
607C22#1171844911yescharacteristic
608C22#1171845111yescharacteristic
609C22#1171845311yescharacteristic
610C22#1171846111yescharacteristic
611C22D13×#10311yescharacteristic
612C22#1171846511yescharacteristic
613C22#1171846811yescharacteristic
614C22#1171847411yescharacteristic
615C22#1171851611yescharacteristic
616C22#1171851911yescharacteristic
617C22#1171852511yescharacteristic
618C22#1171852511yescharacteristic
619C22#1171853511yescharacteristic
620C22#1171853911yescharacteristic
621C22#1171854411yescharacteristic
622C22#1171854811yescharacteristic
623C22C22⋊C4×Dic1311yescharacteristic
624C22#1171861211yescharacteristic
625C22#1171864611yescharacteristic
626C22D8×Dic1311yescharacteristic
627C22SD16×Dic1311yescharacteristic
628C22SD16×Dic1311yescharacteristic
629C22Q16×Dic1311yescharacteristic
630C4—44no—
631C4—82no—
632C4—264no—
633C4—264no—
634C4—1042no—
635C4—1042no—
636C4#1171831411yescharacteristic
637C4#1171831511yescharacteristic
638C4#1171831611yescharacteristic
639C4#1171832911yescharacteristic
640C4C4×C4⋊Dic1311yescharacteristic
641C4#1171861111yescharacteristic
642C4C4⋊C4×Dic1311yescharacteristic
643C4#1171864211yescharacteristic
644C2#1311307011yescharacteristic
645C2#102×Dic1311yescharacteristic
646C2#103×Dic1311yescharacteristic
647C2#1311525811yescharacteristic
648C2#1311526311yescharacteristic
649C2#1311551311yescharacteristic
650C2#1311551411yescharacteristic
651C2#1311552011yescharacteristic
652C2#1311552111yescharacteristic
653C2#1311556311yescharacteristic
654C2#1311556511yescharacteristic
655C2#1311556811yescharacteristic
656C2#1311557011yescharacteristic
657C2#1311579511yescharacteristic
658C2#1311579911yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#10880
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
23. #11718646C4semidirect
24. C13×#340C4semidirect
27. #11718121C4semidirect
150. C2×C8×C13C4⋊C4semidirect
178. C2×#1055C4⋊C4semidirect
292. #340Dic13semidirect
485. C2×C8C4⋊Dic13semidirect
507. C13#10880semidirect

Maximal subgroups

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

subgroupindex
C22×C8×Dic132
C2×#117186462
C2×#117181432
C2×#117181212
#131130652
C2×C13×#3402
#1088013