Finite Group Databasebeta

← #15770827

Subgroups — #15770827

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718634C211yesmaximal, characteristic
2C2×#11718637C211yesmaximal, characteristic
3C2×#11718143C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic
5C2×#11718121C211yesmaximal, characteristic
6C2×#11718142C211yesmaximal, characteristic
7C2×C13×#340C211yesmaximal, characteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×#6101—21no—
14C22×#6101—21no—
15C22×#6101—21no—
16C22×C4×Dic13C2211yescharacteristic
17C23×#1055C2211yescharacteristic
18C2×#88071—21no—
19#11718637—22no—
20#11718637—22no—
21#11718634—22no—
22#11718634C414yescomplemented
23C13×#340—22no—
24#11718143—22no—
25#11718142—22no—
26#11718121—22no—
27#11718121—22no—
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×C13—21no—
40C22×C8×C13—21no—
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⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2×C412yes—
53C2×C13×C4⋊C4D412yes—
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⋊Dic13C2×C412yes—
63C2×C4⋊Dic13D412yes—
64C2×C4⋊Dic13D412yes—
65C2×C4⋊Dic13Q812yes—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—42no—
70C2×#6101—42no—
71C2×#6101—42no—
72C2×#6101—42no—
73C2×#6101—42no—
74C2×#6101—42no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13C2×C412yes—
80C2×C4×Dic13D412yes—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055Q812yes—
88#88071—24no—
89#11207—131nomaximal, Sylow
90C24×C13C2×D411yescharacteristic
91C22×C4×C13—22no—
92C22×C4×C13—22no—
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×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13C22×C411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×Q811yescharacteristic
111C22×C4×C13C2×Q811yescharacteristic
112C22×C4×C13C2×Q811yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—41no—
132C22×Dic13—41no—
133C22×Dic13—41no—
134C22×Dic13—41no—
135C22×Dic13—41no—
136C22×Dic13—41no—
137C22×Dic13—41no—
138C22×Dic13—41no—
139C22×Dic13—41no—
140C22×Dic13—41no—
141C22×Dic13C22⋊C412yes—
142C22×Dic13C22⋊C412yes—
143C22×Dic13D812yes—
144C22×Dic13SD1612yes—
145C22×Dic13SD1612yes—
146C22×Dic13Q1612yes—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13—22no—
150C2×C8×C13—41no—
151C2×C8×C13—41no—
152C2×C8×C13—41no—
153C2×C8×C13—41no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—41no—
162C4⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—41no—
168C4⋊Dic13—41no—
169C4⋊Dic13C4⋊C414yescomplemented
170#6101—48no—
171#6101—48no—
172#6101—48no—
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—41no—
181C2×#1055—41no—
182C2×#1055—41no—
183C2×#1055—41no—
184C2×#389—131no—
185C2×#384—131no—
186C2×#340—131no—
187C2×#340—131no—
188C2×#340—131no—
189C2×#340D1311yescharacteristic
190C2×#336—131no—
191C23×C13C2×C22⋊C411yescharacteristic
192C23×C13#12011yescharacteristic
193C23×C13#12111yescharacteristic
194C23×C13C22⋊Q811yescharacteristic
195C23×C13#12311yescharacteristic
196C23×C13#12411yescharacteristic
197C23×C13C4⋊Q811yescharacteristic
198C23×C13C2×D811yescharacteristic
199C23×C13C2×SD1611yescharacteristic
200C23×C13C2×SD1611yescharacteristic
201C23×C13C2×Q1611yescharacteristic
202C23×C13AGL(1,ℤ/8)11yescharacteristic
203C23×C13AGL(1,ℤ/8)11yescharacteristic
204C23×C13#13711yescharacteristic
205C23×C13#13711yescharacteristic
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—81no—
213C2×C4×C13—81no—
214C2×C4×C13—81no—
215C2×C4×C13—81no—
216C2×C4×C13—81no—
217C2×C4×C13—81no—
218C2×C4×C13—81no—
219C2×C4×C13—81no—
220C2×C4×C13C2×C4⋊C411yescharacteristic
221C2×C4×C13#11711yescharacteristic
222C2×C4×C13C4×D411yescharacteristic
223C2×C4×C13C4×D411yescharacteristic
224C2×C4×C13C4×Q811yescharacteristic
225C2×C4×C13C4×Q811yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13C22⋊Q811yescharacteristic
232C2×C4×C13C22⋊Q811yescharacteristic
233C2×C4×C13C22⋊Q811yescharacteristic
234C2×C4×C13C22⋊Q811yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13C22⋊Q811yescharacteristic
237C2×C4×C13C22⋊Q811yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12311yescharacteristic
240C2×C4×C13#12511yescharacteristic
241C2×C4×C13#12511yescharacteristic
242C2×C4×C13#12511yescharacteristic
243C2×C4×C13#12511yescharacteristic
244C2×C4×C13#12611yescharacteristic
245C2×C4×C13#12611yescharacteristic
246C2×C4×C13C4⋊Q811yescharacteristic
247C2×C4×C13C4⋊Q811yescharacteristic
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—81no—
271C2×Dic13—81no—
272C2×Dic13—81no—
273C2×Dic13—81no—
274C2×Dic13#10214yes—
275C2×Dic13#10314yes—
276C8×C13—42no—
277#1055—42no—
278C23×C8—131no—
279C23×C8C2×D1311yescharacteristic
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—261no—
283C22×C4⋊C4—261no—
284C22×C4⋊C4—261no—
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C4⋊C4C2×D1311yescharacteristic
287C22×C42—131no—
288#389—134no—
289#389—262no—
290#384—262no—
291#384—262no—
292C2×#95—261no—
293#340—22no—
294#340—262no—
295#340—262no—
296#340—262no—
297#336—262no—
298C22×C13#38011yescharacteristic
299C22×C13#38611yescharacteristic
300C22×C13#39111yescharacteristic
301C22×C13#39411yescharacteristic
302C22×C13#39511yescharacteristic
303C22×C13#39811yescharacteristic
304C22×C13#40011yescharacteristic
305C22×C13C2×#10211yescharacteristic
306C22×C13C2×#10311yescharacteristic
307C22×C13#41711yescharacteristic
308C22×C13#41711yescharacteristic
309C22×C13#44711yescharacteristic
310C22×C13#44811yescharacteristic
311C22×C13#45011yescharacteristic
312C22×C13#45111yescharacteristic
313C22×C13#45911yescharacteristic
314C22×C13#46011yescharacteristic
315C22×C13#46111yescharacteristic
316C22×C13#46211yescharacteristic
317C22×C13#47411yescharacteristic
318C22×C13#47511yescharacteristic
319C22×C13#47611yescharacteristic
320C22×C13#47711yescharacteristic
321C22×C13#48011yescharacteristic
322C22×C13#48111yescharacteristic
323C22×C13#48311yescharacteristic
324C22×C13#48411yescharacteristic
325C22×C13#48611yescharacteristic
326C22×C13#48711yescharacteristic
327C22×C13#49011yescharacteristic
328C22×C13#49111yescharacteristic
329C22×C13#49811yescharacteristic
330C22×C13#50011yescharacteristic
331C22×C13#50111yescharacteristic
332C22×C13#50111yescharacteristic
333C4×C13—82no—
334C4×C13—82no—
335C4×C13#38711yescharacteristic
336C4×C13#38711yescharacteristic
337C4×C13#38911yescharacteristic
338C4×C13#38911yescharacteristic
339C4×C13#39611yescharacteristic
340C4×C13#39611yescharacteristic
341C4×C13#39811yescharacteristic
342C4×C13#39811yescharacteristic
343Dic13—24no—
344Dic13—24no—
345Dic13—44no—
346Dic13—82no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—261no—
352C23×C4—261no—
353C23×C4C22×D1311yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—132no—
361C22×C8—261no—
362C22×C8—261no—
363C22×C8—261no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8—261no—
367C22×C8Dic2612yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—132no—
380C2×C4⋊C4—132no—
381C2×C4⋊C4—132no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—522no—
394C2×C4⋊C4—522no—
395C2×C4⋊C4—522no—
396C2×C4⋊C4—522no—
397C2×C4⋊C4—522no—
398C2×C4⋊C4—522no—
399C2×C4⋊C4C4×D1312yes—
400C2×C4⋊C4C22⋊D1312yes—
401C2×C42—132no—
402C2×C42—132no—
403C2×C42—261no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42—261no—
407#95—264no—
408C2×C13#144111yescharacteristic
409C2×C13#180211yescharacteristic
410C2×C13#180311yescharacteristic
411C2×C13#187211yescharacteristic
412C2×C13#187411yescharacteristic
413C2×C13#199011yescharacteristic
414C2×C13#199211yescharacteristic
415C2×C13#204111yescharacteristic
416C2×C13#204311yescharacteristic
417C2×C13#205711yescharacteristic
418C2×C13#205811yescharacteristic
419C2×C13#208311yescharacteristic
420C2×C13#208411yescharacteristic
421C2×C13#209911yescharacteristic
422C2×C13#210011yescharacteristic
423C24D4×D1311yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—132no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4—521no—
459C22×C4—521no—
460C22×C4—521no—
461C22×C4—521no—
462C22×C4—521no—
463C22×C4—521no—
464C22×C4—521no—
465C22×C4—521no—
466C22×C4C2×Dic2611yescharacteristic
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4#612711yescharacteristic
469C22×C4#612711yescharacteristic
470C22×C4#612711yescharacteristic
471C22×C4#612711yescharacteristic
472C22×C4D4×D1311yescharacteristic
473C22×C4D4×D1311yescharacteristic
474C22×C4D4×D1311yescharacteristic
475C22×C4#612911yescharacteristic
476C22×C4#612911yescharacteristic
477C22×C4Q8×D1311yescharacteristic
478C22×C4Q8×D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—262no—
488C2×C8—262no—
489C2×C8—262no—
490C2×C8—521no—
491C2×C8—521no—
492C2×C8—521no—
493C2×C8—521no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—134no—
503C4⋊C4—262no—
504C4⋊C4—262no—
505C4⋊C4—262no—
506C4⋊C4—262no—
507C4⋊C4—262no—
508C4⋊C4—528no—
509C4⋊C4—528no—
510C4⋊C4—528no—
511C4⋊C4—521no—
512C4⋊C4—521no—
513C42—262no—
514C42—262no—
515C42—262no—
516C42—262no—
517C13#1120711yescharacteristic, complemented, Sylow
518C23C22⋊C4×D1311yescharacteristic
519C23#8813711yescharacteristic
520C23#8813811yescharacteristic
521C23#8813911yescharacteristic
522C23#8814211yescharacteristic
523C23#8815011yescharacteristic
524C23D8×D1311yescharacteristic
525C23#8816511yescharacteristic
526C23SD16×D1311yescharacteristic
527C23SD16×D1311yescharacteristic
528C23#8816811yescharacteristic
529C23#8816911yescharacteristic
530C23Q16×D1311yescharacteristic
531C23#8817211yescharacteristic
532C23#8819111yescharacteristic
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—134no—
548C2×C4—134no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—264no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—1041no—
572C2×C4—1041no—
573C2×C4—1041no—
574C2×C4—1041no—
575C2×C4C4×Dic2611yescharacteristic
576C2×C4#8812411yescharacteristic
577C2×C4#8812611yescharacteristic
578C2×C4#8813011yescharacteristic
579C2×C4#8813211yescharacteristic
580C2×C4#8813211yescharacteristic
581C2×C4#8813311yescharacteristic
582C2×C4#8813511yescharacteristic
583C2×C4#8813711yescharacteristic
584C2×C4#8813811yescharacteristic
585C2×C4#8813811yescharacteristic
586C2×C4#8813811yescharacteristic
587C2×C4#8814111yescharacteristic
588C2×C4#8814211yescharacteristic
589C2×C4#8814311yescharacteristic
590C2×C4#8814311yescharacteristic
591C2×C4#8814311yescharacteristic
592C2×C4C4⋊C4×D1311yescharacteristic
593C2×C4#8815011yescharacteristic
594C2×C4#8815011yescharacteristic
595C2×C4#8815011yescharacteristic
596C2×C4#8815011yescharacteristic
597C2×C4#8817811yescharacteristic
598C2×C4C4×C22⋊D1311yescharacteristic
599C2×C4#8818311yescharacteristic
600C2×C4#8819211yescharacteristic
601C2×C4#8819311yescharacteristic
602C2×C4#8819811yescharacteristic
603C8—42no—
604C8—522no—
605C22#1171830711yescharacteristic
606C22#1171831811yescharacteristic
607C22#1171831911yescharacteristic
608C22#1171832811yescharacteristic
609C22#1171842111yescharacteristic
610C22#1171842311yescharacteristic
611C22#1171842511yescharacteristic
612C22D13×#10211yescharacteristic
613C22#1171843211yescharacteristic
614C22#1171843511yescharacteristic
615C22#1171843811yescharacteristic
616C22#1171844711yescharacteristic
617C22#1171845311yescharacteristic
618C22#1171845411yescharacteristic
619C22#1171845811yescharacteristic
620C22D13×#10311yescharacteristic
621C22#1171846411yescharacteristic
622C22#1171846611yescharacteristic
623C22#1171847011yescharacteristic
624C22#1171847911yescharacteristic
625C22#1171851511yescharacteristic
626C22#1171851611yescharacteristic
627C22#1171851711yescharacteristic
628C22#1171853111yescharacteristic
629C22#1171853511yescharacteristic
630C22#1171853611yescharacteristic
631C22#1171853711yescharacteristic
632C22#1171855111yescharacteristic
633C22#1171861711yescharacteristic
634C22#1171862011yescharacteristic
635C22#1171864011yescharacteristic
636C22#1171881711yescharacteristic
637C22#1171883011yescharacteristic
638C22#1171883111yescharacteristic
639C22#1171884711yescharacteristic
640C4—82no—
641C4—82no—
642C4—264no—
643C4—264no—
644C4—524no—
645C4—1042no—
646C4#1171830811yescharacteristic
647C4#1171831311yescharacteristic
648C4#1171831811yescharacteristic
649C4#1171833711yescharacteristic
650C4#1171859411yescharacteristic
651C4#1171860911yescharacteristic
652C4#1171863311yescharacteristic
653C4#1171864111yescharacteristic
654C2#1311308711yescharacteristic
655C2#1311483511yescharacteristic
656C2#1311484011yescharacteristic
657C2#1311514011yescharacteristic
658C2#1311515011yescharacteristic
659C2#1311579511yescharacteristic
660C2#1311580311yescharacteristic
661C2#1311606811yescharacteristic
662C2#1311608011yescharacteristic
663C2#1311616211yescharacteristic
664C2#1311616711yescharacteristic
665C2#1311631111yescharacteristic
666C2#1311631611yescharacteristic
667C2#1311639611yescharacteristic
668C2#1311640111yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#11207
LCSG ▷ C22×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
22. #11718634C4semidirect
169. C4⋊Dic13C4⋊C4semidirect
517. C13#11207semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117186372
C2×#117181432
C2×#117181212
C2×#117181422
C2×C13×#3402
#1120713