Finite Group Databasebeta

← #15768766

Subgroups — #15768766

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88054C211yesmaximal, characteristic
2C2×#11718638C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic
4C2×#11718143C211yesmaximal, characteristic
5C2×#11718121C211yesmaximal, characteristic
6C2×#11718121C211yesmaximal, characteristic
7C2×C13×#340C211yesmaximal, characteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4×Dic13—21no—
14C22×C4×Dic13C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C2×#88071—21no—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88054—22no—
20C2×#88054—22no—
21C2×#88054C414yescomplemented
22#11718638—22no—
23#11718638C414yescomplemented
24C4⋊C4×Dic13—22no—
25C4⋊C4×Dic13C414yescomplemented
26C13×#340—22no—
27#11718143—22no—
28#11718121—22no—
29#11718121—22no—
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13C2×C412yes—
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⋊C4C2×C412yes—
54C2×C13×C4⋊C4D412yes—
55C2×C13×C4⋊C4Q812yes—
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⋊Dic13C2×C412yes—
65C2×C4⋊Dic13C2×C412yes—
66C2×C4⋊Dic13D412yes—
67C2×C4⋊Dic13Q812yes—
68C2×C4×Dic13—24no—
69C2×C4×Dic13—42no—
70C2×C4×Dic13—42no—
71C2×C4×Dic13C2×C412yes—
72C2×C4×Dic13C2×C412yes—
73C2×C4×Dic13C2×C412yes—
74C2×C4×Dic13D412yes—
75C2×C4×Dic13D412yes—
76C2×C4×Dic13Q812yes—
77C22×#1055—21no—
78C22×#1055—21no—
79C22×#1055—21no—
80C22×#1055—21no—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055C2×C412yes—
84#88071—24no—
85#88071—24no—
86#88071—24no—
87#88054—28no—
88#10850—131nomaximal, Sylow
89C24×C13C2×D411yescharacteristic
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
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×C13C22×C411yescharacteristic
105C22×C4×C13C22×C411yescharacteristic
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×Q811yescharacteristic
112C22×C4×C13C2×Q811yescharacteristic
113C22×C4×C13C2×Q811yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
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×Dic13—41no—
139C22×Dic13—41no—
140C22×Dic13C22⋊C412yes—
141C22×Dic13C22⋊C412yes—
142C22×Dic13C22⋊C412yes—
143C22×Dic13C22⋊C412yes—
144C22×Dic13C4⋊C412yes—
145C22×Dic13C4⋊C412yes—
146C2×C8×C13—22no—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13—41no—
150C2×C8×C13—41no—
151C2×C8×C13—41no—
152C2×C8×C13—41no—
153C13×C4⋊C4—22no—
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⋊C4C4⋊C414yes—
161C4⋊Dic13—22no—
162C4⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166C4⋊Dic13—41no—
167C4⋊Dic13—41no—
168C4⋊Dic13C4⋊C414yes—
169C4×Dic13—48no—
170C4×Dic13C4214yes—
171C4×Dic13C22⋊C414yes—
172C4×Dic13C4⋊C414yes—
173C4×Dic13C4⋊C414yes—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—41no—
178C2×#1055—41no—
179C2×#1055—41no—
180C2×#1055—41no—
181C22×C4⋊C8—131no—
182C2×#382—131no—
183C2×C4×C4⋊C4—131no—
184C2×#340—131no—
185C2×#340—131no—
186C2×#340—131no—
187C2×#340D1311yescharacteristic
188C23×C13C2×C22⋊C411yescharacteristic
189C23×C13C2×C22⋊C411yescharacteristic
190C23×C13C2×C4⋊C411yescharacteristic
191C23×C13#12111yescharacteristic
192C23×C13#12111yescharacteristic
193C23×C13C22⋊Q811yescharacteristic
194C23×C13C22⋊Q811yescharacteristic
195C23×C13#13511yescharacteristic
196C23×C13#13511yescharacteristic
197C23×C13#13511yescharacteristic
198C23×C13#13511yescharacteristic
199C23×C13AGL(1,ℤ/8)11yescharacteristic
200C23×C13AGL(1,ℤ/8)11yescharacteristic
201C23×C13#13711yescharacteristic
202C23×C13#13711yescharacteristic
203C2×C4×C13—24no—
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—42no—
212C2×C4×C13—42no—
213C2×C4×C13—81no—
214C2×C4×C13—81no—
215C2×C4×C13—81no—
216C2×C4×C13—81no—
217C2×C4×C13C2×C4211yescharacteristic
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C4⋊C411yescharacteristic
220C2×C4×C13C2×C4⋊C411yescharacteristic
221C2×C4×C13C2×C4⋊C411yescharacteristic
222C2×C4×C13C2×C4⋊C411yescharacteristic
223C2×C4×C13#11711yescharacteristic
224C2×C4×C13#11711yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13C4×D411yescharacteristic
228C2×C4×C13C4×D411yescharacteristic
229C2×C4×C13C4×Q811yescharacteristic
230C2×C4×C13C4×Q811yescharacteristic
231C2×C4×C13C4×Q811yescharacteristic
232C2×C4×C13C4×Q811yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13C22⋊Q811yescharacteristic
237C2×C4×C13#12411yescharacteristic
238C2×C4×C13#12411yescharacteristic
239C2×C4×C13#12511yescharacteristic
240C2×C4×C13#12511yescharacteristic
241C2×C4×C13#12711yescharacteristic
242C2×C4×C13C4⋊Q811yescharacteristic
243C2×C4×C13C4⋊Q811yescharacteristic
244C2×C4×C13C4⋊Q811yescharacteristic
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—22no—
256C2×Dic13—22no—
257C2×Dic13—24no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—81no—
268C2×Dic13—81no—
269C2×Dic13—81no—
270C2×Dic13—81no—
271C2×Dic13#9514yes—
272C2×Dic13#9514yes—
273C8×C13—42no—
274#1055—42no—
275C23×C8—131no—
276C23×C8C2×D1311yescharacteristic
277C22×C4⋊C4—131no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4C2×D1311yescharacteristic
280C22×C4⋊C4C2×D1311yescharacteristic
281C22×C42—131no—
282C22×C42—261no—
283C2×C4⋊C8—134no—
284C2×C4⋊C8—262no—
285C2×C4⋊C8—262no—
286#382—134no—
287#382—262no—
288C4×C4⋊C4—134no—
289C4×C4⋊C4—262no—
290C2×#95—261no—
291C2×#95—261no—
292C2×#95—261no—
293#340—22no—
294#340—262no—
295#340—262no—
296#340—262no—
297C22×C13C2×#9511yescharacteristic
298C22×C13#38011yescharacteristic
299C22×C13#38011yescharacteristic
300C22×C13#38911yescharacteristic
301C22×C13#38911yescharacteristic
302C22×C13#39011yescharacteristic
303C22×C13#39111yescharacteristic
304C22×C13#41611yescharacteristic
305C22×C13#41611yescharacteristic
306C22×C13#41611yescharacteristic
307C22×C13#41611yescharacteristic
308C22×C13#41711yescharacteristic
309C22×C13#41711yescharacteristic
310C22×C13#41811yescharacteristic
311C22×C13#41911yescharacteristic
312C22×C13#42711yescharacteristic
313C22×C13#42711yescharacteristic
314C22×C13#42811yescharacteristic
315C22×C13#42811yescharacteristic
316C22×C13#46311yescharacteristic
317C22×C13#46311yescharacteristic
318C22×C13#46311yescharacteristic
319C22×C13#46311yescharacteristic
320C22×C13#46411yescharacteristic
321C22×C13#46411yescharacteristic
322C22×C13#46411yescharacteristic
323C22×C13#46411yescharacteristic
324C22×C13#47811yescharacteristic
325C22×C13#47811yescharacteristic
326C22×C13#47811yescharacteristic
327C22×C13#47811yescharacteristic
328C22×C13#47911yescharacteristic
329C22×C13#47911yescharacteristic
330C22×C13#47911yescharacteristic
331C22×C13#47911yescharacteristic
332C4×C13—44no—
333C4×C13—82no—
334C4×C13C4×C4⋊C411yescharacteristic
335C4×C13C4×C4⋊C411yescharacteristic
336C4×C13#38211yescharacteristic
337C4×C13#38411yescharacteristic
338C4×C13#38911yescharacteristic
339C4×C13#38911yescharacteristic
340C4×C13#39011yescharacteristic
341C4×C13#39111yescharacteristic
342Dic13—24no—
343Dic13—24no—
344Dic13—44no—
345Dic13—82no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—261no—
351C23×C4—261no—
352C23×C4C22×D1311yescharacteristic
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—132no—
360C22×C8—261no—
361C22×C8—261no—
362C22×C8—261no—
363C22×C8—261no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8C4×D1312yes—
367C2×C4⋊C4—21no—
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—132no—
376C2×C4⋊C4—132no—
377C2×C4⋊C4—132no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4Dic2612yes—
388C2×C4⋊C4C4×D1312yes—
389C2×C4⋊C4C4×D1312yes—
390C2×C4⋊C4C22⋊D1312yes—
391C2×C42—132no—
392C2×C42—132no—
393C2×C42—132no—
394C2×C42—132no—
395C2×C42—132no—
396C2×C42—132no—
397C2×C42—264no—
398C2×C42—522no—
399C2×C42—522no—
400C4⋊C8—268no—
401#95—264no—
402#95—264no—
403#95—264no—
404C2×C13C4⋊#9511yescharacteristic
405C2×C13#173511yescharacteristic
406C2×C13#173611yescharacteristic
407C2×C13#180411yescharacteristic
408C2×C13#180411yescharacteristic
409C2×C13#180511yescharacteristic
410C2×C13#180511yescharacteristic
411C2×C13#194911yescharacteristic
412C2×C13#194911yescharacteristic
413C2×C13#194911yescharacteristic
414C2×C13#194911yescharacteristic
415C2×C13#198311yescharacteristic
416C2×C13#198311yescharacteristic
417C2×C13#198911yescharacteristic
418C2×C13#198911yescharacteristic
419C24D4×D1311yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
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—132no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—132no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—521no—
453C22×C4—521no—
454C22×C4—521no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4—521no—
459C22×C4—521no—
460C22×C4—521no—
461C22×C4—521no—
462C22×C4C2×Dic2611yescharacteristic
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×C4×D1311yescharacteristic
466C22×C4#612711yescharacteristic
467C22×C4#612711yescharacteristic
468C22×C4D4×D1311yescharacteristic
469C22×C4D4×D1311yescharacteristic
470C22×C4D4×D1311yescharacteristic
471C22×C4#612911yescharacteristic
472C22×C4#612911yescharacteristic
473C22×C4Q8×D1311yescharacteristic
474C22×C4Q8×D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—262no—
484C2×C8—262no—
485C2×C8—262no—
486C2×C8—521no—
487C2×C8—521no—
488C2×C8—521no—
489C2×C8—521no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—134no—
498C4⋊C4—262no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C4⋊C4—262no—
503C4⋊C4—521no—
504C4⋊C4—521no—
505C4⋊C4#610114yes—
506C42—134no—
507C42—134no—
508C42—134no—
509C42—134no—
510C42—528no—
511C13#1085011yescharacteristic, complemented, Sylow
512C23#8813211yescharacteristic
513C23C22⋊C4×D1311yescharacteristic
514C23C22⋊C4×D1311yescharacteristic
515C23#8813811yescharacteristic
516C23C4⋊C4×D1311yescharacteristic
517C23#8815011yescharacteristic
518C23#8816511yescharacteristic
519C23#8816611yescharacteristic
520C23#8816811yescharacteristic
521C23#8816911yescharacteristic
522C23#8817011yescharacteristic
523C23#8817011yescharacteristic
524C23#8817211yescharacteristic
525C23#8817311yescharacteristic
526C23#8819311yescharacteristic
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—134no—
542C2×C4—134no—
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—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—264no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—1041no—
566C2×C4—1041no—
567C2×C4—1041no—
568C2×C4—1041no—
569C2×C4C4×Dic2611yescharacteristic
570C2×C4C4×Dic2611yescharacteristic
571C2×C4C42×D1311yescharacteristic
572C2×C4#8812611yescharacteristic
573C2×C4#8813111yescharacteristic
574C2×C4#8813211yescharacteristic
575C2×C4C22⋊C4×D1311yescharacteristic
576C2×C4#8813511yescharacteristic
577C2×C4#8813511yescharacteristic
578C2×C4#8813811yescharacteristic
579C2×C4#8813911yescharacteristic
580C2×C4#8813911yescharacteristic
581C2×C4#8814111yescharacteristic
582C2×C4#8814111yescharacteristic
583C2×C4#8814211yescharacteristic
584C2×C4#8814211yescharacteristic
585C2×C4#8814311yescharacteristic
586C2×C4#8814311yescharacteristic
587C2×C4C4⋊C4×D1311yescharacteristic
588C2×C4C4⋊C4×D1311yescharacteristic
589C2×C4C4⋊C4×D1311yescharacteristic
590C2×C4#8815011yescharacteristic
591C2×C4C2×#610111yescharacteristic
592C2×C4C4×C22⋊D1311yescharacteristic
593C2×C4C4×C22⋊D1311yescharacteristic
594C2×C4#8819311yescharacteristic
595C2×C4#8819411yescharacteristic
596C2×C4#8819811yescharacteristic
597C8—42no—
598C8—522no—
599C22#1171830711yescharacteristic
600C22#1171830811yescharacteristic
601C22D13×#9511yescharacteristic
602C22#1171832811yescharacteristic
603C22#1171842411yescharacteristic
604C22#1171842711yescharacteristic
605C22#1171842811yescharacteristic
606C22#1171843111yescharacteristic
607C22#1171843211yescharacteristic
608C22#1171843311yescharacteristic
609C22#1171843311yescharacteristic
610C22#1171844811yescharacteristic
611C22#1171845711yescharacteristic
612C22#1171845911yescharacteristic
613C22#1171846011yescharacteristic
614C22#1171846311yescharacteristic
615C22#1171846411yescharacteristic
616C22#1171846511yescharacteristic
617C22#1171846511yescharacteristic
618C22#1171848011yescharacteristic
619C22#1171851811yescharacteristic
620C22#1171852111yescharacteristic
621C22#1171852211yescharacteristic
622C22#1171853211yescharacteristic
623C22#1171853811yescharacteristic
624C22#1171854111yescharacteristic
625C22#1171854211yescharacteristic
626C22#1171855211yescharacteristic
627C22#1171860311yescharacteristic
628C22#1171861811yescharacteristic
629C22#1171863311yescharacteristic
630C22#1171881411yescharacteristic
631C22#1171882611yescharacteristic
632C22#1171882711yescharacteristic
633C22#1171884611yescharacteristic
634C4—44no—
635C4—82no—
636C4—264no—
637C4—264no—
638C4—524no—
639C4—1042no—
640C4#1171830711yescharacteristic
641C4#1171830811yescharacteristic
642C4#1171831011yescharacteristic
643C4#1171831111yescharacteristic
644C4C4×#610111yescharacteristic
645C4#1171861811yescharacteristic
646C4#1171863311yescharacteristic
647C4#1171863711yescharacteristic
648C2#1311306411yescharacteristic
649C2#1311455111yescharacteristic
650C2#1311455411yescharacteristic
651C2#1311484411yescharacteristic
652C2#1311484511yescharacteristic
653C2#1311484911yescharacteristic
654C2#1311485011yescharacteristic
655C2#1311560111yescharacteristic
656C2#1311560311yescharacteristic
657C2#1311560511yescharacteristic
658C2#1311560711yescharacteristic
659C2#1311576511yescharacteristic
660C2#1311576711yescharacteristic
661C2#1311579011yescharacteristic
662C2#1311579211yescharacteristic
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#10850
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
21. C2×#88054C4semidirect
23. #11718638C4semidirect
25. C4⋊C4×Dic13C4semidirect
511. C13#10850semidirect

Maximal subgroups

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

subgroupindex
C22×#880542
C2×#117186382
C2×C4⋊C4×Dic132
C2×#117181432
C2×#117181212
C2×C13×#3402
#1085013