Finite Group Databasebeta

← #15770808

Subgroups — #15770808

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718611C211yesmaximal, characteristic
2C2×#11718603C211yesmaximal, characteristic
3C2×#11718118C211yesmaximal, characteristic
4C2×#11718119C211yesmaximal, characteristic
5C2×#11718119C211yesmaximal, characteristic
6#13113058C211yesmaximal, characteristic
7C2×C13×#342C211yesmaximal, characteristic
8C24×Dic13C2211yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C13×C22⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C412yescomplemented
16C22×#6101—21no—
17C2×#88071—21no—
18C2×#88071—22no—
19C2×#88071C412yescomplemented
20#11718611—21no—
21#11718611—22no—
22#11718611—21no—
23#11718603—22no—
24#11718603—22no—
25C13×#342—22no—
26#11718119—22no—
27#11718119—22no—
28#11718118—22no—
29C25×C13C2311yescharacteristic
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13C2×C412yes—
33C23×Dic13—21no—
34C23×Dic13—21no—
35C23×Dic13—21no—
36C23×Dic13—21no—
37C23×Dic13—21no—
38C23×Dic13—21no—
39C23×Dic13—44no—
40C23×Dic13C2×C412yes—
41C23×Dic13C2×C411yescharacteristic
42C23×Dic13C2×C411yescharacteristic
43C23×Dic13D411yescharacteristic
44C23×Dic13D412yes—
45C23×Dic13D411yescharacteristic
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4D412yes—
61C2×C13×C22⋊C4D412yes—
62C2×C13×C22⋊C4Q812yes—
63C2×C13×C22⋊C4Q812yes—
64C2×C22⋊Dic13—21no—
65C2×C22⋊Dic13—21no—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—21no—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13D412yes—
81C2×C22⋊Dic13Q812yes—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—44no—
85C2×#6101—24no—
86C2×#6101—44no—
87#88071—24no—
88#88071—22no—
89#88071—22no—
90#88071—44no—
91#11203—131nomaximal, Sylow
92C24×C13—42no—
93C24×C13—42no—
94C24×C13C22×C411yescharacteristic
95C24×C13C2×D411yescharacteristic
96C24×C13C2×D411yescharacteristic
97C24×C13C2×D411yescharacteristic
98C24×C13C2×D411yescharacteristic
99C24×C13C2×D411yescharacteristic
100C24×C13C2×Q811yescharacteristic
101C24×C13C2×Q811yescharacteristic
102C24×C13C2×Q811yescharacteristic
103C24×C13#4111yescharacteristic
104C24×C13#4111yescharacteristic
105C24×C13#4111yescharacteristic
106C24×C13#4111yescharacteristic
107C24×C13#4111yescharacteristic
108C24×C13#4111yescharacteristic
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13—42no—
116C22×C4×C13—42no—
117C22×C4×C13—42no—
118C22×C4×C13—42no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13C4⋊C414yescomplemented
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—24no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—24no—
134C22×Dic13—24no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—44no—
147C22×Dic13—44no—
148C22×Dic13—44no—
149C22×Dic13—44no—
150C22×Dic13—42no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13—42no—
154C22×Dic13—41no—
155C22×Dic13—41no—
156C22×Dic13—41no—
157C22×Dic13—41no—
158C22×Dic13—42no—
159C22×Dic13—42no—
160C22×Dic13C22⋊C412yes—
161C22×Dic13C22⋊C412yes—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C22⋊Dic13—22no—
175C22⋊Dic13—22no—
176C22⋊Dic13—22no—
177C22⋊Dic13—22no—
178C22⋊Dic13—41no—
179C22⋊Dic13—41no—
180C22⋊Dic13—41no—
181C22⋊Dic13—41no—
182C22⋊Dic13—41no—
183C22⋊Dic13—41no—
184C22⋊Dic13—41no—
185C22⋊Dic13—41no—
186C4⋊Dic13—44no—
187C4⋊Dic13—44no—
188#6101—48no—
189C2×#385—131no—
190C2×#380—131no—
191C2×#342—131no—
192C2×#342—131no—
193C2×#342—131no—
194C2×#342D1311yescharacteristic
195C22⋊#95—131no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13C2×C22⋊C411yescharacteristic
219C23×C13C2×C4⋊C411yescharacteristic
220C23×C13#11711yescharacteristic
221C23×C13C4×D411yescharacteristic
222C23×C13C4×D411yescharacteristic
223C23×C13C4×Q811yescharacteristic
224C23×C13C4×Q811yescharacteristic
225C23×C13#12011yescharacteristic
226C23×C13#12111yescharacteristic
227C23×C13#12111yescharacteristic
228C23×C13#12111yescharacteristic
229C23×C13#12111yescharacteristic
230C23×C13#12111yescharacteristic
231C23×C13#12111yescharacteristic
232C23×C13C22⋊Q811yescharacteristic
233C23×C13C22⋊Q811yescharacteristic
234C23×C13C22⋊Q811yescharacteristic
235C23×C13C22⋊Q811yescharacteristic
236C23×C13C22⋊Q811yescharacteristic
237C23×C13C22⋊Q811yescharacteristic
238C23×C13C22⋊Q811yescharacteristic
239C23×C13C22⋊Q811yescharacteristic
240C23×C13#12311yescharacteristic
241C23×C13#12311yescharacteristic
242C23×C13#12311yescharacteristic
243C23×C13#12411yescharacteristic
244C23×C13#12511yescharacteristic
245C23×C13#12511yescharacteristic
246C23×C13#12511yescharacteristic
247C23×C13#12511yescharacteristic
248C23×C13#12611yescharacteristic
249C23×C13#12611yescharacteristic
250C23×C13C4⋊Q811yescharacteristic
251C23×C13C4⋊Q811yescharacteristic
252C23×C13C4⋊Q811yescharacteristic
253C2×C4×C13—24no—
254C2×C4×C13—44no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—44no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—44no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—82no—
264C2×C4×C13—82no—
265C2×C4×C13—81no—
266C2×C4×C13—81no—
267C2×C4×C13—82no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—44no—
276C2×Dic13—44no—
277C2×Dic13—44no—
278C2×Dic13—44no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—44no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—82no—
291C2×Dic13—82no—
292C2×Dic13—81no—
293C2×Dic13—81no—
294C2×Dic13—82no—
295C2×Dic13—81no—
296C2×Dic13—81no—
297C2×Dic13—81no—
298C2×Dic13—81no—
299C2×Dic13#9914yes—
300C24×C4—131no—
301C22×C4⋊C4—132no—
302C22×C4⋊C4—261no—
303C22×C22⋊C4—131no—
304C22×C22⋊C4—131no—
305C22×C22⋊C4—131no—
306C22×C22⋊C4C2×D1311yescharacteristic
307C22×C22⋊C4C2×D1311yescharacteristic
308C22×C22⋊C4C2×D1311yescharacteristic
309#385—261no—
310#385—262no—
311#385—261no—
312#380—262no—
313#380—262no—
314C2×#95—132no—
315C2×#95—261no—
316C2×#95—262no—
317#342—22no—
318#342—262no—
319#342—262no—
320#342—262no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13#38011yescharacteristic
362C22×C13#38611yescharacteristic
363C22×C13#38711yescharacteristic
364C22×C13#38711yescharacteristic
365C22×C13#38911yescharacteristic
366C22×C13#38911yescharacteristic
367C22×C13#39111yescharacteristic
368C22×C13#39411yescharacteristic
369C22×C13#39511yescharacteristic
370C22×C13#39611yescharacteristic
371C22×C13#39611yescharacteristic
372C22×C13#39811yescharacteristic
373C22×C13#39811yescharacteristic
374C22×C13#39811yescharacteristic
375C22×C13#40011yescharacteristic
376C22×C13C2×#9912yes—
377C22×C13#41012yes—
378C4×C13—44no—
379C4×C13—82no—
380C4×C13—82no—
381Dic13—24no—
382Dic13—42no—
383Dic13—82no—
384Dic13—82no—
385Dic13—81no—
386Dic13—81no—
387C25C22×D1311yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—131no—
391C23×C4—132no—
392C23×C4—132no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—261no—
397C23×C4—261no—
398C23×C4—261no—
399C23×C4—261no—
400C23×C4—261no—
401C23×C4—261no—
402C23×C4—524no—
403C23×C4C4×D1312yes—
404C2×C4⋊C4—262no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—264no—
407C2×C4⋊C4—524no—
408C2×C4⋊C4—524no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—132no—
424C2×C22⋊C4—132no—
425C2×C22⋊C4—261no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4Dic2612yes—
442C2×C22⋊C4Dic2612yes—
443C2×C22⋊C4D5212yes—
444C2×C22⋊C4C22⋊D1312yes—
445#95—262no—
446#95—262no—
447#95—264no—
448#95—524no—
449C2×C13—21no—
450C2×C13—21no—
451C2×C13—21no—
452C2×C13—21no—
453C2×C13—21no—
454C2×C13—21no—
455C2×C13—21no—
456C2×C13—21no—
457C2×C13—21no—
458C2×C13—21no—
459C2×C13—21no—
460C2×C13—21no—
461C2×C13#144111yescharacteristic
462C2×C13#179912yes—
463C2×C13#189811yescharacteristic
464C2×C13#189911yescharacteristic
465C2×C13#199612yes—
466C24—42no—
467C24—42no—
468C24C2×Dic2611yescharacteristic
469C24C2×Dic2611yescharacteristic
470C24C2×C4×D1311yescharacteristic
471C24C2×D5211yescharacteristic
472C24#612711yescharacteristic
473C24#612711yescharacteristic
474C24D4×D1311yescharacteristic
475C24D4×D1311yescharacteristic
476C24D4×D1311yescharacteristic
477C24#612911yescharacteristic
478C24#612911yescharacteristic
479C24#612911yescharacteristic
480C24Q8×D1311yescharacteristic
481C24#613111yescharacteristic
482C24C2×C22⋊D1311yescharacteristic
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—132no—
498C22×C4—132no—
499C22×C4—264no—
500C22×C4—264no—
501C22×C4—264no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—262no—
505C22×C4—261no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—261no—
509C22×C4—262no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—522no—
519C22×C4—522no—
520C22×C4—522no—
521C22×C4—524no—
522C22×C4—524no—
523C22×C4—524no—
524C22×C4—524no—
525C22×C4—522no—
526C22×C4—522no—
527C22×C4—522no—
528C22×C4—522no—
529C22×C4—521no—
530C22×C4—521no—
531C22×C4—521no—
532C22×C4—521no—
533C22×C4—522no—
534C22×C4—522no—
535C22×C4#610114yescomplemented
536C4⋊C4—524no—
537C4⋊C4—528no—
538C4⋊C4—524no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—262no—
552C22⋊C4—262no—
553C22⋊C4—262no—
554C22⋊C4—262no—
555C22⋊C4—521no—
556C22⋊C4—521no—
557C22⋊C4—521no—
558C22⋊C4—521no—
559C22⋊C4—521no—
560C22⋊C4—521no—
561C22⋊C4—521no—
562C22⋊C4—521no—
563C13#1120311yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—41no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23C4×Dic2611yescharacteristic
587C23#8812311yescharacteristic
588C23#8812411yescharacteristic
589C23C4×D5211yescharacteristic
590C23#8813111yescharacteristic
591C23#8813211yescharacteristic
592C23#8813211yescharacteristic
593C23#8813211yescharacteristic
594C23#8813211yescharacteristic
595C23#8813311yescharacteristic
596C23C22⋊C4×D1311yescharacteristic
597C23#8813611yescharacteristic
598C23#8813711yescharacteristic
599C23#8813811yescharacteristic
600C23#8813911yescharacteristic
601C23#8814011yescharacteristic
602C23#8814111yescharacteristic
603C23#8814211yescharacteristic
604C23#8814211yescharacteristic
605C23#8814311yescharacteristic
606C23#8814411yescharacteristic
607C23#8814411yescharacteristic
608C23#8814711yescharacteristic
609C23#8814811yescharacteristic
610C23#8814911yescharacteristic
611C23#8815011yescharacteristic
612C23#8815111yescharacteristic
613C23#8815211yescharacteristic
614C23C2×#610111yescharacteristic
615C23#8817811yescharacteristic
616C23#8818411yescharacteristic
617C23#8819211yescharacteristic
618C23#8819311yescharacteristic
619C23#8819311yescharacteristic
620C23#8820011yescharacteristic
621C2×C4—24no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—82no—
636C2×C4—134no—
637C2×C4—264no—
638C2×C4—264no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—524no—
645C2×C4—524no—
646C2×C4—524no—
647C2×C4—524no—
648C2×C4—522no—
649C2×C4—522no—
650C2×C4—522no—
651C2×C4—522no—
652C2×C4—524no—
653C2×C4—522no—
654C2×C4—522no—
655C2×C4—521no—
656C2×C4—521no—
657C2×C4—522no—
658C2×C4—522no—
659C2×C4—1041no—
660C2×C4—1041no—
661C2×C4—1042no—
662C2×C4—1042no—
663C2×C4—1042no—
664C2×C4—1041no—
665C2×C4—1041no—
666C2×C4—1041no—
667C2×C4—1041no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22#1171830711yescharacteristic
709C22#1171831411yescharacteristic
710C22#1171831511yescharacteristic
711C22#1171831711yescharacteristic
712C22#1171831811yescharacteristic
713C22#1171832111yescharacteristic
714C22#1171832211yescharacteristic
715C22#1171832611yescharacteristic
716C22#1171840112yes—
717C22D13×#9912yes—
718C22#1171858911yescharacteristic
719C22#1171860311yescharacteristic
720C22#1171860911yescharacteristic
721C22#1171862211yescharacteristic
722C22#1171863411yescharacteristic
723C22#1171864511yescharacteristic
724C22#1171865511yescharacteristic
725C4—44no—
726C4—82no—
727C4—82no—
728C4—264no—
729C4—522no—
730C4—1042no—
731C4—1042no—
732C4—1041no—
733C4—1041no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#1311308811yescharacteristic
747C2#1311482212yes—
748C2#1311528811yescharacteristic
749C2#1311529311yescharacteristic
750C2#1311581912yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC24×C13C22×C4
FrattiniC25C22×D13
FittingC2×C13×#342C2
socleC23×C13C2×C22⋊C4
prime radical, cosocleC25×C13C23
hypercenterC2×#342D13
hypocenterC13#11203
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
15. C22×C4⋊Dic13C4semidirect
19. C2×#88071C4semidirect
123. C22×C4×C13C4⋊C4semidirect
535. C22×C4#6101semidirect
563. C13#11203semidirect

Maximal subgroups

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

subgroupindex
C2×#117186112
C2×#117186032
C2×#117181182
C2×#117181192
#131130582
C2×C13×#3422
#1120313