Finite Group Databasebeta

← #15770741

Subgroups — #15770741

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88056C211yesmaximal, characteristic
2C22×#88050C211yesmaximal, characteristic
3C2×#11718635C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic
5C2×#11718142C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7C2×C13×#340C211yesmaximal, characteristic
8C23×Dic26C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C2×#88071—21no—
16C2×#88071—21no—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88056—22no—
20C2×#88056—22no—
21C2×#88056—22no—
22#11718635—22no—
23#11718635—22no—
24C2×#88050—22no—
25C2×#88050—22no—
26C2×#88050C414yescomplemented
27C13×#340—22no—
28#11718142—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×Dic26—21no—
38C22×Dic26—21no—
39C22×Dic26—21no—
40C22×Dic26—21no—
41C22×Dic26—21no—
42C22×Dic26—21no—
43C22×Dic26—21no—
44C22×Dic26—21no—
45C22×Dic26—21no—
46C22×Dic26—21no—
47C22×Dic26—21no—
48C22×Dic26C2×C412yes—
49C22×Dic26D412yes—
50C22×Dic26D412yes—
51C22×C8×C13—21no—
52C22×C8×C13—21no—
53C22×C8×C13—21no—
54C22×C8×C13—21no—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13D412yes—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2×C412yes—
69C2×C13×C4⋊C4D412yes—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13D412yes—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055C2×C412yes—
89#88071—24no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88056—28no—
94#88050—28no—
95#11190—131nomaximal, Sylow
96C24×C13C2×D411yescharacteristic
97C22×C4×C13—22no—
98C22×C4×C13—22no—
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×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C22×C4×C13#4111yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C22×Dic13—22no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—41no—
142C22×Dic13—41no—
143C22×Dic13—41no—
144C22×Dic13—41no—
145C22×Dic13—41no—
146C22×Dic13—41no—
147C22×Dic13—41no—
148C22×Dic13—41no—
149C22×Dic13—41no—
150C22×Dic13—41no—
151C22×Dic13SD1612yes—
152C22×Dic13Q1612yes—
153C2×Dic26—22no—
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26—22no—
157C2×Dic26—22no—
158C2×Dic26—22no—
159C2×Dic26—22no—
160C2×Dic26—22no—
161C2×Dic26—22no—
162C2×Dic26—22no—
163C2×Dic26—22no—
164C2×Dic26—22no—
165C2×Dic26—22no—
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26—41no—
169C2×Dic26—41no—
170C2×Dic26—41no—
171C2×Dic26—41no—
172C2×Dic26—41no—
173C2×Dic26—41no—
174C2×Dic26—41no—
175C2×Dic26—41no—
176C2×Dic26—41no—
177C2×Dic26—41no—
178C2×Dic26—41no—
179C2×Dic26—41no—
180C2×Dic26C22⋊C414yes—
181C2×C8×C13—22no—
182C2×C8×C13—22no—
183C2×C8×C13—22no—
184C2×C8×C13—41no—
185C2×C8×C13—41no—
186C2×C8×C13—41no—
187C2×C8×C13—41no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4—41no—
194C13×C4⋊C4—41no—
195C13×C4⋊C4—41no—
196C4⋊Dic13—22no—
197C4⋊Dic13—22no—
198C4⋊Dic13—41no—
199C4⋊Dic13—41no—
200C4×Dic13—41no—
201C4×Dic13—41no—
202C4×Dic13—41no—
203C4×Dic13—41no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—22no—
207C2×#1055—41no—
208C2×#1055—41no—
209C2×#1055—41no—
210C2×#1055—41no—
211C22×#103—131no—
212C22×#103—131no—
213C2×#391—131no—
214C2×#340—131no—
215C2×#340D1311yescharacteristic
216C2×#336—131no—
217C4⋊#95—131no—
218C23×C13C4×D411yescharacteristic
219C23×C13#12011yescharacteristic
220C23×C13#12111yescharacteristic
221C23×C13#12111yescharacteristic
222C23×C13#12111yescharacteristic
223C23×C13#12311yescharacteristic
224C23×C13#12411yescharacteristic
225C23×C13C2×SD1611yescharacteristic
226C23×C13C2×Q1611yescharacteristic
227C23×C13#13511yescharacteristic
228C23×C13#13511yescharacteristic
229C23×C13AGL(1,ℤ/8)11yescharacteristic
230C23×C13#13711yescharacteristic
231C23×C13#13711yescharacteristic
232C23×C13#13711yescharacteristic
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—81no—
240C2×C4×C13—81no—
241C2×C4×C13—81no—
242C2×C4×C13—81no—
243C2×C4×C13—81no—
244C2×C4×C13—81no—
245C2×C4×C13—81no—
246C2×C4×C13—81no—
247C2×C4×C13C2×C22⋊C411yescharacteristic
248C2×C4×C13#11711yescharacteristic
249C2×C4×C13#11711yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13#12111yescharacteristic
255C2×C4×C13#12111yescharacteristic
256C2×C4×C13#12111yescharacteristic
257C2×C4×C13#12111yescharacteristic
258C2×C4×C13#12111yescharacteristic
259C2×C4×C13#12311yescharacteristic
260C2×C4×C13#12311yescharacteristic
261C2×C4×C13#12311yescharacteristic
262C2×C4×C13#12311yescharacteristic
263C2×C4×C13#12311yescharacteristic
264C2×C4×C13#12311yescharacteristic
265C2×C4×C13#12311yescharacteristic
266C2×C4×C13#12311yescharacteristic
267C2×C4×C13#12311yescharacteristic
268C2×C4×C13#12411yescharacteristic
269C2×C4×C13#12411yescharacteristic
270C2×C4×C13#12411yescharacteristic
271C2×C4×C13#12611yescharacteristic
272C2×C4×C13#12611yescharacteristic
273C2×C4×C13#12611yescharacteristic
274C2×C4×C13#12611yescharacteristic
275C2×Dic13—24no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—81no—
300C2×Dic13—81no—
301C2×Dic13—81no—
302C2×Dic13—81no—
303Dic26—24no—
304Dic26—24no—
305Dic26—42no—
306Dic26—42no—
307Dic26—42no—
308Dic26—42no—
309Dic26—42no—
310Dic26—42no—
311C8×C13—42no—
312#1055—42no—
313C23×Q8—131no—
314C23×C8—131no—
315C23×C8C2×D1311yescharacteristic
316C22×C4⋊C4—131no—
317C22×C4⋊C4C2×D1311yescharacteristic
318C22×C4⋊C4C2×D1311yescharacteristic
319C22×C42—131no—
320C2×#103—134no—
321C2×#103—262no—
322C2×#103—262no—
323C2×#103—262no—
324C2×#103—262no—
325C2×#103—262no—
326#391—262no—
327#391—262no—
328C2×#95—261no—
329C2×#95—261no—
330C2×#95—261no—
331C2×#95—261no—
332#340—22no—
333#340—262no—
334#336—262no—
335C22×C13#38611yescharacteristic
336C22×C13#38811yescharacteristic
337C22×C13#38811yescharacteristic
338C22×C13#39411yescharacteristic
339C22×C13#39411yescharacteristic
340C22×C13#39411yescharacteristic
341C22×C13#39711yescharacteristic
342C22×C13C4×SD1611yescharacteristic
343C22×C13C4×Q1611yescharacteristic
344C22×C13#44011yescharacteristic
345C22×C13#44111yescharacteristic
346C22×C13#44811yescharacteristic
347C22×C13#44911yescharacteristic
348C22×C13#45111yescharacteristic
349C22×C13#45211yescharacteristic
350C22×C13#46011yescharacteristic
351C22×C13#46111yescharacteristic
352C22×C13#46211yescharacteristic
353C22×C13#46211yescharacteristic
354C22×C13#46311yescharacteristic
355C22×C13#46411yescharacteristic
356C22×C13#46411yescharacteristic
357C22×C13#46411yescharacteristic
358C22×C13#46511yescharacteristic
359C22×C13#46711yescharacteristic
360C22×C13#46811yescharacteristic
361C22×C13#47011yescharacteristic
362C22×C13#48311yescharacteristic
363C22×C13#48411yescharacteristic
364C22×C13#48511yescharacteristic
365C22×C13#48511yescharacteristic
366C22×C13#48711yescharacteristic
367C22×C13#48811yescharacteristic
368C22×C13#48911yescharacteristic
369C22×C13#49111yescharacteristic
370C4×C13—82no—
371C4×C13—82no—
372C4×C13#38111yescharacteristic
373C4×C13#38611yescharacteristic
374C4×C13#38811yescharacteristic
375C4×C13#38811yescharacteristic
376C4×C13#39411yescharacteristic
377C4×C13#39711yescharacteristic
378C4×C13#39711yescharacteristic
379C4×C13#39711yescharacteristic
380Dic13—44no—
381Dic13—42no—
382Dic13—42no—
383Dic13—82no—
384C22×Q8—132no—
385C22×Q8—132no—
386C22×Q8—132no—
387C22×Q8—261no—
388C22×Q8—261no—
389C22×Q8—261no—
390C22×Q8—261no—
391C22×Q8—261no—
392C22×Q8—261no—
393C22×Q8—261no—
394C22×Q8—261no—
395C22×Q8—261no—
396C22×Q8—261no—
397C22×Q8—261no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—131no—
401C23×C4—131no—
402C23×C4—261no—
403C23×C4—261no—
404C23×C4C22×D1311yescharacteristic
405C22×C8—21no—
406C22×C8—21no—
407C22×C8—21no—
408C22×C8—21no—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—132no—
412C22×C8—261no—
413C22×C8—261no—
414C22×C8—261no—
415C22×C8—261no—
416C22×C8—261no—
417C22×C8—261no—
418C22×C8D5212yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—132no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4C4×D1312yes—
436C2×C4⋊C4C22⋊D1312yes—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42—261no—
440C2×C42—261no—
441C2×C42—261no—
442C2×C42—261no—
443#103—268no—
444#103—268no—
445#95—264no—
446#95—264no—
447#95—522no—
448#95—522no—
449C2×C13#144011yescharacteristic
450C2×C13#187811yescharacteristic
451C2×C13#188011yescharacteristic
452C2×C13#192711yescharacteristic
453C2×C13#192811yescharacteristic
454C2×C13#193311yescharacteristic
455C2×C13#193511yescharacteristic
456C2×C13#203511yescharacteristic
457C2×C13#203611yescharacteristic
458C2×C13#204211yescharacteristic
459C2×C13#204311yescharacteristic
460C2×C13#205511yescharacteristic
461C2×C13#205611yescharacteristic
462C2×C13#207211yescharacteristic
463C2×C13#207411yescharacteristic
464C24D4×D1311yescharacteristic
465C2×Q8—134no—
466C2×Q8—262no—
467C2×Q8—262no—
468C2×Q8—262no—
469C2×Q8—262no—
470C2×Q8—262no—
471C2×Q8—262no—
472C2×Q8—262no—
473C2×Q8—262no—
474C2×Q8—262no—
475C2×Q8—262no—
476C2×Q8—262no—
477C2×Q8—262no—
478C2×Q8—262no—
479C2×Q8—262no—
480C2×Q8—262no—
481C2×Q8—521no—
482C2×Q8—521no—
483C2×Q8—521no—
484C2×Q8—521no—
485C2×Q8—521no—
486C2×Q8—521no—
487C2×Q8—521no—
488C2×Q8—521no—
489C2×Q8—521no—
490C2×Q8—521no—
491C2×Q8—521no—
492C2×Q8—521no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—132no—
508C22×C4—132no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—261no—
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—261no—
522C22×C4—261no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—521no—
526C22×C4—521no—
527C22×C4—521no—
528C22×C4—521no—
529C22×C4—521no—
530C22×C4—521no—
531C22×C4—521no—
532C22×C4—521no—
533C22×C4—521no—
534C22×C4—521no—
535C22×C4C2×C4×D1311yescharacteristic
536C22×C4C2×D5211yescharacteristic
537C22×C4#612711yescharacteristic
538C22×C4#612711yescharacteristic
539C22×C4#612711yescharacteristic
540C22×C4#612711yescharacteristic
541C22×C4D4×D1311yescharacteristic
542C22×C4D4×D1311yescharacteristic
543C22×C4D4×D1311yescharacteristic
544C22×C4#612911yescharacteristic
545C22×C4#612911yescharacteristic
546C22×C4#613111yescharacteristic
547C22×C4#613111yescharacteristic
548C22×C4C2×C22⋊D1311yescharacteristic
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—262no—
557C2×C8—262no—
558C2×C8—262no—
559C2×C8—521no—
560C2×C8—521no—
561C2×C8—521no—
562C2×C8—521no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—262no—
572C4⋊C4—262no—
573C4⋊C4—521no—
574C4⋊C4—521no—
575C42—521no—
576C42—521no—
577C42—521no—
578C42—521no—
579C13#1119011yescharacteristic, complemented, Sylow
580C23#8813511yescharacteristic
581C23#8813811yescharacteristic
582C23#8813811yescharacteristic
583C23#8813911yescharacteristic
584C23#8814811yescharacteristic
585C23#8814911yescharacteristic
586C23#8816511yescharacteristic
587C23#8816611yescharacteristic
588C23SD16×D1311yescharacteristic
589C23#8816911yescharacteristic
590C23#8816911yescharacteristic
591C23#8817011yescharacteristic
592C23Q16×D1311yescharacteristic
593C23#8817211yescharacteristic
594C23#8819111yescharacteristic
595Q8—264no—
596Q8—264no—
597Q8—522no—
598Q8—522no—
599Q8—522no—
600Q8—522no—
601Q8—522no—
602Q8—522no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—264no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—522no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4—522no—
641C2×C4—1041no—
642C2×C4—1041no—
643C2×C4—1041no—
644C2×C4—1041no—
645C2×C4#8812611yescharacteristic
646C2×C4C4×D5211yescharacteristic
647C2×C4#8812911yescharacteristic
648C2×C4#8813011yescharacteristic
649C2×C4C22⋊C4×D1311yescharacteristic
650C2×C4#8813611yescharacteristic
651C2×C4#8813711yescharacteristic
652C2×C4#8813711yescharacteristic
653C2×C4#8813711yescharacteristic
654C2×C4#8813811yescharacteristic
655C2×C4#8813911yescharacteristic
656C2×C4#8814011yescharacteristic
657C2×C4#8814611yescharacteristic
658C2×C4#8814711yescharacteristic
659C2×C4#8814811yescharacteristic
660C2×C4#8814811yescharacteristic
661C2×C4#8814811yescharacteristic
662C2×C4#8814811yescharacteristic
663C2×C4#8814911yescharacteristic
664C2×C4#8815211yescharacteristic
665C2×C4#8815211yescharacteristic
666C2×C4#8815211yescharacteristic
667C2×C4C4×C22⋊D1311yescharacteristic
668C2×C4#8818311yescharacteristic
669C2×C4#8818411yescharacteristic
670C2×C4#8819211yescharacteristic
671C2×C4#8819311yescharacteristic
672C2×C4#8820111yescharacteristic
673C8—42no—
674C8—522no—
675C22#1171833011yescharacteristic
676C22#1171833111yescharacteristic
677C22#1171833311yescharacteristic
678C22#1171833611yescharacteristic
679C22#1171841811yescharacteristic
680C22#1171841911yescharacteristic
681C22#1171842311yescharacteristic
682C22#1171842611yescharacteristic
683C22#1171842811yescharacteristic
684C22#1171842811yescharacteristic
685C22#1171842911yescharacteristic
686C22#1171844811yescharacteristic
687C22#1171845011yescharacteristic
688C22#1171845111yescharacteristic
689C22#1171845311yescharacteristic
690C22#1171845411yescharacteristic
691C22#1171845411yescharacteristic
692C22#1171845811yescharacteristic
693C22#1171845911yescharacteristic
694C22#1171847911yescharacteristic
695C22#1171852311yescharacteristic
696C22#1171852511yescharacteristic
697C22#1171852811yescharacteristic
698C22#1171852911yescharacteristic
699C22#1171854511yescharacteristic
700C22#1171854711yescharacteristic
701C22#1171854811yescharacteristic
702C22#1171854911yescharacteristic
703C22#1171861711yescharacteristic
704C22#1171862011yescharacteristic
705C22#1171865211yescharacteristic
706C22#1171881911yescharacteristic
707C22#1171883111yescharacteristic
708C22#1171883411yescharacteristic
709C22#1171884711yescharacteristic
710C4—82no—
711C4—82no—
712C4—522no—
713C4—522no—
714C4—524no—
715C4—1042no—
716C4#1171832511yescharacteristic
717C4#1171832611yescharacteristic
718C4#1171833511yescharacteristic
719C4#1171833611yescharacteristic
720C4#1171860111yescharacteristic
721C4#1171862211yescharacteristic
722C4#1171865111yescharacteristic
723C4#1171865411yescharacteristic
724C2#1311308411yescharacteristic
725C2#1311517411yescharacteristic
726C2#1311518811yescharacteristic
727C2#1311546811yescharacteristic
728C2#1311547511yescharacteristic
729C2#1311551311yescharacteristic
730C2#1311552711yescharacteristic
731C2#1311603411yescharacteristic
732C2#1311604111yescharacteristic
733C2#1311607511yescharacteristic
734C2#1311608011yescharacteristic
735C2#1311615511yescharacteristic
736C2#1311616011yescharacteristic
737C2#1311624811yescharacteristic
738C2#1311625811yescharacteristic
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#11190
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
26. C2×#88050C4semidirect
579. C13#11190semidirect

Maximal subgroups

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

subgroupindex
C22×#880562
C22×#880502
C2×#117186352
C2×#117181212
C2×#117181422
#131130652
C2×C13×#3402
#1119013