Finite Group Databasebeta

← #15770739

Subgroups — #15770739

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×#88075C211yesmaximal, characteristic
2C22×#88075C211yesmaximal, characteristic
3C2×#11718121C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic
5C2×#11718116C211yesmaximal, characteristic
6#13113066C211yesmaximal, characteristic
7C2×C13×#391C211yesmaximal, characteristic
8C23×Q8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C23×#1055C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C13×#391—22no—
16C13×#391—22no—
17C2×C13×#95—21no—
18C2×C13×#95—21no—
19C2×#88075—22no—
20C2×#88075—22no—
21C2×#88075—22no—
22C2×#88075—22no—
23C2×#88075—22no—
24C2×#88075C414yescomplemented
25C2×#88071—21no—
26C2×#88071—21no—
27#11718121—22no—
28#11718121—22no—
29#11718116—22no—
30C22×Q8×C13—21no—
31C22×Q8×C13—21no—
32C22×Q8×C13—21no—
33C22×Q8×C13—21no—
34C22×Q8×C13—21no—
35C22×Q8×C13—21no—
36C22×Q8×C13—21no—
37C22×Q8×C13—21no—
38C22×Q8×C13—21no—
39C22×Q8×C13—21no—
40C22×Q8×C13—21no—
41C22×Q8×C13C2×C412yes—
42C22×Q8×C13D412yes—
43C22×Q8×C13D412yes—
44C23×C4×C13—21no—
45C23×C4×C13—21no—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13—21no—
50C23×Dic13—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D412yes—
57C2×C42×C13—21no—
58C2×C42×C13—21no—
59C2×C42×C13—21no—
60C2×C42×C13—21no—
61C2×C42×C13—21no—
62C2×C42×C13—21no—
63C2×C4⋊Dic13—21no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
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×#1055—21no—
80C22×#1055—21no—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055C2×C412yes—
88C22×#1055D412yes—
89C13×#95—24no—
90C13×#95—24no—
91#88075—28no—
92#88075—28no—
93#88071—42no—
94#88071—42no—
95#11190—131nomaximal, Sylow
96C24×C13C2×D411yescharacteristic
97C2×Q8×C13—22no—
98C2×Q8×C13—22no—
99C2×Q8×C13—22no—
100C2×Q8×C13—22no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—22no—
104C2×Q8×C13—22no—
105C2×Q8×C13—22no—
106C2×Q8×C13—22no—
107C2×Q8×C13—22no—
108C2×Q8×C13—22no—
109C2×Q8×C13—22no—
110C2×Q8×C13—22no—
111C2×Q8×C13—22no—
112C2×Q8×C13—41no—
113C2×Q8×C13—41no—
114C2×Q8×C13—41no—
115C2×Q8×C13—41no—
116C2×Q8×C13—41no—
117C2×Q8×C13—41no—
118C2×Q8×C13—41no—
119C2×Q8×C13—41no—
120C2×Q8×C13—41no—
121C2×Q8×C13—41no—
122C2×Q8×C13—41no—
123C2×Q8×C13—41no—
124C2×Q8×C13C22⋊C414yes—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13—41no—
146C22×C4×C13—41no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13—41no—
151C22×C4×C13SD1612yes—
152C22×C4×C13Q1612yes—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C22×C4×C13#4111yescharacteristic
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—41no—
170C22×Dic13—41no—
171C22×Dic13—41no—
172C22×Dic13—41no—
173C22×Dic13—41no—
174C22×Dic13—41no—
175C22×Dic13—41no—
176C22×Dic13—41no—
177C22×Dic13—41no—
178C22×Dic13—41no—
179C22×Dic13—41no—
180C22×Dic13—41no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4—41no—
185C42×C13—41no—
186C42×C13—41no—
187C42×C13—41no—
188C42×C13—41no—
189C4⋊Dic13—22no—
190C4⋊Dic13—22no—
191C4⋊Dic13—22no—
192C4⋊Dic13—22no—
193C4⋊Dic13—41no—
194C4⋊Dic13—41no—
195C4⋊Dic13—41no—
196C4⋊Dic13—41no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—22no—
200C2×#1055—22no—
201C2×#1055—22no—
202C2×#1055—22no—
203C2×#1055—41no—
204C2×#1055—41no—
205C2×#1055—41no—
206C2×#1055—41no—
207C2×#1055—41no—
208C2×#1055—41no—
209C2×#1055—41no—
210C2×#1055—41no—
211C22×#103—131no—
212C22×#103—131no—
213C2×#391D1311yescharacteristic
214C2×#340—131no—
215C2×#340—131no—
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
233Q8×C13—24no—
234Q8×C13—24no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—42no—
238Q8×C13—42no—
239Q8×C13—42no—
240Q8×C13—42no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—81no—
266C2×C4×C13—81no—
267C2×C4×C13—81no—
268C2×C4×C13—81no—
269C2×C4×C13C2×C22⋊C411yescharacteristic
270C2×C4×C13#11711yescharacteristic
271C2×C4×C13#11711yescharacteristic
272C2×C4×C13C4×D411yescharacteristic
273C2×C4×C13C4×D411yescharacteristic
274C2×C4×C13C4×D411yescharacteristic
275C2×C4×C13#12011yescharacteristic
276C2×C4×C13#12111yescharacteristic
277C2×C4×C13#12111yescharacteristic
278C2×C4×C13#12111yescharacteristic
279C2×C4×C13#12111yescharacteristic
280C2×C4×C13#12111yescharacteristic
281C2×C4×C13#12311yescharacteristic
282C2×C4×C13#12311yescharacteristic
283C2×C4×C13#12311yescharacteristic
284C2×C4×C13#12311yescharacteristic
285C2×C4×C13#12311yescharacteristic
286C2×C4×C13#12311yescharacteristic
287C2×C4×C13#12311yescharacteristic
288C2×C4×C13#12311yescharacteristic
289C2×C4×C13#12311yescharacteristic
290C2×C4×C13#12411yescharacteristic
291C2×C4×C13#12411yescharacteristic
292C2×C4×C13#12411yescharacteristic
293C2×C4×C13#12611yescharacteristic
294C2×C4×C13#12611yescharacteristic
295C2×C4×C13#12611yescharacteristic
296C2×C4×C13#12611yescharacteristic
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—81no—
304C2×Dic13—81no—
305C2×Dic13—81no—
306C2×Dic13—81no—
307C2×Dic13—81no—
308C2×Dic13—81no—
309C2×Dic13—81no—
310C2×Dic13—81no—
311#1055—42no—
312#1055—42no—
313C23×Q8C2×D1311yescharacteristic
314C23×C8—131no—
315C23×C8—131no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4C2×D1311yescharacteristic
319C22×C42C2×D1311yescharacteristic
320C2×#103—134no—
321C2×#103—262no—
322C2×#103—262no—
323C2×#103—262no—
324C2×#103—262no—
325C2×#103—262no—
326#391—22no—
327#391—22no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—261no—
331C2×#95—261no—
332#340—262no—
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—44no—
371C4×C13—42no—
372C4×C13—42no—
373C4×C13—82no—
374C4×C13#38111yescharacteristic
375C4×C13#38611yescharacteristic
376C4×C13#38811yescharacteristic
377C4×C13#38811yescharacteristic
378C4×C13#39411yescharacteristic
379C4×C13#39711yescharacteristic
380C4×C13#39711yescharacteristic
381C4×C13#39711yescharacteristic
382Dic13—82no—
383Dic13—82no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8C4×D1312yes—
396C22×Q8D5212yes—
397C22×Q8C22⋊D1312yes—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—261no—
401C23×C4—261no—
402C23×C4C22⋊D1311yescharacteristic
403C23×C4C22⋊D1311yescharacteristic
404C23×C4C22×D1311yescharacteristic
405C22×C8—132no—
406C22×C8—132no—
407C22×C8—261no—
408C22×C8—261no—
409C22×C8—261no—
410C22×C8—261no—
411C22×C8—261no—
412C22×C8—261no—
413C22×C8—261no—
414C22×C8—261no—
415C22×C8—261no—
416C22×C8—261no—
417C22×C8—261no—
418C22×C8—261no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—132no—
425C2×C4⋊C4—132no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4C22⋊D1312yes—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443#103—268no—
444#103—268no—
445#95—24no—
446#95—24no—
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
464C24C2×C22⋊D1311yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8#610314yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—521no—
522C22×C4—521no—
523C22×C4—521no—
524C22×C4—521no—
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#610612yes—
534C22×C4#610712yes—
535C22×C4C2×C4×D1311yescharacteristic
536C22×C4C2×D5211yescharacteristic
537C22×C4#612711yescharacteristic
538C22×C4#612711yescharacteristic
539C22×C4D4×D1311yescharacteristic
540C22×C4D4×D1311yescharacteristic
541C22×C4#612911yescharacteristic
542C22×C4#612911yescharacteristic
543C22×C4#612911yescharacteristic
544C22×C4#612911yescharacteristic
545C22×C4#612911yescharacteristic
546C22×C4#612911yescharacteristic
547C22×C4C2×C22⋊D1311yescharacteristic
548C22×C4C2×C22⋊D1311yescharacteristic
549C2×C8—262no—
550C2×C8—262no—
551C2×C8—262no—
552C2×C8—262no—
553C2×C8—262no—
554C2×C8—262no—
555C2×C8—521no—
556C2×C8—521no—
557C2×C8—521no—
558C2×C8—521no—
559C2×C8—521no—
560C2×C8—521no—
561C2×C8—521no—
562C2×C8—521no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—262no—
568C4⋊C4—262no—
569C4⋊C4—262no—
570C4⋊C4—262no—
571C4⋊C4—521no—
572C4⋊C4—521no—
573C4⋊C4—521no—
574C4⋊C4—521no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C13#1119011yescharacteristic, complemented, Sylow
580C23C4×C22⋊D1311yescharacteristic
581C23#8818411yescharacteristic
582C23#8818911yescharacteristic
583C23#8819011yescharacteristic
584C23#8819211yescharacteristic
585C23#8819311yescharacteristic
586C23C2×#610611yescharacteristic
587C23#8819611yescharacteristic
588C23#8819611yescharacteristic
589C23C2×#610711yescharacteristic
590C23#8820311yescharacteristic
591C23#8820411yescharacteristic
592C23#8820411yescharacteristic
593C23#8820511yescharacteristic
594C23#8820711yescharacteristic
595Q8—24no—
596Q8—24no—
597Q8—42no—
598Q8—42no—
599Q8—42no—
600Q8—42no—
601Q8—42no—
602Q8—42no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—1041no—
638C2×C4—1041no—
639C2×C4—1041no—
640C2×C4—1041no—
641C2×C4—1041no—
642C2×C4—1041no—
643C2×C4—1041no—
644C2×C4—1041no—
645C2×C4#8813111yescharacteristic
646C2×C4#8813111yescharacteristic
647C2×C4#8813311yescharacteristic
648C2×C4#8813311yescharacteristic
649C2×C4#8813311yescharacteristic
650C2×C4#8813311yescharacteristic
651C2×C4#8813511yescharacteristic
652C2×C4#8813511yescharacteristic
653C2×C4#8813611yescharacteristic
654C2×C4#8813711yescharacteristic
655C2×C4#8813711yescharacteristic
656C2×C4#8813911yescharacteristic
657C2×C4#8813911yescharacteristic
658C2×C4#8814011yescharacteristic
659C2×C4#8814011yescharacteristic
660C2×C4#8814011yescharacteristic
661C2×C4C2×#610311yescharacteristic
662C2×C4C4×C22⋊D1311yescharacteristic
663C2×C4#8818311yescharacteristic
664C2×C4#8818411yescharacteristic
665C2×C4#8818911yescharacteristic
666C2×C4#8818911yescharacteristic
667C2×C4#8818911yescharacteristic
668C2×C4#8819011yescharacteristic
669C2×C4#8819211yescharacteristic
670C2×C4#8819311yescharacteristic
671C2×C4#8819311yescharacteristic
672C2×C4#8819311yescharacteristic
673C8—522no—
674C8—522no—
675C22#1171860511yescharacteristic
676C22#1171860611yescharacteristic
677C22#1171861411yescharacteristic
678C22#1171862211yescharacteristic
679C22C4×#610611yescharacteristic
680C22#1171868711yescharacteristic
681C22#1171868811yescharacteristic
682C22#1171868911yescharacteristic
683C22#1171868911yescharacteristic
684C22C4×#610711yescharacteristic
685C22#1171869111yescharacteristic
686C22#1171869211yescharacteristic
687C22#1171870411yescharacteristic
688C22#1171870511yescharacteristic
689C22#1171870611yescharacteristic
690C22#1171870611yescharacteristic
691C22#1171870911yescharacteristic
692C22#1171871011yescharacteristic
693C22#1171871211yescharacteristic
694C22#1171871311yescharacteristic
695C22#1171871511yescharacteristic
696C22#1171871611yescharacteristic
697C22#1171871711yescharacteristic
698C22#1171871811yescharacteristic
699C22#1171874211yescharacteristic
700C22#1171874311yescharacteristic
701C22#1171874411yescharacteristic
702C22#1171875111yescharacteristic
703C22#1171887411yescharacteristic
704C22#1171888311yescharacteristic
705C22#1171888311yescharacteristic
706C22#1171888811yescharacteristic
707C22#1171888911yescharacteristic
708C22#1171889911yescharacteristic
709C22#1171890011yescharacteristic
710C4—42no—
711C4—42no—
712C4—44no—
713C4—82no—
714C4—1042no—
715C4—1042no—
716C4#1171860411yescharacteristic
717C4#1171860511yescharacteristic
718C4#1171860611yescharacteristic
719C4#1171861311yescharacteristic
720C4#1171861311yescharacteristic
721C4#1171861411yescharacteristic
722C4#1171861911yescharacteristic
723C4#1171862211yescharacteristic
724C2#1311308311yescharacteristic
725C2#1311517711yescharacteristic
726C2#1311519111yescharacteristic
727C2#1311546711yescharacteristic
728C2#1311547411yescharacteristic
729C2#1311551511yescharacteristic
730C2#1311552911yescharacteristic
731C2#1311602911yescharacteristic
732C2#1311603611yescharacteristic
733C2#1311607211yescharacteristic
734C2#1311607911yescharacteristic
735C2#1311615111yescharacteristic
736C2#1311615811yescharacteristic
737C2#1311624411yescharacteristic
738C2#1311625411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#391C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#391D13
hypocenterC13#11190
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
24. C2×#88075C4semidirect
579. C13#11190semidirect

Maximal subgroups

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

subgroupindex
C22×#880752
C2×#117181212
C2×#117181162
#131130662
C2×C13×#3912
#1119013