Finite Group Databasebeta

← #15768487

Subgroups — #15768487

Order 3328.

1370 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C22×#88056C211yesmaximal, characteristic
3C22×#88050C211yesmaximal, 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×#6101—21no—
14C22×C4×Dic13—21no—
15C22×C4×Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×#88141—22no—
18C2×#88141—22no—
19C2×#88141—22no—
20C2×#88141—22no—
21C2×#88141—22no—
22C2×#88141C414yescomplemented
23C2×#88071—21no—
24C2×#88071—21no—
25C2×#88056—22no—
26C2×#88056—22no—
27C2×#88056C414yescomplemented
28C2×#88050—22no—
29C2×#88050—22no—
30C2×#88050C414yescomplemented
31C13×#340—22no—
32#11718142—22no—
33#11718121—22no—
34C23×C4×C13—21no—
35C23×C4×C13—21no—
36C23×C4×C13C2311yescharacteristic
37C23×Dic13—21no—
38C23×Dic13—21no—
39C23×Dic13D411yescharacteristic
40C23×Dic13D411yescharacteristic
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×Dic26C2×C412yes—
50C22×Dic26C2×C412yes—
51C22×Dic26D412yes—
52C22×Dic26D412yes—
53C22×Dic26D412yes—
54C22×Dic26Q812yes—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13C2×C412yes—
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⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2×C412yes—
71C2×C13×C4⋊C4C2×C412yes—
72C2×C13×C4⋊C4D412yes—
73C2×C13×C4⋊C4D412yes—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2×C412yes—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13C2×C412yes—
91C2×C4×Dic13D412yes—
92C22×#1055—21no—
93C22×#1055—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055C2×C412yes—
99#88141—28no—
100#88141—28no—
101#88141—28no—
102#88141—28no—
103#88071—42no—
104#88071—42no—
105#88056—28no—
106#88050—28no—
107#10789—131nomaximal, Sylow
108C24×C13C2×D411yescharacteristic
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×Q811yescharacteristic
133C22×C4×C13#4111yescharacteristic
134C22×C4×C13#4111yescharacteristic
135C22×C4×C13#4111yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—41no—
156C22×Dic13—41no—
157C22×Dic13—41no—
158C22×Dic13—41no—
159C22×Dic13—41no—
160C22×Dic13—41no—
161C22×Dic13C22⋊C412yes—
162C22×Dic13C22⋊C412yes—
163C22×Dic13SD1612yes—
164C22×Dic13Q1612yes—
165C2×Dic26—22no—
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26—22no—
169C2×Dic26—22no—
170C2×Dic26—22no—
171C2×Dic26—22no—
172C2×Dic26—22no—
173C2×Dic26—22no—
174C2×Dic26—22no—
175C2×Dic26—22no—
176C2×Dic26—22no—
177C2×Dic26—22no—
178C2×Dic26—22no—
179C2×Dic26—22no—
180C2×Dic26—22no—
181C2×Dic26—22no—
182C2×Dic26—22no—
183C2×Dic26—22no—
184C2×Dic26—22no—
185C2×Dic26—22no—
186C2×Dic26C4214yes—
187C2×Dic26C22⋊C414yes—
188C2×Dic26C22⋊C414yes—
189C2×Dic26C22⋊C414yes—
190C2×Dic26C4⋊C414yes—
191C2×Dic26C4⋊C414yes—
192C2×Dic26C4⋊C414yes—
193C2×C8×C13—22no—
194C2×C8×C13—22no—
195C2×C8×C13—22no—
196C2×C8×C13—41no—
197C2×C8×C13—41no—
198C2×C8×C13—41no—
199C2×C8×C13—41no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—22no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—41no—
206C13×C4⋊C4—41no—
207C13×C4⋊C4C22⋊C414yes—
208C4⋊Dic13—22no—
209C4⋊Dic13—22no—
210C4⋊Dic13—41no—
211C4⋊Dic13—41no—
212#6101—216no—
213C4×Dic13—216no—
214C4×Dic13—22no—
215C4×Dic13—22no—
216C4×Dic13—22no—
217C4×Dic13—22no—
218C2×#1055—22no—
219C2×#1055—22no—
220C2×#1055—22no—
221C2×#1055—41no—
222C2×#1055—41no—
223C2×#1055—41no—
224C2×#1055—41no—
225C22×C4×Q8—131no—
226C22×#103—131no—
227C22×#103—131no—
228C2×#340—131no—
229C2×#340D1311yescharacteristic
230C2×#336—131no—
231C4⋊#95—131no—
232C23×C13C2×C22⋊C411yescharacteristic
233C23×C13C4×D411yescharacteristic
234C23×C13C4×D411yescharacteristic
235C23×C13#12011yescharacteristic
236C23×C13#12011yescharacteristic
237C23×C13#12111yescharacteristic
238C23×C13C22⋊Q811yescharacteristic
239C23×C13C2×SD1611yescharacteristic
240C23×C13C2×Q1611yescharacteristic
241C23×C13#13511yescharacteristic
242C23×C13#13511yescharacteristic
243C23×C13AGL(1,ℤ/8)11yescharacteristic
244C23×C13#13711yescharacteristic
245C23×C13#13711yescharacteristic
246C23×C13#13711yescharacteristic
247C2×C4×C13—24no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—81no—
258C2×C4×C13—81no—
259C2×C4×C13—81no—
260C2×C4×C13—81no—
261C2×C4×C13C2×C4211yescharacteristic
262C2×C4×C13C2×C22⋊C411yescharacteristic
263C2×C4×C13C2×C22⋊C411yescharacteristic
264C2×C4×C13C2×C22⋊C411yescharacteristic
265C2×C4×C13C2×C22⋊C411yescharacteristic
266C2×C4×C13C2×C4⋊C411yescharacteristic
267C2×C4×C13C2×C4⋊C411yescharacteristic
268C2×C4×C13C2×C4⋊C411yescharacteristic
269C2×C4×C13#11711yescharacteristic
270C2×C4×C13#11711yescharacteristic
271C2×C4×C13C4×D411yescharacteristic
272C2×C4×C13C4×D411yescharacteristic
273C2×C4×C13C4×D411yescharacteristic
274C2×C4×C13C4×D411yescharacteristic
275C2×C4×C13C4×D411yescharacteristic
276C2×C4×C13C4×D411yescharacteristic
277C2×C4×C13#12011yescharacteristic
278C2×C4×C13#12011yescharacteristic
279C2×C4×C13#12111yescharacteristic
280C2×C4×C13#12111yescharacteristic
281C2×C4×C13#12111yescharacteristic
282C2×C4×C13C22⋊Q811yescharacteristic
283C2×C4×C13C22⋊Q811yescharacteristic
284C2×C4×C13C22⋊Q811yescharacteristic
285C2×C4×C13#12311yescharacteristic
286C2×C4×C13#12311yescharacteristic
287C2×C4×C13#12311yescharacteristic
288C2×C4×C13#12311yescharacteristic
289C2×Dic13—24no—
290C2×Dic13—22no—
291C2×Dic13—24no—
292C2×Dic13—24no—
293C2×Dic13—24no—
294C2×Dic13—24no—
295C2×Dic13—24no—
296C2×Dic13—24no—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13—42no—
312C2×Dic13—81no—
313C2×Dic13—81no—
314C2×Dic13—81no—
315C2×Dic13—81no—
316C2×Dic13#10314yescomplemented
317Dic26—24no—
318Dic26—24no—
319Dic26—24no—
320Dic26—24no—
321Dic26—24no—
322Dic26—24no—
323Dic26—24no—
324Dic26#9518yescomplemented
325C8×C13—42no—
326#1055—42no—
327C23×Q8—131no—
328C23×C8—131no—
329C23×C8C2×D1311yescharacteristic
330C2×C4×Q8—134no—
331C2×C4×Q8—262no—
332C2×C4×Q8—262no—
333C2×C4×Q8—262no—
334C2×C4×Q8—262no—
335C2×C4×Q8—262no—
336C22×C4⋊C4—131no—
337C22×C4⋊C4—261no—
338C22×C4⋊C4C2×D1311yescharacteristic
339C22×C4⋊C4C2×D1311yescharacteristic
340C22×C42—131no—
341C22×C42—261no—
342C2×#103—134no—
343C2×#103—134no—
344C2×#103—262no—
345C2×#103—262no—
346C2×#103—262no—
347C2×#103—262no—
348C2×#95—261no—
349C2×#95—261no—
350#340—22no—
351#340—262no—
352#336—262no—
353C22×C13C4×C22⋊C411yescharacteristic
354C22×C13#37911yescharacteristic
355C22×C13#38011yescharacteristic
356C22×C13#38511yescharacteristic
357C22×C13#38511yescharacteristic
358C22×C13#38611yescharacteristic
359C22×C13#38611yescharacteristic
360C22×C13C2×#10311yescharacteristic
361C22×C13#41611yescharacteristic
362C22×C13#41711yescharacteristic
363C22×C13#41911yescharacteristic
364C22×C13C4×SD1611yescharacteristic
365C22×C13C4×SD1611yescharacteristic
366C22×C13C4×Q1611yescharacteristic
367C22×C13C4×Q1611yescharacteristic
368C22×C13#44011yescharacteristic
369C22×C13#44011yescharacteristic
370C22×C13#44111yescharacteristic
371C22×C13#44111yescharacteristic
372C22×C13#44811yescharacteristic
373C22×C13#44811yescharacteristic
374C22×C13#44911yescharacteristic
375C22×C13#44911yescharacteristic
376C22×C13#45111yescharacteristic
377C22×C13#45111yescharacteristic
378C22×C13#45211yescharacteristic
379C22×C13#45211yescharacteristic
380C22×C13#46011yescharacteristic
381C22×C13#46211yescharacteristic
382C22×C13#46411yescharacteristic
383C22×C13#46411yescharacteristic
384C22×C13#47511yescharacteristic
385C22×C13#47711yescharacteristic
386C22×C13#47911yescharacteristic
387C22×C13#47911yescharacteristic
388C4×C13—44no—
389C4×C13—82no—
390C4×C13C2×#9511yescharacteristic
391C4×C13C4×C22⋊C411yescharacteristic
392C4×C13#38011yescharacteristic
393C4×C13#38111yescharacteristic
394C4×C13#38511yescharacteristic
395C4×C13#38511yescharacteristic
396C4×C13#38611yescharacteristic
397C4×C13#38611yescharacteristic
398Dic13—28no—
399Dic13—24no—
400Dic13—42no—
401Dic13—82no—
402C22×Q8—132no—
403C22×Q8—132no—
404C22×Q8—132no—
405C22×Q8—132no—
406C22×Q8—132no—
407C22×Q8—132no—
408C22×Q8—132no—
409C22×Q8—261no—
410C22×Q8—261no—
411C22×Q8—261no—
412C22×Q8—261no—
413C22×Q8—261no—
414C22×Q8—261no—
415C22×Q8—261no—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—131no—
419C23×C4—131no—
420C23×C4—261no—
421C23×C4—261no—
422C23×C4C22×D1311yescharacteristic
423C22×C8—21no—
424C22×C8—21no—
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—21no—
428C22×C8—21no—
429C22×C8—132no—
430C22×C8—261no—
431C22×C8—261no—
432C22×C8—261no—
433C22×C8—261no—
434C22×C8—261no—
435C22×C8—261no—
436C22×C8C4×D1312yes—
437C4×Q8—268no—
438C4×Q8—268no—
439C4×Q8—268no—
440C4×Q8—268no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—132no—
450C2×C4⋊C4—264no—
451C2×C4⋊C4—264no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—261no—
454C2×C4⋊C4—261no—
455C2×C4⋊C4—261no—
456C2×C4⋊C4—261no—
457C2×C4⋊C4—261no—
458C2×C4⋊C4C4×D1312yes—
459C2×C4⋊C4C4×D1312yes—
460C2×C4⋊C4D5212yes—
461C2×C4⋊C4C22⋊D1312yes—
462C2×C42—132no—
463C2×C42—132no—
464C2×C42—264no—
465C2×C42—264no—
466C2×C42—264no—
467C2×C42—261no—
468C2×C42—261no—
469C2×C42—261no—
470C2×C42—261no—
471#103—268no—
472#103—268no—
473#95—522no—
474#95—522no—
475C2×C13C22⋊#9511yescharacteristic
476C2×C13C4×#10311yescharacteristic
477C2×C13#176311yescharacteristic
478C2×C13#178711yescharacteristic
479C2×C13#178811yescharacteristic
480C2×C13#180311yescharacteristic
481C2×C13#180511yescharacteristic
482C2×C13#186311yescharacteristic
483C2×C13#186311yescharacteristic
484C2×C13#186511yescharacteristic
485C2×C13#186511yescharacteristic
486C2×C13#187811yescharacteristic
487C2×C13#187811yescharacteristic
488C2×C13#188011yescharacteristic
489C2×C13#188011yescharacteristic
490C24D4×D1311yescharacteristic
491C2×Q8—134no—
492C2×Q8—134no—
493C2×Q8—134no—
494C2×Q8—134no—
495C2×Q8—134no—
496C2×Q8—134no—
497C2×Q8—134no—
498C2×Q8—262no—
499C2×Q8—262no—
500C2×Q8—262no—
501C2×Q8—262no—
502C2×Q8—262no—
503C2×Q8—262no—
504C2×Q8—262no—
505C2×Q8—262no—
506C2×Q8—262no—
507C2×Q8—262no—
508C2×Q8—262no—
509C2×Q8—262no—
510C2×Q8—262no—
511C2×Q8—262no—
512C2×Q8—262no—
513C2×Q8—262no—
514C2×Q8—262no—
515C2×Q8—262no—
516C2×Q8—262no—
517C2×Q8—262no—
518C2×Q8—262no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—132no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—261no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—261no—
545C22×C4—261no—
546C22×C4—261no—
547C22×C4—262no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—262no—
555C22×C4—521no—
556C22×C4—521no—
557C22×C4—521no—
558C22×C4—521no—
559C22×C4—521no—
560C22×C4—521no—
561C22×C4C2×C4×D1311yescharacteristic
562C22×C4C2×C4×D1311yescharacteristic
563C22×C4C2×C4×D1311yescharacteristic
564C22×C4C2×D5211yescharacteristic
565C22×C4#612711yescharacteristic
566C22×C4#612711yescharacteristic
567C22×C4D4×D1311yescharacteristic
568C22×C4D4×D1311yescharacteristic
569C22×C4D4×D1311yescharacteristic
570C22×C4D4×D1311yescharacteristic
571C22×C4#612911yescharacteristic
572C22×C4Q8×D1311yescharacteristic
573C22×C4#613111yescharacteristic
574C22×C4C2×C22⋊D1311yescharacteristic
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—262no—
583C2×C8—262no—
584C2×C8—262no—
585C2×C8—521no—
586C2×C8—521no—
587C2×C8—521no—
588C2×C8—521no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—2616no—
597C4⋊C4—262no—
598C4⋊C4—262no—
599C4⋊C4—521no—
600C4⋊C4—521no—
601C4⋊C4#610314yes—
602C42—2616no—
603C42—262no—
604C42—262no—
605C42—262no—
606C42—262no—
607C13#1078911yescharacteristic, complemented, Sylow
608C23C22⋊C4×D1311yescharacteristic
609C23#8813511yescharacteristic
610C23#8813611yescharacteristic
611C23#8813811yescharacteristic
612C23#8814711yescharacteristic
613C23#8815011yescharacteristic
614C23#8816511yescharacteristic
615C23#8816611yescharacteristic
616C23SD16×D1311yescharacteristic
617C23#8816911yescharacteristic
618C23#8816911yescharacteristic
619C23#8817011yescharacteristic
620C23Q16×D1311yescharacteristic
621C23#8817211yescharacteristic
622C23#8819111yescharacteristic
623Q8—138no—
624Q8—264no—
625Q8—264no—
626Q8—264no—
627Q8—264no—
628Q8—264no—
629Q8—264no—
630Q8—264no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—134no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—264no—
651C2×C4—264no—
652C2×C4—264no—
653C2×C4—264no—
654C2×C4—262no—
655C2×C4—262no—
656C2×C4—264no—
657C2×C4—264no—
658C2×C4—264no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—262no—
662C2×C4—521no—
663C2×C4—521no—
664C2×C4—521no—
665C2×C4—521no—
666C2×C4—522no—
667C2×C4—522no—
668C2×C4—522no—
669C2×C4—1041no—
670C2×C4—1041no—
671C2×C4—1041no—
672C2×C4—1041no—
673C2×C4C42×D1311yescharacteristic
674C2×C4#8812611yescharacteristic
675C2×C4C4×D5211yescharacteristic
676C2×C4C4×D5211yescharacteristic
677C2×C4C22⋊C4×D1311yescharacteristic
678C2×C4C22⋊C4×D1311yescharacteristic
679C2×C4C22⋊C4×D1311yescharacteristic
680C2×C4#8813511yescharacteristic
681C2×C4#8813611yescharacteristic
682C2×C4#8813711yescharacteristic
683C2×C4#8813711yescharacteristic
684C2×C4#8813811yescharacteristic
685C2×C4C4⋊C4×D1311yescharacteristic
686C2×C4C4⋊C4×D1311yescharacteristic
687C2×C4C4⋊C4×D1311yescharacteristic
688C2×C4#8814611yescharacteristic
689C2×C4#8814711yescharacteristic
690C2×C4#8814811yescharacteristic
691C2×C4#8814811yescharacteristic
692C2×C4#8814911yescharacteristic
693C2×C4#8815011yescharacteristic
694C2×C4#8815111yescharacteristic
695C2×C4C2×#610311yescharacteristic
696C2×C4C4×C22⋊D1311yescharacteristic
697C2×C4C4×C22⋊D1311yescharacteristic
698C2×C4#8819111yescharacteristic
699C2×C4#8819211yescharacteristic
700C2×C4#8820011yescharacteristic
701C8—42no—
702C8—522no—
703C22#1171832611yescharacteristic
704C22#1171832711yescharacteristic
705C22#1171832811yescharacteristic
706C22#1171832911yescharacteristic
707C22#1171841811yescharacteristic
708C22#1171841911yescharacteristic
709C22#1171842311yescharacteristic
710C22#1171842811yescharacteristic
711C22#1171843211yescharacteristic
712C22#1171843311yescharacteristic
713C22#1171844211yescharacteristic
714C22#1171844411yescharacteristic
715C22#1171845011yescharacteristic
716C22#1171845111yescharacteristic
717C22#1171845411yescharacteristic
718C22#1171845911yescharacteristic
719C22D13×#10311yescharacteristic
720C22#1171846311yescharacteristic
721C22#1171846711yescharacteristic
722C22#1171846911yescharacteristic
723C22#1171851311yescharacteristic
724C22#1171851411yescharacteristic
725C22#1171851511yescharacteristic
726C22#1171851811yescharacteristic
727C22#1171853411yescharacteristic
728C22#1171853611yescharacteristic
729C22#1171853811yescharacteristic
730C22#1171855011yescharacteristic
731C22#1171861611yescharacteristic
732C22#1171861711yescharacteristic
733C22#1171865011yescharacteristic
734C22#1171881911yescharacteristic
735C22#1171883111yescharacteristic
736C22#1171883411yescharacteristic
737C22#1171884711yescharacteristic
738C4—44no—
739C4—82no—
740C4—264no—
741C4—268no—
742C4—522no—
743C4—1042no—
744C4D13×#9511yescharacteristic
745C4#1171832511yescharacteristic
746C4#1171832611yescharacteristic
747C4#1171832911yescharacteristic
748C4C4×#610311yescharacteristic
749C4#1171861711yescharacteristic
750C4#1171864811yescharacteristic
751C4#1171865011yescharacteristic
752C2#1311305711yescharacteristic
753C2#1311465511yescharacteristic
754C2#1311466511yescharacteristic
755C2#1311476911yescharacteristic
756C2#1311477311yescharacteristic
757C2#1311484011yescharacteristic
758C2#1311485011yescharacteristic
759C2#1311508711yescharacteristic
760C2#1311509111yescharacteristic
761C2#1311510111yescharacteristic
762C2#1311510511yescharacteristic
763C2#1311517411yescharacteristic
764C2#1311517811yescharacteristic
765C2#1311518811yescharacteristic
766C2#1311519211yescharacteristic
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#10789
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
22. C2×#88141C4semidirect
27. C2×#88056C4semidirect
30. C2×#88050C4semidirect
316. C2×Dic13#103semidirect
324. Dic26#95semidirect
607. C13#10789semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C22×#880562
C22×#880502
C2×#117181212
C2×#117181422
#131130652
C2×C13×#3402
#1078913