Finite Group Databasebeta

← #15768482

Subgroups — #15768482

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88147C211yesmaximal, characteristic
2C22×#88061C211yesmaximal, characteristic
3C22×#88049C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic, complemented
5C2×#11718142C211yesmaximal, characteristic, complemented
6#13113065C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×D52C2211yescharacteristic
9C23×C4×D13—21no—
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×#6103—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×#88147—22no—
18C2×#88147—22no—
19C2×#88147—22no—
20C2×#88147—22no—
21C2×#88147—22no—
22C2×#88147C414yescomplemented
23C2×#88071—21no—
24C2×#88071—21no—
25C2×#88061—22no—
26C2×#88061—22no—
27C2×#88061C414yescomplemented
28C2×#88049—22no—
29C2×#88049—22no—
30C2×#88049C414yescomplemented
31C13×#340—22no—
32#11718142—22no—
33#11718121—22no—
34C24×D13—21no—
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—21no—
39C23×Dic13D411yescharacteristic
40C23×Dic13D411yescharacteristic
41C22×D52—21no—
42C22×D52—21no—
43C22×D52—21no—
44C22×D52—21no—
45C22×D52—21no—
46C22×D52—21no—
47C22×D52—21no—
48C22×D52C2×C412yes—
49C22×D52C2×C412yes—
50C22×D52C2×C412yes—
51C22×D52D412yes—
52C22×D52D412yes—
53C22×D52D412yes—
54C22×D52Q812yes—
55C22×C4×D13—24no—
56C22×C4×D13—24no—
57C22×C4×D13—24no—
58C22×C4×D13—42no—
59C22×C4×D13—42no—
60C22×C4×D13—42no—
61C22×C4×D13—42no—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C22×C8×C13—21no—
68C22×C8×C13C2×C412yescomplemented
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2×C412yes—
78C2×C13×C4⋊C4C2×C412yescomplemented
79C2×C13×C4⋊C4D412yes—
80C2×C13×C4⋊C4D412yes—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2×C412yescomplemented
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13C2×C412yes—
95C2×C4×Dic13D412yes—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C22×#1055—21no—
101C22×#1055—21no—
102C22×#1055C2×C412yescomplemented
103#88147—28no—
104#88147—28no—
105#88147—28no—
106#88147—28no—
107#88071—42no—
108#88071—42no—
109#88061—28no—
110#88049—28no—
111#10788—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—41no—
121C23×D13—41no—
122C23×D13—41no—
123C23×D13—41no—
124C23×D13—41no—
125C23×D13—41no—
126C23×D13—41no—
127C23×D13—41no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×Q811yescharacteristic
152C22×C4×C13#4111yescharacteristic
153C22×C4×C13#4111yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—41no—
168C22×Dic13—41no—
169C22×Dic13—41no—
170C22×Dic13—41no—
171C22×Dic13—41no—
172C22×Dic13—41no—
173C22×Dic13C22⋊C412yes—
174C22×Dic13C22⋊C412yes—
175C22×Dic13D812yes—
176C22×Dic13SD1612yes—
177C2×D52—22no—
178C2×D52—22no—
179C2×D52—22no—
180C2×D52—22no—
181C2×D52—22no—
182C2×D52—22no—
183C2×D52—22no—
184C2×D52—22no—
185C2×D52—22no—
186C2×D52—22no—
187C2×D52—22no—
188C2×D52—22no—
189C2×D52—22no—
190C2×D52—22no—
191C2×D52—22no—
192C2×D52—22no—
193C2×D52—22no—
194C2×D52—22no—
195C2×D52—22no—
196C2×D52—22no—
197C2×D52—22no—
198C2×D52C4214yes—
199C2×D52C22⋊C414yes—
200C2×D52C22⋊C414yes—
201C2×D52C22⋊C414yes—
202C2×D52C4⋊C414yes—
203C2×D52C4⋊C414yes—
204C2×D52C4⋊C414yes—
205C2×C4×D13—216no—
206C2×C4×D13—48no—
207C2×C4×D13—48no—
208C2×C4×D13—48no—
209C2×C4×D13—48no—
210C2×C4×D13—48no—
211C2×C4×D13—48no—
212C2×C8×C13—22no—
213C2×C8×C13—22no—
214C2×C8×C13—22no—
215C2×C8×C13—41no—
216C2×C8×C13—41no—
217C2×C8×C13—41no—
218C2×C8×C13—41no—
219C13×C4⋊C4—22no—
220C13×C4⋊C4—22no—
221C13×C4⋊C4—22no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—22no—
224C13×C4⋊C4—41no—
225C13×C4⋊C4—41no—
226C13×C4⋊C4C22⋊C414yes—
227#6103—216no—
228C4⋊Dic13—22no—
229C4⋊Dic13—22no—
230C4⋊Dic13—41no—
231C4⋊Dic13—41no—
232C4×Dic13—22no—
233C4×Dic13—22no—
234C4×Dic13—22no—
235C4×Dic13—22no—
236C2×#1055—22no—
237C2×#1055—22no—
238C2×#1055—22no—
239C2×#1055—41no—
240C2×#1055—41no—
241C2×#1055—41no—
242C2×#1055—41no—
243C22×C4×D4—131no—
244C22×#102—131no—
245C22×#102—131no—
246C2×#340—131no—
247C2×#340D1311yescharacteristic, complemented
248C2×#336—131no—
249C4⋊#95—131no—
250C23×C13C2×C22⋊C411yescharacteristic
251C23×C13C4×D411yescharacteristic
252C23×C13C4×D411yescharacteristic
253C23×C13#12011yescharacteristic
254C23×C13#12011yescharacteristic
255C23×C13#12111yescharacteristic
256C23×C13C22⋊Q811yescharacteristic
257C23×C13C2×D811yescharacteristic
258C23×C13C2×SD1611yescharacteristic
259C23×C13#13511yescharacteristic
260C23×C13#13511yescharacteristic
261C23×C13AGL(1,ℤ/8)11yescharacteristic
262C23×C13AGL(1,ℤ/8)11yescharacteristic
263C23×C13AGL(1,ℤ/8)11yescharacteristic
264C23×C13#13711yescharacteristic
265C22×D13—24no—
266C22×D13—24no—
267C22×D13—24no—
268C22×D13—24no—
269C22×D13—24no—
270C22×D13—24no—
271C22×D13—24no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—42no—
275C22×D13—42no—
276C22×D13—42no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
284C22×D13—42no—
285C22×D13—42no—
286C22×D13—42no—
287C22×D13—42no—
288C22×D13—42no—
289C22×D13—42no—
290C22×D13—42no—
291C22×D13—42no—
292C22×D13—42no—
293C22×D13—42no—
294C22×D13—42no—
295C22×D13—42no—
296C22×D13—42no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—42no—
300C2×C4×C13—24no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—81no—
311C2×C4×C13—81no—
312C2×C4×C13—81no—
313C2×C4×C13—81no—
314C2×C4×C13C2×C4211yescharacteristic
315C2×C4×C13C2×C22⋊C411yescharacteristic
316C2×C4×C13C2×C22⋊C411yescharacteristic
317C2×C4×C13C2×C22⋊C411yescharacteristic
318C2×C4×C13C2×C22⋊C411yescharacteristic
319C2×C4×C13C2×C4⋊C411yescharacteristic
320C2×C4×C13C2×C4⋊C411yescharacteristic
321C2×C4×C13C2×C4⋊C411yescharacteristic
322C2×C4×C13#11711yescharacteristic
323C2×C4×C13#11711yescharacteristic
324C2×C4×C13C4×D411yescharacteristic
325C2×C4×C13C4×D411yescharacteristic
326C2×C4×C13C4×D411yescharacteristic
327C2×C4×C13C4×D411yescharacteristic
328C2×C4×C13C4×D411yescharacteristic
329C2×C4×C13C4×D411yescharacteristic
330C2×C4×C13#12011yescharacteristic
331C2×C4×C13#12011yescharacteristic
332C2×C4×C13#12111yescharacteristic
333C2×C4×C13#12111yescharacteristic
334C2×C4×C13#12111yescharacteristic
335C2×C4×C13C22⋊Q811yescharacteristic
336C2×C4×C13C22⋊Q811yescharacteristic
337C2×C4×C13C22⋊Q811yescharacteristic
338C2×C4×C13#12311yescharacteristic
339C2×C4×C13#12311yescharacteristic
340C2×C4×C13#12311yescharacteristic
341C2×C4×C13#12311yescharacteristic
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—81no—
359C2×Dic13—81no—
360C2×Dic13—81no—
361C2×Dic13—81no—
362C2×Dic13#10214yescomplemented
363D52—24no—
364D52—24no—
365D52—24no—
366D52—24no—
367D52—24no—
368D52—24no—
369D52—24no—
370D52#9518yescomplemented
371C4×D13—432no—
372C8×C13—42no—
373#1055—42no—
374C23×D4—131no—
375C24×C4—261no—
376C23×C8—131no—
377C23×C8C2×D1311yescharacteristic
378C2×C4×D4—134no—
379C2×C4×D4—262no—
380C2×C4×D4—262no—
381C2×C4×D4—262no—
382C2×C4×D4—262no—
383C2×C4×D4—262no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4C2×D1311yescharacteristic
386C22×C4⋊C4C2×D1311yescharacteristic
387C22×C22⋊C4—261no—
388C22×C42—131no—
389C2×#102—134no—
390C2×#102—134no—
391C2×#102—262no—
392C2×#102—262no—
393C2×#102—262no—
394C2×#102—262no—
395C2×#95—261no—
396C2×#95—261no—
397#340—22no—
398#340—262no—
399#336—262no—
400C22×C13C4×C22⋊C411yescharacteristic
401C22×C13#37911yescharacteristic
402C22×C13#38011yescharacteristic
403C22×C13#38511yescharacteristic
404C22×C13#38511yescharacteristic
405C22×C13#38611yescharacteristic
406C22×C13#38611yescharacteristic
407C22×C13C2×#10211yescharacteristic
408C22×C13#41611yescharacteristic
409C22×C13#41711yescharacteristic
410C22×C13#41811yescharacteristic
411C22×C13C4×D811yescharacteristic
412C22×C13C4×D811yescharacteristic
413C22×C13C4×SD1611yescharacteristic
414C22×C13C4×SD1611yescharacteristic
415C22×C13#44011yescharacteristic
416C22×C13#44011yescharacteristic
417C22×C13#44211yescharacteristic
418C22×C13#44211yescharacteristic
419C22×C13#44711yescharacteristic
420C22×C13#44711yescharacteristic
421C22×C13#44911yescharacteristic
422C22×C13#44911yescharacteristic
423C22×C13#45011yescharacteristic
424C22×C13#45011yescharacteristic
425C22×C13#45211yescharacteristic
426C22×C13#45211yescharacteristic
427C22×C13#45911yescharacteristic
428C22×C13#46111yescharacteristic
429C22×C13#46311yescharacteristic
430C22×C13#46311yescharacteristic
431C22×C13#47411yescharacteristic
432C22×C13#47611yescharacteristic
433C22×C13#47811yescharacteristic
434C22×C13#47811yescharacteristic
435C2×D13—28no—
436C2×D13—44no—
437C2×D13—44no—
438C2×D13—44no—
439C2×D13—44no—
440C2×D13—44no—
441C2×D13—44no—
442C2×D13—44no—
443C2×D13—44no—
444C2×D13—44no—
445C2×D13—44no—
446C2×D13—44no—
447C2×D13—44no—
448C2×D13—44no—
449C2×D13—44no—
450C4×C13—44no—
451C4×C13—82no—
452C4×C13C2×#9511yescharacteristic
453C4×C13C4×C22⋊C411yescharacteristic
454C4×C13#38011yescharacteristic
455C4×C13#38111yescharacteristic
456C4×C13#38511yescharacteristic
457C4×C13#38511yescharacteristic
458C4×C13#38611yescharacteristic
459C4×C13#38611yescharacteristic
460Dic13—24no—
461Dic13—42no—
462Dic13—82no—
463C25—261no—
464C22×D4—132no—
465C22×D4—132no—
466C22×D4—132no—
467C22×D4—132no—
468C22×D4—132no—
469C22×D4—132no—
470C22×D4—132no—
471C22×D4—261no—
472C22×D4—261no—
473C22×D4—261no—
474C22×D4—261no—
475C22×D4—261no—
476C22×D4—261no—
477C22×D4—261no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—131no—
481C23×C4—131no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—261no—
486C23×C4—522no—
487C23×C4—522no—
488C23×C4—522no—
489C23×C4—522no—
490C23×C4C22×D1311yescharacteristic
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—132no—
498C22×C8—261no—
499C22×C8—261no—
500C22×C8—261no—
501C22×C8—261no—
502C22×C8—261no—
503C22×C8—261no—
504C22×C8C4×D1312yescomplemented
505C4×D4—268no—
506C4×D4—268no—
507C4×D4—268no—
508C4×D4—268no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—132no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4—261no—
522C2×C4⋊C4—261no—
523C2×C4⋊C4C4×D1312yes—
524C2×C4⋊C4C4×D1312yescomplemented
525C2×C4⋊C4D5212yes—
526C2×C4⋊C4C22⋊D1312yes—
527C2×C22⋊C4—264no—
528C2×C22⋊C4—264no—
529C2×C22⋊C4—264no—
530C2×C42—132no—
531C2×C42—132no—
532C2×C42—261no—
533C2×C42—261no—
534C2×C42—261no—
535C2×C42—261no—
536#102—268no—
537#102—268no—
538#95—522no—
539#95—522no—
540C2×C13C22⋊#9511yescharacteristic
541C2×C13C4×#10211yescharacteristic
542C2×C13#176211yescharacteristic
543C2×C13#178611yescharacteristic
544C2×C13#178811yescharacteristic
545C2×C13#180211yescharacteristic
546C2×C13#180411yescharacteristic
547C2×C13#186211yescharacteristic
548C2×C13#186211yescharacteristic
549C2×C13#186411yescharacteristic
550C2×C13#186411yescharacteristic
551C2×C13#187711yescharacteristic
552C2×C13#187711yescharacteristic
553C2×C13#187911yescharacteristic
554C2×C13#187911yescharacteristic
555D13—48no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—521no—
564C24—521no—
565C24—521no—
566C24—521no—
567C24—521no—
568C24—521no—
569C24—521no—
570C24—521no—
571C24D4×D1311yescharacteristic
572C2×D4—134no—
573C2×D4—134no—
574C2×D4—134no—
575C2×D4—134no—
576C2×D4—134no—
577C2×D4—134no—
578C2×D4—134no—
579C2×D4—262no—
580C2×D4—262no—
581C2×D4—262no—
582C2×D4—262no—
583C2×D4—262no—
584C2×D4—262no—
585C2×D4—262no—
586C2×D4—262no—
587C2×D4—262no—
588C2×D4—262no—
589C2×D4—262no—
590C2×D4—262no—
591C2×D4—262no—
592C2×D4—262no—
593C2×D4—262no—
594C2×D4—262no—
595C2×D4—262no—
596C2×D4—262no—
597C2×D4—262no—
598C2×D4—262no—
599C2×D4—262no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—132no—
618C22×C4—2616no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—262no—
630C22×C4—528no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—528no—
636C22×C4—521no—
637C22×C4—521no—
638C22×C4—521no—
639C22×C4—521no—
640C22×C4—521no—
641C22×C4—521no—
642C22×C4C2×C4×D1311yescharacteristic
643C22×C4C2×C4×D1311yescharacteristic
644C22×C4C2×C4×D1311yescharacteristic
645C22×C4C2×D5211yescharacteristic
646C22×C4#612711yescharacteristic
647C22×C4#612711yescharacteristic
648C22×C4D4×D1311yescharacteristic
649C22×C4D4×D1311yescharacteristic
650C22×C4D4×D1311yescharacteristic
651C22×C4D4×D1311yescharacteristic
652C22×C4#612911yescharacteristic
653C22×C4Q8×D1311yescharacteristic
654C22×C4#613111yescharacteristic
655C22×C4C2×C22⋊D1311yescharacteristic
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—521no—
667C2×C8—521no—
668C2×C8—521no—
669C2×C8—521no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—262no—
678C4⋊C4—262no—
679C4⋊C4—521no—
680C4⋊C4—521no—
681C4⋊C4#610314yes—
682C22⋊C4—2616no—
683C42—262no—
684C42—262no—
685C42—262no—
686C42—262no—
687C13#1078811yescharacteristic, complemented, Sylow
688C23—264no—
689C23—264no—
690C23—264no—
691C23—264no—
692C23—264no—
693C23—264no—
694C23—264no—
695C23—522no—
696C23—522no—
697C23—522no—
698C23—522no—
699C23—522no—
700C23—522no—
701C23—522no—
702C23—522no—
703C23—522no—
704C23—522no—
705C23—522no—
706C23—522no—
707C23—522no—
708C23—522no—
709C23—522no—
710C23—522no—
711C23—522no—
712C23—522no—
713C23—522no—
714C23—522no—
715C23—522no—
716C23—522no—
717C23—522no—
718C23—522no—
719C23—522no—
720C23—522no—
721C23—522no—
722C23—522no—
723C23C22⋊C4×D1311yescharacteristic
724C23#8813511yescharacteristic
725C23#8813611yescharacteristic
726C23#8813811yescharacteristic
727C23#8814711yescharacteristic
728C23#8815011yescharacteristic
729C23D8×D1311yescharacteristic
730C23#8816511yescharacteristic
731C23SD16×D1311yescharacteristic
732C23#8816811yescharacteristic
733C23#8816811yescharacteristic
734C23#8817011yescharacteristic
735C23#8817211yescharacteristic
736C23#8817311yescharacteristic
737C23#8819111yescharacteristic
738D4—138no—
739D4—264no—
740D4—264no—
741D4—264no—
742D4—264no—
743D4—264no—
744D4—264no—
745D4—264no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—134no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—5232no—
771C2×C4—521no—
772C2×C4—521no—
773C2×C4—521no—
774C2×C4—521no—
775C2×C4—522no—
776C2×C4—522no—
777C2×C4—522no—
778C2×C4—1041no—
779C2×C4—1041no—
780C2×C4—1041no—
781C2×C4—1041no—
782C2×C4C42×D1311yescharacteristic
783C2×C4#8812611yescharacteristic
784C2×C4C4×D5211yescharacteristic
785C2×C4C4×D5211yescharacteristic
786C2×C4C22⋊C4×D1311yescharacteristic
787C2×C4C22⋊C4×D1311yescharacteristic
788C2×C4C22⋊C4×D1311yescharacteristic
789C2×C4#8813511yescharacteristic
790C2×C4#8813611yescharacteristic
791C2×C4#8813711yescharacteristic
792C2×C4#8813711yescharacteristic
793C2×C4#8813811yescharacteristic
794C2×C4C4⋊C4×D1311yescharacteristic
795C2×C4C4⋊C4×D1311yescharacteristic
796C2×C4C4⋊C4×D1311yescharacteristic
797C2×C4#8814611yescharacteristic
798C2×C4#8814711yescharacteristic
799C2×C4#8814811yescharacteristic
800C2×C4#8814811yescharacteristic
801C2×C4#8814911yescharacteristic
802C2×C4#8815011yescharacteristic
803C2×C4#8815111yescharacteristic
804C2×C4C2×#610311yescharacteristic
805C2×C4C4×C22⋊D1311yescharacteristic
806C2×C4C4×C22⋊D1311yescharacteristic
807C2×C4#8819111yescharacteristic
808C2×C4#8819211yescharacteristic
809C2×C4#8820011yescharacteristic
810C8—42no—
811C8—522no—
812C22—268no—
813C22—524no—
814C22—524no—
815C22—524no—
816C22—524no—
817C22—524no—
818C22—524no—
819C22—524no—
820C22—524no—
821C22—524no—
822C22—524no—
823C22—524no—
824C22—524no—
825C22—524no—
826C22—524no—
827C22#1171832611yescharacteristic
828C22#1171832711yescharacteristic
829C22#1171832811yescharacteristic
830C22#1171832911yescharacteristic
831C22#1171841711yescharacteristic
832C22D13×#10211yescharacteristic
833C22#1171843111yescharacteristic
834C22#1171843411yescharacteristic
835C22#1171843711yescharacteristic
836C22#1171844611yescharacteristic
837C22#1171844711yescharacteristic
838C22#1171844811yescharacteristic
839C22#1171844911yescharacteristic
840C22#1171846411yescharacteristic
841C22#1171846511yescharacteristic
842C22#1171847111yescharacteristic
843C22#1171847211yescharacteristic
844C22#1171847811yescharacteristic
845C22#1171847911yescharacteristic
846C22#1171848011yescharacteristic
847C22#1171851311yescharacteristic
848C22#1171853011yescharacteristic
849C22#1171853111yescharacteristic
850C22#1171853211yescharacteristic
851C22#1171853311yescharacteristic
852C22#1171855011yescharacteristic
853C22#1171855111yescharacteristic
854C22#1171855211yescharacteristic
855C22#1171861611yescharacteristic
856C22#1171861711yescharacteristic
857C22#1171865011yescharacteristic
858C22#1171881711yescharacteristic
859C22#1171883011yescharacteristic
860C22#1171883311yescharacteristic
861C22#1171884811yescharacteristic
862C4—44no—
863C4—82no—
864C4—264no—
865C4—522no—
866C4—1042no—
867C4D13×#9511yescharacteristic
868C4#1171832511yescharacteristic
869C4#1171832611yescharacteristic
870C4#1171832911yescharacteristic
871C4C4×#610311yescharacteristic
872C4#1171861711yescharacteristic
873C4#1171864811yescharacteristic
874C4#1171865011yescharacteristic
875C2—528no—
876C2#1311305711yescharacteristic
877C2#1311465011yescharacteristic
878C2#1311466011yescharacteristic
879C2#1311476511yescharacteristic
880C2#1311477511yescharacteristic
881C2#1311483511yescharacteristic
882C2#1311484511yescharacteristic
883C2#1311508011yescharacteristic
884C2#1311508411yescharacteristic
885C2#1311509411yescharacteristic
886C2#1311509811yescharacteristic
887C2#1311516711yescharacteristic
888C2#1311517111yescharacteristic
889C2#1311518111yescharacteristic
890C2#1311518511yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#10788
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
4. C2×#11718121C2semidirect
5. C2×#11718142C2semidirect
6. #13113065C2semidirect
7. C2×C13×#340C2semidirect
22. C2×#88147C4semidirect
27. C2×#88061C4semidirect
30. C2×#88049C4semidirect
68. C22×C8×C13C2×C4semidirect
78. C2×C13×C4⋊C4C2×C4semidirect
89. C2×C4⋊Dic13C2×C4semidirect
102. C22×#1055C2×C4semidirect
247. C2×#340D13semidirect
362. C2×Dic13#102semidirect
370. D52#95semidirect
504. C22×C8C4×D13semidirect
524. C2×C4⋊C4C4×D13semidirect
687. C13#10788semidirect

Maximal subgroups

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

subgroupindex
C22×#881472
C22×#880612
C22×#880492
C2×#117181212
C2×#117181422
#131130652
C2×C13×#3402
#1078813