Finite Group Databasebeta

← #15868985

Subgroups — #15868985

Order 3328.

1116 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718788C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×D13×#97C211yesmaximal, characteristic, complemented
4C4×#88192C211yesmaximal, characteristic
5#13115635C211yesmaximal, characteristic, complemented
6#13115557C211yesmaximal, characteristic, complemented
7#13115446C211yesmaximal, characteristic, complemented
8#13115446C211yesmaximal, characteristic, complemented
9#13115125C211yesmaximal, characteristic, complemented
10#13115125C211yesmaximal, characteristic, complemented
11#13114813C211yesmaximal, characteristic, complemented
12#13114708C211yesmaximal, characteristic, complemented
13#13114617C211yesmaximal, characteristic, complemented
14#13114612C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88192C411yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×C4×C22⋊D13C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24C2×C42×D13C2211yescharacteristic
25C13×#435—24no—
26C2×C13×C4⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×C13×#97C2211yescharacteristic
30#11718882C411yescharacteristic
31C4×C22⋊Dic13C2211yescharacteristic
32C4×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718788—24no—
38C8×C22⋊D13—24no—
39C2×#88060C2211yescharacteristic
40C2×#88060C2211yescharacteristic
41C2×#88055C2211yescharacteristic
42C2×#88055C2211yescharacteristic
43C2×#88055C2211yescharacteristic
44C2×#88054C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×C8×Dic13C2211yescharacteristic
47#11718648C411yescharacteristic
48#11718634C411yescharacteristic
49#11718617C411yescharacteristic
50#11718617C411yescharacteristic
51#11718605C411yescharacteristic
52#11718605C411yescharacteristic
53C4×C4⋊Dic13C2211yescharacteristic
54C2×C4⋊#1055C2211yescharacteristic
55C2×#88043C2211yescharacteristic
56D13×#97—24no—
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
63C22×D4×C13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
68C22×C4×D13C2×C411yescharacteristic
69C22×C4×D13C2×C411yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C2×C13×M16—22no—
72C2×C13×M16—22no—
73C2×C13×M16—22no—
74C22×C8×C13—22no—
75C22×C8×C13—22no—
76C22×C8×C13—22no—
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C4×D4×C13—22no—
82C4×D4×C13—22no—
83C2×C13×C4⋊C4C2×C411yescharacteristic
84C2×C13×C22⋊C4C2×C411yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×C22⋊Dic13C2×C411yescharacteristic
92C2×C22⋊Dic13C2×C411yescharacteristic
93#88192—24no—
94C4×C22⋊D13—22no—
95C4×C22⋊D13—22no—
96C4×C22⋊D13—22no—
97C4×C22⋊D13—22no—
98C2×#6103C2×C411yescharacteristic
99C2×#6103C2×C411yescharacteristic
100C2×C4⋊Dic13C2×C411yescharacteristic
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×#6101C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2×C411yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C2×C8×D13—22no—
114C2×C8×D13—22no—
115C2×C8×D13—22no—
116C2×C8×D13—22no—
117C2×C8×D13—22no—
118C2×C8×D13D414yescomplemented
119C42×D13—22no—
120C42×D13—22no—
121C13×C4⋊C8—22no—
122C13×C22⋊C8—22no—
123C13×C22⋊C8—22no—
124C13×#97D414yescomplemented
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131C22⋊#1055—22no—
132C22⋊#1055—22no—
133C22⋊#1055—22no—
134C22⋊#1055—22no—
135#88060—22no—
136#88060—22no—
137#88055—22no—
138#88055—22no—
139#88055—22no—
140#88054—22no—
141#88054—22no—
142C8×Dic13—22no—
143C4⋊#1055—22no—
144#88043—22no—
145#21489—131nomaximal, Sylow
146C24×C13C22×C411yescharacteristic
147C24×C13C22×C411yescharacteristic
148C23×D13C22×C411yescharacteristic
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—41no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C22×C411yescharacteristic
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C2411yescharacteristic
169C2×C22⋊D13—22no—
170C2×C22⋊D13—22no—
171C2×C22⋊D13—22no—
172C2×C22⋊D13—22no—
173C2×C22⋊D13—22no—
174C2×C22⋊D13M1614yescomplemented
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C411yescharacteristic
180C22×Dic13C22×C411yescharacteristic
181C22×Dic13C22×C411yescharacteristic
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—22no—
187C2×C4×D13—22no—
188C2×C4×D13—22no—
189C2×C4×D13—22no—
190C2×C4×D13—41no—
191C2×C4×D13—41no—
192C2×C4×D13C2×D412yes—
193C2×C4×D13#4112yes—
194C13×M16—44no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—44no—
204C2×C8×C13C2×D412yes—
205C2×C8×C13C2×D412yes—
206C2×C8×C13C2×D412yes—
207C2×C8×C13#4112yes—
208C13×C4⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C42×C13C2×D412yes—
212C42×C13#4112yes—
213C22⋊Dic13—22no—
214C22⋊Dic13—22no—
215C22⋊Dic13—22no—
216C22⋊Dic13—22no—
217C22⋊Dic13—41no—
218C22⋊Dic13—41no—
219#6103—22no—
220#6103—22no—
221C4⋊Dic13—22no—
222C4⋊Dic13—41no—
223#6101—22no—
224#6101—22no—
225C4×Dic13—22no—
226C4×Dic13—22no—
227C4×Dic13—21no—
228C4×Dic13—21no—
229C4×Dic13—21no—
230C4×Dic13—21no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055C2×D412yes—
244C2×#1055#4112yes—
245C8×D13—28no—
246C8×D13—28no—
247C2×#435—131no—
248C2×#435D1311yescharacteristic, complemented
249C2×C8×D4—131no—
250C22×#97—131no—
251C4×#121—131no—
252#1955—131no—
253#1940—131no—
254#1924—131no—
255#1924—131no—
256#1869—131no—
257#1869—131no—
258#1797—131no—
259#1771—131no—
260#1753—131no—
261#1752—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13C2×M1612yes—
276C23×C13C23×C411yescharacteristic
277C22×D13—21no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13C4×D412yes—
282C22×D13C2×M1612yes—
283C22×D13#13112yes—
284D4×C13—44no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13C4×D412yes—
304C2×C4×C13C4×D412yes—
305C2×C4×C13C22×D411yescharacteristic
306C2×C4×C13C22×D411yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13C2×#4111yescharacteristic
311C22⋊D13—28no—
312C22⋊D13—44no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13—21no—
328C2×Dic13—21no—
329C2×Dic13—21no—
330C2×Dic13—21no—
331C2×Dic13—21no—
332C2×Dic13C4×D412yes—
333C2×Dic13C2×M1612yes—
334C4×D13—22no—
335C4×D13—22no—
336C4×D13—22no—
337C4×D13—22no—
338C4×D13—44no—
339C4×D13—44no—
340C8×C13—22no—
341C8×C13—41no—
342C8×C13—41no—
343C8×C13#12114yescomplemented
344#1055—22no—
345#1055—22no—
346#1055—41no—
347#1055—41no—
348C22×M16C2×D1311yescharacteristic
349C23×C8—131no—
350C23×C8—131no—
351C23×C8C2×D1311yescharacteristic
352C2×#121—131no—
353C2×C4×D4—131no—
354C2×C4×D4—131no—
355C2×C4×D4C2×D1311yescharacteristic
356C22×C42—131no—
357#435—24no—
358#435—264no—
359C8×D4—264no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8C2×D1311yescharacteristic
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×C22⋊C8—131no—
367C2×C22⋊C8—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×C22⋊C8C2×D1311yescharacteristic
371C2×C22⋊C8C2×D1311yescharacteristic
372C2×#97—131no—
373C2×#97—131no—
374C2×#97—131no—
375C2×#97—131no—
376C2×#97—264no—
377C2×#97C2×D1311yescharacteristic
378C2×C4×C8—131no—
379#390—131no—
380#389—131no—
381#388—131no—
382#388—131no—
383#386—131no—
384#386—131no—
385#380—131no—
386C4×C4⋊C4—131no—
387C4×C22⋊C4—131no—
388C4×C22⋊C4—131no—
389#336—131no—
390#336—131no—
391#336—131no—
392#336—131no—
393#336—131no—
394#336—131no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13C2×C4×D411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C4×#4111yescharacteristic
412C22×C13C22×M1611yescharacteristic
413C22×C13C2×#13111yescharacteristic
414C22×C13#56811yescharacteristic
415C22×C13#56811yescharacteristic
416C2×D13—22no—
417C2×D13—22no—
418C2×D13—22no—
419C2×D13—22no—
420C2×D13—22no—
421C2×D13—22no—
422C2×D13#43514yescomplemented
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13C2×#12111yescharacteristic
428C4×C13#52511yescharacteristic
429C4×C13#52911yescharacteristic
430C4×C13#53211yescharacteristic
431Dic13—22no—
432Dic13—22no—
433Dic13—41no—
434Dic13—41no—
435Dic13—41no—
436Dic13—41no—
437Dic13—41no—
438C22×D4—131no—
439C22×D4—131no—
440C22×D4C4×D1311yescharacteristic
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—134no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—262no—
458C22×C8—262no—
459C22×C8—262no—
460C22×C8—262no—
461C22×C8—262no—
462C22×C8C22×D1311yescharacteristic
463C22×C8C22×D1311yescharacteristic
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466#121—264no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—262no—
470C4×D4—262no—
471C4×D4—262no—
472C4×D4—262no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4C4×D1311yescharacteristic
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4—131no—
485C2×C22⋊C4—131no—
486C2×C22⋊C4C4×D1311yescharacteristic
487C2×C22⋊C4C4×D1311yescharacteristic
488C2×C42—131no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—131no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42C22×D1311yescharacteristic
496C4⋊C8—22no—
497C4⋊C8—262no—
498C4⋊C8—262no—
499C4⋊C8—262no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—262no—
503C22⋊C8—262no—
504C22⋊C8—262no—
505C22⋊C8—262no—
506C22⋊C8—262no—
507C22⋊C8—262no—
508#97—262no—
509#97—262no—
510#97—262no—
511#97—262no—
512#97C22⋊D1314yescomplemented
513C4×C8—262no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95—131no—
518#95—131no—
519#95—131no—
520C2×C13—42no—
521C2×C13—81no—
522C2×C13C4×#12111yescharacteristic
523C2×C13C2×#43511yescharacteristic
524C2×C13#293211yescharacteristic
525C2×C13#293311yescharacteristic
526C2×C13D4×M1611yescharacteristic
527C2×C13#296811yescharacteristic
528C2×C13#297011yescharacteristic
529D13—24no—
530C24—131no—
531C24C2×C4×D1311yescharacteristic
532C24C2×C4×D1311yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—134no—
537C2×D4—262no—
538C2×D4—262no—
539C2×D4—262no—
540C2×D4—262no—
541C2×D4—262no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—131no—
559C22×C4—131no—
560C22×C4—131no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—521no—
572C22×C4—521no—
573C22×C4C2×C4×D1311yescharacteristic
574C22×C4C2×C4×D1311yescharacteristic
575C22×C4C2×C4×D1311yescharacteristic
576C22×C4C2×C4×D1311yescharacteristic
577C22×C4C23×D1311yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—268no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—268no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8D4×D1312yes—
603C2×C8#612912yes—
604C2×C8C2×C22⋊D1312yes—
605C2×C8C2×C22⋊D1312yes—
606C4⋊C4—22no—
607C4⋊C4—262no—
608C4⋊C4—262no—
609C4⋊C4—262no—
610C4⋊C4—521no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—262no—
614C22⋊C4—262no—
615C22⋊C4—262no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—521no—
620C22⋊C4—521no—
621C42—262no—
622C42—262no—
623C42—261no—
624C42—261no—
625C42—261no—
626C42—261no—
627C42—261no—
628C42—261no—
629C42#612712yes—
630C42C2×C22⋊D1312yes—
631C13#2148911yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—132no—
646C23—132no—
647C23—132no—
648C23—261no—
649C23—261no—
650C23—261no—
651C23—261no—
652C23M16×D1312yes—
653C23C22×C4×D1311yescharacteristic
654D4—44no—
655D4—268no—
656D4—524no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—132no—
676C2×C4—132no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—261no—
688C2×C4—261no—
689C2×C4—261no—
690C2×C4—261no—
691C2×C4—261no—
692C2×C4—261no—
693C2×C4—261no—
694C2×C4—261no—
695C2×C4—261no—
696C2×C4—261no—
697C2×C4—261no—
698C2×C4—261no—
699C2×C4—261no—
700C2×C4—524no—
701C2×C4—524no—
702C2×C4C4×C22⋊D1312yes—
703C2×C4C4×C22⋊D1312yes—
704C2×C4C2×#612711yescharacteristic
705C2×C4C2×D4×D1311yescharacteristic
706C2×C4C2×#612911yescharacteristic
707C2×C4#41×D1311yescharacteristic
708C2×C4#41×D1311yescharacteristic
709C2×C4C22×C22⋊D1311yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—262no—
714C8—262no—
715C8—521no—
716C8—521no—
717C8#8819214yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—134no—
733C22—262no—
734C22—262no—
735C22—262no—
736C22—262no—
737C22—262no—
738C22—262no—
739C22C4×#612911yescharacteristic
740C22C4×D4×D1311yescharacteristic
741C22C2×M16×D1311yescharacteristic
742C22#1171945011yescharacteristic
743C22D13×#13111yescharacteristic
744C22#1171945511yescharacteristic
745C22C2×C4×C22⋊D1311yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—262no—
751C4—262no—
752C4—521no—
753C4—521no—
754C4—521no—
755C4—521no—
756C4—521no—
757C4#1171925311yescharacteristic
758C4#1171926211yescharacteristic
759C4C2×#8819211yescharacteristic
760C4#1171953311yescharacteristic
761C2—42no—
762C2—81no—
763C2—264no—
764C2C4×#8819211yescharacteristic
765C2D13×#43511yescharacteristic
766C2#1312355011yescharacteristic
767C2#1312355811yescharacteristic
768C2M16×C22⋊D1311yescharacteristic
769C2#1312382711yescharacteristic
770C2#1312384611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radicalC2×#88192C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#21489
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11718788C2semidirect
2. C2×C8×C22⋊D13C2semidirect
3. C2×D13×#97C2semidirect
5. #13115635C2semidirect
6. #13115557C2semidirect
7. #13115446C2semidirect
8. #13115446C2semidirect
9. #13115125C2semidirect
10. #13115125C2semidirect
11. #13114813C2semidirect
12. #13114708C2semidirect
13. #13114617C2semidirect
14. #13114612C2semidirect
15. C2×C13×#435C2semidirect
118. C2×C8×D13D4semidirect
124. C13×#97D4semidirect
174. C2×C22⋊D13M16semidirect
248. C2×#435D13semidirect
343. C8×C13#121semidirect
422. C2×D13#435semidirect
512. #97C22⋊D13semidirect
631. C13#21489semidirect
717. C8#88192semidirect

Maximal subgroups

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

subgroupindex
C2×#117187882
C2×C8×C22⋊D132
C2×D13×#972
C4×#881922
#131156352
#131155572
#131154462
#131151252
#131148132
#131147082
#131146172
#131146122
C2×C13×#4352
#2148913