Finite Group Databasebeta

← #15860730

Subgroups — #15860730

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719250C211yesmaximal, characteristic
2C2×#11718431C211yesmaximal, characteristic
3C2×D13×#102C211yesmaximal, characteristic
4C2×#11718369C211yesmaximal, characteristic, complemented
5#13117190C211yesmaximal, characteristic, complemented
6#13114663C211yesmaximal, characteristic, complemented
7#13114662C211yesmaximal, characteristic, complemented
8#13114660C211yesmaximal, characteristic, complemented
9C4×#88049C211yesmaximal, characteristic, complemented
10#102×Dic13C211yesmaximal, characteristic, complemented
11C4×#88072C211yesmaximal, characteristic, complemented
12#13114650C211yesmaximal, characteristic, complemented
13#13114554C211yesmaximal, characteristic, complemented
14#13114551C211yesmaximal, characteristic, complemented
15C13×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×C4×C22⋊D13—21no—
20C22×#6103—21no—
21C22×#6094C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23#11719250—24no—
24#11719250C418yescomplemented
25C2×#88147C2211yescharacteristic
26C2×#88146C2211yescharacteristic
27C2×#88146C2211yescharacteristic
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×#88135—21no—
30C2×C22⋊C4×D13—21no—
31C2×C4×D52C2211yescharacteristic
32C2×#88126C2211yescharacteristic
33C2×C13×#102C2211yescharacteristic
34C2×C13×#102C2211yescharacteristic
35C2×C13×#97C2211yescharacteristic, complemented
36C4×C13×C4⋊C4C2211yescharacteristic, complemented
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88061C2211yescharacteristic
40C2×#88061C2211yescharacteristic
41C2×#88055C2211yescharacteristic, complemented
42C2×C8×Dic13C2211yescharacteristic, complemented
43C4⋊C4×Dic13C2211yescharacteristic, complemented
44C4⋊C4×Dic13C2211yescharacteristic, complemented
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C4×#6103—21no—
48C4×C4⋊Dic13C2211yescharacteristic, complemented
49C4×#6101—21no—
50C2×C4×#1055C2211yescharacteristic, complemented
51#11718431C418yescomplemented
52D13×#102C418yescomplemented
53#11718369—24no—
54#11718327—21no—
55#11718310—21no—
56C13×#340C2211yescharacteristic, complemented
57C13×#340C2211yescharacteristic, complemented
58#11718143C2211yescharacteristic, complemented
59#11718143C2211yescharacteristic, complemented
60#11718121C2211yescharacteristic, complemented
61#11718121C2211yescharacteristic, complemented
62#11718121C2211yescharacteristic, complemented
63#11718121C2211yescharacteristic, complemented
64C24×D13—21no—
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C22×C22⋊D13—21no—
68C23×Dic13—21no—
69C2×D4×D13—22no—
70C2×D4×D13—22no—
71C2×D4×D13—22no—
72C2×D4×D13C2×C414yes—
73C2×D4×D13C2×C414yes—
74C2×D4×D13C2×C414yes—
75C22×D52C2311yescharacteristic
76C22×C4×D13—21no—
77C22×C4×D13—21no—
78C22×C4×D13—21no—
79C22×C4×D13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C4×D4×C13—22no—
83C4×D4×C13C2×C414yescomplemented
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C22⋊C4—21no—
88C2×C42×C13—21no—
89C2×C42×C13C2311yescharacteristic
90C2×C22⋊Dic13—21no—
91D4×Dic13—22no—
92D4×Dic13C2×C414yescomplemented
93C4×C22⋊D13—28no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×#6103—21no—
98C2×#6103—28no—
99C2×#6103D411yescharacteristic
100C2×#6103D411yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×#6101—21no—
105C2×#6101D411yescharacteristic
106C2×#6101D411yescharacteristic
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—21no—
110C2×C4×Dic13—21no—
111C2×C4×Dic13—21no—
112C2×C4×Dic13C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C2×#6094—22no—
116C2×#6094—22no—
117C2×#6094C2×C414yescomplemented
118C2×C8×D13—22no—
119C2×C8×D13—22no—
120C2×C8×D13C2×C414yescomplemented
121#88147—22no—
122#88147C2×C414yescomplemented
123#88146—22no—
124#88146—22no—
125#88146C2×C414yes—
126#88146C2×C414yescomplemented
127C4⋊C4×D13—22no—
128C4⋊C4×D13C2×C414yescomplemented
129#88135—28no—
130C22⋊C4×D13—28no—
131C4×D52—22no—
132C4×D52C2×C414yescomplemented
133#88126C2×C414yes—
134#88126D414yes—
135C13×#102C2×C414yescomplemented
136C13×#102C2×C414yescomplemented
137C13×#97—22no—
138C13×#95—21no—
139#88072C2×C414yescomplemented
140#88072C2×C414yescomplemented
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88061C2×C414yescomplemented
145#88061C2×C414yescomplemented
146#88055—22no—
147C8×Dic13—22no—
148#88049C2×C414yescomplemented
149#88049C2×C414yescomplemented
150C4×#1055—22no—
151#20416—131nomaximal, Sylow
152C24×C13—21no—
153C23×D13—21no—
154C23×D13—24no—
155C23×D13—24no—
156C23×D13—24no—
157C23×D13—81no—
158C23×D13—81no—
159C23×D13—81no—
160C23×D13—81no—
161C23×D13C2×D411yescharacteristic
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13C22×C412yes—
166C2×D4×C13C22×C412yes—
167C2×D4×C13C22×C412yes—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—24no—
172C22×C4×C13—81no—
173C22×C4×C13—81no—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2411yescharacteristic
177C2×C22⋊D13—24no—
178C2×C22⋊D13—24no—
179C2×C22⋊D13—24no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—24no—
184C22×Dic13—81no—
185C22×Dic13—81no—
186C22×Dic13C2×D411yescharacteristic
187C22×Dic13C2×D411yescharacteristic
188C22×Dic13C2×D411yescharacteristic
189D4×D13—28no—
190D4×D13—28no—
191D4×D13—28no—
192D4×D13C42116yescomplemented
193C2×D52—21no—
194C2×D52—21no—
195C2×D52—21no—
196C2×D52C22×C412yes—
197C2×D52C22×C412yes—
198C2×D52C22×C412yes—
199C2×C4×D13—24no—
200C2×C4×D13—24no—
201C2×C4×D13—24no—
202C2×C4×D13—81no—
203C2×C4×D13—81no—
204C2×C4×D13—81no—
205C2×C4×D13—81no—
206C2×C4×D13—81no—
207C2×C4×D13—81no—
208C2×C4×D13C22×C412yes—
209C2×C4×D13C22×C412yes—
210C2×C4×D13C22×C412yes—
211C2×C4×D13C2×D412yes—
212C2×C4×D13#4112yes—
213C2×C4×D13#4112yes—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—21no—
217C2×C8×C13—21no—
218C2×C8×C13C22×C412yes—
219C2×C8×C13C22×C412yes—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4C22×C412yes—
224C13×C4⋊C4C22×C412yes—
225C13×C4⋊C4C22×C412yes—
226C13×C22⋊C4—24no—
227C42×C13—81no—
228C42×C13C22×C412yes—
229C42×C13C2×D412yes—
230C22⋊Dic13—24no—
231#6103—24no—
232#6103—24no—
233#6103—24no—
234#6103—24no—
235#6103C22⋊C414yes—
236#6103C22⋊C414yes—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13C22×C412yes—
241C4⋊Dic13C22×C412yes—
242C4⋊Dic13C22×C412yes—
243#6101—24no—
244#6101C22⋊C414yes—
245#6101C22⋊C414yes—
246C4×Dic13—24no—
247C4×Dic13—24no—
248C4×Dic13—81no—
249C4×Dic13—81no—
250C4×Dic13—81no—
251C4×Dic13C22×C412yes—
252C4×Dic13C2×D412yes—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055C22×C412yes—
258C2×#1055C22×C412yes—
259#6094—28no—
260C8×D13—28no—
261C2×#518—131no—
262C2×#418—131no—
263C22×#102—131no—
264C2×#405—131no—
265#2274—131no—
266#1762—131no—
267#1762—131no—
268#1762—131no—
269#1762D1311yescharacteristic, complemented
270C4×#102—131no—
271C4×#102—131no—
272C4×#102—131no—
273C4×#102—131no—
274#1736—131no—
275#1735—131no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13C22×D411yescharacteristic
284C22×D13—21no—
285C22×D13—21no—
286C22×D13—21no—
287C22×D13—21no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—216no—
292C22×D13—41no—
293C22×D13—41no—
294C22×D13—41no—
295C22×D13—41no—
296C22×D13—84no—
297C22×D13—84no—
298C22×D13—84no—
299C22×D13—84no—
300C22×D13—84no—
301C22×D13—84no—
302C22×D13C2×C22⋊C412yes—
303C22×D13C4×D412yes—
304C22×D13C4×D412yes—
305D4×C13—22no—
306D4×C13—22no—
307D4×C13—22no—
308D4×C13C2×C4214yes—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—84no—
323C2×C4×C13C2×C22⋊C412yes—
324C2×C4×C13C2×C22⋊C412yes—
325C2×C4×C13C23×C411yescharacteristic
326C2×C4×C13C23×C411yescharacteristic
327C2×C4×C13C23×C411yescharacteristic
328C2×C4×C13C22×D411yescharacteristic
329C2×C4×C13C2×#4111yescharacteristic
330C2×C4×C13C2×#4111yescharacteristic
331C22⋊D13—216no—
332C2×Dic13—21no—
333C2×Dic13—21no—
334C2×Dic13—21no—
335C2×Dic13—21no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—84no—
346C2×Dic13C2×C22⋊C412yes—
347C2×Dic13C2×C22⋊C412yes—
348C2×Dic13C2×C22⋊C412yes—
349C2×Dic13C4×D412yes—
350C2×Dic13C4×D412yes—
351D52—22no—
352D52—22no—
353D52—22no—
354D52C2×C4214yes—
355C4×D13—84no—
356C4×D13—84no—
357C4×D13—84no—
358C4×D13C2×C4214yes—
359C4×D13#11714yes—
360C4×D13C4×D414yes—
361C4×D13C4×D414yes—
362C8×C13—22no—
363C8×C13—22no—
364#1055—22no—
365#1055—22no—
366C23×D4—131no—
367C22×M16—131no—
368C23×C8—131no—
369#518—138no—
370#518—264no—
371C2×C4×D4—131no—
372C2×C4×D4—131no—
373C2×C4×D4—131no—
374C2×C4×D4—261no—
375C2×C4×D4—261no—
376C2×C4×D4C2×D1311yescharacteristic
377C2×#117—131no—
378C2×#117—131no—
379C2×#117—131no—
380C22×C4⋊C4—131no—
381C22×C22⋊C4—261no—
382C22×C22⋊C4—261no—
383#418—138no—
384C2×#102—131no—
385C2×#102—131no—
386C2×#102—131no—
387C2×#102—131no—
388C2×#102—131no—
389C2×#102—131no—
390C2×#102—138no—
391C2×#102C2×D1311yescharacteristic
392C2×#102C2×D1311yescharacteristic
393#405—264no—
394C2×#97—131no—
395C2×#97C2×D1311yescharacteristic, complemented
396C2×C4×C8—131no—
397C2×C4×C8—131no—
398C4×C4⋊C4—131no—
399C4×C4⋊C4—131no—
400C4×C4⋊C4—131no—
401C4×C4⋊C4—261no—
402C4×C4⋊C4—261no—
403C4×C4⋊C4C2×D1311yescharacteristic, complemented
404C4×C22⋊C4—261no—
405C4×C22⋊C4—261no—
406#340—131no—
407#340—131no—
408#340—131no—
409#340—131no—
410#340—131no—
411#340—131no—
412#340C2×D1311yescharacteristic, complemented
413#340C2×D1311yescharacteristic, complemented
414C22×C13—24no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—42no—
421C22×C13C22×C22⋊C411yescharacteristic
422C22×C13C2×C4×D411yescharacteristic
423C22×C13C2×C4×D411yescharacteristic
424C22×C13#57611yescharacteristic
425C22×C13#57611yescharacteristic
426C22×C13#57711yescharacteristic
427C22×C13#57711yescharacteristic
428C2×D13—22no—
429C2×D13—22no—
430C2×D13—22no—
431C2×D13—22no—
432C2×D13—22no—
433C2×D13—22no—
434C2×D13—24no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—816no—
442C2×D13C4×C22⋊C414yes—
443C4×C13—22no—
444C4×C13—22no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13C22×C4211yescharacteristic
449C4×C13C2×#11711yescharacteristic
450C4×C13C2×C4×D411yescharacteristic
451C4×C13C2×C4×D411yescharacteristic
452Dic13—22no—
453Dic13—22no—
454Dic13—42no—
455Dic13—42no—
456Dic13—42no—
457Dic13C4×C22⋊C414yes—
458C25—261no—
459C22×D4—134no—
460C22×D4—134no—
461C22×D4—134no—
462C22×D4—131no—
463C22×D4—262no—
464C22×D4—262no—
465C22×D4—262no—
466C22×D4—261no—
467C22×D4C22×D1311yescharacteristic
468C23×C4—21no—
469C23×C4—131no—
470C23×C4—261no—
471C23×C4—261no—
472C23×C4—261no—
473C23×C4—261no—
474C2×M16—134no—
475C2×M16—262no—
476C2×M16—262no—
477C22×C8—131no—
478C22×C8—131no—
479C22×C8—134no—
480C22×C8—262no—
481C22×C8—262no—
482C22×C8C22×D1311yescharacteristic
483C22×C8C22×D1311yescharacteristic
484C4×D4—22no—
485C4×D4—134no—
486C4×D4—134no—
487C4×D4—134no—
488C4×D4—262no—
489C4×D4—262no—
490C4×D4—268no—
491C4×D4—268no—
492C4×D4—262no—
493C4×D4C4×D1314yescomplemented
494#117—134no—
495#117—134no—
496#117—134no—
497#117—134no—
498#117—262no—
499#117—262no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4C22×D1311yescharacteristic
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—131no—
513C2×C22⋊C4—131no—
514C2×C22⋊C4—268no—
515C2×C22⋊C4—268no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C42—21no—
522C2×C42—131no—
523C2×C42—261no—
524C2×C42—261no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42—261no—
528C2×C42C22×D1311yescharacteristic
529#102—134no—
530#102—134no—
531#102—134no—
532#102—134no—
533#102—134no—
534#102—134no—
535#102C4×D1314yescomplemented
536#102C4×D1314yescomplemented
537#97—22no—
538#97—262no—
539C4×C8—262no—
540C4×C8—262no—
541#95—21no—
542#95—261no—
543#95—261no—
544#95—261no—
545C2×C13—44no—
546C2×C13C2×C4×C22⋊C411yescharacteristic
547C2×C13#289711yescharacteristic
548C2×C13#289711yescharacteristic
549C2×C13#294611yescharacteristic
550C2×C13#294611yescharacteristic
551C2×C13#294811yescharacteristic
552C2×C13#294911yescharacteristic
553D13—24no—
554D13—44no—
555C24—21no—
556C24—131no—
557C24—264no—
558C24—264no—
559C24—264no—
560C24—261no—
561C24—1041no—
562C24—1041no—
563C24—1041no—
564C24—1041no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—1316no—
569C2×D4—132no—
570C2×D4—132no—
571C2×D4—132no—
572C2×D4—268no—
573C2×D4—268no—
574C2×D4—268no—
575C2×D4—264no—
576C2×D4—264no—
577C2×D4—264no—
578C2×D4—261no—
579C2×D4—261no—
580C2×D4—261no—
581C2×D4C2×C4×D1312yes—
582C2×D4C2×C4×D1312yes—
583C2×D4C2×C4×D1312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—131no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—131no—
598C22×C4—131no—
599C22×C4—264no—
600C22×C4—264no—
601C22×C4—264no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—264no—
606C22×C4—1041no—
607C22×C4—1041no—
608C22×C4—1041no—
609C22×C4—1041no—
610C22×C4—1041no—
611C22×C4—1041no—
612C22×C4—1041no—
613C22×C4—1041no—
614C22×C4D4×D1311yescharacteristic
615C22×C4D4×D1311yescharacteristic
616C22×C4C23×D1311yescharacteristic
617M16—268no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—132no—
623C2×C8—132no—
624C2×C8—268no—
625C2×C8—261no—
626C2×C8—261no—
627C2×C8—261no—
628C2×C8—261no—
629C2×C8C2×C4×D1312yes—
630C2×C8C2×C4×D1312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—134no—
635C4⋊C4—134no—
636C4⋊C4—132no—
637C4⋊C4—132no—
638C4⋊C4—132no—
639C4⋊C4—264no—
640C4⋊C4—261no—
641C4⋊C4—261no—
642C4⋊C4—261no—
643C4⋊C4C2×C4×D1312yes—
644C4⋊C4C2×C4×D1312yes—
645C4⋊C4C2×C4×D1312yes—
646C22⋊C4—24no—
647C22⋊C4—134no—
648C22⋊C4—134no—
649C22⋊C4—264no—
650C22⋊C4—264no—
651C22⋊C4—264no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C42—81no—
655C42—132no—
656C42—132no—
657C42—264no—
658C42—264no—
659C42—1041no—
660C42—1041no—
661C42—1041no—
662C42C2×C4×D1312yes—
663C42D4×D1312yes—
664C13#2041611yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—132no—
673C23—132no—
674C23—132no—
675C23—2616no—
676C23—261no—
677C23—261no—
678C23—261no—
679C23—261no—
680C23—262no—
681C23—262no—
682C23—262no—
683C23—521no—
684C23—521no—
685C23—521no—
686C23—521no—
687C23—1044no—
688C23—1044no—
689C23—1044no—
690C23—1044no—
691C23—1044no—
692C23—1044no—
693C23C2×D4×D1311yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—134no—
698D4—2616no—
699D4—262no—
700D4—262no—
701D4—262no—
702D4C42×D1314yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—132no—
718C2×C4—132no—
719C2×C4—132no—
720C2×C4—134no—
721C2×C4—134no—
722C2×C4—134no—
723C2×C4—134no—
724C2×C4—132no—
725C2×C4—132no—
726C2×C4—261no—
727C2×C4—261no—
728C2×C4—261no—
729C2×C4—261no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—521no—
739C2×C4—1044no—
740C2×C4—1044no—
741C2×C4—1044no—
742C2×C4—1044no—
743C2×C4C22⋊C4×D1312yes—
744C2×C4C22⋊C4×D1312yes—
745C2×C4C22×C4×D1311yescharacteristic
746C2×C4C22×C4×D1311yescharacteristic
747C2×C4C22×C4×D1311yescharacteristic
748C2×C4C2×D4×D1311yescharacteristic
749C2×C4#41×D1311yescharacteristic
750C2×C4#41×D1311yescharacteristic
751C8—22no—
752C8—22no—
753C8—262no—
754C8—262no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—134no—
763C22—262no—
764C22—262no—
765C22—262no—
766C22—262no—
767C22—262no—
768C22—262no—
769C22—264no—
770C22—522no—
771C22—522no—
772C22—522no—
773C22—522no—
774C22—522no—
775C22—522no—
776C22—10416no—
777C22C2×C22⋊C4×D1311yescharacteristic
778C22C4×D4×D1311yescharacteristic
779C22C4×D4×D1311yescharacteristic
780C22#1171947911yescharacteristic
781C22#1171947911yescharacteristic
782C22#1171948011yescharacteristic
783C22#1171948311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—134no—
790C4—262no—
791C4—262no—
792C4—522no—
793C4—522no—
794C4—522no—
795C4C2×C42×D1311yescharacteristic
796C4D13×#11711yescharacteristic
797C4C4×D4×D1311yescharacteristic
798C4C4×D4×D1311yescharacteristic
799C2—44no—
800C2—264no—
801C2—524no—
802C2C4×C22⋊C4×D1311yescharacteristic
803C2#1312336011yescharacteristic
804C2#1312336111yescharacteristic
805C2#1312366511yescharacteristic
806C2#1312366711yescharacteristic
807C2#1312368511yescharacteristic
808C2#1312369211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1762C2
socleC23×C13C22×D4
prime radicalC22×D4×D13C22
cosocleC22×C4×C13C24
hypercenter#1762D13
hypocenterC13#20416
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. C2×#11718369C2semidirect
5. #13117190C2semidirect
6. #13114663C2semidirect
7. #13114662C2semidirect
8. #13114660C2semidirect
9. C4×#88049C2semidirect
10. #102×Dic13C2semidirect
11. C4×#88072C2semidirect
12. #13114650C2semidirect
13. #13114554C2semidirect
14. #13114551C2semidirect
15. C13×#1762C2semidirect
24. #11719250C4semidirect
35. C2×C13×#97C22semidirect
36. C4×C13×C4⋊C4C22semidirect
41. C2×#88055C22semidirect
42. C2×C8×Dic13C22semidirect
43. C4⋊C4×Dic13C22semidirect
44. C4⋊C4×Dic13C22semidirect
48. C4×C4⋊Dic13C22semidirect
50. C2×C4×#1055C22semidirect
51. #11718431C4semidirect
52. D13×#102C4semidirect
56. C13×#340C22semidirect
57. C13×#340C22semidirect
58. #11718143C22semidirect
59. #11718143C22semidirect
60. #11718121C22semidirect
61. #11718121C22semidirect
62. #11718121C22semidirect
63. #11718121C22semidirect
83. C4×D4×C13C2×C4semidirect
92. D4×Dic13C2×C4semidirect
117. C2×#6094C2×C4semidirect
120. C2×C8×D13C2×C4semidirect
122. #88147C2×C4semidirect
126. #88146C2×C4semidirect
128. C4⋊C4×D13C2×C4semidirect
132. C4×D52C2×C4semidirect
135. C13×#102C2×C4semidirect
136. C13×#102C2×C4semidirect
139. #88072C2×C4semidirect
140. #88072C2×C4semidirect
144. #88061C2×C4semidirect
145. #88061C2×C4semidirect
148. #88049C2×C4semidirect
149. #88049C2×C4semidirect
192. D4×D13C42semidirect
269. #1762D13semidirect
395. C2×#97C2×D13semidirect
403. C4×C4⋊C4C2×D13semidirect
412. #340C2×D13semidirect
413. #340C2×D13semidirect
493. C4×D4C4×D13semidirect
535. #102C4×D13semidirect
536. #102C4×D13semidirect
664. C13#20416semidirect

Maximal subgroups

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

subgroupindex
C2×#117192502
C2×#117184312
C2×D13×#1022
C2×#117183692
#131171902
#131146632
#131146622
#131146602
C4×#880492
#102×Dic132
C4×#880722
#131146502
#131145542
#131145512
C13×#17622
#2041613