Finite Group Databasebeta

← C4×#11718899 #15868534

Subgroups — C4×#11718899 #15868534

Order 3328.

1564 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718899C211yesmaximal, characteristic
2C2×C4×#6106C211yesmaximal, characteristic, complemented
3C2×C4×#6104C211yesmaximal, characteristic, complemented
4C4×#88184C211yesmaximal, characteristic, complemented
5#13115191C211yesmaximal, characteristic, complemented
6#13115184C211yesmaximal, characteristic, complemented
7#13115158C211yesmaximal, characteristic, complemented
8#13115097C211yesmaximal, characteristic, complemented
9#13115090C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic, complemented
11#13114776C211yesmaximal, characteristic, complemented
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14C4×C22⋊#1055C211yesmaximal, characteristic, complemented
15C2×C4×C13×#41C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C4×C13×#41—24no—
18C4×C13×#41—24no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117C2211yescharacteristic
27C22×C42×C13—21no—
28C22×C42×C13C2211yescharacteristic
29C22×#6106C2211yescharacteristic
30C22×#6104C2211yescharacteristic
31C2×#88184C2211yescharacteristic
32C2×C4×C22⋊D13—21no—
33C2×C4×D52C2211yescharacteristic
34#11718899C418yesdirect product factor
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41#11718874—21no—
42#11718873C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45C4×#6106—24no—
46C4×#6104—24no—
47C2×#88049C2211yescharacteristic
48C2×#88049C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51#11718601—21no—
52#11718600C2211yescharacteristic
53C4×#6103—21no—
54C4×C4⋊Dic13C2211yescharacteristic
55#11718589C2211yescharacteristic
56C2×C4×#1055C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718116C2211yescharacteristic
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—22no—
69C2×C13×#41C2×C414yescomplemented
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13—21no—
72C22×D4×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13D411yescharacteristic
77C23×C4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—21no—
80C22×D52C2311yescharacteristic
81C22×C4×D13—21no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13—22no—
85C4×Q8×C13D414yescomplemented
86C4×D4×C13—28no—
87C4×D4×C13—28no—
88C4×D4×C13—22no—
89C4×D4×C13—22no—
90C4×D4×C13—22no—
91C4×D4×C13D414yescomplemented
92C13×#117—28no—
93C13×#117—22no—
94C13×#117—22no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C42×C13—28no—
103C2×C42×C13—21no—
104C2×C42×C13—21no—
105C2×C42×C13—21no—
106C2×C42×C13—22no—
107C2×C42×C13—22no—
108C2×C42×C13D411yescharacteristic
109C2×C42×C13D411yescharacteristic
110C2×C42×C13C2311yescharacteristic
111C2×C42×C13C2311yescharacteristic
112C2×C22⋊Dic13—21no—
113C2×#6106—22no—
114C2×#6106—22no—
115C2×#6106C2×C414yescomplemented
116C2×#6104—22no—
117C2×#6104—22no—
118C2×#6104C2×C414yescomplemented
119#88184—22no—
120#88184C2×C414yescomplemented
121C4×C22⋊D13—44no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×#6101—21no—
130C2×C4×Dic13—21no—
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134C22×#1055C2311yescharacteristic
135C4×D52—22no—
136C4×D52—22no—
137#88075—22no—
138#88075—22no—
139#88075C2×C414yescomplemented
140#88072—22no—
141#88072—22no—
142#88072C2×C414yescomplemented
143#88071—21no—
144#88071—21no—
145#88071—21no—
146C22⋊#1055—22no—
147C22⋊#1055C2×C414yescomplemented
148#88049—22no—
149#88049—22no—
150#88048—22no—
151#88047—22no—
152C4×#1055—22no—
153C4×#1055—22no—
154C4×#449—131nomaximal, Sylow
155C24×C13—21no—
156C24×C13C2×D411yescharacteristic
157C23×D13—21no—
158C13×#41—28no—
159C13×#41—28no—
160C13×#41—28no—
161C13×#41—28no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×Q8×C13C22×C412yes—
166C2×Q8×C13C2×D412yes—
167C2×Q8×C13#4112yes—
168C2×D4×C13—24no—
169C2×D4×C13—24no—
170C2×D4×C13—24no—
171C2×D4×C13—21no—
172C2×D4×C13—21no—
173C2×D4×C13—21no—
174C2×D4×C13C22×C412yes—
175C2×D4×C13C2×D412yes—
176C2×D4×C13#4112yes—
177C22×C4×C13—24no—
178C22×C4×C13—24no—
179C22×C4×C13—21no—
180C22×C4×C13—24no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—24no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—24no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—41no—
195C22×C4×C13—42no—
196C22×C4×C13—42no—
197C22×C4×C13—42no—
198C22×C4×C13—42no—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13#4112yes—
206C22×C4×C13C2411yescharacteristic
207C2×C22⋊D13—24no—
208C2×C22⋊D13—42no—
209C2×C22⋊D13—42no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C2×D52—21no—
214C2×D52—21no—
215C2×D52—21no—
216C2×D52—21no—
217C2×D52—21no—
218C2×D52C22×C412yes—
219C2×C4×D13—42no—
220C2×C4×D13—42no—
221C2×C4×D13—42no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4C2×D412yes—
227C13×C4⋊C4C2×D412yes—
228C13×C22⋊C4—24no—
229C13×C22⋊C4—24no—
230C13×C22⋊C4—24no—
231C42×C13—24no—
232C42×C13—24no—
233C42×C13—22no—
234C42×C13—24no—
235C42×C13—22no—
236C42×C13—21no—
237C42×C13—21no—
238C42×C13C2×D412yes—
239C42×C13C2×D412yes—
240C22⋊Dic13—42no—
241#6106—28no—
242#6104—28no—
243#6103—24no—
244#6103—42no—
245#6103—42no—
246#6103—42no—
247C4⋊Dic13—21no—
248C4⋊Dic13—21no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13C22×C412yes—
253#6101—42no—
254C4×Dic13—42no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055C22×C412yes—
266C2×#1055C22×C412yes—
267C2×C4×#41D1311yescharacteristic, complemented
268C2×#449—131no—
269C2×C4×SD16—131no—
270C2×C4×D8—131no—
271C4×#121—131no—
272#1880—131no—
273#1879—131no—
274#1875—131no—
275#1864—131no—
276#1863—131no—
277#1854—131no—
278#1788—131no—
279C4×#103—131no—
280C4×#102—131no—
281C4×C22⋊C8—131no—
282C23×C13—22no—
283C23×C13—21no—
284C23×C13—22no—
285C23×C13—21no—
286C23×C13—22no—
287C23×C13—21no—
288C23×C13—21no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13C4×D412yes—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—41no—
299C22×D13—41no—
300C22×D13—41no—
301C22×D13—41no—
302C22×D13—41no—
303C22×D13—41no—
304Q8×C13—22no—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13C4×D414yescomplemented
308D4×C13—216no—
309D4×C13—22no—
310D4×C13—22no—
311D4×C13—22no—
312D4×C13C4×D414yescomplemented
313C2×C4×C13—216no—
314C2×C4×C13—22no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—22no—
318C2×C4×C13—21no—
319C2×C4×C13—22no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—21no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—44no—
333C2×C4×C13—48no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—44no—
339C2×C4×C13—48no—
340C2×C4×C13C4×D412yes—
341C2×C4×C13#12012yes—
342C2×C4×C13#12012yes—
343C2×C4×C13#13512yes—
344C2×C4×C13#13512yes—
345C2×C4×C13AGL(1,ℤ/8)12yes—
346C2×C4×C13C23×C411yescharacteristic
347C2×C4×C13C22×D411yescharacteristic
348C2×C4×C13C22×D411yescharacteristic
349C2×C4×C13C2×#4111yescharacteristic
350C2×C4×C13C2×#4111yescharacteristic
351C2×C4×C13C2×#4111yescharacteristic
352C22⋊D13—48no—
353C2×Dic13—22no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13—41no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362D52—22no—
363D52—22no—
364D52—41no—
365D52—41no—
366C4×D13—84no—
367#1055—22no—
368#1055—22no—
369#1055—41no—
370#1055—41no—
371C22×#41C2×D1311yescharacteristic
372C22×SD16—131no—
373C22×D8—131no—
374C2×#121—131no—
375C4×#41—24no—
376C4×#41—24no—
377C2×C4×Q8C2×D1311yescharacteristic
378C2×C4×Q8C2×D1311yescharacteristic
379C2×C4×D4—21no—
380C2×C4×D4—21no—
381C2×C4×D4—131no—
382C2×C4×D4—261no—
383C2×C4×D4C2×D1311yescharacteristic
384C2×C4×D4C2×D1311yescharacteristic
385C2×#117—21no—
386C2×#117C2×D1311yescharacteristic
387C22×C42—21no—
388C22×C42C2×D1311yescharacteristic
389#449—138no—
390C4×SD16—264no—
391C4×D8—264no—
392C2×#107—131no—
393C2×#106—131no—
394C2×#103—131no—
395C2×#103—131no—
396C2×#103—131no—
397C2×#102—131no—
398C2×#102—131no—
399C2×#102—131no—
400C2×#102—131no—
401C2×#102—131no—
402C2×C22⋊C8—131no—
403C2×C22⋊C8—131no—
404C2×C4×C8—131no—
405C2×C4×C8—131no—
406#390—131no—
407#389—131no—
408#388—261no—
409#386—261no—
410#380—131no—
411C4×C4⋊C4—131no—
412C4×C22⋊C4—261no—
413#340—131no—
414#340—131no—
415#340—131no—
416#340—131no—
417#336—131no—
418#336—131no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—22no—
422C22×C13—24no—
423C22×C13—41no—
424C22×C13—42no—
425C22×C13—41no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—41no—
430C22×C13—42no—
431C22×C13—41no—
432C22×C13—42no—
433C22×C13C2×C4×D411yescharacteristic
434C22×C13C2×#12011yescharacteristic
435C22×C13#52511yescharacteristic
436C22×C13C2×#13511yescharacteristic
437C22×C13C2×#13511yescharacteristic
438C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
439C22×C13#57511yescharacteristic
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—81no—
444C2×D13—81no—
445C2×D13—81no—
446C2×D13—81no—
447C4×C13—22no—
448C4×C13—22no—
449C4×C13—22no—
450C4×C13—24no—
451C4×C13—41no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13#44914yescomplemented
455C4×C13C2×C4×D411yescharacteristic
456C4×C13C2×C4×D411yescharacteristic
457C4×C13#52511yescharacteristic
458C4×C13#52511yescharacteristic
459Dic13—42no—
460Dic13—81no—
461Dic13—81no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41C4×D1314yescomplemented
468C22×Q8C22×D1311yescharacteristic
469C22×D4—21no—
470C22×D4—131no—
471C22×D4—261no—
472C22×D4C22×D1311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—261no—
477C23×C4C22⋊D1311yescharacteristic
478C23×C4C22⋊D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C2×SD16—134no—
481C2×SD16—262no—
482C2×SD16—262no—
483C2×D8—134no—
484C2×D8—262no—
485C2×D8—262no—
486C22×C8—131no—
487C22×C8—131no—
488C22×C8—131no—
489C22×C8—131no—
490#121—134no—
491#121—262no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8C22⋊D1314yescomplemented
496C4×D4—28no—
497C4×D4—28no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—262no—
502C4×D4—262no—
503C4×D4—524no—
504C4×D4C22⋊D1314yescomplemented
505#117—28no—
506#117—22no—
507#117—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—131no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—131no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4—261no—
524C2×C42—28no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—261no—
531C2×C42C22⋊D1311yescharacteristic
532C2×C42C22⋊D1311yescharacteristic
533C2×C42C22×D1311yescharacteristic
534C2×C42C22×D1311yescharacteristic
535#107—262no—
536#106—262no—
537#103—134no—
538#103—262no—
539#103—262no—
540#102—134no—
541#102—262no—
542#102—262no—
543#102—262no—
544#102—262no—
545C22⋊C8—134no—
546C22⋊C8—262no—
547C4×C8—262no—
548C4×C8—262no—
549#95—261no—
550#95—261no—
551#95—261no—
552C2×C13—42no—
553C2×C13—44no—
554C2×C13C4×#12011yescharacteristic
555C2×C13C4×#13511yescharacteristic
556C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
557C2×C13C2×#44911yescharacteristic
558C2×C13#300211yescharacteristic
559C2×C13#310211yescharacteristic
560C2×C13#310611yescharacteristic
561D13—82no—
562C24—21no—
563C24—261no—
564C24C2×C22⋊D1311yescharacteristic
565#41—28no—
566#41—28no—
567#41—28no—
568#41—28no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C2×C4×D1312yes—
573C2×Q8#612712yes—
574C2×Q8C2×C22⋊D1312yes—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—132no—
582C2×D4—264no—
583C2×D4—261no—
584C2×D4—261no—
585C2×D4—261no—
586C2×D4—261no—
587C2×D4—261no—
588C2×D4—522no—
589C2×D4—522no—
590C2×D4C2×C4×D1312yes—
591C2×D4#612712yes—
592C2×D4C2×C22⋊D1312yes—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—522no—
619C22×C4—522no—
620C22×C4—522no—
621C22×C4C2×C4×D1312yes—
622C22×C4#612712yes—
623C22×C4C2×C22⋊D1311yescharacteristic
624C22×C4C2×C22⋊D1311yescharacteristic
625C22×C4C2×C22⋊D1311yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C22×C4C2×C22⋊D1311yescharacteristic
628C22×C4C23×D1311yescharacteristic
629SD16—268no—
630D8—268no—
631C2×C8—132no—
632C2×C8—132no—
633C2×C8—261no—
634C2×C8—261no—
635C2×C8—261no—
636C2×C8—261no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—132no—
648C4⋊C4—261no—
649C4⋊C4—261no—
650C4⋊C4—261no—
651C4⋊C4—261no—
652C4⋊C4—261no—
653C4⋊C4—522no—
654C4⋊C4C2×C22⋊D1312yes—
655C4⋊C4C2×C22⋊D1312yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—264no—
660C22⋊C4—522no—
661C22⋊C4—522no—
662C22⋊C4—522no—
663C22⋊C4—522no—
664C42—24no—
665C42—24no—
666C42—22no—
667C42—24no—
668C42—22no—
669C42—21no—
670C42—21no—
671C42—522no—
672C42C2×C22⋊D1312yes—
673C42C2×C22⋊D1312yes—
674C13C4×#44911yescharacteristic, complemented, Sylow
675C23—22no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—262no—
689C23—521no—
690C23—521no—
691C23—521no—
692C23—521no—
693C23—521no—
694C23—521no—
695C23C4×C22⋊D1312yes—
696C23C22×C22⋊D1311yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8C4×C22⋊D1314yescomplemented
701D4—216no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—262no—
706D4—262no—
707D4—528no—
708D4—521no—
709D4—521no—
710D4C4×C22⋊D1314yescomplemented
711C2×C4—216no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—44no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—262no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—521no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—1044no—
748C2×C4C4×C22⋊D1312yes—
749C2×C4#8820312yes—
750C2×C4#8820412yes—
751C2×C4#8820412yes—
752C2×C4#8820712yes—
753C2×C4#8820712yes—
754C2×C4C22×C4×D1311yescharacteristic
755C2×C4C2×#612711yescharacteristic
756C2×C4C2×#612711yescharacteristic
757C2×C4C2×#612711yescharacteristic
758C2×C4C22×C22⋊D1311yescharacteristic
759C2×C4C22×C22⋊D1311yescharacteristic
760C8—262no—
761C8—262no—
762C8—521no—
763C8—521no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—24no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—1041no—
782C22—1041no—
783C22—1041no—
784C22—1041no—
785C22C2×C4×C22⋊D1311yescharacteristic
786C22#1171949611yescharacteristic
787C22C2×#8820311yescharacteristic
788C22C2×#8820411yescharacteristic
789C22C2×#8820411yescharacteristic
790C22#1171952711yescharacteristic
791C22C2×#8820711yescharacteristic
792C4—22no—
793C4—24no—
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—42no—
799C4—522no—
800C4—1041no—
801C4—1041no—
802C4#1171889914yesdirect product factor
803C4C2×C4×C22⋊D1311yescharacteristic
804C4C2×C4×C22⋊D1311yescharacteristic
805C4#1171949611yescharacteristic
806C4#1171949611yescharacteristic
807C2—42no—
808C2—44no—
809C2—1042no—
810C2C4×#8820711yescharacteristic
811C2C4×#8820411yescharacteristic
812C2C4×#8820311yescharacteristic
813C2C2×#1171889911yescharacteristic
814C2#1312405411yescharacteristic
815C2#1312485411yescharacteristic
816C2#1312489611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C4×C13×#41C2
socleC23×C13C22×D4
prime radicalC2×#11718899C2
cosocleC22×C4×C13C24
hypercenterC2×C4×#41D13
hypocenterC13C4×#449
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6106C2semidirect
3. C2×C4×#6104C2semidirect
4. C4×#88184C2semidirect
5. #13115191C2semidirect
6. #13115184C2semidirect
7. #13115158C2semidirect
8. #13115097C2semidirect
9. #13115090C2semidirect
10. #13115035C2semidirect
11. #13114776C2semidirect
12. C4×#88075C2semidirect
13. C4×#88072C2semidirect
14. C4×C22⋊#1055C2semidirect
15. C2×C4×C13×#41C2semidirect
34. #11718899C4direct (N × H)
69. C2×C13×#41C2×C4semidirect
85. C4×Q8×C13D4semidirect
91. C4×D4×C13D4semidirect
115. C2×#6106C2×C4semidirect
118. C2×#6104C2×C4semidirect
120. #88184C2×C4semidirect
139. #88075C2×C4semidirect
142. #88072C2×C4semidirect
147. C22⋊#1055C2×C4semidirect
267. C2×C4×#41D13semidirect
307. Q8×C13C4×D4semidirect
312. D4×C13C4×D4semidirect
454. C4×C13#449semidirect
467. C2×#41C4×D13semidirect
495. C4×Q8C22⋊D13semidirect
504. C4×D4C22⋊D13semidirect
674. C13C4×#449semidirect
700. Q8C4×C22⋊D13semidirect
710. D4C4×C22⋊D13semidirect
802. C4#11718899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117188992
C2×C4×#61062
C2×C4×#61042
C4×#881842
#131151912
#131151842
#131151582
#131150972
#131150902
#131150352
#131147762
C4×#880752
C4×#880722
C4×C22⋊#10552
C2×C4×C13×#412
C4×#44913