Finite Group Databasebeta

← #261×#440 #16797409

Subgroups — #261×#440 #16797409

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719106C211yesmaximal, characteristic
2C2×SD16×#261C211yesmaximal, characteristic
3C4×Q8×#261C211yesmaximal, characteristic, complemented
4C4×D4×#261C211yesmaximal, characteristic
5#13130651C211yesmaximal, characteristic, complemented
6#13130650C211yesmaximal, characteristic, complemented
7#107×#261C211yesmaximal, characteristic, complemented
8#13130609C211yesmaximal, characteristic, complemented
9#13130608C211yesmaximal, characteristic, complemented
10#13130607C211yesmaximal, characteristic
11#13130606C211yesmaximal, characteristic
12#103×#261C211yesmaximal, characteristic, complemented
13#102×#261C211yesmaximal, characteristic
14#97×#261C211yesmaximal, characteristic, complemented
15D13×#440C211yesmaximal, characteristic
16C2×Q8×#261C2211yescharacteristic
17C2×Q8×#261C2211yescharacteristic
18C2×D4×#261C2211yescharacteristic
19C2×D4×#261C2211yescharacteristic
20C22×C4×#261—21no—
21C2×SD16×D13C2211yescharacteristic
22C4×Q8×D13C2211yescharacteristic
23C4×D4×D13C2211yescharacteristic
24C2×#88117C2211yescharacteristic
25C2×#88117C2211yescharacteristic
26C2×#88115C2211yescharacteristic
27C2×#88115C2211yescharacteristic
28C4×C22⋊#261—21no—
29#11719106C418yescomplemented
30SD16×#261C418yescomplemented
31C2×#88102C2211yescharacteristic
32C2×#88101C2211yescharacteristic
33C2×#88100C2211yescharacteristic
34C2×#88100C2211yescharacteristic
35C2×C8×#261C2211yescharacteristic
36C2×C8×#261C2211yescharacteristic
37C4⋊C4×#261—21no—
38C4⋊C4×#261—21no—
39C4⋊C4×#261C2211yescharacteristic
40C4⋊C4×#261C2211yescharacteristic
41C4⋊C4×#261C2211yescharacteristic
42C4⋊C4×#261C2211yescharacteristic
43C22⋊C4×#261—21no—
44C22⋊C4×#261—21no—
45C4×C4⋊#261—21no—
46C4×C4⋊#261C2211yescharacteristic
47C4×C4⋊#261C2211yescharacteristic
48C42×#261—21no—
49C42×#261C2211yescharacteristic
50#11719047C2211yescharacteristic
51C13×#440C411yescharacteristic, complemented
52#11718825C411yescharacteristic, complemented
53#11718687C411yescharacteristic, complemented
54#11718679C411yescharacteristic, complemented
55#11718550C411yescharacteristic, complemented
56D13×#107C2211yescharacteristic
57#11718478C411yescharacteristic, complemented
58D13×#103C2211yescharacteristic
59D13×#102C2211yescharacteristic
60#11718418C411yescharacteristic, complemented
61#11718371C411yescharacteristic, complemented
62D13×#97C2211yescharacteristic
63#11718265C2211yescharacteristic
64#11718265C2211yescharacteristic
65#11718246C2211yescharacteristic
66#11718246C2211yescharacteristic
67#11718246C2211yescharacteristic
68#11718246C2211yescharacteristic
69C23×#261—21no—
70C23×#261—21no—
71C2×Q8×D13C2311yescharacteristic
72C2×D4×D13C2311yescharacteristic
73C22×C4×D13—21no—
74C2×C22⋊#261—21no—
75C2×C22⋊#261—21no—
76Q8×#261—22no—
77Q8×#261—22no—
78Q8×#261C2×C414yescomplemented
79Q8×#261C2×C414yescomplemented
80D4×#261—22no—
81D4×#261—22no—
82D4×#261C2×C414yes—
83D4×#261C2×C414yes—
84C2×C4⋊#261—21no—
85C2×C4⋊#261—21no—
86C2×C4⋊#261C2311yescharacteristic
87C2×C4⋊#261C2311yescharacteristic
88C2×C4⋊#261C2311yescharacteristic
89C2×C4⋊#261C2311yescharacteristic
90C2×C4×#261—21no—
91C2×C4×#261—21no—
92C2×C4×#261—21no—
93C2×C4×#261—21no—
94C2×C4×#261—21no—
95C2×C4×#261—21no—
96C2×C4×#261—21no—
97C2×C4×#261—21no—
98C2×C4×#261—44no—
99C2×C4×#261D411yescharacteristic
100C2×C4×#261D411yescharacteristic
101C2×C4×#261D411yescharacteristic
102C2×C4×#261D411yescharacteristic
103C2×C4×#261C2311yescharacteristic
104C2×C4×#261C2311yescharacteristic
105C2×D13⋊C8C2311yescharacteristic
106C2×D13⋊C8C2311yescharacteristic
107C2×C13×SD16C2×C411yescharacteristic
108C4×Q8×C13C2×C411yescharacteristic, complemented
109C4×D4×C13C2×C411yescharacteristic
110Q8×Dic13C2×C411yescharacteristic, complemented
111C2×#6106C2×C411yescharacteristic
112D4×Dic13C2×C411yescharacteristic
113C2×#6105C2×C411yescharacteristic
114C4×C22⋊D13—21no—
115SD16×D13C2×C414yes—
116SD16×D13C2×C414yes—
117C2×#6095C2×C411yescharacteristic
118C2×C8×D13C2311yescharacteristic
119C2×C8×D13C2311yescharacteristic
120#88147C2×C411yescharacteristic
121C4⋊C4×D13—21no—
122C4⋊C4×D13C2311yescharacteristic
123C4⋊C4×D13C2311yescharacteristic
124#88141—21no—
125#88141C2×C411yescharacteristic, complemented
126#88135—21no—
127C22⋊C4×D13—21no—
128C4×D52C2×C411yescharacteristic
129C42×D13—21no—
130C42×D13C2311yescharacteristic
131C4×Dic26—21no—
132C4×Dic26C2×C411yescharacteristic, complemented
133#88117C2×C414yescomplemented
134#88117C2×C414yescomplemented
135#88115C2×C414yes—
136#88115C2×C414yes—
137(C2×#261)⋊C4—21no—
138(C2×#261)⋊C4—21no—
139(C2×#261)⋊C4—21no—
140(C2×#261)⋊C4—21no—
141(C2×#261)⋊C4—21no—
142(C2×#261)⋊C4—21no—
143#88110—21no—
144#88110—21no—
145#88102C2×C414yescomplemented
146#88101C2×C414yescomplemented
147#88100—22no—
148#88100C2×C414yescomplemented
149C8×#261—22no—
150C8×#261C2×C414yescomplemented
151C13×#107C2×C411yescharacteristic, complemented
152C13×#103C2×C411yescharacteristic, complemented
153C13×#102C2×C411yescharacteristic
154C13×#97C2×C411yescharacteristic, complemented
155#88075C2×C411yescharacteristic, complemented
156#88072C2×C411yescharacteristic
157#88061C2×C411yescharacteristic
158#88058C2×C411yescharacteristic, complemented
159#88056C2×C411yescharacteristic, complemented
160#88055C2×C411yescharacteristic, complemented
161#88055C2×C411yescharacteristic, complemented
162#88050C2×C411yescharacteristic, complemented
163#88049C2×C411yescharacteristic
164#88047C2×C411yescharacteristic, complemented
165#88047C2×C411yescharacteristic, complemented
166#88043C2×C411yescharacteristic, complemented
167C4×#440—131nomaximal, Sylow
168C23×D13—21no—
169C22×#261—21no—
170C22×#261—21no—
171C22×#261—21no—
172C22×#261—21no—
173C22×#261—24no—
174C22×#261—24no—
175C22×#261—42no—
176C22×#261—42no—
177C22×#261—42no—
178C22×#261—42no—
179C22×#261C2×D411yescharacteristic
180C22×#261C2×D411yescharacteristic
181C22×#261C2×D411yescharacteristic
182C22×#261C2×D411yescharacteristic
183C2×Q8×C13C22×C411yescharacteristic
184C2×D4×C13C22×C411yescharacteristic
185C22×C4×C13—21no—
186C2×C22⋊D13—21no—
187C22×Dic13—21no—
188Q8×D13—21no—
189Q8×D13—21no—
190Q8×D13C22×C412yes—
191Q8×D13C22×C412yes—
192D4×D13—21no—
193D4×D13—21no—
194D4×D13C22×C412yes—
195D4×D13C22×C412yes—
196C2×D52C22×C411yescharacteristic
197C2×C4×D13—21no—
198C2×C4×D13—21no—
199C2×C4×D13—21no—
200C2×C4×D13—21no—
201C2×C4×D13—21no—
202C2×C4×D13—42no—
203C2×C4×D13—42no—
204C2×C4×D13C2×D411yescharacteristic
205C2×C4×D13C2×D411yescharacteristic
206C2×C4×D13C2411yescharacteristic
207C2×Dic26—21no—
208C2×Dic26C22×C411yescharacteristic
209C22⋊#261—24no—
210C22⋊#261—24no—
211C2×#1057—21no—
212C2×#1057—21no—
213C4⋊#261—24no—
214C4⋊#261—24no—
215C4⋊#261—21no—
216C4⋊#261—21no—
217C4⋊#261—21no—
218C4⋊#261—21no—
219C4⋊#261C22×C412yes—
220C4⋊#261C22×C412yes—
221C4⋊#261C22×C412yes—
222C4⋊#261C22×C412yes—
223C4×#261—24no—
224C4×#261—24no—
225C4×#261—22no—
226C4×#261—22no—
227C4×#261—41no—
228C4×#261—41no—
229C4×#261—42no—
230C4×#261—42no—
231C4×#261—42no—
232C4×#261—42no—
233C4×#261—42no—
234C4×#261—42no—
235C4×#261C22×C412yes—
236C4×#261C22×C412yes—
237C4×#261#4112yes—
238C4×#261#4112yes—
239D13⋊C8—21no—
240D13⋊C8—21no—
241D13⋊C8C22×C412yes—
242D13⋊C8C22×C412yes—
243C13×SD16C4214yescomplemented
244C2×C8×C13C22×C411yescharacteristic
245C2×C8×C13C22×C411yescharacteristic
246C13×C4⋊C4—21no—
247C13×C4⋊C4C22×C411yescharacteristic
248C13×C4⋊C4C22×C411yescharacteristic
249C13×C22⋊C4—21no—
250C42×C13—21no—
251C42×C13C22×C411yescharacteristic
252C22⋊Dic13—21no—
253#6106C4214yescomplemented
254#6105C4214yescomplemented
255#6103—21no—
256#6103—21no—
257C4⋊Dic13—21no—
258C4⋊Dic13C22×C411yescharacteristic
259C4⋊Dic13C22×C411yescharacteristic
260#6101—21no—
261#6101—21no—
262#6101—21no—
263#6101—21no—
264C4×Dic13—21no—
265C4×Dic13—21no—
266C4×Dic13—21no—
267C4×Dic13C22×C411yescharacteristic
268C4×Dic13#4111yescharacteristic
269C4×Dic13#4111yescharacteristic
270C2×#1055C22×C411yescharacteristic
271C2×#1055C22×C411yescharacteristic
272#6095C4214yescomplemented
273C8×D13—21no—
274C8×D13—21no—
275C8×D13C22×C412yes—
276C8×D13C22×C412yes—
277C2×#440—131no—
278C2×#440—131no—
279C2×C4×SD16—131no—
280C42×Q8—131no—
281C42×D4—131no—
282#1776—131no—
283#1776—131no—
284C4×#107—131no—
285#1763—131no—
286#1763—131no—
287#1762—131no—
288#1762—131no—
289C4×#103—131no—
290C4×#102—131no—
291C4×#97—131no—
292C23×C13—21no—
293C22×D13—21no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—41no—
297C22×D13—41no—
298C22×D13—41no—
299C22×D13—41no—
300C22×D13C22×D411yescharacteristic
301C2×#261—21no—
302C2×#261—21no—
303C2×#261—21no—
304C2×#261—21no—
305C2×#261—21no—
306C2×#261—21no—
307C2×#261—22no—
308C2×#261—22no—
309C2×#261—22no—
310C2×#261—22no—
311C2×#261—48no—
312C2×#261—41no—
313C2×#261—41no—
314C2×#261—41no—
315C2×#261—41no—
316C2×#261—41no—
317C2×#261—41no—
318C2×#261—41no—
319C2×#261—41no—
320C2×#261—48no—
321C2×#261C4×D412yes—
322C2×#261C4×D412yes—
323C2×#261C4×D412yes—
324C2×#261C4×D412yes—
325C2×#261AGL(1,ℤ/8)12yes—
326C2×#261#13712yes—
327Q8×C13—21no—
328Q8×C13C2×C4212yescomplemented
329D4×C13—21no—
330D4×C13C2×C4212yes—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—42no—
335C2×C4×C13C4×D411yescharacteristic
336C2×C4×C13C4×D411yescharacteristic
337C2×C4×C13C23×C411yescharacteristic
338C22⋊D13—22no—
339C22⋊D13—22no—
340C2×Dic13—21no—
341C2×Dic13—21no—
342C2×Dic13—21no—
343C2×Dic13—42no—
344C2×Dic13C4×D411yescharacteristic
345C2×Dic13C4×D411yescharacteristic
346C2×Dic13C2×#4111yescharacteristic
347D52—21no—
348D52C2×C4212yes—
349C4×D13—22no—
350C4×D13—22no—
351C4×D13—21no—
352C4×D13—21no—
353C4×D13—21no—
354C4×D13—21no—
355C4×D13—42no—
356C4×D13—42no—
357C4×D13—41no—
358C4×D13—41no—
359C4×D13—41no—
360C4×D13—41no—
361C4×D13C23×C411yescharacteristic
362C4×D13C23×C411yescharacteristic
363C4×D13C2×#4111yescharacteristic
364C4×D13C2×#4111yescharacteristic
365Dic26—21no—
366Dic26—22no—
367Dic26—22no—
368Dic26C2×C4212yescomplemented
369#1057—22no—
370#1057—22no—
371C8×C13—21no—
372C8×C13C2×C4212yescomplemented
373#1055—21no—
374#1055C2×C4212yescomplemented
375C22×SD16—131no—
376C2×C4×Q8—131no—
377C2×C4×Q8—131no—
378C2×C4×Q8—131no—
379C2×C4×D4—131no—
380C2×C4×D4—131no—
381C2×C4×D4—131no—
382C22×C42—261no—
383#440—138no—
384#440—131no—
385#440—131no—
386#440—131no—
387#440—131no—
388#440—131no—
389#440—131no—
390#440—131no—
391#440#26111yescharacteristic, direct product factor
392C4×SD16—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#106—131no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#103—131no—
399C2×#102—131no—
400C2×#102—131no—
401C2×#102—131no—
402C2×#97—131no—
403C2×#97—131no—
404C2×#97—131no—
405C2×#97—131no—
406C2×C4×C8—131no—
407C2×C4×C8—131no—
408C4×C4⋊C4—131no—
409C4×C4⋊C4—131no—
410C4×C4⋊C4—131no—
411C4×C4⋊C4—131no—
412C4×C4⋊C4—131no—
413C4×C4⋊C4—131no—
414C4×C4⋊C4—261no—
415C4×C4⋊C4—261no—
416C4×C4⋊C4—261no—
417C4×C22⋊C4—261no—
418C4×C22⋊C4—261no—
419C4×C22⋊C4—261no—
420C43—131no—
421C43—261no—
422#340—131no—
423#340—131no—
424#340—131no—
425#340—131no—
426#340—131no—
427#340—131no—
428C22×C13—22no—
429C22×C13—41no—
430C22×C13—41no—
431C22×C13C2×C4×D411yescharacteristic
432C2×D13—22no—
433C2×D13—41no—
434C2×D13—41no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13C2×C4×D411yescharacteristic
440C2×D13C2×C4×D411yescharacteristic
441C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
442C2×D13C2×#13711yescharacteristic
443C2×D13#57511yescharacteristic
444C2×D13#57511yescharacteristic
445#261—22no—
446#261—22no—
447#261—22no—
448#261—42no—
449#261—42no—
450#261—42no—
451#261—42no—
452#261#44014yesdirect product factor
453C4×C13—21no—
454C4×C13—21no—
455C4×C13—22no—
456C4×C13—41no—
457C4×C13—41no—
458C4×C13C22×C4211yescharacteristic
459C4×C13C4×#4111yescharacteristic
460Dic13—21no—
461Dic13—21no—
462Dic13—22no—
463Dic13—41no—
464Dic13—41no—
465Dic13C4×#4111yescharacteristic
466Dic13C4×#4111yescharacteristic
467C22×Q8—131no—
468C22×D4—131no—
469C23×C4—261no—
470C23×C4—261no—
471C23×C4—261no—
472C2×SD16—131no—
473C2×SD16—131no—
474C2×SD16—134no—
475C2×SD16—134no—
476C2×SD16—131no—
477C2×SD16C2×#26111yescharacteristic
478C22×C8—131no—
479C22×C8—131no—
480C22×C8—131no—
481C22×C8—131no—
482C4×Q8—134no—
483C4×Q8—134no—
484C4×Q8—131no—
485C4×Q8—131no—
486C4×Q8—131no—
487C4×Q8—261no—
488C4×Q8—261no—
489C4×Q8—262no—
490C4×Q8—262no—
491C4×Q8C2×#26111yescharacteristic, complemented
492C4×D4—134no—
493C4×D4—134no—
494C4×D4—131no—
495C4×D4—131no—
496C4×D4—131no—
497C4×D4—261no—
498C4×D4—261no—
499C4×D4—262no—
500C4×D4—262no—
501C4×D4C2×#26111yescharacteristic
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
505C2×C4⋊C4—131no—
506C2×C4⋊C4—131no—
507C2×C4⋊C4—131no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C42—131no—
515C2×C42—131no—
516C2×C42—131no—
517C2×C42—131no—
518C2×C42—131no—
519C2×C42—131no—
520C2×C42—131no—
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524C2×C42—261no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42—261no—
528C2×C42—261no—
529C2×C42—261no—
530C2×C42—524no—
531#107—134no—
532#107—131no—
533#107—131no—
534#107—131no—
535#107C2×#26111yescharacteristic, complemented
536#106—134no—
537#103—134no—
538#103—134no—
539#103—131no—
540#103—131no—
541#103—131no—
542#103C2×#26111yescharacteristic, complemented
543#102—134no—
544#102—134no—
545#102—131no—
546#102—131no—
547#102—131no—
548#102C2×#26111yescharacteristic
549#97—134no—
550#97—131no—
551#97—131no—
552#97—131no—
553#97—262no—
554#97—261no—
555#97—261no—
556#97C2×#26111yescharacteristic, complemented
557C4×C8—134no—
558C4×C8—262no—
559#95—261no—
560#95—261no—
561#95—261no—
562#95—261no—
563#95—261no—
564#95—261no—
565C2×C13—42no—
566C2×C13C42×D411yescharacteristic
567C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
568C2×C13C4×#13711yescharacteristic
569D13—42no—
570D13C2×#44011yescharacteristic
571D13#294311yescharacteristic
572D13C4×AGL(1,ℤ/8)11yescharacteristic
573D13C4×#13711yescharacteristic
574C24—261no—
575C2×Q8—132no—
576C2×Q8—132no—
577C2×Q8—131no—
578C2×Q8—261no—
579C2×Q8—261no—
580C2×Q8—261no—
581C2×Q8C22×#26111yescharacteristic
582C2×D4—132no—
583C2×D4—132no—
584C2×D4—131no—
585C2×D4—261no—
586C2×D4—261no—
587C2×D4—261no—
588C2×D4C22×#26111yescharacteristic
589C22×C4—21no—
590C22×C4—131no—
591C22×C4—131no—
592C22×C4—131no—
593C22×C4—131no—
594C22×C4—131no—
595C22×C4—131no—
596C22×C4—131no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—264no—
603C22×C4—264no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—522no—
610C22×C4—522no—
611C22×C4—522no—
612C22×C4—522no—
613C22×C4—522no—
614C22×C4—522no—
615SD16—134no—
616SD16—134no—
617SD16—134no—
618SD16C4×#26114yescomplemented
619C2×C8—131no—
620C2×C8—132no—
621C2×C8—132no—
622C2×C8—132no—
623C2×C8—132no—
624C2×C8—131no—
625C2×C8—261no—
626C2×C8—261no—
627C2×C8—261no—
628C2×C8—261no—
629C2×C8—261no—
630C2×C8—261no—
631C2×C8C22×#26111yescharacteristic
632C2×C8C22×#26111yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—132no—
635C4⋊C4—132no—
636C4⋊C4—132no—
637C4⋊C4—132no—
638C4⋊C4—131no—
639C4⋊C4—131no—
640C4⋊C4—261no—
641C4⋊C4—261no—
642C4⋊C4—261no—
643C4⋊C4—261no—
644C4⋊C4—261no—
645C4⋊C4—261no—
646C4⋊C4—261no—
647C4⋊C4—261no—
648C4⋊C4—264no—
649C4⋊C4—264no—
650C4⋊C4—261no—
651C4⋊C4C22×#26111yescharacteristic
652C4⋊C4C22×#26111yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—261no—
655C22⋊C4—261no—
656C22⋊C4—264no—
657C22⋊C4—264no—
658C22⋊C4—261no—
659C42—21no—
660C42—132no—
661C42—132no—
662C42—132no—
663C42—132no—
664C42—131no—
665C42—131no—
666C42—131no—
667C42—261no—
668C42—261no—
669C42—262no—
670C42—262no—
671C42—264no—
672C42—264no—
673C42—261no—
674C42—522no—
675C42—522no—
676C42—521no—
677C42—521no—
678C42—522no—
679C42—522no—
680C42—522no—
681C42—522no—
682C42C22×#26111yescharacteristic
683C13C4×#44011yescharacteristic, complemented, Sylow
684C23—21no—
685C23—131no—
686C23—262no—
687C23—262no—
688C23—261no—
689C23—521no—
690C23—521no—
691C23—521no—
692C23—521no—
693Q8—21no—
694Q8—132no—
695Q8—262no—
696Q8—262no—
697Q8—261no—
698Q8C2×C4×#26112yescomplemented
699D4—21no—
700D4—132no—
701D4—262no—
702D4—262no—
703D4—261no—
704D4C2×C4×#26112yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—132no—
710C2×C4—132no—
711C2×C4—132no—
712C2×C4—131no—
713C2×C4—131no—
714C2×C4—131no—
715C2×C4—131no—
716C2×C4—131no—
717C2×C4—132no—
718C2×C4—132no—
719C2×C4—132no—
720C2×C4—131no—
721C2×C4—131no—
722C2×C4—261no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—261no—
726C2×C4—261no—
727C2×C4—261no—
728C2×C4—261no—
729C2×C4—261no—
730C2×C4—261no—
731C2×C4—261no—
732C2×C4—261no—
733C2×C4—261no—
734C2×C4—261no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—261no—
740C2×C4—261no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—528no—
748C2×C4—522no—
749C2×C4—528no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4D4×#26111yescharacteristic
759C2×C4D4×#26111yescharacteristic
760C2×C4C23×#26111yescharacteristic
761C8—21no—
762C8—132no—
763C8—262no—
764C8—262no—
765C8—261no—
766C8C2×C4×#26112yescomplemented
767C22—22no—
768C22—41no—
769C22—41no—
770C22—131no—
771C22—131no—
772C22—131no—
773C22—131no—
774C22—131no—
775C22—131no—
776C22—262no—
777C22—522no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—521no—
782C22—521no—
783C22C2×D4×#26111yescharacteristic
784C4—22no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—41no—
789C4—134no—
790C4—131no—
791C4—131no—
792C4—262no—
793C4—262no—
794C4—262no—
795C4—262no—
796C4—261no—
797C4—261no—
798C4—522no—
799C4—522no—
800C4—522no—
801C4—522no—
802C4—521no—
803C4—521no—
804C4C22×C4×#26111yescharacteristic
805C4#41×#26111yescharacteristic
806C2—42no—
807C2—131no—
808C2—131no—
809C2—131no—
810C2—131no—
811C2—522no—
812C2C4×D4×#26111yescharacteristic
813C2AGL(1,ℤ/8)×#26111yescharacteristic
814C2#137×#26111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#440C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#440#261
hypocenterC13C4×#440
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×#261C2semidirect
5. #13130651C2semidirect
6. #13130650C2semidirect
7. #107×#261C2semidirect
8. #13130609C2semidirect
9. #13130608C2semidirect
12. #103×#261C2semidirect
14. #97×#261C2semidirect
29. #11719106C4semidirect
30. SD16×#261C4semidirect
51. C13×#440C4semidirect
52. #11718825C4semidirect
53. #11718687C4semidirect
54. #11718679C4semidirect
55. #11718550C4semidirect
57. #11718478C4semidirect
60. #11718418C4semidirect
61. #11718371C4semidirect
78. Q8×#261C2×C4semidirect
79. Q8×#261C2×C4semidirect
108. C4×Q8×C13C2×C4semidirect
110. Q8×Dic13C2×C4semidirect
125. #88141C2×C4semidirect
132. C4×Dic26C2×C4semidirect
133. #88117C2×C4semidirect
134. #88117C2×C4semidirect
145. #88102C2×C4semidirect
146. #88101C2×C4semidirect
148. #88100C2×C4semidirect
150. C8×#261C2×C4semidirect
151. C13×#107C2×C4semidirect
152. C13×#103C2×C4semidirect
154. C13×#97C2×C4semidirect
155. #88075C2×C4semidirect
158. #88058C2×C4semidirect
159. #88056C2×C4semidirect
160. #88055C2×C4semidirect
161. #88055C2×C4semidirect
162. #88050C2×C4semidirect
164. #88047C2×C4semidirect
165. #88047C2×C4semidirect
166. #88043C2×C4semidirect
243. C13×SD16C42semidirect
253. #6106C42semidirect
254. #6105C42semidirect
272. #6095C42semidirect
328. Q8×C13C2×C42semidirect
368. Dic26C2×C42semidirect
372. C8×C13C2×C42semidirect
374. #1055C2×C42semidirect
391. #440#261direct (N × H)
452. #261#440direct (N × H)
491. C4×Q8C2×#261semidirect
535. #107C2×#261semidirect
542. #103C2×#261semidirect
556. #97C2×#261semidirect
618. SD16C4×#261semidirect
683. C13C4×#440semidirect
698. Q8C2×C4×#261semidirect
766. C8C2×C4×#261semidirect

Maximal subgroups

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

subgroupindex
C2×#117191062
C2×SD16×#2612
C4×Q8×#2612
C4×D4×#2612
#131306512
#131306502
#107×#2612
#131306092
#131306082
#131306072
#131306062
#103×#2612
#102×#2612
#97×#2612
D13×#4402
C4×#44013