Finite Group Databasebeta

← #354447

Subgroups — #354447

Order 512.

1682 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#520C211yesmaximal, characteristic
2C2×#1860C211yesmaximal, characteristic
3C2×#1859C211yesmaximal, characteristic
4C4×#428C211yesmaximal, characteristic, complemented
5C4×#417C211yesmaximal, characteristic
6C2×#1759C211yesmaximal, characteristic
7#13779C211yesmaximal, characteristic, complemented
8#10899C211yesmaximal, characteristic, complemented
9#10899C211yesmaximal, characteristic, complemented
10#10892C211yesmaximal, characteristic, complemented
11#10891C211yesmaximal, characteristic, complemented
12#10781C211yesmaximal, characteristic
13#10781C211yesmaximal, characteristic
14C4×#343C211yesmaximal, characteristic, complemented
15#10701C211yesmaximal, characteristic, complemented
16C2×#520C2211yescharacteristic
17C2×#520C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#428C2211yescharacteristic
20C2×#428C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C2×#417C2211yescharacteristic
24C2×#417C2211yescharacteristic
25C2×C4×M16C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27C2×#384C2211yescharacteristic
28C2×#382C2211yescharacteristic
29#2276—21no—
30#2275—22no—
31#2275—21no—
32#2274—21no—
33#2274—21no—
34#2274C2211yescharacteristic
35#2274C2211yescharacteristic
36C42×Q8—21no—
37C42×D4—22no—
38C42×D4—21no—
39C4×#117—21no—
40C4×#117C2211yescharacteristic
41C2×C4×C4⋊C4—21no—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×#376C2211yescharacteristic
45#1860C418yescomplemented
46#1859C418yescomplemented
47#1776—21no—
48#1776—21no—
49C4×#107—21no—
50C4×#106—21no—
51#1763—21no—
52#1762—21no—
53C4×#103—21no—
54C4×#102—21no—
55#1759C418yescomplemented
56C2×#343C2211yescharacteristic
57C2×#343C2211yescharacteristic
58C2×#343C2211yescharacteristic
59C2×#343C2211yescharacteristic
60#1736C2211yescharacteristic
61#1736C2211yescharacteristic
62#1736C2211yescharacteristic
63#1736C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66C2×#339C2211yescharacteristic
67C2×#339C2211yescharacteristic
68C2×#339C2211yescharacteristic
69C2×#339C2211yescharacteristic
70#1436—22no—
71#1436—22no—
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2211yescharacteristic
74C22×#41C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79#520—22no—
80#520—22no—
81#520—22no—
82#520—22no—
83#520—22no—
84#520—22no—
85#520C2×C414yes—
86#520C2×C414yes—
87C4×#41—22no—
88C4×#41—22no—
89C4×#41C2×C414yes—
90C4×#41Q814yes—
91C2×C4×Q8—21no—
92C2×C4×Q8—21no—
93C2×C4×Q8D411yescharacteristic
94C2×C4×Q8D411yescharacteristic
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4D411yescharacteristic
102C2×C4×D4D411yescharacteristic
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117C2311yescharacteristic
107C2×#117C2311yescharacteristic
108C2×#117C2311yescharacteristic
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C42—21no—
117C22×C42—22no—
118C22×C42—21no—
119C22×C42D412yes—
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123#428—22no—
124#428—22no—
125#428C2×C414yescomplemented
126#428C2×C414yescomplemented
127C2×#107—21no—
128C2×#107—21no—
129C2×#106—21no—
130C2×#106—21no—
131C2×#104—22no—
132C2×#104—22no—
133C2×#104C2×C414yes—
134C2×#104C2×C414yes—
135C2×#104C2×C414yes—
136C2×#104C2×C414yes—
137#417—22no—
138#417—22no—
139#417C2×C414yes—
140#417C2×C414yes—
141C2×#103—21no—
142C2×#103—21no—
143C2×#102—21no—
144C2×#102—21no—
145C4×M16—22no—
146C4×M16—22no—
147C4×M16—22no—
148C4×M16C2×C414yescomplemented
149C2×#97—21no—
150C2×#97—21no—
151C2×C4×C8—21no—
152C2×C4×C8—21no—
153#384—22no—
154#384C2×C414yescomplemented
155#382—22no—
156#382C2×C414yescomplemented
157C4×C4⋊C4—22no—
158C4×C4⋊C4—22no—
159C4×C4⋊C4—22no—
160C4×C4⋊C4—22no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—21no—
164C4×C4⋊C4—21no—
165C4×C4⋊C4—21no—
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4D411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C22⋊C4—22no—
184C4×C22⋊C4—22no—
185C4×C22⋊C4—22no—
186C4×C22⋊C4—22no—
187C4×C22⋊C4—22no—
188C4×C22⋊C4—22no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—22no—
192C4×C22⋊C4—22no—
193#376—22no—
194#376—21no—
195#376—22no—
196#376C2×C414yescomplemented
197C2×#95—22no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—22no—
201C2×#95—21no—
202C2×#95—22no—
203C2×#95—22no—
204C2×#95D412yes—
205C43—22no—
206C43—21no—
207#343—22no—
208#343—22no—
209#343C2×C414yescomplemented
210#343C2×C414yescomplemented
211#340—21no—
212#340—21no—
213#340—21no—
214#340—21no—
215#340—21no—
216#340—21no—
217#340—21no—
218#340—21no—
219#339—22no—
220#339—22no—
221#339C2×C414yescomplemented
222#339C2×C414yescomplemented
223#339C2×C414yescomplemented
224#339C2×C414yescomplemented
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41C22×C412yes—
232C2×#41C22×C412yes—
233C2×#41C22×C412yes—
234C2×#41C2×Q812yes—
235C2×#41#4112yes—
236C2×#41#4112yes—
237C22×Q8C2×D411yescharacteristic
238C22×D4—21no—
239C22×D4C2×D411yescharacteristic
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2411yescharacteristic
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16C22×C412yes—
273C2×M16C22×C412yes—
274C2×M16C22×C412yes—
275C2×M16C22×C412yes—
276C2×M16C22×C412yes—
277C2×M16C22×C412yes—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C4×Q8—24no—
283C4×Q8—24no—
284C4×Q8—24no—
285C4×Q8—24no—
286C4×Q8—22no—
287C4×Q8—22no—
288C4×Q8C4⋊C414yescomplemented
289C4×Q8C4⋊C414yescomplemented
290C4×D4—28no—
291C4×D4—28no—
292C4×D4—24no—
293C4×D4—24no—
294C4×D4—24no—
295C4×D4—24no—
296C4×D4—24no—
297C4×D4—24no—
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—24no—
301C4×D4—24no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4C4⋊C414yescomplemented
305C4×D4C4⋊C414yescomplemented
306#117—24no—
307#117—24no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—21no—
312#117—21no—
313#117—21no—
314#117—24no—
315#117—24no—
316#117—24no—
317#117—24no—
318#117C22×C412yes—
319#117C22×C412yes—
320#117C22×C412yes—
321#117C2×Q812yes—
322#117#4112yes—
323#117#4112yes—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—82no—
352C2×C4⋊C4—82no—
353C2×C4⋊C4C22×C412yes—
354C2×C4⋊C4C22×C412yes—
355C2×C4⋊C4C22×C412yes—
356C2×C4⋊C4C22×C412yes—
357C2×C4⋊C4C2×D411yescharacteristic
358C2×C4⋊C4C2×D411yescharacteristic
359C2×C4⋊C4C2×D411yescharacteristic
360C2×C4⋊C4C2×D411yescharacteristic
361C2×C4⋊C4C2×D411yescharacteristic
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4#4112yes—
364C2×C4⋊C4#4112yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—22no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—22no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—84no—
402C2×C42—82no—
403C2×C42—82no—
404C2×C42C22×C412yes—
405C2×C42C22×C412yes—
406C2×C42C22×C412yes—
407C2×C42C22×C412yes—
408C2×C42C22×C412yes—
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×Q812yes—
414C2×C42#4112yes—
415C2×C42#4112yes—
416#107—24no—
417#107—24no—
418#106—24no—
419#106—24no—
420#104—28no—
421#104C42116yescomplemented
422#103—24no—
423#103—24no—
424#102—24no—
425#102—24no—
426#97—24no—
427#97—42no—
428C4×C8—24no—
429C4×C8—42no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—21no—
438#95—22no—
439#95—22no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—41no—
444#95—41no—
445#95—82no—
446#95—82no—
447C24—21no—
448C24C22×D411yescharacteristic
449#41—22no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41C2×C4214yes—
462#41#11714yes—
463#41C4×Q814yes—
464#41C4×Q814yes—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×C4⋊C412yes—
469C2×Q8C4×D412yes—
470C2×Q8C4×D412yes—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×C4⋊C412yes—
481C2×D4C4×D412yes—
482C2×D4C4×D412yes—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4C4×D414yes—
545C22×C4C4×D414yes—
546C22×C4C4×D412yes—
547C22×C4C4×D412yes—
548C22×C4#12011yescharacteristic
549C22×C4#12011yescharacteristic
550C22×C4#12011yescharacteristic
551C22×C4#12011yescharacteristic
552C22×C4C22⋊Q812yes—
553C22×C4C22⋊Q812yes—
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×Q811yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568M16—22no—
569M16—22no—
570M16—22no—
571M16—22no—
572M16—22no—
573M16—22no—
574M16—22no—
575M16—22no—
576M16—22no—
577M16—41no—
578M16—41no—
579M16—41no—
580M16—41no—
581M16—41no—
582M16—41no—
583M16C2×C4214yescomplemented
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—88no—
623C4⋊C4C2×C4⋊C412yes—
624C4⋊C4C2×C4⋊C412yes—
625C4⋊C4C4×D412yes—
626C4⋊C4C4×D412yes—
627C4⋊C4C4×D412yes—
628C4⋊C4C4×D412yes—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C42—28no—
640C42—28no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—24no—
651C42—24no—
652C42—22no—
653C42—22no—
654C42—42no—
655C42—44no—
656C42—42no—
657C42—41no—
658C42—41no—
659C42—81no—
660C42—81no—
661C42—82no—
662C42—82no—
663C42—82no—
664C42—82no—
665C42—82no—
666C42—82no—
667C42—82no—
668C42C2×C4214yescomplemented
669C42C2×C4⋊C412yes—
670C42C2×C4⋊C412yes—
671C42C4×D412yes—
672C42C4×D412yes—
673C42C22⋊Q812yes—
674C42C22⋊Q812yes—
675C42#12312yes—
676C42#12312yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23C2×C4×D411yescharacteristic
689C23C2×C4×D411yescharacteristic
690C23C2×C4×D411yescharacteristic
691C23C2×#12011yescharacteristic
692C23C2×C22⋊Q811yescharacteristic
693C23#52511yescharacteristic
694C23#52511yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8C4×C4⋊C414yes—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—24no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4C4×C4⋊C414yes—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—84no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4#38512yes—
783C2×C4#38512yes—
784C2×C4#38512yes—
785C2×C4#38512yes—
786C2×C4C22×C4211yescharacteristic
787C2×C4C22×C4⋊C411yescharacteristic
788C2×C4C2×#11711yescharacteristic
789C2×C4C2×C4×D411yescharacteristic
790C2×C4C2×C4×D411yescharacteristic
791C2×C4C2×C4×D411yescharacteristic
792C2×C4C2×C4×D411yescharacteristic
793C2×C4C2×C4×D411yescharacteristic
794C2×C4C2×C4×Q811yescharacteristic
795C2×C4C2×C4×Q811yescharacteristic
796C2×C4C4×#4111yescharacteristic
797C2×C4C4×#4111yescharacteristic
798C2×C4C4×#4111yescharacteristic
799C2×C4C4×#4111yescharacteristic
800C2×C4C4×#4111yescharacteristic
801C2×C4C4×#4111yescharacteristic
802C2×C4C2×C22⋊Q811yescharacteristic
803C2×C4C2×#12311yescharacteristic
804C2×C4#52511yescharacteristic
805C2×C4#52511yescharacteristic
806C2×C4#52511yescharacteristic
807C2×C4#52511yescharacteristic
808C2×C4#52911yescharacteristic
809C2×C4#52911yescharacteristic
810C2×C4#52911yescharacteristic
811C2×C4#52911yescharacteristic
812C2×C4#53311yescharacteristic
813C2×C4#53311yescharacteristic
814C8—24no—
815C8—42no—
816C8—42no—
817C8—42no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22C42×D411yescharacteristic
838C22C2×#38511yescharacteristic
839C22#229011yescharacteristic
840C22C4×#12011yescharacteristic
841C22C4×#12011yescharacteristic
842C22C4×C22⋊Q811yescharacteristic
843C22C4×C22⋊Q811yescharacteristic
844C22#301911yescharacteristic
845C22#302011yescharacteristic
846C22#302111yescharacteristic
847C22#302211yescharacteristic
848C4—22no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—44no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4C2×C4×C4⋊C411yescharacteristic
866C4C42×D411yescharacteristic
867C4#229011yescharacteristic
868C4#229611yescharacteristic
869C4C4×#12311yescharacteristic
870C4C4×#12311yescharacteristic
871C4C4×C22⋊Q811yescharacteristic
872C4C4×C22⋊Q811yescharacteristic
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—44no—
878C2C4×#38511yescharacteristic
879C2#2086411yescharacteristic
880C2#2086511yescharacteristic
881C2#2147311yescharacteristic
882C2#2147411yescharacteristic
883C2#2147511yescharacteristic
884C2#2147611yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC22×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C4×#428C2semidirect
7. #13779C2semidirect
8. #10899C2semidirect
9. #10899C2semidirect
10. #10892C2semidirect
11. #10891C2semidirect
14. C4×#343C2semidirect
15. #10701C2semidirect
45. #1860C4semidirect
46. #1859C4semidirect
55. #1759C4semidirect
125. #428C2×C4semidirect
126. #428C2×C4semidirect
148. C4×M16C2×C4semidirect
154. #384C2×C4semidirect
156. #382C2×C4semidirect
196. #376C2×C4semidirect
209. #343C2×C4semidirect
210. #343C2×C4semidirect
221. #339C2×C4semidirect
222. #339C2×C4semidirect
223. #339C2×C4semidirect
224. #339C2×C4semidirect
288. C4×Q8C4⋊C4semidirect
289. C4×Q8C4⋊C4semidirect
304. C4×D4C4⋊C4semidirect
305. C4×D4C4⋊C4semidirect
421. #104C42semidirect
583. M16C2×C42semidirect
668. C42C2×C42semidirect

Maximal subgroups

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

subgroupindex
C4×#5202
C2×#18602
C2×#18592
C4×#4282
C4×#4172
C2×#17592
#137792
#108992
#108922
#108912
#107812
C4×#3432
#107012