Finite Group Databasebeta

← #221532

Subgroups — #221532

Order 512.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D42C211yesmaximal, characteristic
2#22749C211yesmaximal, characteristic, complemented
3#21265C211yesmaximal, characteristic, complemented
4C2×#1486C211yesmaximal, characteristic, complemented
5C2×#1478C211yesmaximal, characteristic, complemented
6#9678C211yesmaximal, characteristic, complemented
7#9648C211yesmaximal, characteristic, complemented
8#9076C211yesmaximal, characteristic, complemented
9#9074C211yesmaximal, characteristic, complemented
10#8944C211yesmaximal, characteristic, complemented
11#8940C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8310C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15#8172C211yesmaximal, characteristic, complemented
16C2×D42C411yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×#431C2211yescharacteristic, complemented
21C2×#431C2211yescharacteristic, complemented
22C2×#431C2211yescharacteristic, complemented
23C2×#423C2211yescharacteristic, complemented
24#2366C411yescharacteristic
25#2361—21no—
26#2361C411yescharacteristic
27#2361C411yescharacteristic
28#2358—21no—
29#2358—21no—
30D4×C4⋊C4C411yescharacteristic
31D4×C4⋊C4C411yescharacteristic
32D4×C22⋊C4—21no—
33D4×C22⋊C4C411yescharacteristic
34D4×C22⋊C4C411yescharacteristic
35C4×#127C2211yescharacteristic
36C4×#121—21no—
37C4×#121C2211yescharacteristic
38C4×#121C2211yescharacteristic
39C4×#120—21no—
40C4×#120—21no—
41C42×D4C2211yescharacteristic
42C42×D4C2211yescharacteristic
43#1955—21no—
44#1940—21no—
45#1924—21no—
46#1924—21no—
47#1924—21no—
48#1916—21no—
49#1870—21no—
50#1831C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1767C2211yescharacteristic, complemented
54C4×C4⋊C8C2211yescharacteristic, complemented
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic, complemented
57C4×C22⋊C8C2211yescharacteristic, complemented
58C4×#97C2211yescharacteristic, complemented
59#1486—24no—
60#1478—24no—
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic, complemented
66C2×D4⋊C8C2211yescharacteristic, complemented
67C2×D4⋊C8C2211yescharacteristic, complemented
68C2×D4⋊C8C2211yescharacteristic, complemented
69C2×D4⋊C8C2211yescharacteristic, complemented
70C2×D4⋊C8C2211yescharacteristic, complemented
71C2×D4⋊C8C2211yescharacteristic, complemented
72C2×D4⋊C8C2211yescharacteristic, complemented
73#1279C2211yescharacteristic, complemented
74#1279C2211yescharacteristic, complemented
75#1279C2211yescharacteristic, complemented
76#1279C2211yescharacteristic, complemented
77C23×D4—21no—
78C23×D4C2×C411yescharacteristic
79C23×D4C2×C411yescharacteristic
80C24×C4—21no—
81C24×C4—21no—
82C22×M16—21no—
83D42—24no—
84D42—24no—
85C2×#127C2×C411yescharacteristic
86C2×#121—21no—
87C2×#121C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×#120—21no—
90C2×#120—21no—
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4—21no—
102C2×C4×D4—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4—21no—
107C2×C4×D4—41no—
108C2×C4×D4—41no—
109C2×C4×D4—41no—
110C2×C4×D4—41no—
111C2×C4×D4—44no—
112C2×C4×D4—44no—
113C2×C4×D4C2×C411yescharacteristic
114C2×C4×D4C2×C411yescharacteristic
115C2×C4×D4C2×C411yescharacteristic
116C2×C4×D4C2×C411yescharacteristic
117C2×C4×D4C2×C411yescharacteristic
118C2×C4×D4C2×C411yescharacteristic
119C2×C4×D4C2×C411yescharacteristic
120C2×C4×D4D411yescharacteristic
121C2×C4×D4D411yescharacteristic
122C2×C4×D4C2311yescharacteristic
123C2×C4×D4C2311yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2×C411yescharacteristic
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C42—21no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135#431—22no—
136#431—22no—
137#431—22no—
138#431—41no—
139#431—41no—
140#431—41no—
141#423—22no—
142#423—41no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—21no—
145C2×C4⋊C8—21no—
146C2×C4⋊C8—21no—
147C2×C4⋊C8C2311yescharacteristic
148C2×C4⋊C8C2311yescharacteristic
149C2×C4⋊C8C2311yescharacteristic
150C2×C4⋊C8C2311yescharacteristic
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C22⋊C8—21no—
158C2×#97—21no—
159C2×#97—21no—
160C2×#97—21no—
161C2×C4×C8—21no—
162C2×C4×C8C2311yescharacteristic
163C2×C4×C8C2311yescharacteristic
164C2×C4×C8C2311yescharacteristic
165C2×C4×C8C2311yescharacteristic
166#390—21no—
167#390—21no—
168#390—21no—
169#390C2×C411yescharacteristic
170#390C2×C411yescharacteristic
171#390C2×C411yescharacteristic
172#390C2×C411yescharacteristic
173#389—21no—
174#389C2×C411yescharacteristic
175#389C2×C411yescharacteristic
176#388—21no—
177#388—21no—
178#388—21no—
179#388—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#386—21no—
186#386—21no—
187#386—21no—
188#386—21no—
189#386—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#385—21no—
195#385—21no—
196#384C2×C411yescharacteristic
197#380—21no—
198#380C2×C411yescharacteristic
199#380C2×C411yescharacteristic
200#379—21no—
201#379—21no—
202C4×C4⋊C4C2×C411yescharacteristic
203C4×C4⋊C4C2×C411yescharacteristic
204C4×C4⋊C4C2×C411yescharacteristic
205C4×C4⋊C4D411yescharacteristic
206C4×C4⋊C4D411yescharacteristic
207C4×C4⋊C4C2311yescharacteristic
208C4×C22⋊C4—21no—
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213C4×C22⋊C4C2×C411yescharacteristic
214C4×C22⋊C4C2×C411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C4×C22⋊C4D411yescharacteristic
218C4×C22⋊C4D411yescharacteristic
219C43C2311yescharacteristic
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227#336—21no—
228D4⋊C8—22no—
229D4⋊C8—22no—
230D4⋊C8—22no—
231D4⋊C8—22no—
232D4⋊C8—22no—
233D4⋊C8—22no—
234D4⋊C8—22no—
235D4⋊C8—41no—
236D4⋊C8—41no—
237D4⋊C8—41no—
238D4⋊C8—41no—
239D4⋊C8D414yescomplemented
240C25—21no—
241C25—21no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—28no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—41no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4C22⋊C411yescharacteristic
263C22×D4M1614yescomplemented
264C22×D4C22×C411yescharacteristic
265C22×D4C22×C411yescharacteristic
266C22×D4C22×C411yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—81no—
287C23×C4—81no—
288C23×C4—81no—
289C23×C4—81no—
290C23×C4C22×C411yescharacteristic
291C23×C4C22×C411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C2×M16—42no—
297C2×M16—42no—
298C2×M16—81no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307#127—22no—
308#127—22no—
309#121—28no—
310#121—22no—
311#121—22no—
312#121—22no—
313#121M1614yescomplemented
314#120—28no—
315#120—28no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—42no—
338C4×D4—42no—
339C4×D4—42no—
340C4×D4—42no—
341C4×D4—41no—
342C4×D4—41no—
343C4×D4—41no—
344C4×D4—41no—
345C4×D4—41no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—42no—
350C4×D4—42no—
351C4×D4—42no—
352C4×D4—42no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4—44no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—81no—
362C4×D4—81no—
363C4×D4C2×D412yes—
364C4×D4#4112yes—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4C22⋊C411yescharacteristic
377C2×C4⋊C4C22⋊C411yescharacteristic
378C2×C4⋊C4C22⋊C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C411yescharacteristic
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4C22⋊C411yescharacteristic
412C2×C22⋊C4C22⋊C411yescharacteristic
413C2×C22⋊C4C22⋊C411yescharacteristic
414C2×C22⋊C4C22⋊C411yescharacteristic
415C2×C22⋊C4C22⋊C411yescharacteristic
416C2×C22⋊C4C22⋊C411yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42C22×C411yescharacteristic
431C2×C42C22×C411yescharacteristic
432C2×C42C22×C411yescharacteristic
433C2×C42C22×C411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2411yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—42no—
451C4⋊C8—42no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454C4⋊C8C2×D412yescomplemented
455C22⋊C8—42no—
456C22⋊C8—42no—
457C22⋊C8—42no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461C22⋊C8—81no—
462#97—42no—
463#97—42no—
464#97—81no—
465C4×C8—21no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8—21no—
471C4×C8—21no—
472C4×C8—42no—
473C4×C8C2×D412yescomplemented
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95C22⋊C411yescharacteristic
482#95C22⋊C411yescharacteristic
483#95C22⋊C411yescharacteristic
484#95C22⋊C411yescharacteristic
485#95C22⋊C411yescharacteristic
486#95C22⋊C411yescharacteristic
487C24—21no—
488C24—24no—
489C24—21no—
490C24—21no—
491C24—24no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—81no—
501C24—81no—
502C24—81no—
503C24—81no—
504C24C2×C22⋊C411yescharacteristic
505C24C2×C22⋊C411yescharacteristic
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—28no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—24no—
528C2×D4—22no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—432no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—44no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4C4×D412yes—
550C2×D4C2×M1612yes—
551C2×D4C2×M1612yes—
552C2×D4C2×M1612yes—
553C2×D4#13112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4C2×C22⋊C411yescharacteristic
638C22×C4C2×C22⋊C411yescharacteristic
639C22×C4C2×C22⋊C411yescharacteristic
640C22×C4C2×C22⋊C411yescharacteristic
641C22×C4C2×C22⋊C411yescharacteristic
642C22×C4C2×C22⋊C411yescharacteristic
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4C2×C22⋊C411yescharacteristic
645C22×C4C2×C22⋊C411yescharacteristic
646C22×C4C2×C22⋊C411yescharacteristic
647C22×C4C2×M1612yes—
648C22×C4C2×M1612yes—
649C22×C4AGL(1,ℤ/8)12yes—
650C22×C4AGL(1,ℤ/8)12yes—
651C22×C4C23×C411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654M16—84no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8—41no—
674C2×C8—41no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—41no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4C4×D412yes—
697C4⋊C4C2×M1612yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—24no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—42no—
724C22⋊C4—81no—
725C22⋊C4—81no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—22no—
749C42—41no—
750C42—42no—
751C42—42no—
752C42—41no—
753C42—41no—
754C42C22×D411yescharacteristic
755C42C2×#4111yescharacteristic
756C42H(5,𝔽2)11yescharacteristic
757C42H(5,𝔽2)11yescharacteristic
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—22no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23—84no—
805C23#40712yes—
806C23#41812yes—
807C23C22×C22⋊C411yescharacteristic
808D4—28no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—48no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—84no—
826D4#43514yes—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—48no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4—84no—
899C2×C4—84no—
900C2×C4—84no—
901C2×C4—84no—
902C2×C4—84no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4#40712yes—
912C2×C4#41812yes—
913C2×C4#42112yes—
914C2×C4C2×C4×D411yescharacteristic
915C2×C4#51811yescharacteristic
916C2×C4D4211yescharacteristic
917C2×C4D4211yescharacteristic
918C2×C4#54611yescharacteristic
919C2×C4#54611yescharacteristic
920C2×C4C22×M1611yescharacteristic
921C2×C4C22×M1611yescharacteristic
922C2×C4C2×#13111yescharacteristic
923C2×C4#56811yescharacteristic
924C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
925C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
926C2×C4#57611yescharacteristic
927C2×C4#57711yescharacteristic
928C8—42no—
929C8—42no—
930C8—42no—
931C8—81no—
932C8—81no—
933C8—81no—
934C8—81no—
935C8—81no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—24no—
942C22—22no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—41no—
952C22—41no—
953C22—42no—
954C22—41no—
955C22—41no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—816no—
964C22—816no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22D4×C22⋊C411yescharacteristic
974C22C2×#40711yescharacteristic
975C22#288011yescharacteristic
976C22C2×#41811yescharacteristic
977C22#289711yescharacteristic
978C22C2×#42111yescharacteristic
979C22#290111yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—21no—
984C4—21no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—42no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C4C2×#43511yescharacteristic
998C4D4×M1611yescharacteristic
999C4#297311yescharacteristic
1000C4#297411yescharacteristic
1001C4#326411yescharacteristic
1002C4#326511yescharacteristic
1003C4#331011yescharacteristic
1004C4#331811yescharacteristic
1005C2—42no—
1006C2—42no—
1007C2—44no—
1008C2—82no—
1009C2—82no—
1010C2#1744811yescharacteristic
1011C2#1745311yescharacteristic
1012C2#1751111yescharacteristic
1013C2#1752211yescharacteristic
1014C2#2239911yescharacteristic
1015C2#2242311yescharacteristic
1016C2#2243511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×D42C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22749C2semidirect
3. #21265C2semidirect
4. C2×#1486C2semidirect
5. C2×#1478C2semidirect
6. #9678C2semidirect
7. #9648C2semidirect
8. #9076C2semidirect
9. #9074C2semidirect
10. #8944C2semidirect
11. #8940C2semidirect
12. #8565C2semidirect
13. #8310C2semidirect
14. #8310C2semidirect
15. #8172C2semidirect
20. C2×#431C22semidirect
21. C2×#431C22semidirect
22. C2×#431C22semidirect
23. C2×#423C22semidirect
50. #1831C22semidirect
51. #1797C22semidirect
52. #1797C22semidirect
53. #1767C22semidirect
54. C4×C4⋊C8C22semidirect
56. C4×C22⋊C8C22semidirect
57. C4×C22⋊C8C22semidirect
58. C4×#97C22semidirect
65. C2×D4⋊C8C22semidirect
66. C2×D4⋊C8C22semidirect
67. C2×D4⋊C8C22semidirect
68. C2×D4⋊C8C22semidirect
69. C2×D4⋊C8C22semidirect
70. C2×D4⋊C8C22semidirect
71. C2×D4⋊C8C22semidirect
72. C2×D4⋊C8C22semidirect
73. #1279C22semidirect
74. #1279C22semidirect
75. #1279C22semidirect
76. #1279C22semidirect
239. D4⋊C8D4semidirect
263. C22×D4M16semidirect
313. #121M16semidirect
454. C4⋊C8C2×D4semidirect
473. C4×C8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C4×D422
#227492
#212652
C2×#14862
C2×#14782
#96782
#96482
#90762
#90742
#89442
#89402
#85652
#83102
#81722