Finite Group Databasebeta

← #221484

Subgroups — #221484

Order 512.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1019 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D42C211yesmaximal, characteristic
2#22748C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4C2×#1478C211yesmaximal, characteristic, complemented
5C22×D4⋊C8C211yesmaximal, characteristic, complemented
6#9674C211yesmaximal, characteristic, complemented
7#9642C211yesmaximal, characteristic, complemented
8#9074C211yesmaximal, characteristic, complemented
9#9072C211yesmaximal, characteristic, complemented
10#8940C211yesmaximal, characteristic, complemented
11#8939C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8310C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15#8170C211yesmaximal, characteristic, complemented
16C2×D42C411yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×#431C2211yescharacteristic, complemented
21C2×#431C2211yescharacteristic, complemented
22C22×C4⋊C8C2211yescharacteristic, complemented
23C22×C4×C8C2211yescharacteristic, 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#1923—21no—
44#1923—21no—
45#1916—21no—
46#1916—21no—
47#1869—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53C4×C4⋊C8C2211yescharacteristic, complemented
54C4×C4⋊C8C2211yescharacteristic, complemented
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic, complemented
57C4×C22⋊C8C2211yescharacteristic, complemented
58#1744C2211yescharacteristic, complemented
59#1478—24no—
60C2×D4⋊C8—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—
82C23×C8—21no—
83C23×C8—21no—
84D42—24no—
85D42C818yescomplemented
86C2×#127C2×C411yescharacteristic
87C2×#121—21no—
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#120—21no—
91C2×#120—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—21no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4—22no—
102C2×C4×D4—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4—41no—
109C2×C4×D4—41no—
110C2×C4×D4—41no—
111C2×C4×D4—41no—
112C2×C4×D4—44no—
113C2×C4×D4—44no—
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×D4C2×C411yescharacteristic
121C2×C4×D4D411yescharacteristic
122C2×C4×D4D411yescharacteristic
123C2×C4×D4C2311yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C2×C4×D4C2311yescharacteristic
126C22×C4⋊C4—21no—
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C4⋊C4C2×C411yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#431—22no—
137#431—22no—
138#431—41no—
139#431—41no—
140C2×C4⋊C8—22no—
141C2×C4⋊C8—21no—
142C2×C4⋊C8—21no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—41no—
145C2×C4⋊C8C2311yescharacteristic
146C2×C4⋊C8C2311yescharacteristic
147C2×C4⋊C8C2311yescharacteristic
148C2×C4⋊C8C2311yescharacteristic
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C4×C8—22no—
156C2×C4×C8—21no—
157C2×C4×C8—21no—
158C2×C4×C8—21no—
159C2×C4×C8—41no—
160C2×C4×C8C2311yescharacteristic
161C2×C4×C8C2311yescharacteristic
162C2×C4×C8C2311yescharacteristic
163C2×C4×C8C2311yescharacteristic
164#390—21no—
165#390—21no—
166#390—21no—
167#390C2×C411yescharacteristic
168#390C2×C411yescharacteristic
169#390C2×C411yescharacteristic
170#390C2×C411yescharacteristic
171#389—21no—
172#389C2×C411yescharacteristic
173#389C2×C411yescharacteristic
174#388—21no—
175#388—21no—
176#388—21no—
177#388—21no—
178#386—21no—
179#386—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#385—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#384C2×C411yescharacteristic
195#380—21no—
196#380C2×C411yescharacteristic
197#380C2×C411yescharacteristic
198#379—21no—
199#379—21no—
200C4×C4⋊C4C2×C411yescharacteristic
201C4×C4⋊C4C2×C411yescharacteristic
202C4×C4⋊C4C2×C411yescharacteristic
203C4×C4⋊C4D411yescharacteristic
204C4×C4⋊C4D411yescharacteristic
205C4×C4⋊C4C2311yescharacteristic
206C4×C22⋊C4—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4—21no—
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4C2×C411yescharacteristic
212C4×C22⋊C4C2×C411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C43C2311yescharacteristic
218#336—21no—
219#336—21no—
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—22no—
245C22×D4—22no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—28no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—41no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4C22⋊C411yescharacteristic
262C22×D4C2×C814yes—
263C22×D4C2×C814yescomplemented
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
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—42no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8—81no—
310#127—22no—
311#127C2×C814yescomplemented
312#121—22no—
313#121—22no—
314#121—28no—
315#121C2×C814yes—
316#121C2×C814yescomplemented
317#120—28no—
318#120—28no—
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×C814yes—
364C4×D4C2×C814yescomplemented
365C4×D4M1614yes—
366C4×D4C2×D412yes—
367C4×D4#4112yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4C22⋊C411yescharacteristic
380C2×C4⋊C4C22⋊C411yescharacteristic
381C2×C4⋊C4C22⋊C411yescharacteristic
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C4⋊C4C22×C411yescharacteristic
386C2×C4⋊C4C22×C411yescharacteristic
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—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4C22⋊C411yescharacteristic
415C2×C22⋊C4C22⋊C411yescharacteristic
416C2×C22⋊C4C22⋊C411yescharacteristic
417C2×C22⋊C4C22⋊C411yescharacteristic
418C2×C22⋊C4C22⋊C411yescharacteristic
419C2×C22⋊C4C22⋊C411yescharacteristic
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—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C411yescharacteristic
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—42no—
454C4⋊C8—42no—
455C4⋊C8—42no—
456C4⋊C8C2×D412yescomplemented
457C22⋊C8—42no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461C22⋊C8—42no—
462C22⋊C8—81no—
463C4×C8—21no—
464C4×C8—21no—
465C4×C8—21no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8—42no—
471C4×C8—42no—
472C4×C8—81no—
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—21no—
489C24—21no—
490C24—24no—
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—28no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
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—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—432no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4C22⋊C814yes—
549C2×D4C4×D412yes—
550C2×D4C22×C812yes—
551C2×D4C22×C812yes—
552C2×D4C22×C812yes—
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—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—42no—
589C22×C4—42no—
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—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—41no—
607C22×C4—41no—
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—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4C2×C22⋊C411yescharacteristic
636C22×C4C2×C22⋊C411yescharacteristic
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×C4C22×C812yes—
646C22×C4C22×C812yes—
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
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—48no—
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—
679C2×C8—84no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4C22⋊C814yes—
697C4⋊C4C4×D412yes—
698C4⋊C4C22×C812yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—41no—
708C22⋊C4—42no—
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—41no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—42no—
723C22⋊C4—81no—
724C22⋊C4—81no—
725C22⋊C4—81no—
726C22⋊C4—81no—
727C22⋊C4C22⋊C814yes—
728C22⋊C4C22⋊C814yes—
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—41no—
748C42—41no—
749C42—42no—
750C42—42no—
751C42—41no—
752C42—41no—
753C42C22×C812yes—
754C42C2×M1612yes—
755C42C22×D411yescharacteristic
756C42C2×#4111yescharacteristic
757C42H(5,𝔽2)11yescharacteristic
758C42H(5,𝔽2)11yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
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—48no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23C2×C22⋊C812yes—
805C23C2×C22⋊C812yes—
806C23#41812yes—
807C23#42112yes—
808C23C22×C22⋊C411yescharacteristic
809D4—28no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4C8×D414yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—22no—
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—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—42no—
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—41no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—84no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4—84no—
899C2×C4—84no—
900C2×C4—84no—
901C2×C4—84no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4C2×C22⋊C812yes—
911C2×C4C2×C22⋊C812yes—
912C2×C4C2×C22⋊C812yes—
913C2×C4C2×C22⋊C812yes—
914C2×C4#41812yes—
915C2×C4C2×C4×D411yescharacteristic
916C2×C4#51811yescharacteristic
917C2×C4D4211yescharacteristic
918C2×C4D4211yescharacteristic
919C2×C4#54611yescharacteristic
920C2×C4#54611yescharacteristic
921C2×C4C23×C811yescharacteristic
922C2×C4C22×M1611yescharacteristic
923C2×C4C2×#13111yescharacteristic
924C2×C4#56811yescharacteristic
925C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
926C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
927C2×C4#57611yescharacteristic
928C2×C4#57711yescharacteristic
929C8—42no—
930C8—42no—
931C8—42no—
932C8—81no—
933C8—81no—
934C8—81no—
935C8—81no—
936C8—81no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—24no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—41no—
952C22—42no—
953C22—41no—
954C22—42no—
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—
973C22#147814yescomplemented
974C22D4×C22⋊C411yescharacteristic
975C22C22×C22⋊C811yescharacteristic
976C22#288011yescharacteristic
977C22C2×#41811yescharacteristic
978C22#289711yescharacteristic
979C22C2×#42111yescharacteristic
980C22#290111yescharacteristic
981C4—22no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—22no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—42no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4C2×C8×D411yescharacteristic
999C4D4×M1611yescharacteristic
1000C4#297211yescharacteristic
1001C4#297411yescharacteristic
1002C4#326411yescharacteristic
1003C4#326511yescharacteristic
1004C4#331011yescharacteristic
1005C4#331811yescharacteristic
1006C2—24no—
1007C2—42no—
1008C2—44no—
1009C2—82no—
1010C2—82no—
1011C2C2×#147811yescharacteristic
1012C2#1743811yescharacteristic
1013C2#1751111yescharacteristic
1014C2#1752111yescharacteristic
1015C2D4×C22⋊C811yescharacteristic
1016C2#2242311yescharacteristic
1017C2#2243411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×D42C4
LCSG ▷ C2×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. #22748C2semidirect
3. #21101C2semidirect
4. C2×#1478C2semidirect
5. C22×D4⋊C8C2semidirect
6. #9674C2semidirect
7. #9642C2semidirect
8. #9074C2semidirect
9. #9072C2semidirect
10. #8940C2semidirect
11. #8939C2semidirect
12. #8565C2semidirect
13. #8310C2semidirect
14. #8310C2semidirect
15. #8170C2semidirect
20. C2×#431C22semidirect
21. C2×#431C22semidirect
22. C22×C4⋊C8C22semidirect
23. C22×C4×C8C22semidirect
50. #1831C22semidirect
51. #1797C22semidirect
52. #1797C22semidirect
53. C4×C4⋊C8C22semidirect
54. C4×C4⋊C8C22semidirect
56. C4×C22⋊C8C22semidirect
57. C4×C22⋊C8C22semidirect
58. #1744C22semidirect
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
85. D42C8semidirect
239. D4⋊C8D4semidirect
263. C22×D4C2×C8semidirect
311. #127C2×C8semidirect
316. #121C2×C8semidirect
364. C4×D4C2×C8semidirect
456. C4⋊C8C2×D4semidirect
473. C4×C8C2×D4semidirect
973. C22#1478semidirect

Maximal subgroups

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

subgroupindex
C4×D422
#227482
#211012
C2×#14782
C22×D4⋊C82
#96742
#96422
#90742
#90722
#89402
#89392
#85652
#83102
#81702