Finite Group Databasebeta

← #221520

Subgroups — #221520

Order 512.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D42C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4C2×#1486C211yesmaximal, characteristic, complemented
5C22×D4⋊C8C211yesmaximal, characteristic, complemented
6#9678C211yesmaximal, characteristic, complemented
7#9644C211yesmaximal, characteristic, complemented
8#9076C211yesmaximal, characteristic, complemented
9#9072C211yesmaximal, characteristic, complemented
10#8944C211yesmaximal, characteristic, complemented
11#8939C211yesmaximal, characteristic, complemented
12#8563C211yesmaximal, characteristic, complemented
13#8310C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15#8174C211yesmaximal, characteristic, complemented
16C2×D42C411yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×#435—21no—
21C2×#431C2211yescharacteristic, complemented
22C2×#423C2211yescharacteristic, complemented
23C22×C4⋊C8C2211yescharacteristic, complemented
24C22×C4×C8C2211yescharacteristic, complemented
25#2366C411yescharacteristic
26#2361—21no—
27#2361C411yescharacteristic
28#2361C411yescharacteristic
29#2358—21no—
30#2358—21no—
31D4×C4⋊C4C411yescharacteristic
32D4×C4⋊C4C411yescharacteristic
33D4×C22⋊C4—21no—
34D4×C22⋊C4C411yescharacteristic
35D4×C22⋊C4C411yescharacteristic
36C4×#127C2211yescharacteristic
37C4×#121—21no—
38C4×#121C2211yescharacteristic
39C4×#121C2211yescharacteristic
40C4×#120—21no—
41C4×#120—21no—
42C42×D4C2211yescharacteristic
43C42×D4C2211yescharacteristic
44#1940—21no—
45#1923—21no—
46#1916—21no—
47#1869—21no—
48#1851—21no—
49#1850—21no—
50#1850—21no—
51#1842C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1797C2211yescharacteristic, complemented
54#1767C2211yescharacteristic, complemented
55C4×C4⋊C8C2211yescharacteristic, complemented
56C4×C22⋊C8C2211yescharacteristic, complemented
57C4×C22⋊C8C2211yescharacteristic, complemented
58#1744C2211yescharacteristic, complemented
59#1486—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—
82C22×M16—21no—
83C23×C8—21no—
84C23×C8—21no—
85D42—24no—
86D42—24no—
87C2×#127C2×C411yescharacteristic
88C2×#121—21no—
89C2×#121C2×C411yescharacteristic
90C2×#121C2×C411yescharacteristic
91C2×#120—21no—
92C2×#120—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
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×D4—22no—
102C2×C4×D4—22no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4—21no—
109C2×C4×D4—41no—
110C2×C4×D4—41no—
111C2×C4×D4—41no—
112C2×C4×D4—41no—
113C2×C4×D4—44no—
114C2×C4×D4—44no—
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×D4C2×C411yescharacteristic
122C2×C4×D4D411yescharacteristic
123C2×C4×D4D411yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C2×C4×D4C2311yescharacteristic
126C2×C4×D4C2311yescharacteristic
127C22×C4⋊C4—21no—
128C22×C4⋊C4C2×C411yescharacteristic
129C22×C4⋊C4C2×C411yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C42—21no—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137#435—44no—
138#431—22no—
139#431—41no—
140#423—22no—
141#423—41no—
142C2×C4⋊C8—22no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—21no—
145C2×C4⋊C8—21no—
146C2×C4⋊C8—21no—
147C2×C4⋊C8—21no—
148C2×C4⋊C8—21no—
149C2×C4⋊C8—41no—
150C2×C4⋊C8C2311yescharacteristic
151C2×C4⋊C8C2311yescharacteristic
152C2×C4⋊C8C2311yescharacteristic
153C2×C4⋊C8C2311yescharacteristic
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C22⋊C8—21no—
158C2×C22⋊C8—21no—
159C2×#97—21no—
160C2×C4×C8—22no—
161C2×C4×C8—21no—
162C2×C4×C8—41no—
163C2×C4×C8C2311yescharacteristic
164C2×C4×C8C2311yescharacteristic
165C2×C4×C8C2311yescharacteristic
166C2×C4×C8C2311yescharacteristic
167#390—21no—
168#390—21no—
169#390—21no—
170#390C2×C411yescharacteristic
171#390C2×C411yescharacteristic
172#390C2×C411yescharacteristic
173#390C2×C411yescharacteristic
174#389—21no—
175#389C2×C411yescharacteristic
176#389C2×C411yescharacteristic
177#388—21no—
178#388—21no—
179#388—21no—
180#388—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#386—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#385—21no—
195#385—21no—
196#385—21no—
197#384C2×C411yescharacteristic
198#380—21no—
199#380C2×C411yescharacteristic
200#380C2×C411yescharacteristic
201#379—21no—
202#379—21no—
203C4×C4⋊C4C2×C411yescharacteristic
204C4×C4⋊C4C2×C411yescharacteristic
205C4×C4⋊C4C2×C411yescharacteristic
206C4×C4⋊C4D411yescharacteristic
207C4×C4⋊C4D411yescharacteristic
208C4×C4⋊C4C2311yescharacteristic
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213C4×C22⋊C4—21no—
214C4×C22⋊C4C2×C411yescharacteristic
215C4×C22⋊C4C2×C411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C4×C22⋊C4D411yescharacteristic
218C4×C22⋊C4D411yescharacteristic
219C4×C22⋊C4D411yescharacteristic
220C43C2311yescharacteristic
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227#336—21no—
228#336—21no—
229D4⋊C8—22no—
230D4⋊C8—22no—
231D4⋊C8—22no—
232D4⋊C8—22no—
233D4⋊C8—22no—
234D4⋊C8—22no—
235D4⋊C8—22no—
236D4⋊C8—41no—
237D4⋊C8—41no—
238D4⋊C8—41no—
239D4⋊C8—41no—
240D4⋊C8D414yescomplemented
241C25—21no—
242C25—21no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—28no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—41no—
260C22×D4—41no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4C22⋊C411yescharacteristic
264C22×D4M1614yescomplemented
265C22×D4C22×C411yescharacteristic
266C22×D4C22×C411yescharacteristic
267C22×D4C22×C411yescharacteristic
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—21no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—81no—
288C23×C4—81no—
289C23×C4—81no—
290C23×C4—81no—
291C23×C4C22×C411yescharacteristic
292C23×C4C22×C411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C2×M16—42no—
298C2×M16—42no—
299C2×M16—81no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—42no—
309C22×C8—42no—
310C22×C8—42no—
311C22×C8—42no—
312C22×C8—42no—
313C22×C8—81no—
314#127—22no—
315#127—22no—
316#121—28no—
317#121—22no—
318#121—22no—
319#121—22no—
320#121M1614yescomplemented
321#120—28no—
322#120—28no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—42no—
343C4×D4—42no—
344C4×D4—42no—
345C4×D4—42no—
346C4×D4—41no—
347C4×D4—41no—
348C4×D4—41no—
349C4×D4—41no—
350C4×D4—41no—
351C4×D4—42no—
352C4×D4—42no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—44no—
357C4×D4—42no—
358C4×D4—42no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—44no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—42no—
365C4×D4—42no—
366C4×D4—81no—
367C4×D4—81no—
368C4×D4D814yes—
369C4×D4SD1614yes—
370C4×D4C2×D412yes—
371C4×D4#4112yes—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4C22⋊C411yescharacteristic
384C2×C4⋊C4C22⋊C411yescharacteristic
385C2×C4⋊C4C22⋊C411yescharacteristic
386C2×C4⋊C4C22×C411yescharacteristic
387C2×C4⋊C4C22×C411yescharacteristic
388C2×C4⋊C4C22×C411yescharacteristic
389C2×C4⋊C4C22×C411yescharacteristic
390C2×C4⋊C4C22×C411yescharacteristic
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—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4C22⋊C411yescharacteristic
419C2×C22⋊C4C22⋊C411yescharacteristic
420C2×C22⋊C4C22⋊C411yescharacteristic
421C2×C22⋊C4C22⋊C411yescharacteristic
422C2×C22⋊C4C22⋊C411yescharacteristic
423C2×C22⋊C4C22⋊C411yescharacteristic
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42C22×C411yescharacteristic
438C2×C42C22×C411yescharacteristic
439C2×C42C22×C411yescharacteristic
440C2×C42C22×C411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2411yescharacteristic
450C4⋊C8—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—42no—
458C4⋊C8—42no—
459C4⋊C8—42no—
460C4⋊C8—42no—
461C4⋊C8—42no—
462C4⋊C8—81no—
463C4⋊C8C2×D412yescomplemented
464C22⋊C8—42no—
465C22⋊C8—42no—
466C22⋊C8—42no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469#97—42no—
470C4×C8—21no—
471C4×C8—21no—
472C4×C8—21no—
473C4×C8—21no—
474C4×C8—21no—
475C4×C8—21no—
476C4×C8—21no—
477C4×C8—42no—
478C4×C8C2×D412yescomplemented
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95C22⋊C411yescharacteristic
487#95C22⋊C411yescharacteristic
488#95C22⋊C411yescharacteristic
489#95C22⋊C411yescharacteristic
490#95C22⋊C411yescharacteristic
491#95C22⋊C411yescharacteristic
492C24—21no—
493C24—24no—
494C24—21no—
495C24—21no—
496C24—24no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—81no—
506C24—81no—
507C24—81no—
508C24—81no—
509C24C2×C22⋊C411yescharacteristic
510C24C2×C22⋊C411yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—28no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
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—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—24no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—432no—
544C2×D4—44no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4#10214yes—
554C2×D4C4×D412yes—
555C2×D4C2×M1612yes—
556C2×D4C2×M1612yes—
557C2×D4C2×M1612yes—
558C2×D4#13112yes—
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—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
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—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4—81no—
639C22×C4—81no—
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×C22⋊C411yescharacteristic
648C22×C4C2×C22⋊C411yescharacteristic
649C22×C4C2×C22⋊C411yescharacteristic
650C22×C4C2×M1612yes—
651C22×C4C2×M1612yes—
652C22×C4C2×D812yes—
653C22×C4C2×D812yes—
654C22×C4C2×SD1612yes—
655C22×C4C2×SD1612yes—
656C22×C4C23×C411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659M16—84no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—48no—
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—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—84no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—41no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—81no—
702C4⋊C4#10214yes—
703C4⋊C4C4×D412yes—
704C4⋊C4C2×M1612yes—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—24no—
712C22⋊C4—22no—
713C22⋊C4—41no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—41no—
724C22⋊C4—41no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C22⋊C4—81no—
732C22⋊C4—81no—
733C22⋊C4#10214yes—
734C22⋊C4#10214yes—
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—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—41no—
754C42—41no—
755C42—41no—
756C42—41no—
757C42—42no—
758C42—42no—
759C42C2×D812yes—
760C42C2×SD1612yes—
761C42C22×D411yescharacteristic
762C42C2×#4111yescharacteristic
763C42H(5,𝔽2)11yescharacteristic
764C42H(5,𝔽2)11yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—48no—
781C23—48no—
782C23—48no—
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—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—48no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23#40712yes—
811C23C2×#10212yes—
812C23C2×#10212yes—
813C23#42112yes—
814C23C22×C22⋊C411yescharacteristic
815D4—28no—
816D4—22no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—48no—
824D4—48no—
825D4—48no—
826D4—48no—
827D4—48no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4#43514yescomplemented
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—48no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—84no—
902C2×C4—84no—
903C2×C4—84no—
904C2×C4—84no—
905C2×C4—84no—
906C2×C4—84no—
907C2×C4—84no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—81no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4#40712yes—
917C2×C4C2×#10212yes—
918C2×C4C2×#10212yes—
919C2×C4C2×#10212yes—
920C2×C4C2×#10212yes—
921C2×C4C2×C4×D411yescharacteristic
922C2×C4#51811yescharacteristic
923C2×C4D4211yescharacteristic
924C2×C4D4211yescharacteristic
925C2×C4#54611yescharacteristic
926C2×C4#54611yescharacteristic
927C2×C4C22×M1611yescharacteristic
928C2×C4C22×M1611yescharacteristic
929C2×C4C2×#13111yescharacteristic
930C2×C4#56811yescharacteristic
931C2×C4C22×D811yescharacteristic
932C2×C4C22×SD1611yescharacteristic
933C2×C4#57611yescharacteristic
934C2×C4#57711yescharacteristic
935C8—42no—
936C8—42no—
937C8—42no—
938C8—81no—
939C8—81no—
940C8—81no—
941C8—81no—
942C8—81no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—24no—
952C22—22no—
953C22—42no—
954C22—41no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—816no—
970C22—816no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—81no—
978C22—81no—
979C22#148614yescomplemented
980C22D4×C22⋊C411yescharacteristic
981C22C2×#40711yescharacteristic
982C22#288011yescharacteristic
983C22C22×#10211yescharacteristic
984C22#289711yescharacteristic
985C22C2×#42111yescharacteristic
986C22#290111yescharacteristic
987C4—22no—
988C4—22no—
989C4—22no—
990C4—22no—
991C4—22no—
992C4—21no—
993C4—21no—
994C4—42no—
995C4—41no—
996C4—41no—
997C4—41no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4C2×#43511yescharacteristic
1005C4D4×M1611yescharacteristic
1006C4#297311yescharacteristic
1007C4#297411yescharacteristic
1008C4D4×D811yescharacteristic
1009C4D4×SD1611yescharacteristic
1010C4#329411yescharacteristic
1011C4#329511yescharacteristic
1012C2—24no—
1013C2—42no—
1014C2—44no—
1015C2—82no—
1016C2—82no—
1017C2C2×#148611yescharacteristic
1018C2#1745311yescharacteristic
1019C2#1750711yescharacteristic
1020C2#1752111yescharacteristic
1021C2#2239911yescharacteristic
1022C2D4×#10211yescharacteristic
1023C2#2243411yescharacteristic
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. #22648C2semidirect
3. #21101C2semidirect
4. C2×#1486C2semidirect
5. C22×D4⋊C8C2semidirect
6. #9678C2semidirect
7. #9644C2semidirect
8. #9076C2semidirect
9. #9072C2semidirect
10. #8944C2semidirect
11. #8939C2semidirect
12. #8563C2semidirect
13. #8310C2semidirect
14. #8310C2semidirect
15. #8174C2semidirect
21. C2×#431C22semidirect
22. C2×#423C22semidirect
23. C22×C4⋊C8C22semidirect
24. C22×C4×C8C22semidirect
51. #1842C22semidirect
52. #1797C22semidirect
53. #1797C22semidirect
54. #1767C22semidirect
55. 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
240. D4⋊C8D4semidirect
264. C22×D4M16semidirect
320. #121M16semidirect
463. C4⋊C8C2×D4semidirect
478. C4×C8C2×D4semidirect
833. D4#435semidirect
979. C22#1486semidirect

Maximal subgroups

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

subgroupindex
C4×D422
#226482
#211012
C2×#14862
C22×D4⋊C82
#96782
#96442
#90762
#90722
#89442
#89392
#85632
#83102
#81742