Finite Group Databasebeta

← #392830

Subgroups — #392830

Order 512.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×M16C211yesmaximal, characteristic, complemented
2C2×#1924C211yesmaximal, characteristic, complemented
3C2×#1923C211yesmaximal, characteristic, complemented
4C2×#1870C211yesmaximal, characteristic
5C2×#1870C211yesmaximal, characteristic
6C2×#1851C211yesmaximal, characteristic, complemented
7C4×#386C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10877C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10798C211yesmaximal, characteristic, complemented
13#10797C211yesmaximal, characteristic, complemented
14#10715C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C2×C4×M16—24no—
29C2×C4×M16—24no—
30C2×C4×M16—24no—
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C2×#386C411yescharacteristic
36C2×#386C411yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40#1924—24no—
41#1923—24no—
42#1870—24no—
43#1870—24no—
44#1851—24no—
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1437C411yescharacteristic
60#1437C411yescharacteristic
61#1436C411yescharacteristic
62#1436C411yescharacteristic
63C22⋊#95C411yescharacteristic
64C22⋊#95C411yescharacteristic
65C4×#95C2211yescharacteristic
66C4×#95C2211yescharacteristic
67C23×D4C2×C411yescharacteristic
68C24×C4C2×C411yescharacteristic
69C24×C4C2×C411yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16D414yes—
85C22×M16D414yes—
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C411yescharacteristic
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C411yescharacteristic
106C22×C22⋊C4C2×C411yescharacteristic
107C22×C22⋊C4C2×C411yescharacteristic
108C22×C22⋊C4C2×C411yescharacteristic
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42C2×C411yescharacteristic
116C22×C42C2×C411yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C2×C4⋊C8—22no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C4×M16—232no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—22no—
150C2×#97—22no—
151C2×#97—22no—
152C2×#97D414yescomplemented
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8D414yescomplemented
159#386—24no—
160#386—24no—
161C4×C22⋊C4—22no—
162C4×C22⋊C4—22no—
163C4×C22⋊C4—22no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C2×#95C2×C411yescharacteristic
168C2×#95C2×C411yescharacteristic
169C2×#95C2×C411yescharacteristic
170C2×#95C2×C411yescharacteristic
171C2×#95C2×C411yescharacteristic
172C2×#95C2×C411yescharacteristic
173C2×#95C2×C411yescharacteristic
174C2×#95C2×C411yescharacteristic
175C2×#95C2×C411yescharacteristic
176C2×#95C2×C411yescharacteristic
177C2×#95C2×C411yescharacteristic
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180C2×#95C2×C411yescharacteristic
181#336—22no—
182#336—22no—
183#336—22no—
184#336—22no—
185#336—22no—
186#336—22no—
187#336—22no—
188#336—22no—
189#336—22no—
190#336—22no—
191#336—22no—
192#336—22no—
193#336—22no—
194#336—22no—
195C25C22×C411yescharacteristic
196C25C22×C411yescharacteristic
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—41no—
203C22×D4—41no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—41no—
237C23×C4—41no—
238C23×C4—41no—
239C23×C4—41no—
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C22×C411yescharacteristic
252C23×C4C2×D412yes—
253C23×C4C2×D412yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4#4112yes—
257C23×C4#4112yes—
258C23×C4C2411yescharacteristic
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—28no—
263C2×M16—28no—
264C2×M16—28no—
265C2×M16—28no—
266C2×M16—28no—
267C2×M16—28no—
268C2×M16—28no—
269C2×M16—28no—
270C2×M16—28no—
271C2×M16—28no—
272C2×M16—28no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
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—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8C2×D412yes—
318C22×C8C2×D412yes—
319C22×C8C2×D412yes—
320C22×C8C2×D412yes—
321C22×C8C2×D412yes—
322C22×C8C2×D412yes—
323C22×C8C2×D412yes—
324C22×C8C2×D412yes—
325C22×C8#4112yes—
326C22×C8#4112yes—
327C22×C8#4112yes—
328C22×C8#4112yes—
329C4×D4—44no—
330C4×D4—44no—
331C4×D4—44no—
332C4×D4—44no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4M1614yescomplemented
360C2×C42—28no—
361C2×C42—28no—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
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—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42C2×D412yes—
397C2×C42C2×D412yes—
398C2×C42#4112yes—
399C2×C42#4112yes—
400C4⋊C8—44no—
401C4⋊C8—44no—
402C22⋊C8—44no—
403C22⋊C8—44no—
404C22⋊C8—44no—
405C22⋊C8—44no—
406C22⋊C8—44no—
407C22⋊C8—44no—
408#97—28no—
409#97—28no—
410C4×C8—28no—
411C4×C8—28no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—41no—
424#95—41no—
425#95M1614yescomplemented
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24#11712yes—
453C24C4×D412yes—
454C24C4×D412yes—
455C24C2×M1612yes—
456C24C23×C411yescharacteristic
457C2×D4—28no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
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—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4#11712yes—
601C22×C4C4×D412yes—
602C22×C4C4×D412yes—
603C22×C4C4×D412yes—
604C22×C4C4×D412yes—
605C22×C4C4×D412yes—
606C22×C4C4×D412yes—
607C22×C4#12114yes—
608C22×C4#12314yes—
609C22×C4#12414yes—
610C22×C4#12614yes—
611C22×C4C2×M1612yes—
612C22×C4C2×M1612yes—
613C22×C4C2×M1612yes—
614C22×C4C2×M1612yes—
615C22×C4C2×M1612yes—
616C22×C4#13112yes—
617C22×C4#13112yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632M16—232no—
633M16—232no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
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—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—41no—
686C2×C8#12014yes—
687C2×C8#12114yes—
688C2×C8#12114yes—
689C2×C8#12314yes—
690C4⋊C4—44no—
691C22⋊C4—28no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C42—28no—
700C42—28no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—41no—
715C42—41no—
716C42—41no—
717C42—41no—
718C42—41no—
719C42—41no—
720C42—41no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
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#38814yes—
791C23C2×#11711yescharacteristic
792C23C2×C4×D411yescharacteristic
793C23C2×C4×D411yescharacteristic
794C23C2×C4×D411yescharacteristic
795C23C2×C4×D411yescharacteristic
796C23C4×#4111yescharacteristic
797C23C4×#4111yescharacteristic
798C23C22×M1611yescharacteristic
799C23C22×M1611yescharacteristic
800C23C2×#13111yescharacteristic
801C23C2×#13111yescharacteristic
802C23#56811yescharacteristic
803C23#56811yescharacteristic
804C23#56811yescharacteristic
805C23#56811yescharacteristic
806D4—416no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
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—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—416no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
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—41no—
877C2×C4—41no—
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—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
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—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4#38814yes—
907C2×C4#43514yes—
908C2×C4#43614yes—
909C2×C4C2×#12011yescharacteristic
910C2×C4C2×#12111yescharacteristic
911C2×C4C2×#12111yescharacteristic
912C2×C4C2×#12111yescharacteristic
913C2×C4C2×#12311yescharacteristic
914C2×C4C2×#12311yescharacteristic
915C2×C4#52511yescharacteristic
916C2×C4#52511yescharacteristic
917C2×C4#52511yescharacteristic
918C2×C4#52511yescharacteristic
919C2×C4#52511yescharacteristic
920C2×C4#52511yescharacteristic
921C2×C4#52511yescharacteristic
922C2×C4#52511yescharacteristic
923C2×C4#52511yescharacteristic
924C2×C4#52511yescharacteristic
925C2×C4C2×#12411yescharacteristic
926C2×C4C2×#12611yescharacteristic
927C2×C4#52911yescharacteristic
928C2×C4#52911yescharacteristic
929C2×C4#52911yescharacteristic
930C2×C4#52911yescharacteristic
931C2×C4#52911yescharacteristic
932C2×C4#52911yescharacteristic
933C2×C4#52911yescharacteristic
934C2×C4#52911yescharacteristic
935C2×C4#53211yescharacteristic
936C2×C4#53211yescharacteristic
937C8—24no—
938C8—24no—
939C8—24no—
940C8—24no—
941C8—81no—
942C8—81no—
943C8—81no—
944C8—81no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22C2×#38811yescharacteristic
976C22#229011yescharacteristic
977C22#229011yescharacteristic
978C22C4×#12011yescharacteristic
979C22C4×#12111yescharacteristic
980C22C4×#12111yescharacteristic
981C22C4×#12311yescharacteristic
982C22#292011yescharacteristic
983C22#292111yescharacteristic
984C22#292211yescharacteristic
985C22#292311yescharacteristic
986C22C2×#43511yescharacteristic
987C22C2×#43611yescharacteristic
988C22#293011yescharacteristic
989C22#293011yescharacteristic
990C22#293311yescharacteristic
991C22#293311yescharacteristic
992C22#293311yescharacteristic
993C22#293311yescharacteristic
994C22D4×M1611yescharacteristic
995C22D4×M1611yescharacteristic
996C22D4×M1611yescharacteristic
997C22D4×M1611yescharacteristic
998C22D4×M1611yescharacteristic
999C22D4×M1611yescharacteristic
1000C22#293511yescharacteristic
1001C22#293511yescharacteristic
1002C22#296511yescharacteristic
1003C22#296511yescharacteristic
1004C22#296711yescharacteristic
1005C22#296711yescharacteristic
1006C22#296911yescharacteristic
1007C22#296911yescharacteristic
1008C22#297011yescharacteristic
1009C22#297111yescharacteristic
1010C4—24no—
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C4—81no—
1022C4#284711yescharacteristic
1023C4#284911yescharacteristic
1024C4#285011yescharacteristic
1025C4#285011yescharacteristic
1026C4#285211yescharacteristic
1027C4#285211yescharacteristic
1028C4#285311yescharacteristic
1029C4#285411yescharacteristic
1030C2—44no—
1031C2—82no—
1032C2#1469611yescharacteristic
1033C2#2104811yescharacteristic
1034C2#2104911yescharacteristic
1035C2#2110211yescharacteristic
1036C2#2110411yescharacteristic
1037C2#2110611yescharacteristic
1038C2#2110811yescharacteristic
1039C2#2143911yescharacteristic
1040C2#2144111yescharacteristic
1041C2#2148611yescharacteristic
1042C2#2148811yescharacteristic
1043C2#2149011yescharacteristic
1044C2#2149011yescharacteristic
1045C2#2156211yescharacteristic
1046C2#2156511yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×C4×M16C2semidirect
2. C2×#1924C2semidirect
3. C2×#1923C2semidirect
6. C2×#1851C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10877C2semidirect
11. #10876C2semidirect
12. #10798C2semidirect
13. #10797C2semidirect
14. #10715C2semidirect
15. #10712C2semidirect
152. C2×#97D4semidirect
158. C2×C4×C8D4semidirect
359. C2×C22⋊C4M16semidirect
425. #95M16semidirect

Maximal subgroups

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

subgroupindex
C22×C4×M162
C2×#19242
C2×#19232
C2×#18702
C2×#18512
C4×#3862
#109222
#109212
#108772
#108762
#107982
#107972
#107152
#107122