Finite Group Databasebeta

← #385874

Subgroups — #385874

Order 512.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1205 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic, complemented
3C2×#1870C211yesmaximal, characteristic, complemented
4C2×#1869C211yesmaximal, characteristic, complemented
5C2×#1869C211yesmaximal, characteristic, complemented
6#11346C211yesmaximal, characteristic, complemented
7#11346C211yesmaximal, characteristic, complemented
8#11147C211yesmaximal, characteristic, complemented
9#11147C211yesmaximal, characteristic, complemented
10#10964C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic, complemented
14#10712C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×#121C411yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C4×#121—24no—
34C4×#121—24no—
35C2×#390C411yescharacteristic
36C2×#389C411yescharacteristic
37C2×#388C411yescharacteristic
38C2×#388C411yescharacteristic
39C2×#386C411yescharacteristic
40C2×#386C411yescharacteristic
41C2×#380C411yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45#1870—24no—
46#1870—24no—
47#1869—24no—
48#1869—24no—
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C23×D4C2×C411yescharacteristic
66C23×D4C2×C411yescharacteristic
67C23×D4C2×C411yescharacteristic
68C24×C4C2×C411yescharacteristic
69C24×C4C2×C411yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—41no—
77C22×M16—41no—
78C22×M16—41no—
79C22×M16—41no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—41no—
84C23×C8—41no—
85C23×C8—41no—
86C23×C8—41no—
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×#121—24no—
96C2×#121—24no—
97C2×#121—24no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4—22no—
102C2×C4×D4—22no—
103C2×C4×D4—22no—
104C2×C4×D4—22no—
105C2×C4×D4—22no—
106C2×C4×D4—41no—
107C2×C4×D4—41no—
108C2×C4×D4—41no—
109C2×C4×D4—41no—
110C2×C4×D4—41no—
111C2×C4×D4—41no—
112C2×C4×D4—41no—
113C2×C4×D4—41no—
114C2×C4×D4D414yes—
115C2×C4×D4D414yes—
116C22×C4⋊C4C2×C411yescharacteristic
117C22×C4⋊C4C2×C411yescharacteristic
118C22×C4⋊C4C2×C411yescharacteristic
119C22×C4⋊C4C2×C411yescharacteristic
120C22×C4⋊C4C2×C411yescharacteristic
121C22×C22⋊C4C2×C411yescharacteristic
122C22×C22⋊C4C2×C411yescharacteristic
123C22×C22⋊C4C2×C411yescharacteristic
124C22×C22⋊C4C2×C411yescharacteristic
125C22×C22⋊C4C2×C411yescharacteristic
126C22×C22⋊C4C2×C411yescharacteristic
127C22×C22⋊C4C2×C411yescharacteristic
128C22×C22⋊C4C2×C411yescharacteristic
129C22×C22⋊C4C2×C411yescharacteristic
130C22×C22⋊C4C2×C411yescharacteristic
131C22×C42—22no—
132C22×C42—22no—
133C22×C42—41no—
134C22×C42—41no—
135C22×C42—41no—
136C22×C42—41no—
137C22×C42C2×C411yescharacteristic
138C22×C42C2×C411yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—22no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—41no—
159C2×C22⋊C8—41no—
160C2×C22⋊C8—41no—
161C2×C22⋊C8—41no—
162C2×C22⋊C8—41no—
163C2×C22⋊C8—41no—
164C2×C22⋊C8—41no—
165C2×C22⋊C8—41no—
166C2×C22⋊C8—41no—
167C2×C22⋊C8—41no—
168C2×C22⋊C8—41no—
169C2×C22⋊C8—41no—
170C2×C22⋊C8—41no—
171C2×C22⋊C8—41no—
172C2×C22⋊C8D414yescomplemented
173#390—24no—
174#389—24no—
175#388—24no—
176#388—24no—
177#386—24no—
178#386—24no—
179#380—24no—
180C4×C4⋊C4—22no—
181C4×C4⋊C4—22no—
182C4×C22⋊C4—22no—
183C4×C22⋊C4—22no—
184C4×C22⋊C4—22no—
185C4×C22⋊C4—22no—
186C2×#95C2×C411yescharacteristic
187C2×#95C2×C411yescharacteristic
188C2×#95C2×C411yescharacteristic
189C2×#95C2×C411yescharacteristic
190C2×#95C2×C411yescharacteristic
191C2×#95C2×C411yescharacteristic
192#336—22no—
193#336—22no—
194#336—22no—
195#336—22no—
196#336—22no—
197#336—22no—
198#336—22no—
199#336—22no—
200#336—41no—
201#336—41no—
202#336—41no—
203#336—41no—
204#336—41no—
205#336—41no—
206#336—41no—
207#336—41no—
208C25C22×C411yescharacteristic
209C25C22×C411yescharacteristic
210C25C22×C411yescharacteristic
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—41no—
228C22×D4—41no—
229C22×D4—41no—
230C22×D4C22⋊C414yes—
231C22×D4M1614yescomplemented
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4C22×C411yescharacteristic
283C23×C4C22×C411yescharacteristic
284C23×C4C22×C411yescharacteristic
285C23×C4C22×C411yescharacteristic
286C23×C4C22×C411yescharacteristic
287C23×C4C22×C411yescharacteristic
288C23×C4C22×C411yescharacteristic
289C23×C4C22×C411yescharacteristic
290C23×C4C22×C411yescharacteristic
291C23×C4C22×C411yescharacteristic
292C23×C4C22×C411yescharacteristic
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4#4112yes—
299C23×C4C2411yescharacteristic
300C2×M16—44no—
301C2×M16—44no—
302C2×M16—44no—
303C2×M16—44no—
304C2×M16—44no—
305C2×M16—44no—
306C2×M16—44no—
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×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—44no—
360C22×C8—44no—
361C22×C8—44no—
362C22×C8—44no—
363C22×C8—44no—
364C22×C8—44no—
365C22×C8—44no—
366C22×C8C2×D412yes—
367C22×C8C2×D412yes—
368C22×C8#4112yes—
369C22×C8#4112yes—
370#121—232no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—44no—
374C4×D4—44no—
375C4×D4—44no—
376C4×D4—44no—
377C4×D4—44no—
378C4×D4—44no—
379C4×D4—44no—
380C4×D4—44no—
381C4×D4—44no—
382C4×D4—44no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4C22⋊C414yes—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—41no—
424C2×C22⋊C4—41no—
425C2×C22⋊C4C22⋊C414yes—
426C2×C22⋊C4C22⋊C414yes—
427C2×C22⋊C4M1614yescomplemented
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—44no—
453C2×C42—44no—
454C2×C42—44no—
455C2×C42—44no—
456C2×C42—41no—
457C2×C42—41no—
458C2×C42—41no—
459C2×C42—41no—
460C2×C42C2×D412yes—
461C2×C42C2×D412yes—
462C22⋊C8—44no—
463C22⋊C8—44no—
464C22⋊C8—44no—
465C22⋊C8—44no—
466C22⋊C8—44no—
467C22⋊C8—44no—
468C22⋊C8—44no—
469C22⋊C8—44no—
470C22⋊C8—44no—
471C22⋊C8—44no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24C2×C22⋊C412yes—
517C24C2×C22⋊C412yes—
518C24C4×D412yes—
519C24C2×M1612yes—
520C24C2×M1612yes—
521C24C2×M1612yes—
522C24#13112yes—
523C24C23×C411yescharacteristic
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—28no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—28no—
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—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—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—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—44no—
709C22×C4C2×C22⋊C412yes—
710C22×C4C2×C22⋊C412yes—
711C22×C4C2×C22⋊C412yes—
712C22×C4C2×C22⋊C412yes—
713C22×C4C4×D412yes—
714C22×C4C2×M1612yes—
715C22×C4C2×M1612yes—
716C22×C4C2×M1612yes—
717C22×C4#13112yes—
718C22×C4#13112yes—
719C22×C4#13112yes—
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D411yescharacteristic
722C22×C4C22×D411yescharacteristic
723C22×C4C2×#4111yescharacteristic
724C22×C4C2×#4111yescharacteristic
725C22×C4C2×#4111yescharacteristic
726C22×C4H(5,𝔽2)11yescharacteristic
727C22×C4H(5,𝔽2)11yescharacteristic
728C22×C4H(5,𝔽2)11yescharacteristic
729C22×C4H(5,𝔽2)11yescharacteristic
730C22×C4H(5,𝔽2)11yescharacteristic
731C22×C4H(5,𝔽2)11yescharacteristic
732C22×C4H(5,𝔽2)11yescharacteristic
733C22×C42−1+411yescharacteristic
734M16—416no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—22no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—22no—
746C2×C8—22no—
747C2×C8—416no—
748C2×C8—41no—
749C2×C8—41no—
750C2×C8—41no—
751C2×C8—41no—
752C2×C8—41no—
753C2×C8—41no—
754C2×C8—41no—
755C2×C8—41no—
756C2×C8—41no—
757C2×C8—41no—
758C2×C8—41no—
759C2×C8—41no—
760C2×C8—41no—
761C2×C8—41no—
762C2×C8—41no—
763C2×C8—41no—
764C2×C8—41no—
765C2×C8—41no—
766C2×C8—41no—
767C2×C8—41no—
768C2×C8—41no—
769C2×C8—41no—
770C2×C8—41no—
771C2×C8—41no—
772C2×C8—41no—
773C2×C8—41no—
774C2×C8—41no—
775C2×C8—41no—
776C2×C8—41no—
777C2×C8—41no—
778C2×C8—41no—
779C2×C8—41no—
780C2×C8—41no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8—41no—
784C2×C8—41no—
785C2×C8—41no—
786C2×C8—41no—
787C2×C8—41no—
788C2×C8—41no—
789C2×C8—41no—
790C2×C8—41no—
791C2×C8—41no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C42—22no—
808C42—22no—
809C42—22no—
810C42—22no—
811C42—44no—
812C42—44no—
813C42—41no—
814C42—41no—
815C42—41no—
816C42—41no—
817C42—41no—
818C42—41no—
819C42—41no—
820C42—41no—
821C42—41no—
822C42—41no—
823C42—41no—
824C42—41no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23#40714yes—
929C23#43514yes—
930C23C22×C22⋊C411yescharacteristic
931C23C2×C4×D411yescharacteristic
932C23C4×#4111yescharacteristic
933C23#51811yescharacteristic
934C23#51811yescharacteristic
935C23#51811yescharacteristic
936C23#52011yescharacteristic
937C23C22×M1611yescharacteristic
938C23C22×M1611yescharacteristic
939C23C2×#13111yescharacteristic
940C23C2×#13111yescharacteristic
941C23C2×#13111yescharacteristic
942C23C2×#13111yescharacteristic
943C23#56811yescharacteristic
944C23#56811yescharacteristic
945D4—416no—
946D4—416no—
947D4—416no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—416no—
979C2×C4—416no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4#40814yes—
1051C2×C4#53411yescharacteristic
1052C2×C4#53411yescharacteristic
1053C2×C4#53411yescharacteristic
1054C2×C4#53411yescharacteristic
1055C2×C4#53411yescharacteristic
1056C2×C4#53711yescharacteristic
1057C2×C4#53811yescharacteristic
1058C2×C4#53811yescharacteristic
1059C2×C4#53811yescharacteristic
1060C2×C4#53911yescharacteristic
1061C2×C4#54011yescharacteristic
1062C2×C4#54011yescharacteristic
1063C2×C4D4211yescharacteristic
1064C2×C4D4211yescharacteristic
1065C2×C4#54611yescharacteristic
1066C2×C4#54611yescharacteristic
1067C2×C4#54611yescharacteristic
1068C2×C4#54611yescharacteristic
1069C2×C4#54611yescharacteristic
1070C2×C4#54611yescharacteristic
1071C2×C4#54711yescharacteristic
1072C2×C4#54711yescharacteristic
1073C2×C4#55311yescharacteristic
1074C2×C4#55311yescharacteristic
1075C2×C4#56011yescharacteristic
1076C2×C4#56011yescharacteristic
1077C2×C4#56211yescharacteristic
1078C2×C4#56211yescharacteristic
1079C8—42no—
1080C8—42no—
1081C8—42no—
1082C8—42no—
1083C8—81no—
1084C8—81no—
1085C8—81no—
1086C8—81no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22#230811yescharacteristic
1133C22#232511yescharacteristic
1134C22#233311yescharacteristic
1135C22D4×C22⋊C411yescharacteristic
1136C22#233911yescharacteristic
1137C22#236411yescharacteristic
1138C22#237711yescharacteristic
1139C22C2×#40711yescharacteristic
1140C22C2×#40811yescharacteristic
1141C22#288011yescharacteristic
1142C22#288011yescharacteristic
1143C22C2×#43511yescharacteristic
1144C22#293111yescharacteristic
1145C22D4×M1611yescharacteristic
1146C22#293511yescharacteristic
1147C22#296511yescharacteristic
1148C22#296611yescharacteristic
1149C22#296911yescharacteristic
1150C22#297011yescharacteristic
1151C22#297311yescharacteristic
1152C22#297411yescharacteristic
1153C22#297411yescharacteristic
1154C22#297411yescharacteristic
1155C22#297411yescharacteristic
1156C22#297411yescharacteristic
1157C22#297611yescharacteristic
1158C22#297611yescharacteristic
1159C22#297711yescharacteristic
1160C22#297811yescharacteristic
1161C22#297911yescharacteristic
1162C22#298111yescharacteristic
1163C22#298911yescharacteristic
1164C22#299011yescharacteristic
1165C22#299311yescharacteristic
1166C22#299411yescharacteristic
1167C4—24no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—81no—
1177C4—81no—
1178C4#266811yescharacteristic
1179C4#266811yescharacteristic
1180C4#267111yescharacteristic
1181C4#267111yescharacteristic
1182C4#268811yescharacteristic
1183C4#268811yescharacteristic
1184C4#270811yescharacteristic
1185C4#270811yescharacteristic
1186C2—44no—
1187C2—44no—
1188C2—82no—
1189C2#1441711yescharacteristic
1190C2#2174011yescharacteristic
1191C2#2174411yescharacteristic
1192C2#2217211yescharacteristic
1193C2#2217411yescharacteristic
1194C2#2233311yescharacteristic
1195C2#2233511yescharacteristic
1196C2#2239911yescharacteristic
1197C2#2240211yescharacteristic
1198C2#2247111yescharacteristic
1199C2#2247411yescharacteristic
1200C2#2311711yescharacteristic
1201C2#2311811yescharacteristic
1202C2#2332911yescharacteristic
1203C2#2333111yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC22×#121C4
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
2. C2×#1870C2semidirect
3. C2×#1870C2semidirect
4. C2×#1869C2semidirect
5. C2×#1869C2semidirect
6. #11346C2semidirect
7. #11346C2semidirect
8. #11147C2semidirect
9. #11147C2semidirect
10. #10964C2semidirect
11. #10964C2semidirect
12. #10715C2semidirect
13. #10714C2semidirect
14. #10712C2semidirect
15. #10712C2semidirect
172. C2×C22⋊C8D4semidirect
231. C22×D4M16semidirect
427. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#18702
C2×#18692
#113462
#111472
#109642
#107152
#107142
#107122