Finite Group Databasebeta

← #368678

Subgroups — #368678

Order 512.

2512 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D4C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic, complemented
4C2×#1869C211yesmaximal, characteristic, complemented
5C2×#1869C211yesmaximal, characteristic, complemented
6C2×#1869C211yesmaximal, characteristic, complemented
7C22×#336C211yesmaximal, characteristic, complemented
8#11202C211yesmaximal, characteristic, complemented
9#11147C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic, complemented
12#10921C211yesmaximal, characteristic, complemented
13#10874C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×#121C411yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×C8×D4—24no—
25C2×C8×D4—24no—
26C2×C8×D4—24no—
27C22×C4⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38C4×#121—24no—
39C4×#121—24no—
40C2×#390C411yescharacteristic
41C2×#389C411yescharacteristic
42C2×#388C411yescharacteristic
43C2×#388C411yescharacteristic
44C2×#386C411yescharacteristic
45C2×#386C411yescharacteristic
46C2×#380C411yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50#1869—24no—
51#1869—24no—
52#1869—24no—
53#1869—24no—
54C2×#336—24no—
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C23×D4C2×C411yescharacteristic
70C23×D4C2×C411yescharacteristic
71C23×D4C2×C411yescharacteristic
72C24×C4C2×C411yescharacteristic
73C24×C4C2×C411yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—22no—
85C23×C8—22no—
86C23×C8—22no—
87C23×C8—22no—
88C23×C8—22no—
89C23×C8—22no—
90C23×C8—22no—
91C23×C8—41no—
92C23×C8—41no—
93C23×C8—41no—
94C23×C8—41no—
95C23×C8—41no—
96C23×C8—41no—
97C23×C8D414yescomplemented
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×#121—24no—
107C2×#121—24no—
108C2×#121C818yescomplemented
109C2×C4×D4—22no—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—22no—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—41no—
124C2×C4×D4—41no—
125C2×C4×D4D414yes—
126C2×C4×D4D414yes—
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C4⋊C4C2×C411yescharacteristic
129C22×C4⋊C4C2×C411yescharacteristic
130C22×C4⋊C4C2×C411yescharacteristic
131C22×C4⋊C4C2×C411yescharacteristic
132C22×C22⋊C4C2×C411yescharacteristic
133C22×C22⋊C4C2×C411yescharacteristic
134C22×C22⋊C4C2×C411yescharacteristic
135C22×C22⋊C4C2×C411yescharacteristic
136C22×C22⋊C4C2×C411yescharacteristic
137C22×C22⋊C4C2×C411yescharacteristic
138C22×C22⋊C4C2×C411yescharacteristic
139C22×C22⋊C4C2×C411yescharacteristic
140C22×C22⋊C4C2×C411yescharacteristic
141C22×C22⋊C4C2×C411yescharacteristic
142C22×C42—22no—
143C22×C42—22no—
144C22×C42—22no—
145C22×C42—22no—
146C22×C42—41no—
147C22×C42—41no—
148C22×C42C2×C411yescharacteristic
149C22×C42C2×C411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C8×D4—232no—
155C2×C4⋊C8—22no—
156C2×C4⋊C8—22no—
157C2×C4⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—22no—
161C2×C22⋊C8—22no—
162C2×C22⋊C8—22no—
163C2×C22⋊C8—22no—
164C2×C22⋊C8—22no—
165C2×C22⋊C8—22no—
166C2×C22⋊C8—22no—
167C2×C22⋊C8—22no—
168C2×C22⋊C8—22no—
169C2×C22⋊C8—22no—
170C2×C22⋊C8—22no—
171C2×C22⋊C8—22no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—22no—
175C2×C22⋊C8—22no—
176C2×C22⋊C8—22no—
177C2×C22⋊C8—22no—
178C2×C22⋊C8—41no—
179C2×C22⋊C8—41no—
180C2×C22⋊C8—41no—
181C2×C22⋊C8—41no—
182C2×C22⋊C8—41no—
183C2×C22⋊C8—41no—
184C2×C22⋊C8D414yescomplemented
185C2×C4×C8—22no—
186C2×C4×C8—22no—
187C2×C4×C8—22no—
188#390—24no—
189#389—24no—
190#388—24no—
191#388—24no—
192#386—24no—
193#386—24no—
194#380—24no—
195C4×C4⋊C4—22no—
196C4×C4⋊C4—22no—
197C4×C22⋊C4—22no—
198C4×C22⋊C4—22no—
199C4×C22⋊C4—22no—
200C4×C22⋊C4—22no—
201C2×#95C2×C411yescharacteristic
202C2×#95C2×C411yescharacteristic
203C2×#95C2×C411yescharacteristic
204C2×#95C2×C411yescharacteristic
205C2×#95C2×C411yescharacteristic
206C2×#95C2×C411yescharacteristic
207#336—22no—
208#336—22no—
209#336—22no—
210#336—22no—
211#336—22no—
212#336—22no—
213#336—22no—
214#336—22no—
215#336—22no—
216#336—22no—
217#336—22no—
218#336—41no—
219#336—41no—
220#336D414yescomplemented
221C25C22×C411yescharacteristic
222C25C22×C411yescharacteristic
223C25C22×C411yescharacteristic
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—41no—
239C22×D4—41no—
240C22×D4C22⋊C414yes—
241C22×D4C2×C814yes—
242C22×D4C2×C814yescomplemented
243C22×D4C2×C814yescomplemented
244C22×D4M1614yes—
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—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
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—21no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—41no—
289C23×C4—41no—
290C23×C4—41no—
291C23×C4—41no—
292C23×C4C2×C814yescomplemented
293C23×C4C22×C411yescharacteristic
294C23×C4C22×C411yescharacteristic
295C23×C4C22×C411yescharacteristic
296C23×C4C22×C411yescharacteristic
297C23×C4C22×C411yescharacteristic
298C23×C4C22×C411yescharacteristic
299C23×C4C22×C411yescharacteristic
300C23×C4C22×C411yescharacteristic
301C23×C4C22×C411yescharacteristic
302C23×C4C22×C411yescharacteristic
303C23×C4C22×C411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D412yes—
309C23×C4C2×D412yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4C2411yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—28no—
318C22×C8—28no—
319C22×C8—28no—
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—28no—
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—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—44no—
366C22×C8—44no—
367C22×C8—44no—
368C22×C8—44no—
369C22×C8—44no—
370C22×C8—44no—
371C22×C8—44no—
372C22×C8—44no—
373C22×C8—44no—
374C22×C8—44no—
375C22×C8—44no—
376C22×C8—44no—
377C22×C8—44no—
378C22×C8—44no—
379C22×C8—44no—
380C22×C8—44no—
381C22×C8—44no—
382C22×C8C2×D412yes—
383C22×C8C2×D412yes—
384C22×C8C2×D412yes—
385C22×C8C2×D412yes—
386C22×C8C2×D412yes—
387C22×C8C2×D412yes—
388C22×C8#4112yes—
389C22×C8#4112yes—
390#121—232no—
391C4×D4—28no—
392C4×D4—28no—
393C4×D4—28no—
394C4×D4—28no—
395C4×D4—44no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—44no—
399C4×D4—44no—
400C4×D4—44no—
401C4×D4—44no—
402C4×D4—44no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4C22⋊C414yes—
417C2×C4⋊C4C2×C814yescomplemented
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4C22⋊C414yes—
445C2×C22⋊C4C22⋊C414yes—
446C2×C22⋊C4C2×C814yescomplemented
447C2×C22⋊C4C2×C814yescomplemented
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—44no—
473C2×C42—44no—
474C2×C42—44no—
475C2×C42—44no—
476C2×C42—41no—
477C2×C42—41no—
478C2×C42C2×D412yes—
479C2×C42C2×D412yes—
480C2×C42C2×D412yes—
481C2×C42#4112yes—
482C4⋊C8—28no—
483C22⋊C8—28no—
484C22⋊C8—28no—
485C22⋊C8—44no—
486C22⋊C8—44no—
487C22⋊C8—44no—
488C22⋊C8—44no—
489C22⋊C8—44no—
490C22⋊C8—44no—
491C22⋊C8—44no—
492C4×C8—28no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
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—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×C22⋊C412yes—
534C24C2×C22⋊C412yes—
535C24C4×D412yes—
536C24C4×D412yes—
537C24C22×C812yes—
538C24C22×C812yes—
539C24C22×C812yes—
540C24C2×M1612yes—
541C24C2×M1612yes—
542C24#13112yes—
543C24#13112yes—
544C24C23×C411yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4C22⋊C8116yescomplemented
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—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—28no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
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—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4C2×C22⋊C412yes—
723C22×C4C2×C22⋊C412yes—
724C22×C4C2×C22⋊C412yes—
725C22×C4C2×C22⋊C412yes—
726C22×C4C4×D412yes—
727C22×C4C4×D412yes—
728C22×C4C4×D412yes—
729C22×C4C4×D412yes—
730C22×C4#12014yes—
731C22×C4#12114yes—
732C22×C4#12114yes—
733C22×C4#12314yes—
734C22×C4C22×C812yes—
735C22×C4C22×C812yes—
736C22×C4C22×C812yes—
737C22×C4C22×C812yes—
738C22×C4C2×M1612yes—
739C22×C4#13112yes—
740C22×C4#13112yes—
741C22×C4C22×D411yescharacteristic
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D411yescharacteristic
745C22×C4C22×D411yescharacteristic
746C22×C4C2×#4111yescharacteristic
747C22×C4C2×#4111yescharacteristic
748C22×C4C2×#4111yescharacteristic
749C22×C4C2×#4111yescharacteristic
750C22×C4C2×#4111yescharacteristic
751C22×C4H(5,𝔽2)11yescharacteristic
752C22×C4H(5,𝔽2)11yescharacteristic
753C22×C4H(5,𝔽2)11yescharacteristic
754C22×C42−1+411yescharacteristic
755C2×C8—22no—
756C2×C8—22no—
757C2×C8—22no—
758C2×C8—22no—
759C2×C8—22no—
760C2×C8—22no—
761C2×C8—22no—
762C2×C8—22no—
763C2×C8—22no—
764C2×C8—22no—
765C2×C8—22no—
766C2×C8—22no—
767C2×C8—22no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—416no—
777C2×C8—416no—
778C2×C8—416no—
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—
792C2×C8—41no—
793C2×C8—41no—
794C2×C8—41no—
795C2×C8—41no—
796C2×C8—41no—
797C2×C8—41no—
798C2×C8—41no—
799C2×C8—41no—
800C2×C8—41no—
801C2×C8—41no—
802C2×C8—41no—
803C2×C8—41no—
804C2×C8—41no—
805C2×C8—41no—
806C2×C8—41no—
807C2×C8—41no—
808C2×C8—41no—
809C2×C8—41no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8#12114yescomplemented
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—22no—
837C42—44no—
838C42—44no—
839C42—41no—
840C42—41no—
841C42—41no—
842C42—41no—
843C42—41no—
844C42—41no—
845C42—41no—
846C42—41no—
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—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
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—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23#38614yes—
945C23C2×C22⋊C814yes—
946C23C2×C22⋊C814yes—
947C23#40814yes—
948C23C8×D414yes—
949C23C8×D414yes—
950C23#43514yes—
951C23#43514yes—
952C23C22×C22⋊C411yescharacteristic
953C23C2×C4×D411yescharacteristic
954C23C2×C4×D411yescharacteristic
955C23C2×C4×D411yescharacteristic
956C23C4×#4111yescharacteristic
957C23#51811yescharacteristic
958C23#52011yescharacteristic
959C23C23×C811yescharacteristic
960C23C22×M1611yescharacteristic
961C23C2×#13111yescharacteristic
962C23C2×#13111yescharacteristic
963C23C2×#13111yescharacteristic
964C23C2×#13111yescharacteristic
965C23#56811yescharacteristic
966C23#56811yescharacteristic
967D4—232no—
968D4—416no—
969D4—416no—
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—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—416no—
1015C2×C4—416no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—81no—
1063C2×C4—81no—
1064C2×C4—81no—
1065C2×C4—81no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—81no—
1069C2×C4—81no—
1070C2×C4#38614yes—
1071C2×C4C2×C22⋊C814yes—
1072C2×C4C8×D414yescomplemented
1073C2×C4C2×#12011yescharacteristic
1074C2×C4C2×#12111yescharacteristic
1075C2×C4C2×#12111yescharacteristic
1076C2×C4C2×#12111yescharacteristic
1077C2×C4C2×#12311yescharacteristic
1078C2×C4#52511yescharacteristic
1079C2×C4#52911yescharacteristic
1080C2×C4#53211yescharacteristic
1081C2×C4#53411yescharacteristic
1082C2×C4#53711yescharacteristic
1083C2×C4#53811yescharacteristic
1084C2×C4#53911yescharacteristic
1085C2×C4D4211yescharacteristic
1086C2×C4D4211yescharacteristic
1087C2×C4D4211yescharacteristic
1088C2×C4#54611yescharacteristic
1089C2×C4#54611yescharacteristic
1090C2×C4#54611yescharacteristic
1091C2×C4#54611yescharacteristic
1092C2×C4#54611yescharacteristic
1093C2×C4#54611yescharacteristic
1094C2×C4#54711yescharacteristic
1095C2×C4#54711yescharacteristic
1096C2×C4#54711yescharacteristic
1097C2×C4#54811yescharacteristic
1098C2×C4#55311yescharacteristic
1099C2×C4#55311yescharacteristic
1100C2×C4#55311yescharacteristic
1101C8—24no—
1102C8—42no—
1103C8—42no—
1104C8—42no—
1105C8—42no—
1106C8—42no—
1107C8—81no—
1108C8—81no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22#186918yescomplemented
1154C22C2×#38611yescharacteristic
1155C22C4×#12111yescharacteristic
1156C22#232511yescharacteristic
1157C22D4×C22⋊C411yescharacteristic
1158C22#233911yescharacteristic
1159C22#236111yescharacteristic
1160C22#236411yescharacteristic
1161C22C22×C22⋊C811yescharacteristic
1162C22C2×#40811yescharacteristic
1163C22#288011yescharacteristic
1164C22#288011yescharacteristic
1165C22C2×C8×D411yescharacteristic
1166C22C2×C8×D411yescharacteristic
1167C22C2×C8×D411yescharacteristic
1168C22C2×#43511yescharacteristic
1169C22C2×#43511yescharacteristic
1170C22#292911yescharacteristic
1171C22#293111yescharacteristic
1172C22#293211yescharacteristic
1173C22#293311yescharacteristic
1174C22D4×M1611yescharacteristic
1175C22#293511yescharacteristic
1176C22#293511yescharacteristic
1177C22C8×#4111yescharacteristic
1178C22#296611yescharacteristic
1179C22#296811yescharacteristic
1180C22#297011yescharacteristic
1181C22#297211yescharacteristic
1182C22#297411yescharacteristic
1183C22#297611yescharacteristic
1184C22#297711yescharacteristic
1185C22#298811yescharacteristic
1186C22#299011yescharacteristic
1187C22#299211yescharacteristic
1188C22#299411yescharacteristic
1189C4—24no—
1190C4—24no—
1191C4—24no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—81no—
1200C4#241011yescharacteristic
1201C4#241611yescharacteristic
1202C4#242411yescharacteristic
1203C4#242511yescharacteristic
1204C4#243011yescharacteristic
1205C4#244311yescharacteristic
1206C4#244411yescharacteristic
1207C4#254311yescharacteristic
1208C2—28no—
1209C2—44no—
1210C2—82no—
1211C2#1402311yescharacteristic
1212C2C2×#186911yescharacteristic
1213C2#2090011yescharacteristic
1214C2C8×#12111yescharacteristic
1215C2#2148911yescharacteristic
1216C2#2216811yescharacteristic
1217C2#2217211yescharacteristic
1218C2D4×C22⋊C811yescharacteristic
1219C2#2239811yescharacteristic
1220C2#2246911yescharacteristic
1221C2#2247011yescharacteristic
1222C2#2298511yescharacteristic
1223C2#2298711yescharacteristic
1224C2#2311611yescharacteristic
1225C2#2311711yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC22×#121C4
LCSG ▷ C23 ▷ 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×C8×D4C2semidirect
3. C2×#1869C2semidirect
4. C2×#1869C2semidirect
5. C2×#1869C2semidirect
6. C2×#1869C2semidirect
7. C22×#336C2semidirect
8. #11202C2semidirect
9. #11147C2semidirect
10. #11042C2semidirect
11. #10964C2semidirect
12. #10921C2semidirect
13. #10874C2semidirect
14. #10714C2semidirect
15. #10712C2semidirect
97. C23×C8D4semidirect
108. C2×#121C8semidirect
184. C2×C22⋊C8D4semidirect
220. #336D4semidirect
242. C22×D4C2×C8semidirect
243. C22×D4C2×C8semidirect
292. C23×C4C2×C8semidirect
417. C2×C4⋊C4C2×C8semidirect
446. C2×C22⋊C4C2×C8semidirect
447. C2×C22⋊C4C2×C8semidirect
565. C2×D4C22⋊C8semidirect
813. C2×C8#121semidirect
1072. C2×C4C8×D4semidirect
1153. C22#1869semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D42
C2×C4×#1212
C2×#18692
C22×#3362
#112022
#111472
#110422
#109642
#109212
#108742
#107142
#107122