Finite Group Databasebeta

← #361435

Subgroups — #361435

Order 512.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2290C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic
4C2×#1851C211yesmaximal, characteristic, complemented
5C2×#1850C211yesmaximal, characteristic, complemented
6C2×#1797C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#11202C211yesmaximal, characteristic, complemented
9#11202C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#11042C211yesmaximal, characteristic, complemented
12#10833C211yesmaximal, characteristic, complemented
13#10796C211yesmaximal, characteristic, complemented
14#10713C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31#2290—24no—
32#2290—24no—
33C2×#388C411yescharacteristic
34C2×#388C411yescharacteristic
35C2×#387C411yescharacteristic
36C2×#387C411yescharacteristic
37C2×#386C411yescharacteristic
38C2×#386C411yescharacteristic
39C2×#385C411yescharacteristic
40C2×#385C411yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×#376C2211yescharacteristic
45#1870—24no—
46#1869—24no—
47#1851—24no—
48#1850—24no—
49#1797—24no—
50#1729—24no—
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
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
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—41no—
78C22×M16—41no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—41no—
85C23×C8—41no—
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×D4D414yes—
99C2×C4×D4Q814yes—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—41no—
105C2×#117—41no—
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C4⋊C4C2×C411yescharacteristic
110C22×C4⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C411yescharacteristic
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C22⋊C4C2×C411yescharacteristic
118C22×C22⋊C4C2×C411yescharacteristic
119C22×C42—22no—
120C22×C42—22no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—41no—
124C22×C42—41no—
125C22×C42C2×C411yescharacteristic
126C22×C42C2×C411yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C2×C4⋊C8—22no—
133C2×C4⋊C8—22no—
134C2×C4⋊C8—22no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×C4⋊C8—22no—
138C2×C4⋊C8—22no—
139C2×C4⋊C8—22no—
140C2×C4⋊C8—41no—
141C2×C4⋊C8—41no—
142C2×C4⋊C8—41no—
143C2×C4⋊C8—41no—
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—
162#388—24no—
163#388—24no—
164#387—24no—
165#387—24no—
166#386—24no—
167#386—24no—
168#385—24no—
169#385—24no—
170C4×C4⋊C4—22no—
171C4×C4⋊C4—22no—
172C4×C22⋊C4—22no—
173C4×C22⋊C4—22no—
174C4×C22⋊C4D414yes—
175C4×C22⋊C4D414yes—
176#376—22no—
177#376—22no—
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180C2×#95C2×C411yescharacteristic
181C2×#95C2×C411yescharacteristic
182C2×#95C2×C411yescharacteristic
183C2×#95C2×C411yescharacteristic
184C2×#95C2×C411yescharacteristic
185C2×#95C2×C411yescharacteristic
186C2×#95C2×C411yescharacteristic
187C2×#95C2×C411yescharacteristic
188#336—22no—
189#336—22no—
190#336—22no—
191#336—22no—
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—22no—
201#336—41no—
202#336—41no—
203#336D414yescomplemented
204C25C22×C411yescharacteristic
205C25C22×C411yescharacteristic
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4C4⋊C414yes—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
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—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—41no—
242C23×C4—41no—
243C23×C4—41no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—41no—
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C22×C411yescharacteristic
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C22×C411yescharacteristic
255C23×C4C22×C411yescharacteristic
256C23×C4C22×C411yescharacteristic
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×Q812yes—
264C23×C4C2×Q812yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4C2411yescharacteristic
268C2×M16—28no—
269C2×M16—44no—
270C2×M16—44no—
271C2×M16—44no—
272C2×M16—44no—
273C2×M16—44no—
274C2×M16—44no—
275C22×C8—28no—
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×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—44no—
329C22×C8—44no—
330C22×C8—44no—
331C22×C8—44no—
332C22×C8—44no—
333C22×C8—44no—
334C22×C8C2×D412yes—
335C22×C8C2×D412yes—
336C22×C8#4112yes—
337C22×C8#4112yes—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—28no—
342#117—44no—
343#117—44no—
344#117—44no—
345#117—44no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4C4⋊C414yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4C22⋊C414yes—
382C2×C22⋊C4C22⋊C414yes—
383C2×C22⋊C4C4⋊C414yes—
384C2×C22⋊C4C4⋊C414yes—
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×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—44no—
412C2×C42—44no—
413C2×C42—44no—
414C2×C42—44no—
415C2×C42—41no—
416C2×C42—41no—
417C2×C42C2×D412yes—
418C2×C42C2×D412yes—
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2×D412yes—
422C2×C42C2×D412yes—
423C2×C42C2×Q812yes—
424C2×C42#4112yes—
425C4⋊C8—44no—
426C4⋊C8—44no—
427C4⋊C8—44no—
428C4⋊C8—44no—
429C22⋊C8—44no—
430C22⋊C8—44no—
431C22⋊C8—44no—
432C22⋊C8—44no—
433C22⋊C8—44no—
434C22⋊C8—44no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95C22⋊C414yes—
444#95C22⋊C414yes—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24C2×C22⋊C412yes—
470C24C2×C4⋊C412yes—
471C24C2×C4⋊C412yes—
472C24#11712yes—
473C24#13112yes—
474C24#13112yes—
475C24C23×C411yescharacteristic
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
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—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
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—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
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—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—44no—
619C22×C4C2×C22⋊C412yes—
620C22×C4C2×C22⋊C412yes—
621C22×C4C2×C22⋊C412yes—
622C22×C4C2×C22⋊C412yes—
623C22×C4C2×C22⋊C412yes—
624C22×C4C2×C4⋊C412yes—
625C22×C4C2×C4⋊C412yes—
626C22×C4C2×C4⋊C412yes—
627C22×C4C2×C4⋊C412yes—
628C22×C4#11712yes—
629C22×C4C4×D412yes—
630C22×C4C4×D412yes—
631C22×C4#12114yes—
632C22×C4#12114yes—
633C22×C4C22⋊Q814yes—
634C22×C4C22⋊Q814yes—
635C22×C4#13112yes—
636C22×C4#13112yes—
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×Q811yescharacteristic
642C22×C4C2×#4111yescharacteristic
643C22×C4C2×#4111yescharacteristic
644C22×C4C2×#4111yescharacteristic
645C22×C4C2×#4111yescharacteristic
646C22×C4C2×#4111yescharacteristic
647C22×C4H(5,𝔽2)11yescharacteristic
648C22×C4H(5,𝔽2)11yescharacteristic
649C22×C4H(5,𝔽2)11yescharacteristic
650C22×C42−1+411yescharacteristic
651M16—416no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—416no—
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—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—41no—
703C2×C8—41no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—41no—
707C2×C8—41no—
708C2×C8—41no—
709C4⋊C4—28no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—22no—
736C42—22no—
737C42—22no—
738C42—44no—
739C42—44no—
740C42—41no—
741C42—41no—
742C42—41no—
743C42—41no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23#38014yes—
813C23#42414yes—
814C23C22×C22⋊C411yescharacteristic
815C23C22×C4⋊C411yescharacteristic
816C23C2×#11711yescharacteristic
817C23C2×C4×D411yescharacteristic
818C23C4×#4111yescharacteristic
819C23#51811yescharacteristic
820C23#52011yescharacteristic
821C23C2×#13111yescharacteristic
822C23C2×#13111yescharacteristic
823C23C2×#13111yescharacteristic
824C23C2×#13111yescharacteristic
825C23#56811yescharacteristic
826C23#56811yescharacteristic
827C23#56811yescharacteristic
828C23#56811yescharacteristic
829D4—416no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
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—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
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—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—416no—
875C2×C4—416no—
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—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#38014yes—
931C2×C4#40814yes—
932C2×C4C2×#12111yescharacteristic
933C2×C4C2×#12111yescharacteristic
934C2×C4C2×C22⋊Q811yescharacteristic
935C2×C4C2×C22⋊Q811yescharacteristic
936C2×C4#52511yescharacteristic
937C2×C4#52511yescharacteristic
938C2×C4#52911yescharacteristic
939C2×C4#52911yescharacteristic
940C2×C4#53811yescharacteristic
941C2×C4#53811yescharacteristic
942C2×C4#53911yescharacteristic
943C2×C4#53911yescharacteristic
944C2×C4D4211yescharacteristic
945C2×C4D4211yescharacteristic
946C2×C4D4211yescharacteristic
947C2×C4#54611yescharacteristic
948C2×C4#54611yescharacteristic
949C2×C4#54611yescharacteristic
950C2×C4#54611yescharacteristic
951C2×C4#54611yescharacteristic
952C2×C4#54611yescharacteristic
953C2×C4#54711yescharacteristic
954C2×C4#54711yescharacteristic
955C2×C4#54711yescharacteristic
956C2×C4D4×Q811yescharacteristic
957C2×C4#55411yescharacteristic
958C2×C4#55411yescharacteristic
959C2×C4#55411yescharacteristic
960C8—42no—
961C8—42no—
962C8—42no—
963C8—42no—
964C8—81no—
965C8—81no—
966C8—81no—
967C8—81no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22C2×#38011yescharacteristic
999C22#229011yescharacteristic
1000C22#231811yescharacteristic
1001C22D4×C22⋊C411yescharacteristic
1002C22#233911yescharacteristic
1003C22D4×C4⋊C411yescharacteristic
1004C22#234911yescharacteristic
1005C22C2×#40811yescharacteristic
1006C22#287911yescharacteristic
1007C22#288011yescharacteristic
1008C22#288011yescharacteristic
1009C22C2×#42411yescharacteristic
1010C22#290511yescharacteristic
1011C22#290611yescharacteristic
1012C22#290611yescharacteristic
1013C22#292411yescharacteristic
1014C22#292411yescharacteristic
1015C22#292511yescharacteristic
1016C22#292511yescharacteristic
1017C22#292911yescharacteristic
1018C22#293011yescharacteristic
1019C22#293311yescharacteristic
1020C22#293311yescharacteristic
1021C22#296611yescharacteristic
1022C22#296711yescharacteristic
1023C22#296811yescharacteristic
1024C22#296911yescharacteristic
1025C22#297611yescharacteristic
1026C22#297611yescharacteristic
1027C22#297711yescharacteristic
1028C22#297811yescharacteristic
1029C22#299211yescharacteristic
1030C22#299311yescharacteristic
1031C22#299411yescharacteristic
1032C22#299511yescharacteristic
1033C4—24no—
1034C4—24no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—81no—
1045C4#242411yescharacteristic
1046C4#242411yescharacteristic
1047C4#242511yescharacteristic
1048C4#242511yescharacteristic
1049C4#244911yescharacteristic
1050C4#244911yescharacteristic
1051C4#245011yescharacteristic
1052C4#245011yescharacteristic
1053C2—44no—
1054C2—44no—
1055C2#1389911yescharacteristic
1056C2#2062811yescharacteristic
1057C2#2062911yescharacteristic
1058C2#2110911yescharacteristic
1059C2#2111211yescharacteristic
1060C2#2200411yescharacteristic
1061C2#2200611yescharacteristic
1062C2#2239811yescharacteristic
1063C2#2240011yescharacteristic
1064C2#2247411yescharacteristic
1065C2#2247511yescharacteristic
1066C2#2264711yescharacteristic
1067C2#2264911yescharacteristic
1068C2#2269711yescharacteristic
1069C2#2269911yescharacteristic
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
4. C2×#1851C2semidirect
5. C2×#1850C2semidirect
6. C2×#1797C2semidirect
7. C2×#1729C2semidirect
8. #11202C2semidirect
9. #11202C2semidirect
10. #11042C2semidirect
11. #11042C2semidirect
12. #10833C2semidirect
13. #10796C2semidirect
14. #10713C2semidirect
15. #10712C2semidirect
203. #336D4semidirect

Maximal subgroups

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

subgroupindex
C2×#22902
C2×#18702
C2×#18692
C2×#18512
C2×#18502
C2×#17972
C2×#17292
#112022
#110422
#108332
#107962
#107132
#107122