Finite Group Databasebeta

← #362638

Subgroups — #362638

Order 512.

1784 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2290C211yesmaximal, characteristic
2C2×#1955C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic
4C2×#1940C211yesmaximal, characteristic, complemented
5C2×#1939C211yesmaximal, characteristic, complemented
6C2×#1798C211yesmaximal, characteristic, complemented
7C2×#1797C211yesmaximal, characteristic, complemented
8#11042C211yesmaximal, characteristic, complemented
9#11042C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#11042C211yesmaximal, characteristic, complemented
12#10833C211yesmaximal, characteristic, complemented
13#10713C211yesmaximal, characteristic, complemented
14#10712C211yesmaximal, characteristic, complemented
15#10694C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
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
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35#2290—24no—
36#2290—24no—
37C2×#388C411yescharacteristic
38C2×#388C411yescharacteristic
39C2×#387C411yescharacteristic
40C2×#387C411yescharacteristic
41C2×#386C411yescharacteristic
42C2×#386C411yescharacteristic
43C2×#385C411yescharacteristic
44C2×#385C411yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48C2×#376C2211yescharacteristic
49#1955—24no—
50#1954—24no—
51#1940—24no—
52#1939—24no—
53#1798—24no—
54#1797—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
67C23×D4C2×C411yescharacteristic
68C24×C4C2×C411yescharacteristic
69C24×C4C2×C411yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4D414yes—
85C2×C4×D4Q814yes—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—41no—
91C2×#117—41no—
92C22×C4⋊C4C2×C411yescharacteristic
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C4⋊C4C2×C411yescharacteristic
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C4⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C22⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C411yescharacteristic
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42—41no—
110C22×C42—41no—
111C22×C42C2×C411yescharacteristic
112C22×C42C2×C411yescharacteristic
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
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×C4⋊C8—22no—
129C2×C4⋊C8—22no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8—22no—
132C2×C4⋊C8—41no—
133C2×C4⋊C8—41no—
134C2×C4⋊C8—41no—
135C2×C4⋊C8—41no—
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—
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—41no—
153C2×C22⋊C8—41no—
154C2×C22⋊C8—41no—
155C2×C22⋊C8—41no—
156C2×C22⋊C8—41no—
157C2×C22⋊C8—41no—
158C2×C22⋊C8—41no—
159C2×C22⋊C8—41no—
160C2×#97—22no—
161C2×#97—22no—
162C2×#97—22no—
163C2×C4×C8—22no—
164C2×C4×C8—22no—
165C2×C4×C8—22no—
166#388—24no—
167#388—24no—
168#387—24no—
169#387—24no—
170#386—24no—
171#386—24no—
172#385—24no—
173#385—24no—
174C4×C4⋊C4D414yes—
175C4×C4⋊C4D414yes—
176C4×C22⋊C4—22no—
177C4×C22⋊C4—22no—
178C4×C22⋊C4—22no—
179C4×C22⋊C4—22no—
180#376—22no—
181#376—22no—
182C2×#95C2×C411yescharacteristic
183C2×#95C2×C411yescharacteristic
184C2×#95C2×C411yescharacteristic
185C2×#95C2×C411yescharacteristic
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—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—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
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—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—41no—
246C23×C4—41no—
247C23×C4—41no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—41no—
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×C4C22×C411yescharacteristic
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×Q812yes—
266C23×C4C2×Q812yes—
267C23×C4C2411yescharacteristic
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
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×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8C2×D412yes—
321C22×C8C2×D412yes—
322C22×C8#4112yes—
323C22×C8#4112yes—
324C4×D4—28no—
325C4×D4—28no—
326C4×D4—28no—
327C4×D4—28no—
328#117—44no—
329#117—44no—
330#117—44no—
331#117—44no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4C22⋊C414yes—
345C2×C4⋊C4C22⋊C414yes—
346C2×C4⋊C4C4⋊C414yes—
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—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4C4⋊C414yes—
370C2×C22⋊C4C4⋊C414yes—
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—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—44no—
394C2×C42—44no—
395C2×C42—44no—
396C2×C42—44no—
397C2×C42—41no—
398C2×C42—41no—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2×D412yes—
404C2×C42C2×D412yes—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×Q812yes—
408C2×C42#4112yes—
409C2×C42#4112yes—
410C2×C42#4112yes—
411C4⋊C8—44no—
412C4⋊C8—44no—
413C4⋊C8—44no—
414C4⋊C8—44no—
415C4⋊C8—44no—
416C4⋊C8—44no—
417C22⋊C8—44no—
418C22⋊C8—44no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421C22⋊C8—44no—
422C22⋊C8—44no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425#97—44no—
426C4×C8—44no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95C22⋊C414yes—
436#95C22⋊C414yes—
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—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24C2×C4⋊C412yes—
464C24C2×C4⋊C412yes—
465C24#13112yes—
466C24#13112yes—
467C24C23×C411yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—28no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
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—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
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—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
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—41no—
601C22×C4—41no—
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—44no—
613C22×C4C2×C22⋊C412yes—
614C22×C4C2×C22⋊C412yes—
615C22×C4C2×C22⋊C412yes—
616C22×C4C2×C22⋊C412yes—
617C22×C4C2×C22⋊C412yes—
618C22×C4C2×C22⋊C412yes—
619C22×C4C2×C4⋊C412yes—
620C22×C4C2×C4⋊C412yes—
621C22×C4C2×C4⋊C412yes—
622C22×C4C2×C4⋊C412yes—
623C22×C4#11712yes—
624C22×C4#11712yes—
625C22×C4C4×D412yes—
626C22×C4C4×D412yes—
627C22×C4#13112yes—
628C22×C4#13112yes—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×Q811yescharacteristic
634C22×C4C2×#4111yescharacteristic
635C22×C4C2×#4111yescharacteristic
636C22×C4C2×#4111yescharacteristic
637C22×C4C2×#4111yescharacteristic
638C22×C4C2×#4111yescharacteristic
639C22×C4H(5,𝔽2)11yescharacteristic
640C22×C4H(5,𝔽2)11yescharacteristic
641C22×C4H(5,𝔽2)11yescharacteristic
642C22×C42−1+411yescharacteristic
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—41no—
656C2×C8—41no—
657C2×C8—41no—
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—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—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—44no—
725C42—44no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42#12114yes—
731C42#12114yes—
732C42C22⋊Q814yes—
733C42C22⋊Q814yes—
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—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—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—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#42414yes—
804C23C22×C22⋊C411yescharacteristic
805C23C22×C4⋊C411yescharacteristic
806C23C2×#11711yescharacteristic
807C23C2×C4×D411yescharacteristic
808C23C4×#4111yescharacteristic
809C23#51811yescharacteristic
810C23#52011yescharacteristic
811C23C2×#13111yescharacteristic
812C23C2×#13111yescharacteristic
813C23C2×#13111yescharacteristic
814C23C2×#13111yescharacteristic
815C23#56811yescharacteristic
816C23#56811yescharacteristic
817C23#56811yescharacteristic
818C23#56811yescharacteristic
819D4—416no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
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—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—416no—
860C2×C4—416no—
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—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4#38014yes—
920C2×C4#38014yes—
921C2×C4#40814yes—
922C2×C4C2×#12111yescharacteristic
923C2×C4C2×#12111yescharacteristic
924C2×C4C2×C22⋊Q811yescharacteristic
925C2×C4C2×C22⋊Q811yescharacteristic
926C2×C4#52911yescharacteristic
927C2×C4#52911yescharacteristic
928C2×C4#53211yescharacteristic
929C2×C4#53211yescharacteristic
930C2×C4#54011yescharacteristic
931C2×C4#54011yescharacteristic
932C2×C4#54211yescharacteristic
933C2×C4#54211yescharacteristic
934C2×C4D4211yescharacteristic
935C2×C4D4211yescharacteristic
936C2×C4D4211yescharacteristic
937C2×C4#54611yescharacteristic
938C2×C4#54611yescharacteristic
939C2×C4#54611yescharacteristic
940C2×C4#54611yescharacteristic
941C2×C4#54711yescharacteristic
942C2×C4#54811yescharacteristic
943C2×C4#54811yescharacteristic
944C2×C4D4×Q811yescharacteristic
945C2×C4#55011yescharacteristic
946C2×C4#55011yescharacteristic
947C2×C4#55411yescharacteristic
948C2×C4#55411yescharacteristic
949C2×C4#55411yescharacteristic
950C8—42no—
951C8—42no—
952C8—42no—
953C8—42no—
954C8—81no—
955C8—81no—
956C8—81no—
957C8—81no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22C2×#38011yescharacteristic
989C22#229311yescharacteristic
990C22#231911yescharacteristic
991C22D4×C22⋊C411yescharacteristic
992C22#234111yescharacteristic
993C22D4×C4⋊C411yescharacteristic
994C22#234911yescharacteristic
995C22C2×#40811yescharacteristic
996C22#287911yescharacteristic
997C22#288011yescharacteristic
998C22#288011yescharacteristic
999C22C2×#42411yescharacteristic
1000C22#290511yescharacteristic
1001C22#290611yescharacteristic
1002C22#290611yescharacteristic
1003C22#292411yescharacteristic
1004C22#292411yescharacteristic
1005C22#292511yescharacteristic
1006C22#292511yescharacteristic
1007C22#292911yescharacteristic
1008C22#293011yescharacteristic
1009C22#293311yescharacteristic
1010C22#293311yescharacteristic
1011C22#296611yescharacteristic
1012C22#296711yescharacteristic
1013C22#296811yescharacteristic
1014C22#296911yescharacteristic
1015C22#297611yescharacteristic
1016C22#297611yescharacteristic
1017C22#297711yescharacteristic
1018C22#297811yescharacteristic
1019C22#299211yescharacteristic
1020C22#299311yescharacteristic
1021C22#299411yescharacteristic
1022C22#299511yescharacteristic
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—81no—
1034C4—81no—
1035C4#242711yescharacteristic
1036C4#242711yescharacteristic
1037C4#242811yescharacteristic
1038C4#242811yescharacteristic
1039C4#245211yescharacteristic
1040C4#245211yescharacteristic
1041C4#245411yescharacteristic
1042C4#245411yescharacteristic
1043C2—44no—
1044C2—82no—
1045C2#1392011yescharacteristic
1046C2#2062811yescharacteristic
1047C2#2062911yescharacteristic
1048C2#2127211yescharacteristic
1049C2#2127311yescharacteristic
1050C2#2201611yescharacteristic
1051C2#2201711yescharacteristic
1052C2#2239811yescharacteristic
1053C2#2240011yescharacteristic
1054C2#2253111yescharacteristic
1055C2#2253311yescharacteristic
1056C2#2264711yescharacteristic
1057C2#2264911yescharacteristic
1058C2#2269711yescharacteristic
1059C2#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×#1940C2semidirect
5. C2×#1939C2semidirect
6. C2×#1798C2semidirect
7. C2×#1797C2semidirect
8. #11042C2semidirect
9. #11042C2semidirect
10. #11042C2semidirect
11. #11042C2semidirect
12. #10833C2semidirect
13. #10713C2semidirect
14. #10712C2semidirect
15. #10694C2semidirect
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×#19552
C2×#19542
C2×#19402
C2×#19392
C2×#17982
C2×#17972
#110422
#108332
#107132
#107122
#106942