Finite Group Databasebeta

← #366966

Subgroups — #366966

Order 512.

2198 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1954C211yesmaximal, characteristic, complemented
3C2×#1954C212yesmaximal, complemented
4C2×#1954C211yesmaximal, characteristic, complemented
5C2×#1939C211yesmaximal, characteristic, complemented
6C2×#1797C211yesmaximal, characteristic, complemented
7C2×C8×C4⋊C4C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
9#11042C212yesmaximal, complemented
10#10964C212yesmaximal, complemented
11#10921C212yesmaximal, complemented
12C22×#121C411yescharacteristic
13C22×C4×D4C2211yescharacteristic
14C22×C4×D4C2212yes—
15C23×C42C2211yescharacteristic
16C22×C4⋊C8C2211yescharacteristic
17C22×C4⋊C8C2212yes—
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×C22⋊C8C2212yes—
23C22×C22⋊C8C2212yes—
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2212yes—
26C22×C4×C8C2211yescharacteristic
27C22×C4×C8C2212yes—
28C22×C4×C8C2211yescharacteristic
29C4×#121—24no—
30C4×#121—24no—
31C2×#390C411yescharacteristic
32C2×#389C411yescharacteristic
33C2×#388C412yes—
34C2×#386C412yes—
35C2×#380C411yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2212yes—
38#1954—24no—
39#1954—28no—
40#1954—24no—
41#1939—24no—
42#1797—24no—
43C8×C4⋊C4—24no—
44C4×C22⋊C8—24no—
45C2×#336C2211yescharacteristic
46C2×#336C2212yes—
47C2×#336C2212yes—
48C2×#336C2211yescharacteristic
49C2×#336C2212yes—
50C23×D4C2×C411yescharacteristic
51C23×D4C2×C412yes—
52C24×C4C2×C411yescharacteristic
53C24×C4C2×C411yescharacteristic
54C24×C4C2312yes—
55C24×C4C2311yescharacteristic
56C23×C8C2312yes—
57C23×C8C2311yescharacteristic
58C23×C8C2312yes—
59C23×C8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C2×#121—24no—
63C2×#121—24no—
64C2×#121C818yescomplemented
65C2×C4×D4—24no—
66C2×C4×D4—24no—
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—24no—
70C2×C4×D4—24no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—42no—
76C2×C4×D4—42no—
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C412yes—
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C412yes—
82C22×C22⋊C4C2×C412yes—
83C22×C22⋊C4C2×C412yes—
84C22×C22⋊C4C2×C412yes—
85C22×C22⋊C4C2×C412yes—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42C2×C411yescharacteristic
93C22×C42C2×C411yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2312yes—
96C22×C42C2311yescharacteristic
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—24no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—24no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—42no—
105C2×C4⋊C8D414yescomplemented
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—24no—
112C2×C22⋊C8—24no—
113C2×C22⋊C8—24no—
114C2×C22⋊C8—24no—
115C2×C22⋊C8—24no—
116C2×C22⋊C8—24no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—24no—
119C2×C22⋊C8—24no—
120C2×C22⋊C8—24no—
121C2×C22⋊C8—42no—
122C2×C22⋊C8—42no—
123C2×C22⋊C8—42no—
124C2×C22⋊C8—42no—
125C2×C22⋊C8—42no—
126C2×C22⋊C8D414yescomplemented
127C2×C4×C8—22no—
128C2×C4×C8—22no—
129C2×C4×C8—24no—
130C2×C4×C8—22no—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—24no—
134C2×C4×C8—42no—
135C2×C4×C8D414yescomplemented
136#390—24no—
137#389—24no—
138#388—28no—
139#386—28no—
140#380—24no—
141C4×C4⋊C4D414yes—
142C4×C4⋊C4D414yes—
143C4×C22⋊C4—24no—
144C4×C22⋊C4—24no—
145C2×#95C2×C412yes—
146C2×#95C2×C412yes—
147C2×#95C2×C412yes—
148#336—24no—
149#336—22no—
150#336—22no—
151#336—24no—
152#336—24no—
153C25C22×C412yes—
154C25C22×C411yescharacteristic
155C22×D4—24no—
156C22×D4—24no—
157C22×D4—24no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—24no—
162C22×D4—22no—
163C22×D4—22no—
164C22×D4—22no—
165C22×D4—42no—
166C22×D4—42no—
167C22×D4C2×C814yes—
168C22×D4C2×C818yes—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—41no—
207C23×C4—41no—
208C23×C4C2×C814yes—
209C23×C4C22×C412yes—
210C23×C4C22×C412yes—
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C412yes—
216C23×C4C22×C411yescharacteristic
217C23×C4C2×D412yes—
218C23×C4#4112yes—
219C23×C4C2411yescharacteristic
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—22no—
229C22×C8—21no—
230C22×C8—22no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—22no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—22no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8C2×D412yes—
256C22×C8C2×D414yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C22×C8C2×D412yes—
260C22×C8#4112yes—
261C22×C8#4112yes—
262#121—232no—
263C4×D4—48no—
264C4×D4—48no—
265C4×D4—48no—
266C4×D4—48no—
267C4×D4—44no—
268C4×D4—44no—
269C4×D4—44no—
270C4×D4—44no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4C22⋊C414yes—
280C2×C4⋊C4C22⋊C414yes—
281C2×C4⋊C4C2×C814yes—
282C2×C4⋊C4M1614yes—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4C2×C818yes—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—44no—
315C2×C42—44no—
316C2×C42—44no—
317C2×C42—44no—
318C2×C42C2×D414yes—
319C2×C42C2×D414yes—
320C2×C42C2×D412yes—
321C2×C42C2×D412yes—
322C2×C42C2×D412yes—
323C2×C42C2×D412yes—
324C2×C42#4112yes—
325C2×C42#4112yes—
326C4⋊C8—28no—
327C4⋊C8—48no—
328C4⋊C8—44no—
329C22⋊C8—28no—
330C22⋊C8—28no—
331C22⋊C8—48no—
332C22⋊C8—48no—
333C22⋊C8—48no—
334C22⋊C8—48no—
335C22⋊C8—48no—
336C4×C8—28no—
337C4×C8—48no—
338C4×C8—44no—
339#95—24no—
340#95—24no—
341#95C22⋊C418yes—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24C4×D412yes—
369C24C22×C814yes—
370C24C22×C812yes—
371C24#13112yes—
372C24C23×C411yescharacteristic
373C2×D4—216no—
374C2×D4—216no—
375C2×D4—28no—
376C2×D4—28no—
377C2×D4—28no—
378C2×D4—48no—
379C2×D4—48no—
380C2×D4—48no—
381C2×D4—48no—
382C2×D4—48no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—28no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4C2×C22⋊C414yes—
497C22×C4C2×C22⋊C412yes—
498C22×C4C2×C22⋊C414yes—
499C22×C4C2×C22⋊C412yes—
500C22×C4C4×D412yes—
501C22×C4C4×D412yes—
502C22×C4C4×D412yes—
503C22×C4C4×D412yes—
504C22×C4C4×D412yes—
505C22×C4C22×C812yes—
506C22×C4C22×C814yes—
507C22×C4C22×C812yes—
508C22×C4C2×M1614yes—
509C22×C4C2×M1612yes—
510C22×C4#13112yes—
511C22×C4#13112yes—
512C22×C4#13112yes—
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4H(5,𝔽2)11yescharacteristic
524C22×C4H(5,𝔽2)11yescharacteristic
525C22×C4H(5,𝔽2)11yescharacteristic
526C22×C42−1+411yescharacteristic
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—24no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—24no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—24no—
544C2×C8—22no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—42no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—42no—
551C2×C8—42no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—42no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—42no—
564C2×C8—42no—
565C2×C8—42no—
566C2×C8—42no—
567C2×C8—42no—
568C2×C8#12114yescomplemented
569C4⋊C4—28no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4C22⋊C8116yescomplemented
573C22⋊C4—216no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C42—24no—
579C42—24no—
580C42—24no—
581C42—24no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—44no—
587C42—44no—
588C42#12114yes—
589C42#12114yes—
590C42#12414yes—
591C42#12714yes—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C8×D414yes—
662C23C22×C22⋊C411yescharacteristic
663C23C2×C4×D411yescharacteristic
664C23C2×C4×D411yescharacteristic
665C23C2×C4×D411yescharacteristic
666C23C4×#4111yescharacteristic
667C23#51811yescharacteristic
668C23#52011yescharacteristic
669C23C23×C811yescharacteristic
670C23C22×M1611yescharacteristic
671C23C2×#13111yescharacteristic
672C23C2×#13111yescharacteristic
673C23C2×#13111yescharacteristic
674C23C2×#13111yescharacteristic
675C23#56811yescharacteristic
676C23#56811yescharacteristic
677D4—432no—
678D4—416no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4#39014yes—
745C2×C4#39014yes—
746C2×C4C2×C22⋊C818yes—
747C2×C4C2×C22⋊C814yes—
748C2×C4#40814yes—
749C2×C4C8×D414yes—
750C2×C4C8×D414yes—
751C2×C4#43614yes—
752C2×C4#43614yes—
753C2×C4C2×#12111yescharacteristic
754C2×C4C2×#12111yescharacteristic
755C2×C4C2×#12111yescharacteristic
756C2×C4#52511yescharacteristic
757C2×C4C2×#12411yescharacteristic
758C2×C4#52911yescharacteristic
759C2×C4C2×#12711yescharacteristic
760C2×C4#53211yescharacteristic
761C2×C4#53511yescharacteristic
762C2×C4#53711yescharacteristic
763C2×C4#54011yescharacteristic
764C2×C4#54211yescharacteristic
765C2×C4D4211yescharacteristic
766C2×C4D4211yescharacteristic
767C2×C4D4211yescharacteristic
768C2×C4#54611yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54711yescharacteristic
772C2×C4#54811yescharacteristic
773C2×C4#54811yescharacteristic
774C2×C4#54811yescharacteristic
775C2×C4#55011yescharacteristic
776C2×C4#55011yescharacteristic
777C2×C4#55011yescharacteristic
778C2×C4#55311yescharacteristic
779C2×C4#55311yescharacteristic
780C2×C4#55511yescharacteristic
781C8—24no—
782C8—42no—
783C8—44no—
784C8—42no—
785C8—42no—
786C8—82no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22C2×#39011yescharacteristic
818C22C4×#12111yescharacteristic
819C22#232411yescharacteristic
820C22D4×C22⋊C411yescharacteristic
821C22#234111yescharacteristic
822C22#236111yescharacteristic
823C22#236311yescharacteristic
824C22C22×C22⋊C811yescharacteristic
825C22C2×#40811yescharacteristic
826C22#288011yescharacteristic
827C22#288011yescharacteristic
828C22C2×C8×D411yescharacteristic
829C22C2×C8×D411yescharacteristic
830C22C2×C8×D411yescharacteristic
831C22C2×#43611yescharacteristic
832C22C2×#43611yescharacteristic
833C22#292911yescharacteristic
834C22#293011yescharacteristic
835C22#293111yescharacteristic
836C22#293311yescharacteristic
837C22#293311yescharacteristic
838C22D4×M1611yescharacteristic
839C22#293511yescharacteristic
840C22C8×#4111yescharacteristic
841C22#296611yescharacteristic
842C22#296911yescharacteristic
843C22#297111yescharacteristic
844C22#297211yescharacteristic
845C22#297411yescharacteristic
846C22#297911yescharacteristic
847C22#298111yescharacteristic
848C22#298811yescharacteristic
849C22#299111yescharacteristic
850C22#299311yescharacteristic
851C22#299411yescharacteristic
852C4—28no—
853C4—24no—
854C4—44no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—82no—
859C4#195418yescomplemented
860C4#241411yescharacteristic
861C4#241611yescharacteristic
862C4#242611yescharacteristic
863C4#242811yescharacteristic
864C4#249011yescharacteristic
865C4#249111yescharacteristic
866C4#254011yescharacteristic
867C4#254111yescharacteristic
868C2—44no—
869C2—84no—
870C2#1399811yescharacteristic
871C2C2×#195411yescharacteristic
872C2#2119111yescharacteristic
873C2C8×#12111yescharacteristic
874C2#2148811yescharacteristic
875C2#2213311yescharacteristic
876C2#2213711yescharacteristic
877C2D4×C22⋊C811yescharacteristic
878C2#2240211yescharacteristic
879C2#2253011yescharacteristic
880C2#2253111yescharacteristic
881C2#2298511yescharacteristic
882C2#2299011yescharacteristic
883C2#2308311yescharacteristic
884C2#2308811yescharacteristic
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
2. C2×#1954C2semidirect
3. C2×#1954C2semidirect
4. C2×#1954C2semidirect
5. C2×#1939C2semidirect
6. C2×#1797C2semidirect
7. C2×C8×C4⋊C4C2semidirect
8. C2×C4×C22⋊C8C2semidirect
9. #11042C2semidirect
10. #10964C2semidirect
11. #10921C2semidirect
64. C2×#121C8semidirect
105. C2×C4⋊C8D4semidirect
126. C2×C22⋊C8D4semidirect
135. C2×C4×C8D4semidirect
568. C2×C8#121semidirect
572. C4⋊C4C22⋊C8semidirect
859. C4#1954semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#19542
C2×#19392
C2×#17972
C2×C8×C4⋊C42
C2×C4×C22⋊C82
#110422
#109642
#109212