Finite Group Databasebeta

← #356597

Subgroups — #356597

Order 512.

1896 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2293C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic
4C2×#1752C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×#1750C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#10922C211yesmaximal, characteristic, complemented
9#10922C211yesmaximal, characteristic, complemented
10#10875C211yesmaximal, characteristic, complemented
11#10874C211yesmaximal, characteristic, complemented
12#10795C211yesmaximal, characteristic, complemented
13#10713C211yesmaximal, characteristic, complemented
14#10713C211yesmaximal, characteristic, complemented
15#10693C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2293—24no—
32#2293—24no—
33C2×#390C412yes—
34C2×#389C412yes—
35C2×#388C412yes—
36C2×#388C412yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C43C2211yescharacteristic
41#1870C418yescomplemented
42#1869C418yescomplemented
43#1753—24no—
44#1752—24no—
45#1750—24no—
46#1729—24no—
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
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
63C23×D4C2×C411yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16C2×C414yes—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8C2×C414yes—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4C2×C414yes—
93C2×C4×D4C2×C414yes—
94C2×#117—22no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—41no—
103C2×#117—41no—
104C2×#117—41no—
105C2×#117—41no—
106C22×C4⋊C4C2×C412yes—
107C22×C4⋊C4C2×C412yes—
108C22×C4⋊C4C2×C412yes—
109C22×C4⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C412yes—
111C22×C22⋊C4C2×C412yes—
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C412yes—
115C22×C22⋊C4C2×C412yes—
116C22×C42C2×C412yes—
117C22×C42C2×C412yes—
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8—41no—
135C2×C22⋊C8C2×C414yes—
136C2×C22⋊C8C2×C414yes—
137C2×C22⋊C8C2×C414yes—
138C2×C22⋊C8C2×C414yes—
139C2×C22⋊C8C2×C414yes—
140C2×C22⋊C8C2×C414yes—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—41no—
148C2×#97—41no—
149C2×#97—41no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—41no—
153#390—28no—
154#389—28no—
155#388—28no—
156#388—28no—
157C4×C4⋊C4—22no—
158C4×C4⋊C4—22no—
159C4×C22⋊C4—22no—
160C4×C22⋊C4—22no—
161C4×C22⋊C4D414yes—
162C4×C22⋊C4D414yes—
163C2×#95C2×C412yes—
164C2×#95C2×C412yes—
165C2×#95C2×C412yes—
166C43—22no—
167C43—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—41no—
178#336—41no—
179#336C2×C414yes—
180#336C2×C414yes—
181#336C2×C414yes—
182#336C2×C414yes—
183#336D414yescomplemented
184C25C22×C411yescharacteristic
185C25C22×C411yescharacteristic
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—24no—
189C22×D4—42no—
190C22×D4C4214yes—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C22×C412yes—
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C412yes—
217C23×C4C22×C412yes—
218C23×C4C22×C412yes—
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C412yes—
222C23×C4C22×C412yes—
223C23×C4C2×D412yes—
224C23×C4C2×D412yes—
225C23×C4#4112yes—
226C23×C4#4112yes—
227C23×C4C2411yescharacteristic
228C2×M16—28no—
229C2×M16—28no—
230C2×M16—44no—
231C2×M16—44no—
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—28no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
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—28no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C22×C412yes—
293C22×C8C22×C412yes—
294C22×C8C2×D412yes—
295C22×C8C2×D412yes—
296C22×C8#4112yes—
297C22×C8#4112yes—
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—28no—
301C4×D4—28no—
302#117—44no—
303#117—44no—
304#117—44no—
305#117—44no—
306#117—44no—
307#117—44no—
308#117—44no—
309#117—44no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4C4214yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4C4214yes—
338C2×C22⋊C4C4214yes—
339C2×C22⋊C4C22⋊C418yes—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42C22×C412yes—
369C2×C42C22×C412yes—
370C2×C42C2×D412yes—
371C2×C42C2×D412yes—
372C2×C42C2×D412yes—
373C2×C42C2×D412yes—
374C2×C42C2×D412yes—
375C2×C42#4112yes—
376C22⋊C8—28no—
377C22⋊C8—28no—
378C22⋊C8—28no—
379C22⋊C8—28no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382#97—44no—
383#97—44no—
384#97—44no—
385C4×C8—44no—
386#95—24no—
387#95—24no—
388#95C22⋊C418yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24C2×C4212yes—
408C24C2×C4212yes—
409C24C2×C22⋊C412yes—
410C24#11712yes—
411C24C23×C411yescharacteristic
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—44no—
415C2×D4—48no—
416C2×D4—48no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
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—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4C2×C4212yes—
512C22×C4C2×C4212yes—
513C22×C4C2×C4212yes—
514C22×C4C2×C4212yes—
515C22×C4C2×C22⋊C414yes—
516C22×C4C2×C22⋊C414yes—
517C22×C4C2×C22⋊C412yes—
518C22×C4#11712yes—
519C22×C4C4×D414yes—
520C22×C4C4×D414yes—
521C22×C4C4×D414yes—
522C22×C4C4×D414yes—
523C22×C4C4×D414yes—
524C22×C4#13114yes—
525C22×C4C23×C411yescharacteristic
526C22×C4C23×C411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4H(5,𝔽2)11yescharacteristic
536C22×C4H(5,𝔽2)11yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C42−1+411yescharacteristic
539M16—416no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—416no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8C4×D414yes—
596C2×C8C4×D414yes—
597C4⋊C4—28no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—48no—
624C42—48no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C4×C22⋊C414yes—
675C23C22×C4211yescharacteristic
676C23C22×C22⋊C411yescharacteristic
677C23C2×#11711yescharacteristic
678C23C2×C4×D411yescharacteristic
679C23C4×#4111yescharacteristic
680C23#51811yescharacteristic
681C23#52011yescharacteristic
682C23C2×#13112yes—
683C23#56812yes—
684C23#56812yes—
685C23#56812yes—
686D4—416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
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—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4C4×C22⋊C414yes—
754C2×C4#40514yes—
755C2×C4C2×C4×D411yescharacteristic
756C2×C4C2×C4×D411yescharacteristic
757C2×C4C2×C4×D411yescharacteristic
758C2×C4C2×C4×D411yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C4×#4111yescharacteristic
762C2×C4C4×#4111yescharacteristic
763C2×C4#51811yescharacteristic
764C2×C4#51811yescharacteristic
765C2×C4#52011yescharacteristic
766C2×C4#52011yescharacteristic
767C2×C4D4211yescharacteristic
768C2×C4D4211yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54611yescharacteristic
772C2×C4#54611yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4#54711yescharacteristic
775C2×C4#54711yescharacteristic
776C2×C4#54811yescharacteristic
777C2×C4#55111yescharacteristic
778C2×C4#55111yescharacteristic
779C2×C4#55211yescharacteristic
780C2×C4#55311yescharacteristic
781C2×C4#55311yescharacteristic
782C2×C4#55311yescharacteristic
783C8—24no—
784C8—24no—
785C8—42no—
786C8—42no—
787C8—42no—
788C8—42no—
789C8—42no—
790C8—42no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22C2×C4×C22⋊C411yescharacteristic
814C22C42×D411yescharacteristic
815C22#227511yescharacteristic
816C22D4×C22⋊C411yescharacteristic
817C22#233911yescharacteristic
818C22#235211yescharacteristic
819C22#235311yescharacteristic
820C22C2×#40511yescharacteristic
821C22#287311yescharacteristic
822C22#287511yescharacteristic
823C22#287511yescharacteristic
824C22#287912yes—
825C22#288012yes—
826C22#292312yes—
827C22#292412yes—
828C22#293212yes—
829C22#293512yes—
830C22#296712yes—
831C22#296912yes—
832C22#298012yes—
833C22#298112yes—
834C22#299312yes—
835C22#299512yes—
836C4—24no—
837C4—24no—
838C4—44no—
839C4—44no—
840C4—42no—
841C4—44no—
842C4—42no—
843C4—82no—
844C4#235811yescharacteristic
845C4#235811yescharacteristic
846C4#235911yescharacteristic
847C4#235911yescharacteristic
848C4#236111yescharacteristic
849C4#236111yescharacteristic
850C4#236411yescharacteristic
851C4#236411yescharacteristic
852C2—44no—
853C2—82no—
854C2#1381311yescharacteristic
855C2#2037511yescharacteristic
856C2#2037911yescharacteristic
857C2#2048811yescharacteristic
858C2#2049511yescharacteristic
859C2#2056311yescharacteristic
860C2#2056511yescharacteristic
861C2#2240312yes—
862C2#2247212yes—
863C2#2275712yes—
864C2#2279012yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C22×C42
socleC24C23×C4
prime radicalC23×D4C2×C4
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
4. C2×#1752C2semidirect
5. C2×#1753C2semidirect
6. C2×#1750C2semidirect
7. C2×#1729C2semidirect
8. #10922C2semidirect
9. #10922C2semidirect
10. #10875C2semidirect
11. #10874C2semidirect
12. #10795C2semidirect
13. #10713C2semidirect
14. #10713C2semidirect
15. #10693C2semidirect
41. #1870C4semidirect
42. #1869C4semidirect
183. #336D4semidirect

Maximal subgroups

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

subgroupindex
C2×#22932
C2×#18702
C2×#18692
C2×#17522
C2×#17532
C2×#17502
C2×#17292
#109222
#108752
#108742
#107952
#107132
#106932