Finite Group Databasebeta

← #356631

Subgroups — #356631

Order 512.

1868 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#436C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1752C211yesmaximal, characteristic, complemented
4C2×#1753C211yesmaximal, characteristic, complemented
5C2×#1750C211yesmaximal, characteristic, complemented
6C2×#1729C211yesmaximal, characteristic, complemented
7#13839C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10922C211yesmaximal, characteristic, complemented
10#10877C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10797C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10715C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#436—24no—
22C2×#436—24no—
23C2×#436C418yescomplemented
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#1869C418yescomplemented
39#1753—24no—
40#1752—24no—
41#1750—24no—
42#1729—24no—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1441C412yes—
58#1440C412yes—
59#1439C412yes—
60#1438C412yes—
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63C23×D4C2×C411yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C22×M16—41no—
77C22×M16—41no—
78C22×M16C2×C414yes—
79C22×M16C2×C414yes—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—41no—
85C23×C8—41no—
86C23×C8C2×C414yes—
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4C2×C414yes—
100C2×C4×D4C2×C414yes—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—41no—
106C2×#117—41no—
107C22×C4⋊C4C2×C412yes—
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C412yes—
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C412yes—
113C22×C22⋊C4C2×C412yes—
114C22×C22⋊C4C2×C412yes—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120#436—232no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8C2×C414yes—
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—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yes—
135C2×C22⋊C8C2×C414yes—
136C2×C22⋊C8C2×C414yes—
137C2×C22⋊C8D414yes—
138C2×C22⋊C8D414yes—
139C2×#97—22no—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—41no—
146C2×#97—41no—
147C2×#97—41no—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—41no—
153C2×C4×C8C2×C414yes—
154C4×C22⋊C4—22no—
155C4×C22⋊C4—22no—
156C4×C22⋊C4—22no—
157C4×C22⋊C4—22no—
158C4×C22⋊C4—41no—
159C4×C22⋊C4—41no—
160C2×#95C2×C412yes—
161C2×#95C2×C412yes—
162C2×#95C2×C412yes—
163C2×#95C2×C412yes—
164C2×#95C2×C412yes—
165C2×#95C2×C412yes—
166C2×#95C2×C412yes—
167#336—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—41no—
177#336—41no—
178#336C2×C414yes—
179#336C2×C414yes—
180#336D414yescomplemented
181C25C22×C411yescharacteristic
182C25C22×C411yescharacteristic
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—24no—
186C22×D4—42no—
187C22×D4C4214yes—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
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×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C412yes—
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C412yes—
219C23×C4C22×C412yes—
220C23×C4C2×D412yes—
221C23×C4C2×D412yes—
222C23×C4#4112yes—
223C23×C4#4112yes—
224C23×C4C2411yescharacteristic
225C2×M16—28no—
226C2×M16—28no—
227C2×M16—28no—
228C2×M16—28no—
229C2×M16—44no—
230C2×M16—44no—
231C2×M16—44no—
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C2×M16—44no—
236C2×M16—44no—
237C2×M16—44no—
238C2×M16—44no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
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—28no—
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×C8C2×D412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299C22×C8C2×D412yes—
300C22×C8#4112yes—
301C22×C8#4112yes—
302C4×D4—28no—
303C4×D4—28no—
304C4×D4—28no—
305C4×D4—28no—
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—42no—
315C2×C4⋊C4C4214yes—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4C4214yes—
333C2×C22⋊C4C4214yes—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
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—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42C22×C412yes—
361C2×C42C22×C412yes—
362C2×C42C2×D412yes—
363C2×C42#4112yes—
364C4⋊C8—28no—
365C22⋊C8—28no—
366C22⋊C8—28no—
367C22⋊C8—28no—
368C22⋊C8—44no—
369C22⋊C8C22⋊C4116yescomplemented
370#97—44no—
371#97—44no—
372#97—44no—
373C4×C8—28no—
374C4×C8—44no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95—42no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24C2×C4212yes—
401C24C2×C4212yes—
402C24C4×D412yes—
403C24C4×D412yes—
404C24C23×C411yescharacteristic
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—44no—
408C2×D4—48no—
409C2×D4—48no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
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—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—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
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—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
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×C4C2×C4212yes—
507C22×C4C2×C4212yes—
508C22×C4C2×C4212yes—
509C22×C4C2×C4212yes—
510C22×C4C2×C22⋊C414yes—
511C22×C4#11714yes—
512C22×C4C4×D414yes—
513C22×C4C4×D414yes—
514C22×C4C4×D414yes—
515C22×C4C4×D412yes—
516C22×C4C4×D412yes—
517C22×C4#13114yes—
518C22×C4C23×C411yescharacteristic
519C22×C4C23×C411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C4H(5,𝔽2)11yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C42−1+411yescharacteristic
532M16—416no—
533M16—416no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
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×C8C2×C22⋊C414yes—
588C2×C8C2×C22⋊C414yes—
589C2×C8C4×D414yes—
590C2×C8C4×D414yes—
591C4⋊C4—28no—
592C4⋊C4—48no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C4×C22⋊C414yes—
665C23C22×C4211yescharacteristic
666C23C2×C4×D411yescharacteristic
667C23C2×C4×D411yescharacteristic
668C23C2×C4×D411yescharacteristic
669C23C4×#4111yescharacteristic
670C23#51811yescharacteristic
671C23#52011yescharacteristic
672C23C2×#13112yes—
673C23#56812yes—
674C23#56812yes—
675C23#56812yes—
676D4—416no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
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×C4C4×C22⋊C414yes—
744C2×C4#40514yes—
745C2×C4C22×C22⋊C411yescharacteristic
746C2×C4C2×#11711yescharacteristic
747C2×C4C2×C4×D411yescharacteristic
748C2×C4C2×C4×D411yescharacteristic
749C2×C4C2×C4×D411yescharacteristic
750C2×C4C2×C4×D411yescharacteristic
751C2×C4C4×#4111yescharacteristic
752C2×C4C4×#4111yescharacteristic
753C2×C4#51811yescharacteristic
754C2×C4#51811yescharacteristic
755C2×C4#52011yescharacteristic
756C2×C4#52011yescharacteristic
757C2×C4D4211yescharacteristic
758C2×C4D4211yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#54711yescharacteristic
765C2×C4#54711yescharacteristic
766C2×C4#54811yescharacteristic
767C2×C4#55111yescharacteristic
768C2×C4#55111yescharacteristic
769C2×C4#55211yescharacteristic
770C2×C4#55311yescharacteristic
771C2×C4#55311yescharacteristic
772C2×C4#55311yescharacteristic
773C8—24no—
774C8—24no—
775C8—24no—
776C8—24no—
777C8—42no—
778C8—42no—
779C8—42no—
780C8—42no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22C2×C4×C22⋊C411yescharacteristic
804C22C42×D411yescharacteristic
805C22#227511yescharacteristic
806C22#235811yescharacteristic
807C22#235911yescharacteristic
808C22#236111yescharacteristic
809C22#236411yescharacteristic
810C22C2×#40511yescharacteristic
811C22#287311yescharacteristic
812C22#287511yescharacteristic
813C22#287511yescharacteristic
814C22#293012yes—
815C22#293012yes—
816C22#293212yes—
817C22#293312yes—
818C22#293312yes—
819C22#293512yes—
820C22#296712yes—
821C22#296912yes—
822C22#297812yes—
823C22#298112yes—
824C22#299312yes—
825C22#299512yes—
826C4—24no—
827C4—24no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4D4×C22⋊C411yescharacteristic
835C4#233911yescharacteristic
836C4#235211yescharacteristic
837C4#235311yescharacteristic
838C4#235811yescharacteristic
839C4#235911yescharacteristic
840C4#236111yescharacteristic
841C4#236411yescharacteristic
842C2—44no—
843C2—82no—
844C2#1381311yescharacteristic
845C2#2038411yescharacteristic
846C2#2038911yescharacteristic
847C2#2048711yescharacteristic
848C2#2049511yescharacteristic
849C2#2056411yescharacteristic
850C2#2056511yescharacteristic
851C2#2284912yes—
852C2#2290712yes—
853C2#2299412yes—
854C2#2312512yes—
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
3. C2×#1752C2semidirect
4. C2×#1753C2semidirect
5. C2×#1750C2semidirect
6. C2×#1729C2semidirect
8. #10922C2semidirect
9. #10922C2semidirect
10. #10877C2semidirect
11. #10876C2semidirect
12. #10797C2semidirect
13. #10715C2semidirect
14. #10715C2semidirect
15. #10696C2semidirect
23. C2×#436C4semidirect
38. #1869C4semidirect
180. #336D4semidirect
369. C22⋊C8C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4362
C2×#18692
C2×#17522
C2×#17532
C2×#17502
C2×#17292
#138392
#109222
#108772
#108762
#107972
#107152
#106962