Finite Group Databasebeta

← #355424

Subgroups — #355424

Order 512.

1930 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1753C211yesmaximal, characteristic, complemented
4C2×#1728C211yesmaximal, characteristic, complemented
5C4×#386C211yesmaximal, characteristic
6#10922C211yesmaximal, characteristic, complemented
7#10921C211yesmaximal, characteristic, complemented
8#10877C211yesmaximal, characteristic, complemented
9#10876C211yesmaximal, characteristic, complemented
10#10798C211yesmaximal, characteristic, complemented
11#10798C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#435—24no—
22C2×#435—24no—
23C2×#435C418yescomplemented
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C2×#386C412yes—
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1870C418yescomplemented
38#1753—24no—
39#1728—24no—
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
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
56#1437C412yes—
57#1436C412yes—
58C22⋊#95C412yes—
59C4×#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C23×D4C2×C411yescharacteristic
62C24×C4C2×C412yes—
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—41no—
68C22×M16—41no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16—41no—
73C22×M16—41no—
74C22×M16—41no—
75C22×M16C2×C414yes—
76C22×M16C2×C414yes—
77C22×M16D414yes—
78C22×M16D414yes—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—41no—
82C23×C8—41no—
83C23×C8—41no—
84C23×C8—41no—
85C23×C8C2×C414yescomplemented
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×D4C2×C414yes—
99C2×C4×D4C2×C414yes—
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C412yes—
102C22×C22⋊C4C2×C412yes—
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C412yes—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—41no—
109C22×C42—41no—
110C22×C42—41no—
111C22×C42—41no—
112C22×C42C2×C412yes—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118#435—232no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8C2×C414yescomplemented
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yescomplemented
135C2×C22⋊C8C2×C414yescomplemented
136C2×C22⋊C8C2×C414yescomplemented
137C2×#97—22no—
138C2×#97—22no—
139C2×#97—22no—
140C2×#97—41no—
141C2×#97—41no—
142C2×#97C2×C414yescomplemented
143C2×C4×C8—22no—
144C2×C4×C8—41no—
145C2×C4×C8—41no—
146#386—28no—
147C4×C22⋊C4—22no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—41no—
150C4×C22⋊C4—41no—
151C4×C22⋊C4—41no—
152C4×C22⋊C4—41no—
153C2×#95C2×C412yes—
154C2×#95C2×C412yes—
155C2×#95C2×C412yes—
156C2×#95C2×C412yes—
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159C2×#95C2×C412yes—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—41no—
167#336—41no—
168#336—41no—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
173#336—41no—
174#336C2×C414yescomplemented
175#336C2×C414yescomplemented
176C25C22×C411yescharacteristic
177C25C22×C411yescharacteristic
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—24no—
181C22×D4—42no—
182C22×D4C4214yes—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
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—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4C22×C412yes—
211C23×C4C22×C411yescharacteristic
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×C412yes—
221C23×C4C22×C412yes—
222C23×C4C2×D412yes—
223C23×C4C2×D412yes—
224C23×C4#4112yes—
225C23×C4#4112yes—
226C23×C4C2411yescharacteristic
227C2×M16—28no—
228C2×M16—44no—
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—
239C2×M16—44no—
240C2×M16C22⋊C4116yescomplemented
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—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—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—28no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8C22×C412yes—
293C22×C8C22×C412yes—
294C22×C8C22×C412yes—
295C22×C8C22×C412yes—
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C412yes—
299C22×C8C22×C412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C22×C8C2×D412yes—
303C22×C8C2×D412yes—
304C4×D4—28no—
305C4×D4—28no—
306C4×D4—28no—
307C4×D4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4C4214yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4C4214yes—
324C2×C22⋊C4C4214yes—
325C2×C22⋊C4M1618yescomplemented
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—24no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
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—42no—
356C2×C42—42no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42—44no—
361C2×C42C22×C412yes—
362C2×C42C22×C412yes—
363C4⋊C8—28no—
364C22⋊C8—28no—
365C22⋊C8—28no—
366C22⋊C8—28no—
367C22⋊C8—44no—
368C22⋊C8—44no—
369#97—28no—
370#97—44no—
371C4×C8—44no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—42no—
377#95—42no—
378#95—42no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24C2×C4212yes—
397C24C2×C4212yes—
398C24C4×D412yes—
399C24C4×D412yes—
400C24C2×M1614yes—
401C24C23×C411yescharacteristic
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—44no—
405C2×D4—48no—
406C2×D4—48no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
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—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
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—48no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
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×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4C2×C4212yes—
510C22×C4C2×C4212yes—
511C22×C4C2×C4212yes—
512C22×C4C2×C4212yes—
513C22×C4C2×C22⋊C414yes—
514C22×C4#11714yes—
515C22×C4C4×D414yes—
516C22×C4C4×D414yes—
517C22×C4C4×D412yes—
518C22×C4C4×D412yes—
519C22×C4C2×M1614yes—
520C22×C4C2×M1614yes—
521C22×C4#13114yes—
522C22×C4C23×C411yescharacteristic
523C22×C4C23×C411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C4H(5,𝔽2)11yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C4H(5,𝔽2)11yescharacteristic
533C22×C4H(5,𝔽2)11yescharacteristic
534C22×C42−1+411yescharacteristic
535C22×C42−1+411yescharacteristic
536M16—416no—
537M16—416no—
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—416no—
569C2×C8—41no—
570C2×C8—41no—
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×C8C2×C22⋊C414yes—
594C2×C8C2×C22⋊C414yes—
595C4⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—28no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—48no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
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—
664C23—42no—
665C23—42no—
666C23C4×C22⋊C414yes—
667C23C4×M1614yes—
668C23C22×C4211yescharacteristic
669C23C2×C4×D411yescharacteristic
670C23C2×C4×D411yescharacteristic
671C23#51811yescharacteristic
672C23#51811yescharacteristic
673C23#52011yescharacteristic
674C23#52011yescharacteristic
675C23C22×M1612yes—
676C23C2×#13112yes—
677C23#56812yes—
678C23#56812yes—
679D4—416no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
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—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—432no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
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×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4C4×C22⋊C414yes—
749C2×C4C22×C22⋊C411yescharacteristic
750C2×C4C2×#11711yescharacteristic
751C2×C4C2×C4×D411yescharacteristic
752C2×C4C2×C4×D411yescharacteristic
753C2×C4#51811yescharacteristic
754C2×C4#51811yescharacteristic
755C2×C4#51811yescharacteristic
756C2×C4#51811yescharacteristic
757C2×C4#52011yescharacteristic
758C2×C4#52011yescharacteristic
759C2×C4#52011yescharacteristic
760C2×C4#52011yescharacteristic
761C2×C4#53411yescharacteristic
762C2×C4#53411yescharacteristic
763C2×C4#53411yescharacteristic
764C2×C4#53411yescharacteristic
765C2×C4#53511yescharacteristic
766C2×C4#53611yescharacteristic
767C2×C4#53711yescharacteristic
768C2×C4#53711yescharacteristic
769C2×C4#53811yescharacteristic
770C2×C4#53811yescharacteristic
771C2×C4#53811yescharacteristic
772C2×C4#53811yescharacteristic
773C2×C4#53911yescharacteristic
774C2×C4#53911yescharacteristic
775C2×C4#53911yescharacteristic
776C2×C4#53911yescharacteristic
777C8—24no—
778C8—24no—
779C8—42no—
780C8—42no—
781C8—42no—
782C8—42no—
783C8—42no—
784C8—42no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22C2×C4×C22⋊C411yescharacteristic
808C22#227511yescharacteristic
809C22#227511yescharacteristic
810C22#232111yescharacteristic
811C22#232211yescharacteristic
812C22#232511yescharacteristic
813C22#232511yescharacteristic
814C22C2×C4×M1611yescharacteristic
815C22#287311yescharacteristic
816C22C4×#13111yescharacteristic
817C22#287511yescharacteristic
818C22#293312yes—
819C22D4×M1612yes—
820C22D4×M1612yes—
821C22#293512yes—
822C22#297312yes—
823C22#297412yes—
824C22#297612yes—
825C22#297812yes—
826C22#298912yes—
827C22#299012yes—
828C22#299312yes—
829C22#299512yes—
830C4—24no—
831C4—44no—
832C4—44no—
833C4—44no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—82no—
838C4#230811yescharacteristic
839C4#231111yescharacteristic
840C4#231811yescharacteristic
841C4#231811yescharacteristic
842C4#232111yescharacteristic
843C4#232211yescharacteristic
844C4#232511yescharacteristic
845C4#232511yescharacteristic
846C2—44no—
847C2—44no—
848C2#1378411yescharacteristic
849C2#2038711yescharacteristic
850C2C22⋊C4×M1611yescharacteristic
851C2#2055611yescharacteristic
852C2#2055911yescharacteristic
853C2#2056111yescharacteristic
854C2#2056411yescharacteristic
855C2#2203612yes—
856C2#2207112yes—
857C2#2217012yes—
858C2#2217412yes—
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×#1753C2semidirect
4. C2×#1728C2semidirect
6. #10922C2semidirect
7. #10921C2semidirect
8. #10877C2semidirect
9. #10876C2semidirect
10. #10798C2semidirect
11. #10798C2semidirect
12. #10715C2semidirect
13. #10714C2semidirect
14. #10714C2semidirect
15. #10712C2semidirect
23. C2×#435C4semidirect
37. #1870C4semidirect
85. C23×C8C2×C4semidirect
121. C2×C4⋊C8C2×C4semidirect
134. C2×C22⋊C8C2×C4semidirect
135. C2×C22⋊C8C2×C4semidirect
136. C2×C22⋊C8C2×C4semidirect
142. C2×#97C2×C4semidirect
174. #336C2×C4semidirect
175. #336C2×C4semidirect
240. C2×M16C22⋊C4semidirect
325. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×#18702
C2×#17532
C2×#17282
C4×#3862
#109222
#109212
#108772
#108762
#107982
#107152
#107142
#107122