Finite Group Databasebeta

← #357213

Subgroups — #357213

Order 512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1955C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1752C211yesmaximal, characteristic, complemented
4C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#1749C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
7C4×#386C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10922C211yesmaximal, characteristic, complemented
10#10921C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10877C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10696C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
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×#97C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C2×#386C412yes—
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#1955C418yescomplemented
39#1869C418yescomplemented
40#1752—24no—
41C8×C22⋊C4—24no—
42#1749—24no—
43C4×C22⋊C8—24no—
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
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—41no—
70C23×C8—41no—
71C23×C8C2×C414yescomplemented
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4×D4—41no—
81C2×C4×D4—41no—
82C2×C4×D4—41no—
83C2×C4×D4—41no—
84C2×C4×D4C2×C414yes—
85C2×C4×D4C2×C414yes—
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C22⋊C4C2×C412yes—
88C22×C22⋊C4C2×C412yes—
89C22×C22⋊C4C2×C412yes—
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42—22no—
96C22×C42—41no—
97C22×C42—41no—
98C22×C42C2×C412yes—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—41no—
105C2×C4⋊C8—41no—
106C2×C4⋊C8C2×C414yescomplemented
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8C2×C414yes—
122C2×C22⋊C8C2×C414yes—
123C2×C22⋊C8C2×C414yes—
124C2×C22⋊C8C2×C414yes—
125C2×C22⋊C8C2×C414yescomplemented
126C2×C22⋊C8C2×C414yescomplemented
127C2×C22⋊C8C2×C414yescomplemented
128C2×#97—22no—
129C2×#97—22no—
130C2×#97—22no—
131C2×#97—22no—
132C2×#97—22no—
133C2×#97—22no—
134C2×#97—41no—
135C2×#97—41no—
136C2×#97—41no—
137C2×#97—41no—
138C2×#97—41no—
139C2×#97C2×C414yescomplemented
140C2×C4×C8—22no—
141C2×C4×C8—22no—
142C2×C4×C8—22no—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145C2×C4×C8—22no—
146C2×C4×C8—41no—
147C2×C4×C8—41no—
148C2×C4×C8—41no—
149#386—28no—
150C4×C22⋊C4—22no—
151C4×C22⋊C4—22no—
152C4×C22⋊C4—22no—
153C4×C22⋊C4—22no—
154C4×C22⋊C4—41no—
155C4×C22⋊C4—41no—
156C2×#95C2×C412yes—
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159C2×#95C2×C412yes—
160C2×#95C2×C412yes—
161C2×#95C2×C412yes—
162C2×#95C2×C412yes—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—41no—
170#336—41no—
171#336C2×C414yescomplemented
172#336C2×C414yescomplemented
173#336D414yescomplemented
174#336D414yescomplemented
175C25C22×C411yescharacteristic
176C25C22×C411yescharacteristic
177C22×D4—24no—
178C22×D4—24no—
179C22×D4—41no—
180C22×D4—41no—
181C22×D4C4214yes—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—24no—
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—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4C22×C412yes—
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C412yes—
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C22×C412yes—
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C22×C412yes—
225C23×C4C2411yescharacteristic
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
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—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—28no—
267C22×C8—28no—
268C22×C8—44no—
269C22×C8—44no—
270C22×C8—44no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C22×C412yes—
280C22×C8C22×C412yes—
281C22×C8C2×D412yes—
282C22×C8C2×D412yes—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8#4112yes—
286C22×C8#4112yes—
287C22×C8#4112yes—
288C22×C8#4112yes—
289C4×D4—44no—
290C4×D4—44no—
291C4×D4—44no—
292C4×D4—44no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4C4214yes—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4C4214yes—
309C2×C22⋊C4C4214yes—
310C2×C22⋊C4M1618yes—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42—44no—
340C2×C42—44no—
341C2×C42—42no—
342C2×C42C22×C412yes—
343C2×C42C22×C412yes—
344C2×C42C2×D412yes—
345C2×C42C2×D412yes—
346C2×C42#4112yes—
347C2×C42#4112yes—
348C4⋊C8—44no—
349C22⋊C8—28no—
350C22⋊C8—28no—
351C22⋊C8—28no—
352C22⋊C8—28no—
353C22⋊C8—28no—
354C22⋊C8—28no—
355C22⋊C8—44no—
356#97—44no—
357#97—44no—
358#97—44no—
359#97—44no—
360C4×C8—44no—
361C4×C8—44no—
362C4×C8—44no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—42no—
369#95—42no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24C2×C4212yes—
389C24C2×C4212yes—
390C24C2×M1614yes—
391C24#13114yes—
392C24C23×C411yescharacteristic
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—44no—
396C2×D4—48no—
397C2×D4—48no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—216no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
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—22no—
449C22×C4—22no—
450C22×C4—22no—
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—48no—
467C22×C4—48no—
468C22×C4—48no—
469C22×C4—48no—
470C22×C4—48no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
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—48no—
504C22×C4C2×C4212yes—
505C22×C4C2×C4212yes—
506C22×C4C2×C4212yes—
507C22×C4C2×C4212yes—
508C22×C4C4×D414yes—
509C22×C4C4×D414yes—
510C22×C4C2×M1614yes—
511C22×C4C2×M1614yes—
512C22×C4#13114yes—
513C22×C4C23×C411yescharacteristic
514C22×C4C23×C411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C2×#4111yescharacteristic
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×C4H(5,𝔽2)11yescharacteristic
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—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—416no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
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×C8C4×D414yes—
581C2×C8C4×D414yes—
582C2×C8C4×D414yes—
583C2×C8C4×D414yes—
584C4⋊C4—44no—
585C22⋊C4—216no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—48no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C4×M1614yes—
656C23#40514yes—
657C23C22×C4211yescharacteristic
658C23C2×C4×D411yescharacteristic
659C23C2×C4×D411yescharacteristic
660C23C4×#4111yescharacteristic
661C23C4×#4111yescharacteristic
662C23#51811yescharacteristic
663C23#51811yescharacteristic
664C23C22×M1612yes—
665C23C2×#13112yes—
666C23C2×#13112yes—
667C23#56812yes—
668D4—416no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—432no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
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#43518yes—
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C4×#4111yescharacteristic
743C2×C4C4×#4111yescharacteristic
744C2×C4C4×#4111yescharacteristic
745C2×C4C4×#4111yescharacteristic
746C2×C4#51811yescharacteristic
747C2×C4#51811yescharacteristic
748C2×C4#51811yescharacteristic
749C2×C4#51811yescharacteristic
750C2×C4D4211yescharacteristic
751C2×C4#54611yescharacteristic
752C2×C4#54611yescharacteristic
753C2×C4#54611yescharacteristic
754C2×C4#54611yescharacteristic
755C2×C4#55011yescharacteristic
756C2×C4#55011yescharacteristic
757C2×C4#55111yescharacteristic
758C2×C4#55111yescharacteristic
759C2×C4#55311yescharacteristic
760C2×C4#55311yescharacteristic
761C2×C4#55311yescharacteristic
762C2×C4#55311yescharacteristic
763C2×C4#55511yescharacteristic
764C2×C4#55511yescharacteristic
765C2×C4#55911yescharacteristic
766C8—24no—
767C8—24no—
768C8—24no—
769C8—24no—
770C8—42no—
771C8—42no—
772C8—42no—
773C8—42no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—44no—
796C22C42×D411yescharacteristic
797C22C42×D411yescharacteristic
798C22#227311yescharacteristic
799C22#235811yescharacteristic
800C22#236311yescharacteristic
801C22#236311yescharacteristic
802C22#237411yescharacteristic
803C22C2×C4×M1611yescharacteristic
804C22C2×#40511yescharacteristic
805C22C4×#13111yescharacteristic
806C22#287511yescharacteristic
807C22C2×#43512yes—
808C22#292912yes—
809C22#293312yes—
810C22D4×M1612yes—
811C22#296512yes—
812C22#296612yes—
813C22#296812yes—
814C22#297012yes—
815C22#297412yes—
816C22#297412yes—
817C22#297612yes—
818C22#298112yes—
819C4—28no—
820C4—42no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—82no—
827C4#235811yescharacteristic
828C4#236311yescharacteristic
829C4#236311yescharacteristic
830C4#236411yescharacteristic
831C4#236411yescharacteristic
832C4#236611yescharacteristic
833C4#237211yescharacteristic
834C4#237411yescharacteristic
835C2—44no—
836C2—44no—
837C2#1382411yescharacteristic
838C2#2048411yescharacteristic
839C2C4×#43511yescharacteristic
840C2#2049111yescharacteristic
841C2#2049311yescharacteristic
842C2#2052511yescharacteristic
843C2#2053111yescharacteristic
844C2#2284612yes—
845C2#2308412yes—
846C2#2308512yes—
847C2#2330012yes—
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×C8×C22⋊C4C2semidirect
5. C2×#1749C2semidirect
6. C2×C4×C22⋊C8C2semidirect
8. #10922C2semidirect
9. #10922C2semidirect
10. #10921C2semidirect
11. #10921C2semidirect
12. #10877C2semidirect
13. #10876C2semidirect
14. #10696C2semidirect
15. #10696C2semidirect
38. #1955C4semidirect
39. #1869C4semidirect
71. C23×C8C2×C4semidirect
106. C2×C4⋊C8C2×C4semidirect
125. C2×C22⋊C8C2×C4semidirect
126. C2×C22⋊C8C2×C4semidirect
127. C2×C22⋊C8C2×C4semidirect
139. C2×#97C2×C4semidirect
171. #336C2×C4semidirect
172. #336C2×C4semidirect
173. #336D4semidirect
174. #336D4semidirect

Maximal subgroups

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

subgroupindex
C2×#19552
C2×#18692
C2×#17522
C2×C8×C22⋊C42
C2×#17492
C2×C4×C22⋊C82
C4×#3862
#109222
#109212
#108772
#108762
#106962