Finite Group Databasebeta

← #365782

Subgroups — #365782

Order 512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1916C211yesmaximal, characteristic, complemented
2C2×#1797C211yesmaximal, characteristic
3C2×C8×C22⋊C4C211yesmaximal, characteristic
4C22×#336C211yesmaximal, characteristic
5C4×#385C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic, complemented
7#11298C211yesmaximal, characteristic, complemented
8#11255C211yesmaximal, characteristic, complemented
9#11202C211yesmaximal, characteristic, complemented
10#10876C211yesmaximal, characteristic, complemented
11#10874C211yesmaximal, characteristic, complemented
12#10797C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic
14#10714C211yesmaximal, characteristic
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C2×#385C411yescharacteristic
26C2×#385C411yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31#1916—24no—
32#1797—24no—
33C8×C22⋊C4—24no—
34C2×#336—24no—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
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
55#1436C411yescharacteristic
56#1436C411yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59C22⋊#95C411yescharacteristic
60C22⋊#95C411yescharacteristic
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63C24×C4C2×C411yescharacteristic
64C24×C4C2×C411yescharacteristic
65C24×C4C2311yescharacteristic
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8Q814yes—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—41no—
101C22×C42—41no—
102C22×C42C2×C411yescharacteristic
103C22×C42C2×C411yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—41no—
115C2×C4⋊C8—41no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8D414yes—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8—41no—
127C2×C4×C8—41no—
128#385—24no—
129#385C818yescomplemented
130C4×C4⋊C4—22no—
131C4×C4⋊C4—22no—
132C4×C4⋊C4—41no—
133C4×C4⋊C4—41no—
134C4×C22⋊C4—22no—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C2×#95C2×C411yescharacteristic
141C2×#95C2×C411yescharacteristic
142C2×#95C2×C411yescharacteristic
143C2×#95C2×C411yescharacteristic
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—22no—
167#336—41no—
168#336—41no—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
173#336D414yes—
174C25C22×C411yescharacteristic
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4—41no—
195C23×C4—41no—
196C23×C4C2×C814yes—
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C2×D412yes—
211C23×C4C2×Q812yes—
212C23×C4#4112yes—
213C23×C4#4112yes—
214C23×C4#4112yes—
215C23×C4#4112yes—
216C23×C4C2411yescharacteristic
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—28no—
222C22×C8—28no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
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—28no—
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—44no—
269C22×C8—44no—
270C22×C8—44no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8—44no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8C2×D412yes—
280C22×C8C2×D412yes—
281C22×C8C2×D412yes—
282C22×C8C2×D412yes—
283C22×C8C2×Q812yes—
284C22×C8C2×Q812yes—
285C22×C8#4112yes—
286C22×C8#4112yes—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4C2×C814yescomplemented
298C2×C4⋊C4C2×C814yescomplemented
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4C2×C814yes—
309C2×C22⋊C4C2×C814yes—
310C2×C22⋊C4M1614yes—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
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—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—44no—
350C2×C42—44no—
351C2×C42—44no—
352C2×C42—44no—
353C2×C42—41no—
354C2×C42—41no—
355C2×C42C2×D412yes—
356C2×C42#4112yes—
357C4⋊C8—44no—
358C4⋊C8—44no—
359C22⋊C8—28no—
360C22⋊C8—44no—
361C4×C8—44no—
362C4×C8—44no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—41no—
374#95—41no—
375#95—41no—
376#95—41no—
377#95C2×C814yescomplemented
378#95C2×C814yescomplemented
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24#11712yes—
388C24C4×D412yes—
389C24C4×Q812yes—
390C24C22×C812yes—
391C24C2×M1612yes—
392C24#13112yes—
393C24#13112yes—
394C24C23×C411yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
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—28no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
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—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4#11712yes—
510C22×C4C4×D412yes—
511C22×C4C4×D412yes—
512C22×C4C4×D412yes—
513C22×C4C4×Q812yes—
514C22×C4C22⋊Q814yes—
515C22×C4#12314yes—
516C22×C4#12514yes—
517C22×C4#12614yes—
518C22×C4C22×C812yes—
519C22×C4C22×C812yes—
520C22×C4C22×C812yes—
521C22×C4C22×C812yes—
522C22×C4C22×C812yes—
523C22×C4C22×C812yes—
524C22×C4C2×M1612yes—
525C22×C4C2×M1612yes—
526C22×C4#13112yes—
527C22×C4#13112yes—
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×Q811yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4H(5,𝔽2)11yescharacteristic
539C22×C4H(5,𝔽2)11yescharacteristic
540C22×C4H(5,𝔽2)11yescharacteristic
541C22×C42−1+411yescharacteristic
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—416no—
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×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×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8C22⋊Q814yes—
600C4⋊C4—28no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—44no—
613C42—44no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23#38714yes—
663C23#43114yes—
664C23#43314yes—
665C23C8×D414yes—
666C23#43514yes—
667C23C8×Q814yes—
668C23#44614yes—
669C23C2×#11711yescharacteristic
670C23C2×C4×D411yescharacteristic
671C23C2×C4×D411yescharacteristic
672C23C2×C4×Q811yescharacteristic
673C23C4×#4111yescharacteristic
674C23#51811yescharacteristic
675C23#52011yescharacteristic
676C23C23×C811yescharacteristic
677C23C22×M1611yescharacteristic
678C23C2×#13111yescharacteristic
679C23C2×#13111yescharacteristic
680C23C2×#13111yescharacteristic
681C23C2×#13111yescharacteristic
682C23#56811yescharacteristic
683C23#56811yescharacteristic
684C2×C4—22no—
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—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4#38714yes—
784C2×C4C8×D414yes—
785C2×C4C2×C22⋊Q811yescharacteristic
786C2×C4C2×C22⋊Q811yescharacteristic
787C2×C4C2×#12311yescharacteristic
788C2×C4#52511yescharacteristic
789C2×C4C2×#12511yescharacteristic
790C2×C4C2×#12611yescharacteristic
791C2×C4#52911yescharacteristic
792C2×C4#53311yescharacteristic
793C2×C4#53811yescharacteristic
794C2×C4#53911yescharacteristic
795C2×C4#54311yescharacteristic
796C2×C4#54411yescharacteristic
797C2×C4D4211yescharacteristic
798C2×C4#54611yescharacteristic
799C2×C4#54611yescharacteristic
800C2×C4#54611yescharacteristic
801C2×C4#54611yescharacteristic
802C2×C4#54711yescharacteristic
803C2×C4#54811yescharacteristic
804C2×C4#55111yescharacteristic
805C2×C4#55111yescharacteristic
806C2×C4#55111yescharacteristic
807C2×C4#55111yescharacteristic
808C2×C4#55211yescharacteristic
809C2×C4#55211yescharacteristic
810C2×C4#55311yescharacteristic
811C2×C4#55311yescharacteristic
812C2×C4#55311yescharacteristic
813C8—24no—
814C8—42no—
815C8—42no—
816C8—42no—
817C8—42no—
818C8—42no—
819C8—81no—
820C8—81no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22#191618yescomplemented
836C22C2×#38711yescharacteristic
837C22C4×C22⋊Q811yescharacteristic
838C22#232911yescharacteristic
839C22#235211yescharacteristic
840C22#235311yescharacteristic
841C22#235811yescharacteristic
842C22#235911yescharacteristic
843C22C2×#43111yescharacteristic
844C22C2×#43311yescharacteristic
845C22#292511yescharacteristic
846C22#292511yescharacteristic
847C22C2×C8×D411yescharacteristic
848C22C2×C8×D411yescharacteristic
849C22C2×#43511yescharacteristic
850C22#292911yescharacteristic
851C22#293311yescharacteristic
852C22#293311yescharacteristic
853C22#293311yescharacteristic
854C22D4×M1611yescharacteristic
855C22C2×C8×Q811yescharacteristic
856C22C2×#44611yescharacteristic
857C22#296011yescharacteristic
858C22#296111yescharacteristic
859C22C8×#4111yescharacteristic
860C22#296611yescharacteristic
861C22#296811yescharacteristic
862C22#297011yescharacteristic
863C22#297211yescharacteristic
864C22#297411yescharacteristic
865C22#297611yescharacteristic
866C22#297711yescharacteristic
867C22#298811yescharacteristic
868C22#299011yescharacteristic
869C22#299211yescharacteristic
870C22#299411yescharacteristic
871C4—24no—
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—81no—
883C4—81no—
884C4#243711yescharacteristic
885C4#243811yescharacteristic
886C4#244211yescharacteristic
887C4#244311yescharacteristic
888C4#244411yescharacteristic
889C4#248011yescharacteristic
890C4#249311yescharacteristic
891C4#256911yescharacteristic
892C2—28no—
893C2#1398011yescharacteristic
894C2C2×#191611yescharacteristic
895C2#2102711yescharacteristic
896C2C8×C22⋊Q811yescharacteristic
897C2#2159911yescharacteristic
898C2#2228711yescharacteristic
899C2#2229111yescharacteristic
900C2#2274811yescharacteristic
901C2#2275411yescharacteristic
902C2#2278511yescharacteristic
903C2#2279111yescharacteristic
904C2#2284211yescharacteristic
905C2#2284611yescharacteristic
906C2#2290011yescharacteristic
907C2#2290811yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC25C22×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
1. C2×#1916C2semidirect
6. #11346C2semidirect
7. #11298C2semidirect
8. #11255C2semidirect
9. #11202C2semidirect
10. #10876C2semidirect
11. #10874C2semidirect
12. #10797C2semidirect
129. #385C8semidirect
297. C2×C4⋊C4C2×C8semidirect
298. C2×C4⋊C4C2×C8semidirect
377. #95C2×C8semidirect
378. #95C2×C8semidirect
835. C22#1916semidirect

Maximal subgroups

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

subgroupindex
C2×#19162
C2×#17972
C2×C8×C22⋊C42
C22×#3362
C4×#3852
#113462
#112982
#112552
#112022
#108762
#108742
#107972
#107142