Finite Group Databasebeta

← #372846

Subgroups — #372846

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#126C211yesmaximal, characteristic
2C2×#1923C211yesmaximal, characteristic
3C2×C8×C22⋊C4C211yesmaximal, characteristic
4#11346C211yesmaximal, characteristic, complemented
5#11202C211yesmaximal, characteristic, complemented
6#11147C211yesmaximal, characteristic
7#11147C211yesmaximal, characteristic
8#10874C211yesmaximal, characteristic, complemented
9#10874C211yesmaximal, characteristic, complemented
10#10874C211yesmaximal, characteristic, complemented
11#10834C211yesmaximal, characteristic, complemented
12#10795C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic
14#10714C211yesmaximal, characteristic
15C4×#336C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×#126C411yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C4×#126—24no—
26C4×#126—24no—
27C2×#388C411yescharacteristic
28C2×#388C411yescharacteristic
29C2×#388C411yescharacteristic
30C2×#387C411yescharacteristic
31C2×#387C411yescharacteristic
32C2×#387C411yescharacteristic
33C2×#383C411yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C43C2211yescharacteristic
41#1923—24no—
42C8×C22⋊C4—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
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—41no—
70C23×C8—41no—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×#126—24no—
80C2×#126—24no—
81C2×#126C818yescomplemented
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4C2×C411yescharacteristic
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic
94C22×C42C2×C411yescharacteristic
95C22×C42C2×C411yescharacteristic
96C22×C42C2×C411yescharacteristic
97C22×C42C2×C411yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—41no—
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—41no—
115C2×C22⋊C8—41no—
116C2×C4×C8—22no—
117C2×C4×C8—22no—
118C2×C4×C8—22no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8—22no—
122C2×C4×C8—41no—
123C2×C4×C8—41no—
124C2×C4×C8—41no—
125#388—24no—
126#388—24no—
127#388—24no—
128#387—24no—
129#387—24no—
130#387—24no—
131#383—24no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—22no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C22⋊C4—22no—
139C4×C22⋊C4—22no—
140C4×C22⋊C4—22no—
141C4×C22⋊C4—22no—
142C4×C22⋊C4D414yes—
143C4×C22⋊C4D414yes—
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
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C43—22no—
157C43—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—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—41no—
175#336—41no—
176#336—41no—
177#336—41no—
178C25C22×C411yescharacteristic
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
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×C4C22×C411yescharacteristic
192C23×C4C22×C411yescharacteristic
193C23×C4C22×C411yescharacteristic
194C23×C4C22×C411yescharacteristic
195C23×C4C22×C411yescharacteristic
196C23×C4C22×C411yescharacteristic
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C2×D412yes—
205C23×C4C2×D412yes—
206C23×C4C2411yescharacteristic
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—28no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
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—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—44no—
257C22×C8—44no—
258C22×C8—44no—
259C22×C8—44no—
260C22×C8—44no—
261C22×C8—44no—
262C22×C8#4112yes—
263C22×C8#4112yes—
264C22×C8#4112yes—
265C22×C8#4112yes—
266C22×C8#4112yes—
267C22×C8#4112yes—
268C22×C8#4112yes—
269C22×C8#4112yes—
270#126—232no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4C2×C814yescomplemented
287C2×C4⋊C4C2×C814yescomplemented
288C2×C4⋊C4C2×C814yescomplemented
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—41no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4C22⋊C414yes—
302C2×C22⋊C4C22⋊C414yes—
303C2×C22⋊C4C2×C814yes—
304C2×C22⋊C4C2×C814yes—
305C2×C22⋊C4C2×C814yes—
306C2×C22⋊C4M1614yes—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
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—41no—
349C2×C42—41no—
350C2×C42C2×C814yescomplemented
351C2×C42C2×D412yes—
352C2×C42C2×D412yes—
353C2×C42C2×D412yes—
354C2×C42C2×D412yes—
355C4⋊C8—44no—
356C22⋊C8—28no—
357C22⋊C8—44no—
358C22⋊C8—44no—
359C4×C8—44no—
360C4×C8—44no—
361C4×C8—44no—
362#95—22no—
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#95C22⋊C414yes—
373#95C22⋊C414yes—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24C2×C22⋊C412yes—
387C24C22×C812yes—
388C24C2×M1612yes—
389C24C23×C411yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
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—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
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—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—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—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×C4C2×C22⋊C412yes—
493C22×C4C2×C22⋊C412yes—
494C22×C4C2×C22⋊C412yes—
495C22×C4C2×C22⋊C412yes—
496C22×C4C2×C22⋊C412yes—
497C22×C4C22×C812yes—
498C22×C4C22×C812yes—
499C22×C4C22×C812yes—
500C22×C4C22×C812yes—
501C22×C4C22×C812yes—
502C22×C4C22×C812yes—
503C22×C4C2×M1612yes—
504C22×C4C2×M1612yes—
505C22×C4#13112yes—
506C22×C4#13112yes—
507C22×C4#13112yes—
508C22×C4#13112yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4H(5,𝔽2)11yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C42−1+411yescharacteristic
522C22×C42−1+411yescharacteristic
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
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—416no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
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#12614yescomplemented
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4C22⋊C8116yes—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—28no—
601C42—44no—
602C42—44no—
603C42—41no—
604C42—41no—
605C42—41no—
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—44no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23C2×C22⋊C814yes—
655C23C22×C22⋊C411yescharacteristic
656C23C4×#4111yescharacteristic
657C23C4×#4111yescharacteristic
658C23C4×#4111yescharacteristic
659C23C4×#4111yescharacteristic
660C23#52011yescharacteristic
661C23#52011yescharacteristic
662C23C23×C811yescharacteristic
663C23C22×M1611yescharacteristic
664C23C2×#13111yescharacteristic
665C23C2×#13111yescharacteristic
666C23C2×#13111yescharacteristic
667C23C2×#13111yescharacteristic
668C23#56811yescharacteristic
669C23#56811yescharacteristic
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
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—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
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—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
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×C4C2×C22⋊C814yes—
767C2×C4C2×C22⋊C814yes—
768C2×C4#40814yes—
769C2×C4#52511yescharacteristic
770C2×C4#52511yescharacteristic
771C2×C4C2×#12611yescharacteristic
772C2×C4#52911yescharacteristic
773C2×C4#52911yescharacteristic
774C2×C4#52911yescharacteristic
775C2×C4#53211yescharacteristic
776C2×C4#53211yescharacteristic
777C2×C4#53811yescharacteristic
778C2×C4#53911yescharacteristic
779C2×C4#54111yescharacteristic
780C2×C4#54211yescharacteristic
781C2×C4#54611yescharacteristic
782C2×C4#54611yescharacteristic
783C2×C4#54611yescharacteristic
784C2×C4#54611yescharacteristic
785C2×C4#54711yescharacteristic
786C2×C4#54711yescharacteristic
787C2×C4#54711yescharacteristic
788C2×C4#54711yescharacteristic
789C2×C4#55111yescharacteristic
790C2×C4#55111yescharacteristic
791C2×C4#55211yescharacteristic
792C2×C4#55211yescharacteristic
793C2×C4#55311yescharacteristic
794C2×C4#55311yescharacteristic
795C2×C4#55611yescharacteristic
796C2×C4#55611yescharacteristic
797C8—24no—
798C8—42no—
799C8—42no—
800C8—42no—
801C8—42no—
802C8—42no—
803C8—81no—
804C8—81no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22#229711yescharacteristic
821C22C4×#12611yescharacteristic
822C22#233411yescharacteristic
823C22#233911yescharacteristic
824C22#233911yescharacteristic
825C22#237311yescharacteristic
826C22#237311yescharacteristic
827C22C22×C22⋊C811yescharacteristic
828C22C2×#40811yescharacteristic
829C22#288011yescharacteristic
830C22#288011yescharacteristic
831C22C8×#4111yescharacteristic
832C22C8×#4111yescharacteristic
833C22C8×#4111yescharacteristic
834C22C8×#4111yescharacteristic
835C22#296511yescharacteristic
836C22#296511yescharacteristic
837C22#296611yescharacteristic
838C22#296611yescharacteristic
839C22#296611yescharacteristic
840C22#296711yescharacteristic
841C22#296811yescharacteristic
842C22#296811yescharacteristic
843C22#296911yescharacteristic
844C22#296911yescharacteristic
845C22#297011yescharacteristic
846C22#297011yescharacteristic
847C22#298811yescharacteristic
848C22#298811yescharacteristic
849C22#299011yescharacteristic
850C22#299011yescharacteristic
851C22#299211yescharacteristic
852C22#299311yescharacteristic
853C22#299411yescharacteristic
854C22#299411yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4#246611yescharacteristic
869C4#246811yescharacteristic
870C4#247811yescharacteristic
871C4#248011yescharacteristic
872C4#249611yescharacteristic
873C4#252111yescharacteristic
874C4#255311yescharacteristic
875C4#255911yescharacteristic
876C2—44no—
877C2#1410211yescharacteristic
878C2#2137311yescharacteristic
879C2#2138111yescharacteristic
880C2C8×#12611yescharacteristic
881C2#2166511yescharacteristic
882C2#2234111yescharacteristic
883C2#2234511yescharacteristic
884C2#2246911yescharacteristic
885C2#2246911yescharacteristic
886C2#2247011yescharacteristic
887C2#2247411yescharacteristic
888C2#2327811yescharacteristic
889C2#2327811yescharacteristic
890C2#2328211yescharacteristic
891C2#2328811yescharacteristic
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
4. #11346C2semidirect
5. #11202C2semidirect
8. #10874C2semidirect
9. #10874C2semidirect
10. #10874C2semidirect
11. #10834C2semidirect
12. #10795C2semidirect
15. C4×#336C2semidirect
81. C2×#126C8semidirect
286. C2×C4⋊C4C2×C8semidirect
287. C2×C4⋊C4C2×C8semidirect
288. C2×C4⋊C4C2×C8semidirect
350. C2×C42C2×C8semidirect
579. C2×C8#126semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1262
C2×#19232
C2×C8×C22⋊C42
#113462
#112022
#111472
#108742
#108342
#107952
#107142
C4×#3362