Finite Group Databasebeta

← #373300

Subgroups — #373300

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1939C211yesmaximal, characteristic, complemented
2C2×#1923C211yesmaximal, characteristic
3C2×#1850C211yesmaximal, characteristic
4C2×C8×C22⋊C4C211yesmaximal, characteristic
5C4×#388C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic, complemented
7#11202C211yesmaximal, characteristic, complemented
8#11042C211yesmaximal, characteristic
9#11042C211yesmaximal, characteristic
10#10876C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10876C211yesmaximal, characteristic, complemented
13#10832C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic
15C4×#336C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C2×#388C411yescharacteristic
29C2×#388C411yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C43C2211yescharacteristic
35#1939—24no—
36#1923—24no—
37#1850—24no—
38C8×C22⋊C4—24no—
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#1437C411yescharacteristic
56#1437C411yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59#1434C411yescharacteristic
60#1434C411yescharacteristic
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
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
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C22⋊C4C2×C411yescharacteristic
85C22×C22⋊C4C2×C411yescharacteristic
86C22×C22⋊C4C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—41no—
109C2×C4⋊C8—41no—
110C2×C4⋊C8—41no—
111C2×C4⋊C8—41no—
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×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—41no—
128C2×C4×C8—41no—
129C2×C4×C8—41no—
130#388—24no—
131#388C818yescomplemented
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C22⋊C4—22no—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—41no—
137C4×C22⋊C4—41no—
138C4×C22⋊C4D414yes—
139C4×C22⋊C4Q814yes—
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
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C43—41no—
157C43—41no—
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—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—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C22×C411yescharacteristic
188C23×C4C22×C411yescharacteristic
189C23×C4C22×C411yescharacteristic
190C23×C4C22×C411yescharacteristic
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×C4C2×D412yes—
201C23×C4C2×Q812yes—
202C23×C4C2411yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—28no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
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—44no—
253C22×C8—44no—
254C22×C8—44no—
255C22×C8—44no—
256C22×C8—44no—
257C22×C8—44no—
258C22×C8C2×D412yes—
259C22×C8C2×D412yes—
260C22×C8#4112yes—
261C22×C8#4112yes—
262C22×C8#4112yes—
263C22×C8#4112yes—
264C22×C8#4112yes—
265C22×C8#4112yes—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4C2×C814yescomplemented
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4—41no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4C4⋊C414yes—
285C2×C22⋊C4C4⋊C414yes—
286C2×C22⋊C4C2×C814yes—
287C2×C22⋊C4C2×C814yes—
288C2×C22⋊C4C2×C814yes—
289C2×C22⋊C4M1614yes—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—21no—
308C2×C42—21no—
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—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—41no—
326C2×C42—41no—
327C2×C42—41no—
328C2×C42—41no—
329C2×C42—41no—
330C2×C42—41no—
331C2×C42C2×C814yescomplemented
332C2×C42C2×D412yes—
333C2×C42C2×D412yes—
334C2×C42C2×D412yes—
335C2×C42C2×Q812yes—
336C2×C42C2×Q812yes—
337C2×C42#4112yes—
338C4⋊C8—44no—
339C4⋊C8—44no—
340C4⋊C8—44no—
341C4⋊C8—44no—
342C4⋊C8—44no—
343C22⋊C8—28no—
344C22⋊C8—44no—
345C22⋊C8—44no—
346C4×C8—44no—
347C4×C8—44no—
348C4×C8—44no—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—41no—
359#95—41no—
360#95—41no—
361#95C4⋊C414yes—
362#95C4⋊C414yes—
363#95C2×C814yescomplemented
364#95C2×C814yescomplemented
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24C2×C4⋊C412yes—
378C24C22×C812yes—
379C24C2×M1612yes—
380C24C23×C411yescharacteristic
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
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—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—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—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
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×C4C2×C4⋊C412yes—
482C22×C4C2×C4⋊C412yes—
483C22×C4C2×C4⋊C412yes—
484C22×C4C2×C4⋊C412yes—
485C22×C4C2×C4⋊C412yes—
486C22×C4C4×D412yes—
487C22×C4C4×D412yes—
488C22×C4C22×C812yes—
489C22×C4C22×C812yes—
490C22×C4C22×C812yes—
491C22×C4C22×C812yes—
492C22×C4C22×C812yes—
493C22×C4C22×C812yes—
494C22×C4C2×M1612yes—
495C22×C4C2×M1612yes—
496C22×C4#13112yes—
497C22×C4#13112yes—
498C22×C4#13112yes—
499C22×C4#13112yes—
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C4H(5,𝔽2)11yescharacteristic
513C22×C42−1+411yescharacteristic
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
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—416no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
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#12414yes—
571C4⋊C4—28no—
572C4⋊C4—44no—
573C22⋊C4—28no—
574C22⋊C4—28no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4C4⋊C8116yescomplemented
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—44no—
592C42—44no—
593C42—44no—
594C42—44no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23C2×C4⋊C814yes—
642C23C22×C4⋊C411yescharacteristic
643C23C2×C4×D411yescharacteristic
644C23C4×#4111yescharacteristic
645C23C4×#4111yescharacteristic
646C23C4×#4111yescharacteristic
647C23#51811yescharacteristic
648C23#52011yescharacteristic
649C23C23×C811yescharacteristic
650C23C22×M1611yescharacteristic
651C23C2×#13111yescharacteristic
652C23C2×#13111yescharacteristic
653C23C2×#13111yescharacteristic
654C23C2×#13111yescharacteristic
655C23#56811yescharacteristic
656C23#56811yescharacteristic
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
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—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
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—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
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×C4C2×C4⋊C814yes—
753C2×C4C2×C4⋊C814yes—
754C2×C4#42414yes—
755C2×C4C8×D414yes—
756C2×C4#52511yescharacteristic
757C2×C4#52511yescharacteristic
758C2×C4C2×#12411yescharacteristic
759C2×C4#52911yescharacteristic
760C2×C4#52911yescharacteristic
761C2×C4#53211yescharacteristic
762C2×C4#53311yescharacteristic
763C2×C4#53311yescharacteristic
764C2×C4#53811yescharacteristic
765C2×C4#53911yescharacteristic
766C2×C4#54011yescharacteristic
767C2×C4#54211yescharacteristic
768C2×C4D4211yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54611yescharacteristic
772C2×C4#54611yescharacteristic
773C2×C4#54711yescharacteristic
774C2×C4D4×Q811yescharacteristic
775C2×C4#55111yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55311yescharacteristic
778C2×C4#55311yescharacteristic
779C2×C4#55311yescharacteristic
780C2×C4#55411yescharacteristic
781C2×C4#55411yescharacteristic
782C2×C4#55411yescharacteristic
783C2×C4#55611yescharacteristic
784C8—24no—
785C8—42no—
786C8—42no—
787C8—42no—
788C8—42no—
789C8—42no—
790C8—81no—
791C8—81no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22#229611yescharacteristic
808C22C4×#12411yescharacteristic
809C22#233511yescharacteristic
810C22D4×C4⋊C411yescharacteristic
811C22#234911yescharacteristic
812C22#236411yescharacteristic
813C22#237311yescharacteristic
814C22C22×C4⋊C811yescharacteristic
815C22C2×#42411yescharacteristic
816C22#290611yescharacteristic
817C22#290611yescharacteristic
818C22C2×C8×D411yescharacteristic
819C22#293111yescharacteristic
820C22D4×M1611yescharacteristic
821C22#293511yescharacteristic
822C22C8×#4111yescharacteristic
823C22C8×#4111yescharacteristic
824C22C8×#4111yescharacteristic
825C22#296511yescharacteristic
826C22#296511yescharacteristic
827C22#296611yescharacteristic
828C22#296611yescharacteristic
829C22#296711yescharacteristic
830C22#296811yescharacteristic
831C22#296811yescharacteristic
832C22#296911yescharacteristic
833C22#297011yescharacteristic
834C22#297211yescharacteristic
835C22#297411yescharacteristic
836C22#297611yescharacteristic
837C22#297711yescharacteristic
838C22#298811yescharacteristic
839C22#299011yescharacteristic
840C22#299311yescharacteristic
841C22#299411yescharacteristic
842C4—24no—
843C4—24no—
844C4—24no—
845C4—24no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—81no—
854C4—81no—
855C4#246411yescharacteristic
856C4#246611yescharacteristic
857C4#247011yescharacteristic
858C4#247211yescharacteristic
859C4#249211yescharacteristic
860C4#252211yescharacteristic
861C4#255611yescharacteristic
862C4#258711yescharacteristic
863C2—44no—
864C2#1411611yescharacteristic
865C2#2134911yescharacteristic
866C2#2135711yescharacteristic
867C2C8×#12411yescharacteristic
868C2#2163211yescharacteristic
869C2#2235711yescharacteristic
870C2#2236111yescharacteristic
871C2D4×C4⋊C811yescharacteristic
872C2#2265111yescharacteristic
873C2#2269611yescharacteristic
874C2#2269711yescharacteristic
875C2#2311611yescharacteristic
876C2#2311811yescharacteristic
877C2#2327811yescharacteristic
878C2#2328211yescharacteristic
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×#1939C2semidirect
6. #11255C2semidirect
7. #11202C2semidirect
10. #10876C2semidirect
11. #10876C2semidirect
12. #10876C2semidirect
13. #10832C2semidirect
15. C4×#336C2semidirect
131. #388C8semidirect
271. C2×C4⋊C4C2×C8semidirect
331. C2×C42C2×C8semidirect
363. #95C2×C8semidirect
364. #95C2×C8semidirect
578. C22⋊C4C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#19392
C2×#19232
C2×#18502
C2×C8×C22⋊C42
C4×#3882
#112552
#112022
#110422
#108762
#108322
#107142
C4×#3362