Finite Group Databasebeta

← #356283

Subgroups — #356283

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic
2C2×#1804C211yesmaximal, characteristic
3C2×#1771C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic
5#13804C211yesmaximal, characteristic, complemented
6#10931C211yesmaximal, characteristic
7#10931C211yesmaximal, characteristic
8#10927C211yesmaximal, characteristic
9#10925C211yesmaximal, characteristic
10#10849C211yesmaximal, characteristic, complemented
11#10843C211yesmaximal, characteristic, complemented
12#10807C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10703C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#117—21no—
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#97C2211yescharacteristic
24C22×#97C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26#2354—24no—
27#2354C418yescomplemented
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#388—21no—
31C2×#388—21no—
32C2×#384C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×#380—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#1804C418yescomplemented
42#1771—24no—
43#1762C418yescomplemented
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1436—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63C4×#95—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4C2×C414yes—
74C2×C4×D4C2×C414yes—
75C2×C4×D4C2×C414yes—
76C2×#117—28no—
77C2×#117—44no—
78C2×#117—44no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4D411yescharacteristic
82C22×C4⋊C4D411yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42—21no—
98C22×C42—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8C2×C414yes—
106C2×#102—22no—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102C2×C414yes—
115C2×#102C2×C414yes—
116C2×#102C2×C414yes—
117C2×#102C2×C414yes—
118C2×#97—22no—
119C2×#97—22no—
120C2×#97—22no—
121C2×#97—22no—
122C2×#97—41no—
123C2×#97C2×C414yes—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8—41no—
127#390—22no—
128#390—22no—
129#390C2×C414yes—
130#390C2×C414yes—
131#388—28no—
132#388—28no—
133#384—22no—
134#384C2×C414yes—
135#382—22no—
136#382C2×C414yes—
137#380—28no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—41no—
144C4×C4⋊C4—41no—
145C4×C4⋊C4C2×C414yes—
146C4×C4⋊C4C2×C414yes—
147C4×C4⋊C4C2×C414yes—
148C4×C4⋊C4C2×C414yes—
149C4×C4⋊C4D414yes—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95D411yescharacteristic
162C2×#95D411yescharacteristic
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340C2×C414yes—
172#340C2×C414yes—
173#340C2×C414yes—
174#340C2×C414yes—
175#336—22no—
176#336—22no—
177C25—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4C22×C412yes—
190C22×D4C22×C412yes—
191C22×D4C22×C412yes—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—24no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2411yescharacteristic
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×C8C22×C412yes—
236C22×C8C22×C412yes—
237C22×C8C22×C412yes—
238C22×C8C22×C412yes—
239C22×C8#4112yes—
240C22×C8#4112yes—
241C4×D4—28no—
242C4×D4—28no—
243C4×D4—28no—
244C4×D4C42116yescomplemented
245#117—432no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4C22⋊C414yes—
288C2×C4⋊C4C22⋊C414yes—
289C2×C4⋊C4C22×C412yes—
290C2×C4⋊C4C22×C412yes—
291C2×C4⋊C4C22×C412yes—
292C2×C4⋊C4C22×C412yes—
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C412yes—
295C2×C4⋊C4C22×C412yes—
296C2×C4⋊C4C22×C412yes—
297C2×C4⋊C4C22×C412yes—
298C2×C4⋊C4#4112yes—
299C2×C4⋊C4#4112yes—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
313C2×C22⋊C4—81no—
314C2×C22⋊C4—81no—
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—24no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—81no—
335C2×C42—81no—
336C2×C42—81no—
337C2×C42—81no—
338C2×C42C22×C412yes—
339C2×C42C22×C412yes—
340C2×C42C22×C412yes—
341C2×C42C22×C412yes—
342C2×C42C22×C412yes—
343C2×C42C2×D412yes—
344C2×C42C2×D412yes—
345C2×C42C2×D412yes—
346C2×C42#4112yes—
347C2×C42#4112yes—
348C4⋊C8—28no—
349#102—28no—
350#102—28no—
351#102—44no—
352#102—44no—
353#97—28no—
354#97—44no—
355C4×C8—44no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—81no—
366#95—81no—
367#95C22⋊C414yes—
368#95C22⋊C414yes—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24C22×D411yescharacteristic
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C2×C4214yes—
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—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
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—216no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—48no—
456C22×C4—48no—
457C22×C4—48no—
458C22×C4—48no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
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×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×C4C2×C22⋊C412yes—
500C22×C4C2×C22⋊C412yes—
501C22×C4C2×C22⋊C412yes—
502C22×C4C2×C22⋊C412yes—
503C22×C4C2×C22⋊C412yes—
504C22×C4C2×C22⋊C412yes—
505C22×C4C4×D412yes—
506C22×C4C4×D412yes—
507C22×C4C4×D412yes—
508C22×C4C4×D412yes—
509C22×C4AGL(1,ℤ/8)12yes—
510C22×C4AGL(1,ℤ/8)12yes—
511C22×C4C23×C411yescharacteristic
512C22×C4C23×C411yescharacteristic
513C22×C4C23×C411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C42−1+411yescharacteristic
524C22×C42−1+411yescharacteristic
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—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#11714yescomplemented
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—28no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—44no—
571C4⋊C4—48no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—84no—
583C4⋊C4C2×C4214yes—
584C4⋊C4#11714yescomplemented
585C22⋊C4—216no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—48no—
599C42—48no—
600C42—84no—
601C42—84no—
602C42—84no—
603C42C2×C4214yes—
604C42#11714yes—
605C42C4×D414yes—
606C42C4×D414yes—
607C23—24no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23C22×C22⋊C411yescharacteristic
643C23C2×C4×D411yescharacteristic
644C23C2×C4×D411yescharacteristic
645C23#54611yescharacteristic
646C23#54711yescharacteristic
647C23#54811yescharacteristic
648C23#55011yescharacteristic
649C23C2×AGL(1,ℤ/8)11yescharacteristic
650C23C2×AGL(1,ℤ/8)11yescharacteristic
651C23#57511yescharacteristic
652C23#57511yescharacteristic
653C23#57611yescharacteristic
654C23#57711yescharacteristic
655C23#57711yescharacteristic
656C23#57811yescharacteristic
657D4—24no—
658D4—24no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
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—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—432no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
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—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C4×C22⋊C414yes—
755C2×C4C4×C22⋊C414yes—
756C2×C4#41814yes—
757C2×C4C22×C4211yescharacteristic
758C2×C4C2×#11711yescharacteristic
759C2×C4C2×#11711yescharacteristic
760C2×C4C2×#11711yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C4×#4111yescharacteristic
764C2×C4C4×#4111yescharacteristic
765C2×C4C4×#4111yescharacteristic
766C2×C4C4×#4111yescharacteristic
767C2×C4#51811yescharacteristic
768C2×C4#51911yescharacteristic
769C2×C4#52011yescharacteristic
770C2×C4#52011yescharacteristic
771C2×C4#52011yescharacteristic
772C2×C4#52011yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4#54711yescharacteristic
775C2×C4#54811yescharacteristic
776C2×C4#55011yescharacteristic
777C2×C4#55211yescharacteristic
778C2×C4#55211yescharacteristic
779C2×C4#55311yescharacteristic
780C2×C4#55311yescharacteristic
781C2×C4#55511yescharacteristic
782C2×C4#55511yescharacteristic
783C2×C4#55611yescharacteristic
784C2×C4#55611yescharacteristic
785C8—24no—
786C8—42no—
787C8—42no—
788C8—42no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22C2×C4×C22⋊C411yescharacteristic
805C22#233911yescharacteristic
806C22#234111yescharacteristic
807C22#235211yescharacteristic
808C22#235411yescharacteristic
809C22#236211yescharacteristic
810C22#236311yescharacteristic
811C22C2×#41811yescharacteristic
812C22#289611yescharacteristic
813C22#289711yescharacteristic
814C22#289811yescharacteristic
815C22C4×AGL(1,ℤ/8)11yescharacteristic
816C22C4×AGL(1,ℤ/8)11yescharacteristic
817C22C4×AGL(1,ℤ/8)11yescharacteristic
818C22C4×AGL(1,ℤ/8)11yescharacteristic
819C22#294611yescharacteristic
820C22#294711yescharacteristic
821C22#295111yescharacteristic
822C22#295211yescharacteristic
823C22#330611yescharacteristic
824C22#330811yescharacteristic
825C22#331911yescharacteristic
826C22#332111yescharacteristic
827C22#334311yescharacteristic
828C22#334511yescharacteristic
829C22#334711yescharacteristic
830C22#334811yescharacteristic
831C22#336611yescharacteristic
832C22#336811yescharacteristic
833C22#337611yescharacteristic
834C22#337711yescharacteristic
835C22#339711yescharacteristic
836C22#339911yescharacteristic
837C22#340111yescharacteristic
838C22#340211yescharacteristic
839C4—24no—
840C4—24no—
841C4—24no—
842C4—44no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—44no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4C4×#11711yescharacteristic
853C4#227411yescharacteristic
854C4#234611yescharacteristic
855C4#234711yescharacteristic
856C4#235211yescharacteristic
857C4#235411yescharacteristic
858C4#236211yescharacteristic
859C4#236311yescharacteristic
860C2—84no—
861C2#1380111yescharacteristic
862C2C4×#41811yescharacteristic
863C2#2041511yescharacteristic
864C2#2249211yescharacteristic
865C2#2249511yescharacteristic
866C2#2254511yescharacteristic
867C2#2254811yescharacteristic
868C2#2278011yescharacteristic
869C2#2278111yescharacteristic
870C2#2281711yescharacteristic
871C2#2282011yescharacteristic
872C2#2307211yescharacteristic
873C2#2307611yescharacteristic
874C2#2310511yescharacteristic
875C2#2310911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#1771C2semidirect
5. #13804C2semidirect
10. #10849C2semidirect
11. #10843C2semidirect
12. #10807C2semidirect
13. #10806C2semidirect
14. #10703C2semidirect
15. C4×#340C2semidirect
27. #2354C4semidirect
41. #1804C4semidirect
43. #1762C4semidirect
244. C4×D4C42semidirect
552. C2×C8#117semidirect
584. C4⋊C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×#18042
C2×#17712
C2×#17622
#138042
#109312
#109272
#109252
#108492
#108432
#108072
#108062
#107032
C4×#3402