Finite Group Databasebeta

← #356286

Subgroups — #356286

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2357C211yesmaximal, characteristic
2C2×#1802C211yesmaximal, characteristic
3C2×#1771C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic
5C4⋊C42C211yesmaximal, characteristic, complemented
6#10931C211yesmaximal, characteristic
7#10931C211yesmaximal, characteristic
8#10927C211yesmaximal, characteristic
9#10925C211yesmaximal, characteristic
10#10850C211yesmaximal, 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×C4⋊C8C2211yescharacteristic
18C22×#102C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#97C2211yescharacteristic
23C22×#97C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25#2357—24no—
26#2357C418yescomplemented
27C2×#390C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#388—21no—
30C2×#388—21no—
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×#381—21no—
34C2×C4×C4⋊C4—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
41C2×C4×C22⋊C4—21no—
42#1802C418yescomplemented
43#1771—24no—
44#1762C418yescomplemented
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1436—21no—
60#1436—21no—
61C4⋊#95—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
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—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4D411yescharacteristic
79C22×C4⋊C4D411yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C42—21no—
93C22×C42—21no—
94C22×C42—21no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8C2×C414yes—
103C2×#102—22no—
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—22no—
107C2×#102—41no—
108C2×#102—41no—
109C2×#102—41no—
110C2×#102—41no—
111C2×#102C2×C414yes—
112C2×#102C2×C414yes—
113C2×#102C2×C414yes—
114C2×#102C2×C414yes—
115C2×#97—22no—
116C2×#97—22no—
117C2×#97—22no—
118C2×#97—22no—
119C2×#97—41no—
120C2×#97C2×C414yes—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—41no—
124#390—22no—
125#390—22no—
126#390C2×C414yes—
127#390C2×C414yes—
128#388—28no—
129#388—28no—
130#384—22no—
131#384C2×C414yes—
132#382—22no—
133#382C2×C414yes—
134#381—28no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
142C4×C4⋊C4—44no—
143C4×C4⋊C4C2×C414yes—
144C4×C4⋊C4C2×C414yes—
145C4×C4⋊C4C2×C414yes—
146C4×C4⋊C4C2×C414yes—
147C4×C4⋊C4D414yes—
148C4×C22⋊C4—28no—
149C2×#95—21no—
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×#95D411yescharacteristic
161C2×#95D411yescharacteristic
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340C2×C414yes—
171#340C2×C414yes—
172#340C2×C414yes—
173#340C2×C414yes—
174#336—22no—
175#336—22no—
176C25—21no—
177C22×D4—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×D4C22×C412yes—
189C22×D4C22×C412yes—
190C22×D4C22×C412yes—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—81no—
202C23×C4—81no—
203C23×C4—81no—
204C23×C4—81no—
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2411yescharacteristic
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×C8C22×C412yes—
235C22×C8C22×C412yes—
236C22×C8C22×C412yes—
237C22×C8C22×C412yes—
238C22×C8#4112yes—
239C22×C8#4112yes—
240C4×D4—28no—
241C4×D4—28no—
242C4×D4—28no—
243C4×D4C42116yescomplemented
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
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—24no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4C22⋊C414yes—
286C2×C4⋊C4C22⋊C414yes—
287C2×C4⋊C4C22×C412yes—
288C2×C4⋊C4C22×C412yes—
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⋊C4#4112yes—
297C2×C4⋊C4#4112yes—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
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—24no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—81no—
331C2×C42—81no—
332C2×C42—81no—
333C2×C42—81no—
334C2×C42—81no—
335C2×C42—81no—
336C2×C42C22×C412yes—
337C2×C42C22×C412yes—
338C2×C42C22×C412yes—
339C2×C42C22×C412yes—
340C2×C42C22×C412yes—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C2×C42C2×D412yes—
344C2×C42#4112yes—
345C2×C42#4112yes—
346C4⋊C8—28no—
347#102—28no—
348#102—28no—
349#102—44no—
350#102—44no—
351#97—28no—
352#97—44no—
353C4×C8—44no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—81no—
364#95—81no—
365#95C22⋊C414yes—
366#95C22⋊C414yes—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24C22×D411yescharacteristic
383C2×D4—22no—
384C2×D4—22no—
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—41no—
399C2×D4—41no—
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×D4C2×C4214yes—
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—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
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—216no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
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—84no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4C2×C22⋊C412yes—
498C22×C4C2×C22⋊C412yes—
499C22×C4C2×C22⋊C412yes—
500C22×C4C2×C22⋊C412yes—
501C22×C4C2×C22⋊C412yes—
502C22×C4C2×C22⋊C412yes—
503C22×C4C4×D412yes—
504C22×C4C4×D412yes—
505C22×C4C4×D412yes—
506C22×C4C4×D412yes—
507C22×C4AGL(1,ℤ/8)12yes—
508C22×C4#13712yes—
509C22×C4C23×C411yescharacteristic
510C22×C4C23×C411yescharacteristic
511C22×C4C23×C411yescharacteristic
512C22×C4C22×D411yescharacteristic
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—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#11714yes—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—28no—
558C4⋊C4—22no—
559C4⋊C4—22no—
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—44no—
569C4⋊C4—48no—
570C4⋊C4—41no—
571C4⋊C4—41no—
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—84no—
581C4⋊C4C2×C4214yes—
582C4⋊C4#11714yes—
583C22⋊C4—216no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—48no—
597C42—84no—
598C42—84no—
599C42—84no—
600C42—84no—
601C42C2×C4214yes—
602C42#11714yes—
603C42C4×D414yes—
604C42C4×D414yes—
605C23—24no—
606C23—42no—
607C23—42no—
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—81no—
625C23—81no—
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—
640C23C22×C22⋊C411yescharacteristic
641C23C2×C4×D411yescharacteristic
642C23C2×C4×D411yescharacteristic
643C23#54611yescharacteristic
644C23#54711yescharacteristic
645C23#54811yescharacteristic
646C23#55011yescharacteristic
647C23C2×AGL(1,ℤ/8)11yescharacteristic
648C23C2×#13711yescharacteristic
649C23#57511yescharacteristic
650C23#57511yescharacteristic
651C23#57611yescharacteristic
652C23#57611yescharacteristic
653C23#57711yescharacteristic
654C23#57711yescharacteristic
655D4—24no—
656D4—24no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
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—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
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—816no—
732C2×C4—81no—
733C2×C4—81no—
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×C4C4×C22⋊C414yes—
753C2×C4C4×C22⋊C414yes—
754C2×C4#41714yes—
755C2×C4C22×C4211yescharacteristic
756C2×C4C2×#11711yescharacteristic
757C2×C4C2×#11711yescharacteristic
758C2×C4C2×#11711yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C4×#4111yescharacteristic
762C2×C4C4×#4111yescharacteristic
763C2×C4C4×#4111yescharacteristic
764C2×C4C4×#4111yescharacteristic
765C2×C4#51811yescharacteristic
766C2×C4#51911yescharacteristic
767C2×C4#52011yescharacteristic
768C2×C4#52011yescharacteristic
769C2×C4#52011yescharacteristic
770C2×C4#52011yescharacteristic
771C2×C4#54611yescharacteristic
772C2×C4#54711yescharacteristic
773C2×C4#54811yescharacteristic
774C2×C4#55011yescharacteristic
775C2×C4#55211yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55311yescharacteristic
778C2×C4#55311yescharacteristic
779C2×C4#55511yescharacteristic
780C2×C4#55511yescharacteristic
781C2×C4#55611yescharacteristic
782C2×C4#55611yescharacteristic
783C8—24no—
784C8—42no—
785C8—42no—
786C8—42no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22C2×C4×C22⋊C411yescharacteristic
803C22#233911yescharacteristic
804C22#234111yescharacteristic
805C22#235211yescharacteristic
806C22#235411yescharacteristic
807C22#236211yescharacteristic
808C22#236311yescharacteristic
809C22C2×#41711yescharacteristic
810C22#289611yescharacteristic
811C22#289711yescharacteristic
812C22#289711yescharacteristic
813C22C4×AGL(1,ℤ/8)11yescharacteristic
814C22C4×AGL(1,ℤ/8)11yescharacteristic
815C22C4×#13711yescharacteristic
816C22C4×#13711yescharacteristic
817C22#294611yescharacteristic
818C22#294611yescharacteristic
819C22#294811yescharacteristic
820C22#294911yescharacteristic
821C22#330711yescharacteristic
822C22#330911yescharacteristic
823C22#331811yescharacteristic
824C22#332011yescharacteristic
825C22#334511yescharacteristic
826C22#334611yescharacteristic
827C22#334711yescharacteristic
828C22#335011yescharacteristic
829C22#337011yescharacteristic
830C22#337111yescharacteristic
831C22#337311yescharacteristic
832C22#337511yescharacteristic
833C22#339911yescharacteristic
834C22#340011yescharacteristic
835C22#340111yescharacteristic
836C22#340311yescharacteristic
837C4—24no—
838C4—24no—
839C4—24no—
840C4—44no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—44no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4C4×#11711yescharacteristic
851C4#227411yescharacteristic
852C4#234611yescharacteristic
853C4#234711yescharacteristic
854C4#235211yescharacteristic
855C4#235411yescharacteristic
856C4#236211yescharacteristic
857C4#236311yescharacteristic
858C2—84no—
859C2#1380111yescharacteristic
860C2C4×#41711yescharacteristic
861C2#2041611yescharacteristic
862C2#2249311yescharacteristic
863C2#2249811yescharacteristic
864C2#2254611yescharacteristic
865C2#2254911yescharacteristic
866C2#2277411yescharacteristic
867C2#2277511yescharacteristic
868C2#2281711yescharacteristic
869C2#2281911yescharacteristic
870C2#2307511yescharacteristic
871C2#2307911yescharacteristic
872C2#2310811yescharacteristic
873C2#2311211yescharacteristic
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. C4⋊C42C2semidirect
10. #10850C2semidirect
11. #10843C2semidirect
12. #10807C2semidirect
13. #10806C2semidirect
14. #10703C2semidirect
15. C4×#340C2semidirect
26. #2357C4semidirect
42. #1802C4semidirect
44. #1762C4semidirect
243. C4×D4C42semidirect

Maximal subgroups

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

subgroupindex
C2×#23572
C2×#18022
C2×#17712
C2×#17622
C4⋊C422
#109312
#109272
#109252
#108502
#108432
#108072
#108062
#107032
C4×#3402