Finite Group Databasebeta

← #374456

Subgroups — #374456

Order 512.

2082 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C22×#428C211yesmaximal, characteristic, complemented
3C2×#1973C211yesmaximal, characteristic, complemented
4C2×#1968C211yesmaximal, characteristic, complemented
5C2×#1875C211yesmaximal, characteristic
6C2×#1872C211yesmaximal, characteristic, complemented
7C2×#1753C211yesmaximal, characteristic, complemented
8#14138C211yesmaximal, characteristic, complemented
9#14137C211yesmaximal, characteristic
10#11124C211yesmaximal, characteristic, complemented
11#11123C211yesmaximal, characteristic, complemented
12#11122C211yesmaximal, characteristic, complemented
13#11121C211yesmaximal, characteristic, complemented
14#10863C211yesmaximal, characteristic, complemented
15#10862C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C2×#468—24no—
23C2×#468—24no—
24C2×#468C418yescomplemented
25C2×#428—24no—
26C2×#428—24no—
27C2×#428—24no—
28C22×#107C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×#107C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×#97C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#386—22no—
47C2×C4×C22⋊C4C2211yescharacteristic
48#1973—24no—
49#1968—24no—
50#1875—24no—
51#1872—24no—
52#1753—24no—
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1440—22no—
60#1439—22no—
61#1436—22no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×SD16—22no—
72C22×SD16—22no—
73C22×SD16—22no—
74C22×SD16—22no—
75C22×SD16—22no—
76C22×SD16—22no—
77C22×SD16C2×C414yescomplemented
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16C2×C414yes—
83C22×M16D414yes—
84C22×M16D414yes—
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8—22no—
91C2×C22⋊Q8—22no—
92C2×C22⋊Q8—22no—
93C2×C22⋊Q8—22no—
94C2×C22⋊Q8C2×C414yes—
95C2×#121—22no—
96C2×#121—22no—
97C2×#121—22no—
98C2×#121—22no—
99C2×#121—22no—
100C2×#121C2×C414yes—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—41no—
106C2×#117—41no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4—22no—
109C22×C4⋊C4—22no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—41no—
114C22×C4⋊C4—41no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—22no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4D412yes—
127C22×C42—21no—
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130#468—232no—
131#428—232no—
132C2×#107—22no—
133C2×#107—22no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107—22no—
137C2×#107—22no—
138C2×#107—22no—
139C2×#107C2×C414yescomplemented
140C2×#107D414yescomplemented
141C2×#106—22no—
142C2×#106—22no—
143C2×#106—22no—
144C2×#106—22no—
145C2×#106—22no—
146C2×#106D414yescomplemented
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#103—22no—
151C2×#103—22no—
152C2×#103—22no—
153C2×#103—41no—
154C2×#103—41no—
155C2×#103C2×C414yescomplemented
156C2×#102—22no—
157C2×#102—22no—
158C2×#102—22no—
159C2×#102—22no—
160C2×#102—22no—
161C2×#102—22no—
162C2×#102—41no—
163C2×#102—41no—
164C2×#102C2×C414yescomplemented
165C2×C22⋊C8—22no—
166C2×C22⋊C8—22no—
167C2×C22⋊C8D414yes—
168C2×#97—22no—
169C2×#97—22no—
170C2×#97—22no—
171C2×C4×C8—22no—
172C2×C4×C8—22no—
173C2×C4×C8—22no—
174#391—22no—
175#391—22no—
176#391—41no—
177#391—41no—
178#390—22no—
179#390—22no—
180#390—41no—
181#390—41no—
182#386—48no—
183C4×C22⋊C4—22no—
184C4×C22⋊C4—22no—
185C2×#95—22no—
186C2×#95—22no—
187C2×#95—22no—
188C2×#95—22no—
189C2×#95—22no—
190C2×#95—22no—
191C2×#95D412yes—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#336—22no—
197#336—22no—
198C25—21no—
199C25C2×D411yescharacteristic
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8C22×C412yes—
214C22×D4—24no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4C22×C412yes—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—44no—
252C23×C4—82no—
253C23×C4C22×C412yes—
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D412yes—
260C23×C4#4112yes—
261C23×C4#4112yes—
262C23×C4C2411yescharacteristic
263C2×SD16—28no—
264C2×SD16—28no—
265C2×SD16—28no—
266C2×SD16—44no—
267C2×SD16—44no—
268C2×SD16—44no—
269C2×SD16—44no—
270C2×M16—28no—
271C2×M16—28no—
272C2×M16—28no—
273C2×M16—28no—
274C2×M16—28no—
275C2×M16—28no—
276C2×M16C22⋊C4116yescomplemented
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8C22×C412yes—
294C22×C8C22×C412yes—
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299C22×C8C2×D412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C22×C8C2×D412yes—
303C22×C8#4112yes—
304C22×C8#4112yes—
305C22⋊Q8—28no—
306C22⋊Q8—28no—
307C22⋊Q8—44no—
308C22⋊Q8—44no—
309#121—28no—
310#121—28no—
311#121—44no—
312#121—44no—
313#117—28no—
314#117—44no—
315#117—44no—
316#117—44no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4C22×C412yes—
358C2×C4⋊C4C22×C412yes—
359C2×C4⋊C4C2×D412yes—
360C2×C4⋊C4C2×D412yes—
361C2×C4⋊C4C2×D412yes—
362C2×C4⋊C4C2×D412yes—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—82no—
380C2×C22⋊C4—82no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396#107—28no—
397#107—28no—
398#107—28no—
399#106—28no—
400#106—28no—
401#103—28no—
402#103—44no—
403#103—44no—
404#102—28no—
405#102—44no—
406#102—44no—
407C22⋊C8—28no—
408#97—44no—
409C4×C8—44no—
410#95—24no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24C4×D412yes—
437C24#12112yes—
438C24#12712yes—
439C24C22×D411yescharacteristic
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—416no—
475C2×D4—48no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—88no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—48no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4C2×C22⋊C414yes—
585C22×C4C4×D414yes—
586C22×C4C4×D412yes—
587C22×C4#12114yes—
588C22×C4#12112yes—
589C22×C4#12414yes—
590C22×C4#12712yes—
591C22×C4AGL(1,ℤ/8)14yes—
592C22×C4C23×C411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4H(5,𝔽2)11yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C42−1+411yescharacteristic
605C22×C42−1+411yescharacteristic
606SD16—416no—
607M16—232no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8C2×C22⋊C414yes—
629C2×C8C2×C22⋊C414yes—
630C2×C8C4×D414yes—
631C2×C8C4×D414yes—
632C2×C8#12014yes—
633C2×C8#12114yes—
634C2×C8#12114yes—
635C2×C8#12314yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—48no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—88no—
667C22⋊C4—88no—
668C42—48no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—41no—
674C42—41no—
675C42—41no—
676C42—41no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—44no—
703C23—42no—
704C23—82no—
705C23—82no—
706C23—82no—
707C23—82no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—81no—
717C23—82no—
718C23—82no—
719C23—82no—
720C23—82no—
721C23—82no—
722C23#39014yes—
723C23C2×C4×D411yescharacteristic
724C23C2×#12111yescharacteristic
725C23C2×#12711yescharacteristic
726C23D4211yescharacteristic
727C23D4211yescharacteristic
728C23#54711yescharacteristic
729C23#54711yescharacteristic
730C23C2×AGL(1,ℤ/8)12yes—
731C23#57512yes—
732C23#57712yes—
733C23#57812yes—
734Q8—42no—
735Q8—42no—
736Q8—42no—
737Q8—42no—
738Q8—81no—
739Q8—81no—
740Q8—81no—
741Q8—81no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—816no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—816no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—81no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4#39014yes—
818C2×C4C22×C22⋊C411yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4C2×C4×D411yescharacteristic
822C2×C4#52011yescharacteristic
823C2×C4#52011yescharacteristic
824C2×C4C2×#12011yescharacteristic
825C2×C4C2×#12111yescharacteristic
826C2×C4C2×#12111yescharacteristic
827C2×C4C2×#12111yescharacteristic
828C2×C4C2×#12311yescharacteristic
829C2×C4C2×#12411yescharacteristic
830C2×C4#53511yescharacteristic
831C2×C4#53611yescharacteristic
832C2×C4#53711yescharacteristic
833C2×C4#53711yescharacteristic
834C2×C4D4211yescharacteristic
835C2×C4D4211yescharacteristic
836C2×C4#54711yescharacteristic
837C2×C4#54711yescharacteristic
838C2×C4#54811yescharacteristic
839C2×C4#54811yescharacteristic
840C2×C4#54811yescharacteristic
841C2×C4#54811yescharacteristic
842C2×C4#55311yescharacteristic
843C2×C4#55311yescharacteristic
844C2×C4#55311yescharacteristic
845C2×C4#55311yescharacteristic
846C8—24no—
847C8—42no—
848C8—42no—
849C8#38618yescomplemented
850C22—24no—
851C22—24no—
852C22—24no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—84no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—84no—
866C22—161no—
867C22—161no—
868C22—161no—
869C22—161no—
870C22—162no—
871C22—162no—
872C22C2×#39011yescharacteristic
873C22#236111yescharacteristic
874C22#236111yescharacteristic
875C22#241611yescharacteristic
876C22#241611yescharacteristic
877C22#243311yescharacteristic
878C22#250111yescharacteristic
879C22C4×AGL(1,ℤ/8)12yes—
880C22#294712yes—
881C22#305512yes—
882C22#306312yes—
883C22#315111yescharacteristic
884C22#315311yescharacteristic
885C22#315411yescharacteristic
886C22#315611yescharacteristic
887C22#326512yes—
888C22#326912yes—
889C22#327212yes—
890C22#327712yes—
891C22#334312yes—
892C22#335012yes—
893C22#335112yes—
894C22#335312yes—
895C4—24no—
896C4—44no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4C2×#38611yescharacteristic
906C4#231111yescharacteristic
907C4#236111yescharacteristic
908C4#236111yescharacteristic
909C4#241611yescharacteristic
910C4#241611yescharacteristic
911C4#243611yescharacteristic
912C4#250411yescharacteristic
913C2—44no—
914C2—162no—
915C2#1413711yescharacteristic
916C2#2123411yescharacteristic
917C2#2123611yescharacteristic
918C2#2303412yes—
919C2#2304012yes—
920C2#2478912yes—
921C2#2479412yes—
922C2#2579111yescharacteristic
923C2#2579211yescharacteristic
924C2#2794411yescharacteristic
925C2#2794711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#428C2semidirect
3. C2×#1973C2semidirect
4. C2×#1968C2semidirect
6. C2×#1872C2semidirect
7. C2×#1753C2semidirect
8. #14138C2semidirect
10. #11124C2semidirect
11. #11123C2semidirect
12. #11122C2semidirect
13. #11121C2semidirect
14. #10863C2semidirect
15. #10862C2semidirect
24. C2×#468C4semidirect
77. C22×SD16C2×C4semidirect
139. C2×#107C2×C4semidirect
140. C2×#107D4semidirect
146. C2×#106D4semidirect
155. C2×#103C2×C4semidirect
164. C2×#102C2×C4semidirect
276. C2×M16C22⋊C4semidirect
849. C8#386semidirect

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4282
C2×#19732
C2×#19682
C2×#18752
C2×#18722
C2×#17532
#141382
#141372
#111242
#111232
#111222
#111212
#108632
#108622