Finite Group Databasebeta

← #370976

Subgroups — #370976

Order 512.

1706 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2346C211yesmaximal, characteristic, complemented
2C2×#1875C211yesmaximal, characteristic
3C2×#1862C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic, complemented
5#13970C211yesmaximal, characteristic
6#11292C211yesmaximal, characteristic, complemented
7#11096C211yesmaximal, characteristic, complemented
8#11066C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10922C211yesmaximal, characteristic, complemented
12#10907C211yesmaximal, characteristic, complemented
13#10881C211yesmaximal, characteristic, complemented
14#10807C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×#97C2211yescharacteristic
27#2346—24no—
28#2346—24no—
29C2×#390C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#388—21no—
33C2×#388—21no—
34C2×#386—21no—
35C2×#382—21no—
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×#376—21no—
42#1875C418yescomplemented
43#1862—24no—
44#1762—24no—
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
58C2×#336C2211yescharacteristic
59#1440—21no—
60#1438—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C22⋊#95—21no—
64C23×D4—21no—
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×#121—22no—
73C2×#121—22no—
74C2×#121—22no—
75C2×#121—41no—
76C2×#121—41no—
77C2×#121C2×C414yes—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—41no—
83C2×C4×D4—41no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117C2×C414yescomplemented
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4D411yescharacteristic
107C22×C22⋊C4D411yescharacteristic
108C22×C42—21no—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—41no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—41no—
126C2×#102C2×C414yes—
127C2×#102C2×C414yes—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8C2×C414yescomplemented
134C2×#97—22no—
135C2×#97—41no—
136C2×#97—41no—
137#390—22no—
138#390—41no—
139#389—22no—
140#389—22no—
141#389—22no—
142#389D414yescomplemented
143#388—28no—
144#388—28no—
145#386—44no—
146#382—28no—
147#380—22no—
148#380—22no—
149#380—22no—
150#380—41no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4D414yescomplemented
155C4×C22⋊C4—22no—
156C4×C22⋊C4—22no—
157#376—28no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95D411yescharacteristic
169C2×#95D411yescharacteristic
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340C2×C414yescomplemented
180#340C2×C414yescomplemented
181#336—22no—
182#336—22no—
183#336—41no—
184C25—21no—
185C25C2×D411yescharacteristic
186C22×D4—24no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—42no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4—42no—
202C22×D4—81no—
203C22×D4—81no—
204C22×D4C22×C412yes—
205C22×D4#4112yes—
206C22×D4#4112yes—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4C22×C412yes—
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4#4112yes—
240C23×C4C2411yescharacteristic
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—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8C22×C412yes—
267C22×C8C22×C412yes—
268C22×C8#4112yes—
269#121—28no—
270#121—44no—
271#121—44no—
272#121—44no—
273C4×D4—28no—
274C4×D4—44no—
275C4×D4—44no—
276C4×D4—44no—
277#117—28no—
278#117—28no—
279#117—28no—
280#117—28no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—81no—
316C2×C4⋊C4—81no—
317C2×C4⋊C4—81no—
318C2×C4⋊C4—81no—
319C2×C4⋊C4C22×C412yes—
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4C2×D412yes—
324C2×C4⋊C4C2×D412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4#4112yes—
327C2×C4⋊C4#4112yes—
328C2×C4⋊C4#4112yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—81no—
352C2×C22⋊C4—81no—
353C2×C22⋊C4—81no—
354C2×C22⋊C4—81no—
355C2×C22⋊C4—81no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42C2×D412yes—
376C2×C42C2×D412yes—
377#107—44no—
378#102—28no—
379#102—28no—
380#102—28no—
381#102—44no—
382C22⋊C8—44no—
383C22⋊C8—44no—
384#97—44no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—22no—
391#95—22no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—81no—
396#95—81no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24C4×D412yes—
427C24C22×D411yescharacteristic
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—84no—
458C2×D4—84no—
459C2×D4—84no—
460C2×D4—84no—
461C2×D4—84no—
462C2×D4#11714yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—48no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
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—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4C4×D412yes—
579C22×C4#12012yes—
580C22×C4#12012yes—
581C22×C4AGL(1,ℤ/8)12yes—
582C22×C4C23×C411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C2×#4111yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C4H(5,𝔽2)11yescharacteristic
594C22×C4H(5,𝔽2)11yescharacteristic
595C22×C42−1+411yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4C4×D414yes—
653C4⋊C4C4×D414yes—
654C22⋊C4—216no—
655C22⋊C4—44no—
656C22⋊C4—48no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C42—216no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—48no—
669C42—48no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—41no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—41no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—81no—
729C23—81no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23C2×C4×D411yescharacteristic
745C23C2×#12011yescharacteristic
746C23#52511yescharacteristic
747C23#54611yescharacteristic
748C23#54611yescharacteristic
749C23#54611yescharacteristic
750C23#54711yescharacteristic
751C23C2×AGL(1,ℤ/8)11yescharacteristic
752C23#57511yescharacteristic
753C23#57511yescharacteristic
754C23#57511yescharacteristic
755C23#57611yescharacteristic
756C23#57611yescharacteristic
757C23#57711yescharacteristic
758C23#57811yescharacteristic
759D4—24no—
760D4—24no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—816no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—816no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4C2×#11711yescharacteristic
862C2×C4C2×C4×D411yescharacteristic
863C2×C4C2×C4×D411yescharacteristic
864C2×C4C4×#4111yescharacteristic
865C2×C4#51811yescharacteristic
866C2×C4#52011yescharacteristic
867C2×C4#52511yescharacteristic
868C2×C4#52511yescharacteristic
869C2×C4#52511yescharacteristic
870C2×C4#52511yescharacteristic
871C2×C4#52911yescharacteristic
872C2×C4#52911yescharacteristic
873C2×C4#53511yescharacteristic
874C2×C4#53711yescharacteristic
875C2×C4#54011yescharacteristic
876C2×C4#54211yescharacteristic
877C2×C4#54611yescharacteristic
878C2×C4#54611yescharacteristic
879C2×C4#54811yescharacteristic
880C2×C4#55011yescharacteristic
881C2×C4#55111yescharacteristic
882C2×C4#55111yescharacteristic
883C2×C4#55111yescharacteristic
884C2×C4#55211yescharacteristic
885C2×C4#55211yescharacteristic
886C2×C4#55311yescharacteristic
887C2×C4#55311yescharacteristic
888C2×C4#55511yescharacteristic
889C8—42no—
890C8—42no—
891C8—42no—
892C8—81no—
893C22—42no—
894C22—44no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—44no—
903C22—81no—
904C22—82no—
905C22—81no—
906C22—82no—
907C22—81no—
908C22—82no—
909C22—81no—
910C22—82no—
911C22—81no—
912C22—82no—
913C22—81no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—81no—
919C22—81no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22C4×#12011yescharacteristic
924C22#234211yescharacteristic
925C22#235911yescharacteristic
926C22#240411yescharacteristic
927C22#240711yescharacteristic
928C22#247011yescharacteristic
929C22#247611yescharacteristic
930C22#294311yescharacteristic
931C22C4×AGL(1,ℤ/8)11yescharacteristic
932C22#294611yescharacteristic
933C22#295111yescharacteristic
934C22#300511yescharacteristic
935C22#300611yescharacteristic
936C22#300811yescharacteristic
937C22#301311yescharacteristic
938C22#311111yescharacteristic
939C22#311511yescharacteristic
940C22#311911yescharacteristic
941C22#312411yescharacteristic
942C22#331011yescharacteristic
943C22#331511yescharacteristic
944C22#331511yescharacteristic
945C22#331711yescharacteristic
946C22#331911yescharacteristic
947C22#331911yescharacteristic
948C22#331911yescharacteristic
949C22#331911yescharacteristic
950C22#332311yescharacteristic
951C22#332511yescharacteristic
952C22#332511yescharacteristic
953C22#332711yescharacteristic
954C22#334311yescharacteristic
955C22#334711yescharacteristic
956C22#334711yescharacteristic
957C22#334811yescharacteristic
958C4—42no—
959C4—42no—
960C4—42no—
961C4—44no—
962C4—44no—
963C4—42no—
964C4—82no—
965C4—81no—
966C4—82no—
967C4—82no—
968C4—82no—
969C4—161no—
970C4#229011yescharacteristic
971C4#232411yescharacteristic
972C4#235211yescharacteristic
973C4#236311yescharacteristic
974C4#247111yescharacteristic
975C4#247711yescharacteristic
976C4#259811yescharacteristic
977C4#260911yescharacteristic
978C2—82no—
979C2—84no—
980C2#1406411yescharacteristic
981C2#2145611yescharacteristic
982C2#2146011yescharacteristic
983C2#2256411yescharacteristic
984C2#2258411yescharacteristic
985C2#2293511yescharacteristic
986C2#2294611yescharacteristic
987C2#2397611yescharacteristic
988C2#2397811yescharacteristic
989C2#2412911yescharacteristic
990C2#2413711yescharacteristic
991C2#2718211yescharacteristic
992C2#2718711yescharacteristic
993C2#2741411yescharacteristic
994C2#2741911yescharacteristic
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
1. C2×#2346C2semidirect
3. C2×#1862C2semidirect
4. C2×#1762C2semidirect
6. #11292C2semidirect
7. #11096C2semidirect
8. #11066C2semidirect
10. #10931C2semidirect
11. #10922C2semidirect
12. #10907C2semidirect
13. #10881C2semidirect
14. #10807C2semidirect
15. #10731C2semidirect
42. #1875C4semidirect
89. C2×#117C2×C4semidirect
133. C2×C22⋊C8C2×C4semidirect
142. #389D4semidirect
154. C4×C4⋊C4D4semidirect
179. #340C2×C4semidirect
180. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23462
C2×#18752
C2×#18622
C2×#17622
#139702
#112922
#110962
#110662
#109692
#109312
#109222
#109072
#108812
#108072
#107312