Finite Group Databasebeta

← #356649

Subgroups — #356649

Order 512.

1904 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34136C211yesmaximal, characteristic
2C2×#1896C211yesmaximal, characteristic
3C2×#1871C211yesmaximal, characteristic
4C2×#1759C211yesmaximal, characteristic, complemented
5C22⋊C4×M16C211yesmaximal, characteristic, complemented
6C22×#339C211yesmaximal, characteristic, complemented
7#13753C211yesmaximal, characteristic, complemented
8#10933C211yesmaximal, characteristic, complemented
9#10924C211yesmaximal, characteristic, complemented
10#10886C211yesmaximal, characteristic, complemented
11#10879C211yesmaximal, characteristic, complemented
12#10808C211yesmaximal, characteristic, complemented
13#10790C211yesmaximal, characteristic, complemented
14#10733C211yesmaximal, characteristic, complemented
15#10701C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C2×#407C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28#2363C412yescomplemented
29#2362C412yescomplemented
30#2361C412yescomplemented
31#2360C412yescomplemented
32#2359—22no—
33#2358—22no—
34#2297C2211yescharacteristic
35#2296C2211yescharacteristic
36#2293—21no—
37#2290—21no—
38#2290—21no—
39C42×D4—21no—
40C4×#117C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×#376C2211yescharacteristic
44C2×#376C2211yescharacteristic
45#1896C418yescomplemented
46#1871C418yescomplemented
47#1759—24no—
48#1753—21no—
49#1753—21no—
50#1752—21no—
51C8×C22⋊C4—21no—
52C2×#339—24no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1434—22no—
68C22⋊#95—22no—
69C4×#95C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C24×C4—21no—
73C24×C4C2311yescharacteristic
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—41no—
79C22×M16—41no—
80C22×M16C2×C414yescomplemented
81C22×M16C2311yescharacteristic
82C22×M16C2311yescharacteristic
83C22×M16C2311yescharacteristic
84C22×M16C2311yescharacteristic
85C23×C8—21no—
86#525—22no—
87#525—22no—
88#525C2×C414yes—
89#525C2×C414yes—
90C2×#123—21no—
91C2×C22⋊Q8C2×C411yescharacteristic
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×#121C2×C411yescharacteristic
94C2×#121C2×C411yescharacteristic
95C2×#120—21no—
96C4×#41—22no—
97C4×#41—22no—
98C4×#41—41no—
99C4×#41—41no—
100C2×C4×Q8C2×C412yescomplemented
101C2×C4×D4—21no—
102C2×C4×D4—21no—
103C2×C4×D4—22no—
104C2×C4×D4—22no—
105C2×C4×D4C2×C412yescomplemented
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—41no—
112C2×#117—41no—
113C2×#117C2×C412yes—
114C2×#117C2311yescharacteristic
115C2×#117C2311yescharacteristic
116C2×#117C2311yescharacteristic
117C22×C4⋊C4C2×C412yes—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4D412yes—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—21no—
124C22×C42—21no—
125C22×C42—22no—
126C22×C42—21no—
127C22×C42—41no—
128C22×C42—41no—
129C22×C42C2×C414yescomplemented
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C2×#104—22no—
137C2×#104—22no—
138C2×#104—22no—
139C2×#104—22no—
140C2×#104—41no—
141C2×#104—41no—
142C2×#104—41no—
143C2×#104—41no—
144C2×#104C2×C414yescomplemented
145C2×#104C2×C414yescomplemented
146C2×#104C2×C414yescomplemented
147C2×#104C2×C414yescomplemented
148#407—22no—
149#407C2×C414yescomplemented
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C4×M16—22no—
153C4×M16—22no—
154C4×M16—41no—
155C4×M16—41no—
156C2×#97—21no—
157C2×#97—21no—
158C2×C4×C8—21no—
159C2×C4×C8—21no—
160#391C2×C412yescomplemented
161#390—22no—
162#390C2×C412yescomplemented
163#389—22no—
164#389C2×C412yescomplemented
165#389C2×C412yescomplemented
166#388—22no—
167#388—22no—
168#388—22no—
169#388—22no—
170#387—22no—
171#387—22no—
172#386—22no—
173#386—22no—
174#386—22no—
175#385—22no—
176#385—22no—
177#385—22no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4—22no—
181C4×C4⋊C4C2×C412yescomplemented
182C4×C4⋊C4C2×C412yescomplemented
183C4×C22⋊C4—22no—
184C4×C22⋊C4—22no—
185C4×C22⋊C4—22no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—22no—
189C4×C22⋊C4C2×C412yes—
190C4×C22⋊C4C2×C412yes—
191C4×C22⋊C4C2×C414yescomplemented
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196#376—21no—
197#376—22no—
198#376—22no—
199#376—41no—
200#376—41no—
201C2×#95—21no—
202C2×#95—22no—
203C2×#95—22no—
204C2×#95—22no—
205C2×#95—22no—
206C2×#95D412yes—
207C43—21no—
208#339—22no—
209#339—22no—
210#339—22no—
211#339—22no—
212#339—22no—
213#339—41no—
214#339—41no—
215#339C2×C414yescomplemented
216#339C2×C414yescomplemented
217#339C2×C414yescomplemented
218#339C2×C414yescomplemented
219#339D414yescomplemented
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224C25C2×D411yescharacteristic
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41C22×C412yes—
236C2×#41C22×C412yes—
237C22×Q8C22×C411yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4C22×C411yescharacteristic
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—24no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C412yes—
265C23×C4C22×C412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4#4112yes—
272C23×C4#4112yes—
273C23×C4C2411yescharacteristic
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—24no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—28no—
294C2×M16—42no—
295C2×M16—42no—
296C2×M16—44no—
297C2×M16—44no—
298C2×M16—44no—
299C2×M16C22×C412yes—
300C2×M16C22×C412yes—
301C2×M16C22×C412yes—
302C2×M16C22×C412yes—
303C2×M16C2×D412yes—
304C2×M16#4112yes—
305C22×C8—21no—
306C22×C8—24no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—42no—
311C22×C8—42no—
312#123—24no—
313#123—24no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8C4214yes—
317C22⋊Q8C4214yes—
318#121—22no—
319#121—22no—
320#121C4214yes—
321#121C4214yes—
322#120—24no—
323#120—24no—
324C4×Q8—24no—
325C4×Q8—42no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—42no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—48no—
335#117—21no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—24no—
344#117—42no—
345#117—42no—
346#117—42no—
347#117—42no—
348#117—42no—
349#117—42no—
350#117—42no—
351#117C22×C412yes—
352#117C22×C412yes—
353#117C2×D412yes—
354#117#4112yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4C22×C412yes—
364C2×C4⋊C4C22×C411yescharacteristic
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C412yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4C22⋊C412yes—
384C2×C22⋊C4C22⋊C412yes—
385C2×C22⋊C4C22⋊C412yes—
386C2×C22⋊C4C22⋊C412yes—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—28no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—22no—
422C2×C42—44no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—44no—
428C2×C42—44no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42C22×C412yes—
432C2×C42C22×C412yes—
433C2×C42C22×C412yes—
434C2×C42C22×C412yes—
435C2×C42C22×C412yes—
436C2×C42C22×C412yes—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D412yes—
442C2×C42#4112yes—
443#104—28no—
444#104—28no—
445#104—44no—
446#104—44no—
447C22⋊C8—24no—
448C22⋊C8—24no—
449#97—42no—
450#97—42no—
451C4×C8—42no—
452C4×C8—42no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95C22⋊C412yes—
465#95C22⋊C412yes—
466#95C22⋊C412yes—
467#95C22⋊C412yes—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—24no—
473C24—21no—
474C24—42no—
475C24C2×C22⋊C411yescharacteristic
476C24C2×C22⋊C411yescharacteristic
477C24C4×D412yes—
478C24C4×D412yes—
479C24C22×D411yescharacteristic
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×C4212yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—44no—
516C2×D4—82no—
517C2×D4C2×C4212yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—48no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—44no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4C2×C4212yes—
605C22×C4C2×C4212yes—
606C22×C4C2×C22⋊C412yes—
607C22×C4C2×C22⋊C412yes—
608C22×C4C2×C22⋊C412yes—
609C22×C4C2×C22⋊C412yes—
610C22×C4C2×C22⋊C411yescharacteristic
611C22×C4C2×C22⋊C411yescharacteristic
612C22×C4#11712yes—
613C22×C4#11712yes—
614C22×C4C4×D412yes—
615C22×C4C4×D412yes—
616C22×C4C4×D412yes—
617C22×C4C4×D412yes—
618C22×C4C4×D412yes—
619C22×C4C4×D412yes—
620C22×C4C23×C411yescharacteristic
621C22×C4C23×C411yescharacteristic
622C22×C4C23×C411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4H(5,𝔽2)11yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C42−1+411yescharacteristic
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—22no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—48no—
644M16—41no—
645M16—41no—
646M16—41no—
647M16—41no—
648M16—41no—
649M16—41no—
650M16C4×D414yescomplemented
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—48no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—82no—
675C4⋊C4C2×C4212yes—
676C4⋊C4C2×C4212yes—
677C4⋊C4C4×D414yes—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—48no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—82no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—22no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—22no—
711C42—21no—
712C42—22no—
713C42—21no—
714C42—21no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—48no—
723C42—44no—
724C42—44no—
725C42—44no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—82no—
735C42C4×D414yescomplemented
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—24no—
750C23—24no—
751C23—22no—
752C23—42no—
753C23—42no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—41no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23C4×C22⋊C412yes—
763C23C4×C22⋊C412yes—
764C23#42114yes—
765C23C22×C22⋊C411yescharacteristic
766C23C2×C4×D411yescharacteristic
767C23C2×C4×D411yescharacteristic
768C23D4211yescharacteristic
769C23#54611yescharacteristic
770C23#54611yescharacteristic
771C23#54711yescharacteristic
772Q8—22no—
773Q8—22no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—42no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—84no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—432no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—82no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—88no—
861C2×C4—88no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C4×C22⋊C412yes—
867C2×C4C4×C22⋊C412yes—
868C2×C4C22×C4211yescharacteristic
869C2×C4C2×#11711yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C2×C4×D411yescharacteristic
872C2×C4C2×C4×D411yescharacteristic
873C2×C4C2×C4×D411yescharacteristic
874C2×C4C2×C4×D411yescharacteristic
875C2×C4C4×#4111yescharacteristic
876C2×C4C4×#4111yescharacteristic
877C2×C4C4×#4111yescharacteristic
878C2×C4#51811yescharacteristic
879C2×C4#51811yescharacteristic
880C2×C4#51811yescharacteristic
881C2×C4#52011yescharacteristic
882C2×C4#52011yescharacteristic
883C2×C4#52011yescharacteristic
884C2×C4D4211yescharacteristic
885C2×C4#54611yescharacteristic
886C2×C4#54611yescharacteristic
887C2×C4#54611yescharacteristic
888C2×C4#54711yescharacteristic
889C2×C4#54811yescharacteristic
890C2×C4#55111yescharacteristic
891C2×C4#55111yescharacteristic
892C2×C4#55211yescharacteristic
893C2×C4#55311yescharacteristic
894C2×C4#55311yescharacteristic
895C2×C4#55311yescharacteristic
896C8—24no—
897C8—42no—
898C8—42no—
899C8—42no—
900C22—22no—
901C22—22no—
902C22—24no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—24no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—82no—
925C22—82no—
926C22#175914yescomplemented
927C22C2×C4×C22⋊C411yescharacteristic
928C22D4×C22⋊C411yescharacteristic
929C22#233911yescharacteristic
930C22#235811yescharacteristic
931C22#235911yescharacteristic
932C22#236111yescharacteristic
933C22#236411yescharacteristic
934C22C2×#42112yes—
935C22#290112yes—
936C4—22no—
937C4—22no—
938C4—44no—
939C4—44no—
940C4—42no—
941C4—42no—
942C4—44no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4C42×D411yescharacteristic
952C4#227511yescharacteristic
953C4#235211yescharacteristic
954C4#235311yescharacteristic
955C4#235811yescharacteristic
956C4#235911yescharacteristic
957C4#236111yescharacteristic
958C4#236411yescharacteristic
959C2—21no—
960C2—21no—
961C2—21no—
962C2—21no—
963C2—24no—
964C2—42no—
965C2—82no—
966C2#1381311yescharacteristic
967C2C2×#175911yescharacteristic
968C2#2040511yescharacteristic
969C2#2243412yes—
970C2#2250612yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1759C2semidirect
5. C22⋊C4×M16C2semidirect
6. C22×#339C2semidirect
7. #13753C2semidirect
8. #10933C2semidirect
9. #10924C2semidirect
10. #10886C2semidirect
11. #10879C2semidirect
12. #10808C2semidirect
13. #10790C2semidirect
14. #10733C2semidirect
15. #10701C2semidirect
28. #2363C4semidirect
29. #2362C4semidirect
30. #2361C4semidirect
31. #2360C4semidirect
45. #1896C4semidirect
46. #1871C4semidirect
80. C22×M16C2×C4semidirect
100. C2×C4×Q8C2×C4semidirect
105. C2×C4×D4C2×C4semidirect
129. C22×C42C2×C4semidirect
144. C2×#104C2×C4semidirect
145. C2×#104C2×C4semidirect
146. C2×#104C2×C4semidirect
147. C2×#104C2×C4semidirect
149. #407C2×C4semidirect
160. #391C2×C4semidirect
162. #390C2×C4semidirect
164. #389C2×C4semidirect
165. #389C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect
182. C4×C4⋊C4C2×C4semidirect
191. C4×C22⋊C4C2×C4semidirect
215. #339C2×C4semidirect
216. #339C2×C4semidirect
217. #339C2×C4semidirect
218. #339C2×C4semidirect
219. #339D4semidirect
650. M16C4×D4semidirect
735. C42C4×D4semidirect
926. C22#1759semidirect

Maximal subgroups

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

subgroupindex
#341362
C2×#18962
C2×#18712
C2×#17592
C22⋊C4×M162
C22×#3392
#137532
#109332
#109242
#108862
#108792
#108082
#107902
#107332
#107012