Finite Group Databasebeta

← #356647

Subgroups — #356647

Order 512.

2080 conjugacy classes of subgroups.

The subgroup lattice has 979 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×C4×#104C211yesmaximal, characteristic, complemented
5C22⋊C4×M16C211yesmaximal, characteristic, complemented
6C22×#339C211yesmaximal, characteristic, complemented
7C42×C22⋊C4C211yesmaximal, characteristic, complemented
8#10933C211yesmaximal, characteristic, complemented
9#10923C211yesmaximal, characteristic, complemented
10#10886C211yesmaximal, characteristic, complemented
11#10878C211yesmaximal, characteristic, complemented
12#10808C211yesmaximal, characteristic, complemented
13#10790C211yesmaximal, characteristic, complemented
14#10733C211yesmaximal, characteristic, complemented
15C4×#339C211yesmaximal, 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⋊C4—22no—
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C43C2211yescharacteristic
45C2×C43C2211yescharacteristic
46#1896C418yescomplemented
47#1871C418yescomplemented
48C4×#104—24no—
49#1753—21no—
50#1753—21no—
51#1752—21no—
52C8×C22⋊C4—21no—
53C2×#339—24no—
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66#1728C2211yescharacteristic
67#1728C2211yescharacteristic
68C4×#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—22no—
127C22×C42—22no—
128C22×C42—21no—
129C22×C42—41no—
130C22×C42—41no—
131C22×C42C2×C414yescomplemented
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C2×#104—22no—
139C2×#104—22no—
140C2×#104—22no—
141C2×#104—22no—
142C2×#104—41no—
143C2×#104—41no—
144C2×#104—41no—
145C2×#104—41no—
146C2×#104C2×C414yescomplemented
147C2×#104C2×C414yescomplemented
148C2×#104C2×C414yescomplemented
149C2×#104C2×C414yescomplemented
150#407—22no—
151#407C2×C414yescomplemented
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C4×M16—22no—
155C4×M16—22no—
156C4×M16—41no—
157C4×M16—41no—
158C2×#97—21no—
159C2×#97—21no—
160C2×C4×C8—21no—
161C2×C4×C8—21no—
162#391C2×C412yescomplemented
163#390—22no—
164#390C2×C412yescomplemented
165#389—22no—
166#389C2×C412yescomplemented
167#389C2×C412yescomplemented
168#388—22no—
169#388—22no—
170#388—22no—
171#388—22no—
172#387—22no—
173#387—22no—
174#386—22no—
175#386—22no—
176#386—22no—
177#385—22no—
178#385—22no—
179#385—22no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4—21no—
182C4×C4⋊C4—22no—
183C4×C4⋊C4C2×C412yescomplemented
184C4×C4⋊C4C2×C412yescomplemented
185C4×C22⋊C4—216no—
186C4×C22⋊C4—22no—
187C4×C22⋊C4—22no—
188C4×C22⋊C4—22no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—22no—
192C4×C22⋊C4C2×C412yes—
193C4×C22⋊C4C2×C412yes—
194C4×C22⋊C4C2×C414yescomplemented
195C4×C22⋊C4D411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199#376—21no—
200C2×#95—21no—
201C2×#95—22no—
202C2×#95—22no—
203C2×#95D412yes—
204C43—21no—
205C43—22no—
206C43—22no—
207C43—41no—
208C43—41no—
209#339—22no—
210#339—22no—
211#339—22no—
212#339—22no—
213#339—22no—
214#339—41no—
215#339—41no—
216#339C2×C414yescomplemented
217#339C2×C414yescomplemented
218#339C2×C414yescomplemented
219#339C2×C414yescomplemented
220#339D414yescomplemented
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225C25C2×D411yescharacteristic
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×#41—21no—
236C2×#41C22×C412yes—
237C2×#41C22×C412yes—
238C22×Q8C22×C411yescharacteristic
239C22×D4—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4C22×C411yescharacteristic
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—28no—
253C23×C4—24no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—44no—
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C412yes—
266C23×C4C22×C412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4C2411yescharacteristic
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—24no—
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—21no—
294C2×M16—28no—
295C2×M16—42no—
296C2×M16—42no—
297C2×M16—44no—
298C2×M16—44no—
299C2×M16—44no—
300C2×M16C22×C412yes—
301C2×M16C22×C412yes—
302C2×M16C22×C412yes—
303C2×M16C22×C412yes—
304C2×M16C2×D412yes—
305C2×M16#4112yes—
306C22×C8—21no—
307C22×C8—24no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—42no—
312C22×C8—42no—
313#123—24no—
314#123—24no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8C4214yescomplemented
318C22⋊Q8C4214yescomplemented
319#121—22no—
320#121—22no—
321#121C4214yescomplemented
322#121C4214yescomplemented
323#120—24no—
324#120—24no—
325C4×Q8—24no—
326C4×Q8—42no—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—42no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4—48no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—21no—
344#117—24no—
345#117—42no—
346#117—42no—
347#117—42no—
348#117—42no—
349#117—42no—
350#117—42no—
351#117—42no—
352#117C22×C412yes—
353#117C22×C412yes—
354#117C2×D412yes—
355#117#4112yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C412yes—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4C22⋊C412yes—
385C2×C22⋊C4C22⋊C412yes—
386C2×C22⋊C4C22⋊C412yes—
387C2×C22⋊C4C22⋊C412yes—
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—21no—
413C2×C42—28no—
414C2×C42—28no—
415C2×C42—28no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—22no—
425C2×C42—44no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—44no—
431C2×C42—44no—
432C2×C42—44no—
433C2×C42—44no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42C22×C412yes—
439C2×C42C22×C412yes—
440C2×C42C22×C412yes—
441C2×C42C22×C412yes—
442C2×C42C22×C412yes—
443C2×C42C22×C412yes—
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D412yes—
449C2×C42#4112yes—
450#104—28no—
451#104—28no—
452#104—44no—
453#104—44no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456#97—42no—
457#97—42no—
458C4×C8—42no—
459C4×C8—42no—
460#95—28no—
461#95—28no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—24no—
469#95C22⋊C412yes—
470#95C22⋊C412yes—
471#95C22⋊C412yes—
472#95C22⋊C412yes—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—24no—
478C24—21no—
479C24—42no—
480C24C2×C22⋊C411yescharacteristic
481C24C2×C22⋊C411yescharacteristic
482C24C4×D412yes—
483C24C4×D412yes—
484C24C22×D411yescharacteristic
485#41—22no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×C4212yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—44no—
521C2×D4—82no—
522C2×D4C2×C4212yes—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—216no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4C2×C4212yes—
610C22×C4C2×C4212yes—
611C22×C4C2×C22⋊C412yes—
612C22×C4C2×C22⋊C412yes—
613C22×C4C2×C22⋊C411yescharacteristic
614C22×C4C2×C22⋊C411yescharacteristic
615C22×C4C2×C22⋊C412yes—
616C22×C4C2×C22⋊C412yes—
617C22×C4#11712yes—
618C22×C4#11712yes—
619C22×C4C4×D412yes—
620C22×C4C4×D412yes—
621C22×C4C4×D412yes—
622C22×C4C4×D412yes—
623C22×C4C4×D412yes—
624C22×C4C4×D412yes—
625C22×C4C23×C411yescharacteristic
626C22×C4C23×C411yescharacteristic
627C22×C4C23×C411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632C22×C4C2×#4111yescharacteristic
633C22×C4C2×#4111yescharacteristic
634C22×C4C2×#4111yescharacteristic
635C22×C4H(5,𝔽2)11yescharacteristic
636C22×C4H(5,𝔽2)11yescharacteristic
637C22×C4H(5,𝔽2)11yescharacteristic
638C22×C42−1+411yescharacteristic
639M16—22no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—48no—
649M16—41no—
650M16—41no—
651M16—41no—
652M16—41no—
653M16—41no—
654M16—41no—
655M16C4×D414yescomplemented
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—48no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—82no—
680C4⋊C4C2×C4212yes—
681C4⋊C4C2×C4212yes—
682C4⋊C4C4×D414yes—
683C22⋊C4—216no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—44no—
700C22⋊C4—82no—
701C22⋊C4#10418yescomplemented
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—22no—
716C42—21no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—48no—
728C42—44no—
729C42—44no—
730C42—416no—
731C42—416no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—41no—
736C42—41no—
737C42—41no—
738C42—41no—
739C42—41no—
740C42—44no—
741C42—82no—
742C42C4×D414yescomplemented
743C23—21no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—24no—
757C23—24no—
758C23—22no—
759C23—42no—
760C23—42no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23C4×C22⋊C412yes—
770C23C4×C22⋊C412yes—
771C23C2×#10414yes—
772C23C22×C22⋊C411yescharacteristic
773C23C2×C4×D411yescharacteristic
774C23C2×C4×D411yescharacteristic
775C23D4211yescharacteristic
776C23#54611yescharacteristic
777C23#54611yescharacteristic
778C23#54711yescharacteristic
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783D4—22no—
784D4—22no—
785D4—42no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—48no—
790D4—41no—
791D4—41no—
792D4—84no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
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—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—432no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—88no—
870C2×C4—88no—
871C2×C4C4×C22⋊C412yes—
872C2×C4C4×C22⋊C412yes—
873C2×C4C2×#10414yes—
874C2×C4C2×#10414yes—
875C2×C4C22×C4211yescharacteristic
876C2×C4C2×#11711yescharacteristic
877C2×C4C2×C4×D411yescharacteristic
878C2×C4C2×C4×D411yescharacteristic
879C2×C4C2×C4×D411yescharacteristic
880C2×C4C2×C4×D411yescharacteristic
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C4×#4111yescharacteristic
883C2×C4C4×#4111yescharacteristic
884C2×C4C4×#4111yescharacteristic
885C2×C4#51811yescharacteristic
886C2×C4#51811yescharacteristic
887C2×C4#51811yescharacteristic
888C2×C4#52011yescharacteristic
889C2×C4#52011yescharacteristic
890C2×C4#52011yescharacteristic
891C2×C4D4211yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#54611yescharacteristic
894C2×C4#54611yescharacteristic
895C2×C4#54711yescharacteristic
896C2×C4#54811yescharacteristic
897C2×C4#55111yescharacteristic
898C2×C4#55111yescharacteristic
899C2×C4#55211yescharacteristic
900C2×C4#55311yescharacteristic
901C2×C4#55311yescharacteristic
902C2×C4#55311yescharacteristic
903C8—24no—
904C8—42no—
905C8—42no—
906C8—42no—
907C22—22no—
908C22—22no—
909C22—24no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—24no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—82no—
932C22—82no—
933C22C4×#10414yescomplemented
934C22C2×C4×C22⋊C411yescharacteristic
935C22D4×C22⋊C411yescharacteristic
936C22#233911yescharacteristic
937C22#235811yescharacteristic
938C22#235911yescharacteristic
939C22#236111yescharacteristic
940C22#236411yescharacteristic
941C22C22×#10412yes—
942C22#290112yes—
943C4—28no—
944C4—24no—
945C4—24no—
946C4—22no—
947C4—22no—
948C4—44no—
949C4—44no—
950C4—44no—
951C4—42no—
952C4—44no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—82no—
958C4C42×D411yescharacteristic
959C4#227511yescharacteristic
960C4#235211yescharacteristic
961C4#235311yescharacteristic
962C4#235811yescharacteristic
963C4#235911yescharacteristic
964C4#236111yescharacteristic
965C4#236411yescharacteristic
966C2—21no—
967C2—21no—
968C2—21no—
969C2—21no—
970C2—24no—
971C2—42no—
972C2—82no—
973C2#1381311yescharacteristic
974C2C2×C4×#10411yescharacteristic
975C2#2040511yescharacteristic
976C2D4×#10412yes—
977C2#2250512yes—
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×C4×#104C2semidirect
5. C22⋊C4×M16C2semidirect
6. C22×#339C2semidirect
7. C42×C22⋊C4C2semidirect
8. #10933C2semidirect
9. #10923C2semidirect
10. #10886C2semidirect
11. #10878C2semidirect
12. #10808C2semidirect
13. #10790C2semidirect
14. #10733C2semidirect
15. C4×#339C2semidirect
28. #2363C4semidirect
29. #2362C4semidirect
30. #2361C4semidirect
31. #2360C4semidirect
46. #1896C4semidirect
47. #1871C4semidirect
80. C22×M16C2×C4semidirect
100. C2×C4×Q8C2×C4semidirect
105. C2×C4×D4C2×C4semidirect
131. C22×C42C2×C4semidirect
146. C2×#104C2×C4semidirect
147. C2×#104C2×C4semidirect
148. C2×#104C2×C4semidirect
149. C2×#104C2×C4semidirect
151. #407C2×C4semidirect
162. #391C2×C4semidirect
164. #390C2×C4semidirect
166. #389C2×C4semidirect
167. #389C2×C4semidirect
183. C4×C4⋊C4C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect
194. C4×C22⋊C4C2×C4semidirect
216. #339C2×C4semidirect
217. #339C2×C4semidirect
218. #339C2×C4semidirect
219. #339C2×C4semidirect
220. #339D4semidirect
317. C22⋊Q8C42semidirect
318. C22⋊Q8C42semidirect
321. #121C42semidirect
322. #121C42semidirect
655. M16C4×D4semidirect
701. C22⋊C4#104semidirect
742. C42C4×D4semidirect
933. C22C4×#104semidirect

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×C4×#1042
C22⋊C4×M162
C22×#3392
C42×C22⋊C42
#109332
#109232
#108862
#108782
#108082
#107902
#107332
C4×#3392