Finite Group Databasebeta

← #387052

Subgroups — #387052

Order 512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 1011 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34947C211yesmaximal, characteristic
2#21023C211yesmaximal, characteristic, complemented
3C4×#387C211yesmaximal, characteristic, complemented
4#11386C211yesmaximal, characteristic, complemented
5#11386C211yesmaximal, characteristic, complemented
6#11370C211yesmaximal, characteristic, complemented
7#11359C211yesmaximal, characteristic, complemented
8#11075C211yesmaximal, characteristic
9#11053C211yesmaximal, characteristic
10#10933C211yesmaximal, characteristic
11#10923C211yesmaximal, characteristic
12#10851C211yesmaximal, characteristic, complemented
13#10839C211yesmaximal, characteristic, complemented
14#10790C211yesmaximal, characteristic
15#10790C211yesmaximal, characteristic
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C22×#104C2211yescharacteristic
20C22×#104C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C2×C4×M16C2211yescharacteristic
24#2568C411yescharacteristic, complemented
25#2567C411yescharacteristic, complemented
26#2566C411yescharacteristic, complemented
27#2566C411yescharacteristic, complemented
28#2565C411yescharacteristic, complemented
29#2565C411yescharacteristic, complemented
30#2564—21no—
31#2564—21no—
32#2563C411yescharacteristic, complemented
33#2542C411yescharacteristic, complemented
34#2417—21no—
35#2417—21no—
36#2396—21no—
37#2396—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40#2297C2211yescharacteristic
41#2297C2211yescharacteristic
42C2×#387—21no—
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C43C2211yescharacteristic
48#1917—21no—
49#1917—21no—
50#1916—21no—
51#1916—21no—
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64#1728C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1728C2211yescharacteristic
68#1436—21no—
69#1436—21no—
70#1434—21no—
71C4×#95C2211yescharacteristic
72C4×#95C2211yescharacteristic
73C4×#95C2211yescharacteristic
74C4×#95C2211yescharacteristic
75C22×#41C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80#533—41no—
81#533—41no—
82#533—41no—
83#533—41no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×#125C2×C411yescharacteristic
87C2×#125C2×C411yescharacteristic
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C4×#41—41no—
93C4×#41—41no—
94C4×#41—41no—
95C4×#41—41no—
96C2×C4×Q8—21no—
97C2×C4×Q8—21no—
98C2×C4×Q8C2×C411yescharacteristic
99C2×C4×Q8C2×C411yescharacteristic
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4C2×C411yescharacteristic
103C2×C4×D4C2×C411yescharacteristic
104C2×#117—21no—
105C2×#117C2311yescharacteristic
106C2×#117C2311yescharacteristic
107C2×#117C2311yescharacteristic
108C22×C4⋊C4—21no—
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4D411yescharacteristic
111C22×C42—21no—
112C22×C42—21no—
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121#423—22no—
122#423—41no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×#104—22no—
126C2×#104—22no—
127C2×#104—22no—
128C2×#104—22no—
129C2×#104—22no—
130C2×#104—41no—
131C2×#104—41no—
132C2×#104—41no—
133C2×#104—41no—
134C2×#104—41no—
135C2×#104—41no—
136C2×#104Q814yescomplemented
137C4×M16—22no—
138C4×M16—41no—
139C2×#97—21no—
140C2×C4×C8—21no—
141#400—21no—
142#400—21no—
143#399—21no—
144#399—21no—
145#398—21no—
146#398—21no—
147#398—21no—
148#398—21no—
149#396—21no—
150#396—21no—
151#396—21no—
152#396—21no—
153#395—21no—
154#395—21no—
155#393—21no—
156#393—21no—
157#391—21no—
158#391—21no—
159#391C2×C411yescharacteristic
160#391C2×C411yescharacteristic
161#391C2×C411yescharacteristic
162#391C2×C411yescharacteristic
163#390C2×C411yescharacteristic
164#390C2×C411yescharacteristic
165#390C2×C411yescharacteristic
166#390C2×C411yescharacteristic
167#389—21no—
168#389—21no—
169#387—28no—
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#384C2×C411yescharacteristic
183#384C2×C411yescharacteristic
184#384C2×C411yescharacteristic
185#384C2×C411yescharacteristic
186#382C2×C411yescharacteristic
187#382C2×C411yescharacteristic
188#382C2×C411yescharacteristic
189#382C2×C411yescharacteristic
190#380—21no—
191#380—21no—
192#380—21no—
193#380—21no—
194#380—21no—
195#380—21no—
196C4×C4⋊C4—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—22no—
201C4×C4⋊C4—41no—
202C4×C4⋊C4C2×C411yescharacteristic
203C4×C4⋊C4C2×C411yescharacteristic
204C4×C4⋊C4C2×C411yescharacteristic
205C4×C4⋊C4C2×C411yescharacteristic
206C4×C4⋊C4D411yescharacteristic
207C4×C4⋊C4D411yescharacteristic
208C4×C4⋊C4D411yescharacteristic
209C4×C4⋊C4D411yescharacteristic
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4—21no—
213C4×C22⋊C4—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95D411yescharacteristic
224C2×#95D411yescharacteristic
225C43—22no—
226C43—41no—
227#339—41no—
228#339—41no—
229#339—41no—
230#339—41no—
231#339—41no—
232#339—41no—
233#339—41no—
234#339—41no—
235#339—41no—
236#339—41no—
237#339—41no—
238#339—41no—
239#336—21no—
240#336—21no—
241#336—21no—
242#336—21no—
243#336—21no—
244#336—21no—
245#336—21no—
246#336—21no—
247C2×#41—21no—
248C2×#41—21no—
249C2×#41—21no—
250C2×#41—21no—
251C2×#41—21no—
252C2×#41—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—21no—
257C2×#41C2×Q812yes—
258C2×#41#4112yes—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×Q8C22×C411yescharacteristic
262C22×D4—21no—
263C22×D4C22×C411yescharacteristic
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2411yescharacteristic
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—21no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16C2×Q812yes—
301C2×M16#4112yes—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C4⋊Q8—41no—
307C4⋊Q8—41no—
308C4⋊Q8—41no—
309C4⋊Q8—41no—
310#125—41no—
311#125—41no—
312#125—41no—
313#125—41no—
314C22⋊Q8—44no—
315C22⋊Q8—42no—
316C22⋊Q8—42no—
317C22⋊Q8—42no—
318C22⋊Q8—42no—
319C22⋊Q8—44no—
320C4×Q8—41no—
321C4×Q8—41no—
322C4×Q8—41no—
323C4×Q8—41no—
324C4×Q8—42no—
325C4×Q8—42no—
326C4×Q8—42no—
327C4×Q8—42no—
328C4×D4—41no—
329C4×D4—41no—
330C4×D4—41no—
331C4×D4—41no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—42no—
335C4×D4—42no—
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—21no—
345#117—21no—
346#117—21no—
347#117—21no—
348#117—42no—
349#117—42no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4C22⋊C411yescharacteristic
372C2×C4⋊C4C22⋊C411yescharacteristic
373C2×C4⋊C4C22⋊C411yescharacteristic
374C2×C4⋊C4C22⋊C411yescharacteristic
375C2×C4⋊C4C22⋊C411yescharacteristic
376C2×C4⋊C4C22⋊C411yescharacteristic
377C2×C4⋊C4C22⋊C411yescharacteristic
378C2×C4⋊C4C22⋊C411yescharacteristic
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C411yescharacteristic
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—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—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—24no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42C22×C411yescharacteristic
446C2×C42C22×C411yescharacteristic
447C2×C42C22×C411yescharacteristic
448C2×C42C22×C411yescharacteristic
449C2×C42C22×C411yescharacteristic
450C2×C42C22×C411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×Q812yes—
458C2×C42#4112yes—
459C4⋊C8—42no—
460C4⋊C8—42no—
461#104—44no—
462#104—44no—
463#104—44no—
464#104—44no—
465#97—42no—
466C4×C8—42no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—42no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—42no—
492#95C22⋊C411yescharacteristic
493#95C22⋊C411yescharacteristic
494#95C22⋊C411yescharacteristic
495#95C22⋊C411yescharacteristic
496#95C22⋊C411yescharacteristic
497#95C22⋊C411yescharacteristic
498#95C22⋊C411yescharacteristic
499#95C22⋊C411yescharacteristic
500C24—21no—
501C24C22×D411yescharacteristic
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—22no—
508#41—22no—
509#41—22no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516#41—41no—
517#41—41no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—81no—
528C2×Q8—81no—
529C2×Q8C4×Q812yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4C4×Q812yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
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—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
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—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×C22⋊C411yescharacteristic
614C22×C4C2×C22⋊C411yescharacteristic
615C22×C4C2×C22⋊C411yescharacteristic
616C22×C4C2×C22⋊C411yescharacteristic
617C22×C4C2×C22⋊C411yescharacteristic
618C22×C4C2×C22⋊C411yescharacteristic
619C22×C4C2×C22⋊C411yescharacteristic
620C22×C4C2×C22⋊C411yescharacteristic
621C22×C4C2×C22⋊C411yescharacteristic
622C22×C4C2×C22⋊C411yescharacteristic
623C22×C4C2×C22⋊C411yescharacteristic
624C22×C4C2×C22⋊C411yescharacteristic
625C22×C4C23×C411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×Q811yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C4H(5,𝔽2)11yescharacteristic
634C22×C4H(5,𝔽2)11yescharacteristic
635C22×C4H(5,𝔽2)11yescharacteristic
636C22×C42−1+411yescharacteristic
637C22×C42−1+411yescharacteristic
638C22×C42−1+411yescharacteristic
639M16—22no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—41no—
644M16—41no—
645M16—41no—
646M16—41no—
647M16—41no—
648M16—41no—
649M16—41no—
650M16—41no—
651M16—41no—
652M16—41no—
653M16—41no—
654M16—41no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—48no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—81no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—81no—
703C4⋊C4#10414yescomplemented
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C22⋊C4—41no—
710C22⋊C4—41no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—81no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4—81no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—22no—
745C42—22no—
746C42—22no—
747C42—22no—
748C42—48no—
749C42—42no—
750C42—42no—
751C42—48no—
752C42—41no—
753C42—41no—
754C42—41no—
755C42—41no—
756C42—41no—
757C42—41no—
758C42—41no—
759C42—41no—
760C42—41no—
761C42—41no—
762C42—41no—
763C42—41no—
764C42—41no—
765C42—41no—
766C42—41no—
767C42—41no—
768C42—41no—
769C42—41no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23C22×C22⋊C411yescharacteristic
782C23#53511yescharacteristic
783C23#53511yescharacteristic
784C23#54611yescharacteristic
785C23#54711yescharacteristic
786C23#54811yescharacteristic
787C23D4×Q811yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—41no—
791Q8—41no—
792Q8—84no—
793Q8—84no—
794D4—22no—
795D4—22no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—41no—
801D4—41no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—42no—
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—41no—
856C2×C4—41no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—84no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—84no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4C2×#10412yes—
902C2×C4C2×#10412yes—
903C2×C4C2×#10412yes—
904C2×C4#42112yes—
905C2×C4C2×C4×Q811yescharacteristic
906C2×C4C4×#4111yescharacteristic
907C2×C4#51811yescharacteristic
908C2×C4#51811yescharacteristic
909C2×C4#51911yescharacteristic
910C2×C4#52011yescharacteristic
911C2×C4#53511yescharacteristic
912C2×C4#53511yescharacteristic
913C2×C4#53811yescharacteristic
914C2×C4#53911yescharacteristic
915C2×C4#53911yescharacteristic
916C2×C4#53911yescharacteristic
917C2×C4#54211yescharacteristic
918C2×C4#54211yescharacteristic
919C2×C4#54311yescharacteristic
920C2×C4#54411yescharacteristic
921C2×C4#54611yescharacteristic
922C2×C4#54711yescharacteristic
923C2×C4#54811yescharacteristic
924C2×C4D4×Q811yescharacteristic
925C2×C4#55111yescharacteristic
926C2×C4#55111yescharacteristic
927C2×C4#55411yescharacteristic
928C2×C4#55411yescharacteristic
929C2×C4#56211yescharacteristic
930C2×C4#56211yescharacteristic
931C2×C4#56311yescharacteristic
932C2×C4#56311yescharacteristic
933C8—42no—
934C8—42no—
935C8—81no—
936C8—81no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22#230911yescharacteristic
957C22#233911yescharacteristic
958C22Q8×C22⋊C411yescharacteristic
959C22#269211yescharacteristic
960C22#269611yescharacteristic
961C22#272011yescharacteristic
962C22#272311yescharacteristic
963C22C22×#10411yescharacteristic
964C22C2×#42111yescharacteristic
965C22#290111yescharacteristic
966C22#290111yescharacteristic
967C4—22no—
968C4—22no—
969C4—22no—
970C4—22no—
971C4—44no—
972C4—44no—
973C4—41no—
974C4—41no—
975C4—41no—
976C4—42no—
977C4—41no—
978C4—41no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—82no—
983C4—82no—
984C4—81no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C4—81no—
990C4#232911yescharacteristic
991C4#233211yescharacteristic
992C4#236811yescharacteristic
993C4#237811yescharacteristic
994C4#269211yescharacteristic
995C4#269611yescharacteristic
996C4#272011yescharacteristic
997C4#272311yescharacteristic
998C2—21no—
999C2—21no—
1000C2—21no—
1001C2—21no—
1002C2—82no—
1003C2#1444811yescharacteristic
1004C2#2181511yescharacteristic
1005C2#2181711yescharacteristic
1006C2#2250511yescharacteristic
1007C2#2250611yescharacteristic
1008C2Q8×#10411yescharacteristic
1009C2#2252911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21023C2semidirect
3. C4×#387C2semidirect
4. #11386C2semidirect
5. #11386C2semidirect
6. #11370C2semidirect
7. #11359C2semidirect
12. #10851C2semidirect
13. #10839C2semidirect
24. #2568C4semidirect
25. #2567C4semidirect
26. #2566C4semidirect
27. #2566C4semidirect
28. #2565C4semidirect
29. #2565C4semidirect
32. #2563C4semidirect
33. #2542C4semidirect
136. C2×#104Q8semidirect
703. C4⋊C4#104semidirect

Maximal subgroups

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

subgroupindex
#349472
#210232
C4×#3872
#113862
#113702
#113592
#110752
#110532
#109332
#109232
#108512
#108392
#107902