Finite Group Databasebeta

← #383334

Subgroups — #383334

Order 512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34742C211yesmaximal, characteristic
2#21049C211yesmaximal, characteristic, complemented
3C2×#1896C211yesmaximal, characteristic
4C2×#1806C211yesmaximal, characteristic, complemented
5C4×#385C211yesmaximal, characteristic, complemented
6#11370C211yesmaximal, characteristic, complemented
7#11226C211yesmaximal, characteristic, complemented
8#11209C211yesmaximal, characteristic, complemented
9#11201C211yesmaximal, characteristic, complemented
10#11075C211yesmaximal, characteristic, complemented
11#10971C211yesmaximal, characteristic
12#10933C211yesmaximal, characteristic, complemented
13#10851C211yesmaximal, characteristic, complemented
14#10790C211yesmaximal, characteristic, complemented
15#10719C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×#104C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C2×#407C2211yescharacteristic
25C2×#407C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27#2423C411yescharacteristic, complemented
28#2423C411yescharacteristic, complemented
29#2422C411yescharacteristic, complemented
30#2422C411yescharacteristic, complemented
31#2421C411yescharacteristic, complemented
32#2421C411yescharacteristic, complemented
33#2420C411yescharacteristic, complemented
34#2420C411yescharacteristic, complemented
35#2419—21no—
36#2419—21no—
37#2418—21no—
38#2418—21no—
39#2395—21no—
40#2395—21no—
41C4×#123—21no—
42C4×#123—21no—
43#2297C2211yescharacteristic
44#2296C2211yescharacteristic
45C2×#385—21no—
46#2285C2211yescharacteristic
47#2280C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52#1924—21no—
53#1924—21no—
54#1923—21no—
55#1923—21no—
56#1896—24no—
57#1806—24no—
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66C2×#339C2211yescharacteristic
67C2×#339C2211yescharacteristic
68C2×#339C2211yescharacteristic
69C2×#339C2211yescharacteristic
70#1728C2211yescharacteristic
71#1728C2211yescharacteristic
72#1436—21no—
73#1436—21no—
74C22⋊#95—21no—
75C4×#95C2211yescharacteristic
76C4×#95C2211yescharacteristic
77C22×#41C2311yescharacteristic
78C24×C4—21no—
79C24×C4C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C22×M16C2311yescharacteristic
83C22×M16C2311yescharacteristic
84#525—22no—
85#525—22no—
86#525—41no—
87#525—41no—
88C2×#123—21no—
89C2×#123—21no—
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×C411yescharacteristic, complemented
101C2×C4×Q8C2×C411yescharacteristic, complemented
102C2×C4×D4—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4C2×C411yescharacteristic, complemented
107C2×C4×D4C2×C411yescharacteristic, complemented
108C2×#117—21no—
109C2×#117C2311yescharacteristic
110C2×#117C2311yescharacteristic
111C2×#117C2311yescharacteristic
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4D411yescharacteristic
116C22×C22⋊C4D411yescharacteristic
117C22×C42—21no—
118C22×C42—22no—
119C22×C42—22no—
120C22×C42—21no—
121C22×C42—41no—
122C22×C42—41no—
123C22×C42—41no—
124C22×C42—41no—
125C22×C42C2311yescharacteristic
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131#423—22no—
132#423—41no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×#104—22no—
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×#104—41no—
145C2×#104—41no—
146C2×#104D414yes—
147#407—22no—
148#407—22no—
149#407—41no—
150#407—41no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C4×M16—22no—
156C4×M16—41no—
157C2×#97—21no—
158C2×C4×C8—21no—
159#400—21no—
160#400—21no—
161#399—21no—
162#399—21no—
163#398—21no—
164#398—21no—
165#397—21no—
166#397—21no—
167#397—21no—
168#397—21no—
169#397—21no—
170#397—21no—
171#394—21no—
172#394—21no—
173#394—21no—
174#394—21no—
175#391C2×C411yescharacteristic, complemented
176#391C2×C411yescharacteristic, complemented
177#390C2×C411yescharacteristic, complemented
178#390C2×C411yescharacteristic, complemented
179#389C2×C411yescharacteristic, complemented
180#389C2×C411yescharacteristic, complemented
181#389C2×C411yescharacteristic, complemented
182#389C2×C411yescharacteristic, complemented
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187#387—21no—
188#387—21no—
189#387—21no—
190#387—21no—
191#386—21no—
192#386—21no—
193#386—21no—
194#386—21no—
195#385—28no—
196#385—21no—
197#385—21no—
198#385—21no—
199#385—21no—
200#384C2×C411yescharacteristic, complemented
201#384C2×C411yescharacteristic, complemented
202#382C2×C411yescharacteristic, complemented
203#382C2×C411yescharacteristic, complemented
204#381—21no—
205#381—21no—
206#381—21no—
207#380—21no—
208#380—21no—
209#380C2×C411yescharacteristic
210#380C2×C411yescharacteristic
211#380C2×C411yescharacteristic
212#380C2×C411yescharacteristic
213#379—21no—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—22no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—41no—
221C4×C4⋊C4—41no—
222C4×C22⋊C4—21no—
223C4×C22⋊C4—21no—
224C4×C22⋊C4—21no—
225C4×C22⋊C4—21no—
226C4×C22⋊C4—41no—
227C4×C22⋊C4—41no—
228C4×C22⋊C4C2×C411yescharacteristic
229C4×C22⋊C4C2×C411yescharacteristic
230C4×C22⋊C4C2×C411yescharacteristic
231C4×C22⋊C4C2×C411yescharacteristic
232C4×C22⋊C4D411yescharacteristic
233C4×C22⋊C4D411yescharacteristic
234C4×C22⋊C4D411yescharacteristic
235C4×C22⋊C4D411yescharacteristic
236C2×#95—21no—
237C2×#95—21no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95D411yescharacteristic
244C2×#95D411yescharacteristic
245#339—22no—
246#339—22no—
247#339—22no—
248#339—22no—
249#339—41no—
250#339—41no—
251#339—41no—
252#339—41no—
253#339—41no—
254#339—41no—
255#339—41no—
256#339—41no—
257#336—21no—
258#336—21no—
259#336—21no—
260#336—21no—
261C25C2×D411yescharacteristic
262C2×#41—21no—
263C2×#41—21no—
264C2×#41—21no—
265C2×#41—21no—
266C2×#41—21no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41C2×D412yes—
273C2×#41#4112yes—
274C22×Q8C22×C411yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4C22×C411yescharacteristic
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—24no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4C22×C411yescharacteristic
306C23×C4C22×C411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×M16—21no—
316C2×M16—21no—
317C2×M16—21no—
318C2×M16—21no—
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16C2×D412yes—
338C2×M16#4112yes—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343#123—44no—
344#123—42no—
345#123—42no—
346#123—44no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—41no—
350C22⋊Q8—41no—
351#121—22no—
352#121—22no—
353#121—41no—
354#121—41no—
355#120—42no—
356#120—42no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—41no—
360C4×Q8—41no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—41no—
364C4×D4—41no—
365C4×D4—42no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—42no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—42no—
386#117—42no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4C22×C411yescharacteristic
406C2×C4⋊C4C22×C411yescharacteristic
407C2×C4⋊C4C22×C411yescharacteristic
408C2×C4⋊C4C22×C411yescharacteristic
409C2×C4⋊C4C22×C411yescharacteristic
410C2×C4⋊C4C22×C411yescharacteristic
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4C22⋊C411yescharacteristic
434C2×C22⋊C4C22⋊C411yescharacteristic
435C2×C22⋊C4C22⋊C411yescharacteristic
436C2×C22⋊C4C22⋊C411yescharacteristic
437C2×C22⋊C4C22⋊C411yescharacteristic
438C2×C22⋊C4C22⋊C411yescharacteristic
439C2×C22⋊C4C22⋊C411yescharacteristic
440C2×C22⋊C4C22⋊C411yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—44no—
477C2×C42—42no—
478C2×C42—42no—
479C2×C42—44no—
480C2×C42—44no—
481C2×C42—42no—
482C2×C42—42no—
483C2×C42—42no—
484C2×C42—44no—
485C2×C42C22×C411yescharacteristic
486C2×C42C22×C411yescharacteristic
487C2×C42C22×C411yescharacteristic
488C2×C42C22×C411yescharacteristic
489C2×C42C2×D412yes—
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42#4112yes—
495C4⋊C8—42no—
496C4⋊C8—42no—
497#104—44no—
498#104—44no—
499#104—44no—
500#104—44no—
501C22⋊C8—42no—
502C22⋊C8—42no—
503C22⋊C8—42no—
504C22⋊C8—42no—
505#97—42no—
506C4×C8—42no—
507#95—24no—
508#95—24no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—42no—
526#95—42no—
527#95—42no—
528#95—42no—
529#95—42no—
530#95C22⋊C411yescharacteristic
531#95C22⋊C411yescharacteristic
532#95C22⋊C411yescharacteristic
533#95C22⋊C411yescharacteristic
534#95C22⋊C411yescharacteristic
535#95C22⋊C411yescharacteristic
536#95C22⋊C411yescharacteristic
537#95C22⋊C411yescharacteristic
538C24—21no—
539C24—21no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—41no—
548C24—41no—
549C24C2×C22⋊C411yescharacteristic
550C24C2×C22⋊C411yescharacteristic
551C24C22×D411yescharacteristic
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C4×D412yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4C4×D412yes—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—48no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4—81no—
708C22×C4C2×C22⋊C411yescharacteristic
709C22×C4C2×C22⋊C411yescharacteristic
710C22×C4C2×C22⋊C411yescharacteristic
711C22×C4C2×C22⋊C411yescharacteristic
712C22×C4C2×C22⋊C411yescharacteristic
713C22×C4C2×C22⋊C411yescharacteristic
714C22×C4C2×C22⋊C411yescharacteristic
715C22×C4C2×C22⋊C411yescharacteristic
716C22×C4C2×C22⋊C411yescharacteristic
717C22×C4C2×C22⋊C411yescharacteristic
718C22×C4C23×C411yescharacteristic
719C22×C4C22×D411yescharacteristic
720C22×C4C22×D411yescharacteristic
721C22×C4C2×#4111yescharacteristic
722C22×C4C2×#4111yescharacteristic
723C22×C4C2×#4111yescharacteristic
724C22×C4H(5,𝔽2)11yescharacteristic
725C22×C4H(5,𝔽2)11yescharacteristic
726C22×C4H(5,𝔽2)11yescharacteristic
727C22×C4H(5,𝔽2)11yescharacteristic
728C22×C4H(5,𝔽2)11yescharacteristic
729C22×C42−1+411yescharacteristic
730C22×C42−1+411yescharacteristic
731C22×C42−1+411yescharacteristic
732M16—22no—
733M16—22no—
734M16—22no—
735M16—22no—
736M16—41no—
737M16—41no—
738M16—41no—
739M16—41no—
740M16—41no—
741M16—41no—
742M16—41no—
743M16—41no—
744M16—41no—
745M16—41no—
746M16—41no—
747M16—41no—
748C2×C8—22no—
749C2×C8—22no—
750C2×C8—41no—
751C2×C8—41no—
752C2×C8—41no—
753C2×C8—41no—
754C2×C8—41no—
755C2×C8—41no—
756C2×C8—41no—
757C2×C8—41no—
758C2×C8—41no—
759C2×C8—41no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—42no—
779C4⋊C4—42no—
780C4⋊C4—42no—
781C4⋊C4—42no—
782C4⋊C4—81no—
783C4⋊C4—81no—
784C4⋊C4—81no—
785C4⋊C4—81no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—41no—
792C22⋊C4—41no—
793C22⋊C4—42no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—42no—
800C22⋊C4—48no—
801C22⋊C4—41no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—81no—
811C22⋊C4—81no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4#10414yescomplemented
815C42—21no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—21no—
822C42—21no—
823C42—21no—
824C42—21no—
825C42—21no—
826C42—21no—
827C42—21no—
828C42—21no—
829C42—21no—
830C42—21no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—42no—
836C42—42no—
837C42—48no—
838C42—41no—
839C42—41no—
840C42—41no—
841C42—41no—
842C42—41no—
843C42—41no—
844C42—41no—
845C42—41no—
846C42—41no—
847C42—41no—
848C42—41no—
849C42—41no—
850C42—41no—
851C42—41no—
852C42—41no—
853C42—41no—
854C42—41no—
855C42—41no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—24no—
861C23—24no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23C2×#10412yes—
896C23#42112yes—
897C23C22×C22⋊C411yescharacteristic
898C23#53511yescharacteristic
899C23#53611yescharacteristic
900C23D4211yescharacteristic
901C23#54611yescharacteristic
902C23#54611yescharacteristic
903C23#54711yescharacteristic
904Q8—22no—
905Q8—22no—
906Q8—41no—
907Q8—41no—
908D4—22no—
909D4—22no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—41no—
915D4—41no—
916D4—84no—
917D4—84no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—432no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—42no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—42no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—84no—
1017C2×C4—81no—
1018C2×C4—81no—
1019C2×C4—81no—
1020C2×C4—81no—
1021C2×C4—84no—
1022C2×C4—81no—
1023C2×C4—81no—
1024C2×C4—81no—
1025C2×C4—81no—
1026C2×C4—81no—
1027C2×C4—81no—
1028C2×C4—81no—
1029C2×C4—81no—
1030C2×C4C2×#10412yes—
1031C2×C4C2×#10412yes—
1032C2×C4C2×C4×D411yescharacteristic
1033C2×C4C4×#4111yescharacteristic
1034C2×C4#51811yescharacteristic
1035C2×C4#52011yescharacteristic
1036C2×C4#52011yescharacteristic
1037C2×C4#52011yescharacteristic
1038C2×C4#53411yescharacteristic
1039C2×C4#53611yescharacteristic
1040C2×C4#53711yescharacteristic
1041C2×C4#53711yescharacteristic
1042C2×C4#53811yescharacteristic
1043C2×C4#53911yescharacteristic
1044C2×C4#53911yescharacteristic
1045C2×C4#53911yescharacteristic
1046C2×C4#54011yescharacteristic
1047C2×C4#54211yescharacteristic
1048C2×C4D4211yescharacteristic
1049C2×C4#54611yescharacteristic
1050C2×C4#54611yescharacteristic
1051C2×C4#54611yescharacteristic
1052C2×C4#54711yescharacteristic
1053C2×C4#54711yescharacteristic
1054C2×C4#55111yescharacteristic
1055C2×C4#55211yescharacteristic
1056C2×C4#56011yescharacteristic
1057C2×C4#56211yescharacteristic
1058C2×C4#56211yescharacteristic
1059C2×C4#56311yescharacteristic
1060C8—42no—
1061C8—42no—
1062C8—81no—
1063C8—81no—
1064C22—21no—
1065C22—21no—
1066C22—21no—
1067C22—21no—
1068C22—21no—
1069C22—21no—
1070C22—21no—
1071C22—21no—
1072C22—21no—
1073C22—21no—
1074C22—21no—
1075C22—21no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22#231111yescharacteristic
1102C22D4×C22⋊C411yescharacteristic
1103C22#233911yescharacteristic
1104C22#267811yescharacteristic
1105C22#268011yescharacteristic
1106C22#268711yescharacteristic
1107C22#270611yescharacteristic
1108C22C22×#10411yescharacteristic
1109C22C2×#42111yescharacteristic
1110C22#290111yescharacteristic
1111C22#290111yescharacteristic
1112C4—22no—
1113C4—22no—
1114C4—44no—
1115C4—44no—
1116C4—41no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—82no—
1126C4—82no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4#232211yescharacteristic
1134C4#233511yescharacteristic
1135C4#235911yescharacteristic
1136C4#237611yescharacteristic
1137C4#267111yescharacteristic
1138C4#267211yescharacteristic
1139C4#269311yescharacteristic
1140C4#269511yescharacteristic
1141C2—21no—
1142C2—21no—
1143C2—21no—
1144C2—21no—
1145C2—42no—
1146C2—42no—
1147C2—82no—
1148C2#1435911yescharacteristic
1149C2#2189911yescharacteristic
1150C2#2190111yescharacteristic
1151C2D4×#10411yescharacteristic
1152C2#2243411yescharacteristic
1153C2#2250511yescharacteristic
1154C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C22×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
2. #21049C2semidirect
4. C2×#1806C2semidirect
5. C4×#385C2semidirect
6. #11370C2semidirect
7. #11226C2semidirect
8. #11209C2semidirect
9. #11201C2semidirect
10. #11075C2semidirect
12. #10933C2semidirect
13. #10851C2semidirect
14. #10790C2semidirect
15. #10719C2semidirect
27. #2423C4semidirect
28. #2423C4semidirect
29. #2422C4semidirect
30. #2422C4semidirect
31. #2421C4semidirect
32. #2421C4semidirect
33. #2420C4semidirect
34. #2420C4semidirect
100. C2×C4×Q8C2×C4semidirect
101. C2×C4×Q8C2×C4semidirect
106. C2×C4×D4C2×C4semidirect
107. C2×C4×D4C2×C4semidirect
175. #391C2×C4semidirect
176. #391C2×C4semidirect
177. #390C2×C4semidirect
178. #390C2×C4semidirect
179. #389C2×C4semidirect
180. #389C2×C4semidirect
181. #389C2×C4semidirect
182. #389C2×C4semidirect
200. #384C2×C4semidirect
201. #384C2×C4semidirect
202. #382C2×C4semidirect
203. #382C2×C4semidirect
814. C22⋊C4#104semidirect

Maximal subgroups

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

subgroupindex
#347422
#210492
C2×#18962
C2×#18062
C4×#3852
#113702
#112262
#112092
#112012
#110752
#109712
#109332
#108512
#107902
#107192