Finite Group Databasebeta

← #361508

Subgroups — #361508

Order 512.

1876 conjugacy classes of subgroups.

The subgroup lattice has 1202 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
4#20837C211yesmaximal, characteristic, complemented
5C2×#1806C211yesmaximal, characteristic, complemented
6C22×#339C211yesmaximal, characteristic, complemented
7C4×#385C211yesmaximal, characteristic, complemented
8#11226C211yesmaximal, characteristic, complemented
9#11209C211yesmaximal, characteristic, complemented
10#11075C211yesmaximal, characteristic, complemented
11#11053C211yesmaximal, characteristic, complemented
12#10852C211yesmaximal, characteristic, complemented
13#10808C211yesmaximal, characteristic, complemented
14#10790C211yesmaximal, characteristic, complemented
15#10733C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C22×#104C2211yescharacteristic
26C22×#104C2211yescharacteristic
27C2×#407C2211yescharacteristic
28#2363C411yescharacteristic, complemented
29#2363C411yescharacteristic, complemented
30#2362C411yescharacteristic, complemented
31#2362C411yescharacteristic, complemented
32#2361C411yescharacteristic, complemented
33#2361C411yescharacteristic, complemented
34#2360C411yescharacteristic, complemented
35#2360C411yescharacteristic, complemented
36#2359—21no—
37#2359—21no—
38#2358—21no—
39#2358—21no—
40#2297C2211yescharacteristic
41#2296C2211yescharacteristic
42#2293—21no—
43#2290—21no—
44#2290—21no—
45C2×#385—21no—
46C42×D4—21no—
47C4×#117C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52#1896—24no—
53#1871—24no—
54#1851—21no—
55#1851—21no—
56#1850—21no—
57#1850—21no—
58#1806—24no—
59C2×#339—24no—
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66C2×#339C2211yescharacteristic
67C2×#339C2211yescharacteristic
68C2×#339C2211yescharacteristic
69C2×#339C2211yescharacteristic
70C2×#339C2211yescharacteristic
71C2×#339C2211yescharacteristic
72#1728C2211yescharacteristic
73#1728C2211yescharacteristic
74#1436—21no—
75#1436—21no—
76C22⋊#95—21no—
77C4×#95C2211yescharacteristic
78C4×#95C2211yescharacteristic
79C22×#41C2311yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—41no—
88C22×M16—41no—
89C22×M16C2311yescharacteristic
90C22×M16C2311yescharacteristic
91C22×M16C2311yescharacteristic
92C22×M16C2311yescharacteristic
93C23×C8—21no—
94#525—22no—
95#525—22no—
96#525D414yes—
97#525Q814yes—
98C2×#123—21no—
99C2×C22⋊Q8C2×C411yescharacteristic
100C2×C22⋊Q8C2×C411yescharacteristic
101C2×#121C2×C411yescharacteristic
102C2×#121C2×C411yescharacteristic
103C2×#120—21no—
104C4×#41—22no—
105C4×#41—22no—
106C4×#41—41no—
107C4×#41—41no—
108C2×C4×Q8C2×C411yescharacteristic, complemented
109C2×C4×Q8C2×C411yescharacteristic, complemented
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×C4×D4—21no—
113C2×C4×D4—21no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4C2×C411yescharacteristic, complemented
117C2×C4×D4C2×C411yescharacteristic, complemented
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—41no—
124C2×#117—41no—
125C2×#117C2×C411yescharacteristic
126C2×#117C2×C411yescharacteristic
127C2×#117C2311yescharacteristic
128C2×#117C2311yescharacteristic
129C2×#117C2311yescharacteristic
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2×C411yescharacteristic
133C22×C4⋊C4C2×C411yescharacteristic
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4D411yescharacteristic
137C22×C22⋊C4D411yescharacteristic
138C22×C42—22no—
139C22×C42—22no—
140C22×C42—22no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42—22no—
144C22×C42—21no—
145C22×C42—41no—
146C22×C42—41no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#423—22no—
154#423—22no—
155#423—41no—
156#423—41no—
157C2×C4⋊C8—21no—
158C2×C4⋊C8—21no—
159C2×C4⋊C8—21no—
160C2×C4⋊C8—21no—
161C2×#104—22no—
162C2×#104—22no—
163C2×#104—22no—
164C2×#104—22no—
165C2×#104—22no—
166C2×#104—22no—
167C2×#104—22no—
168C2×#104—22no—
169C2×#104—41no—
170C2×#104—41no—
171C2×#104—41no—
172C2×#104—41no—
173#407—22no—
174#407—22no—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—21no—
177#391C2×C411yescharacteristic, complemented
178#391C2×C411yescharacteristic, complemented
179#390—21no—
180#390—21no—
181#390C2×C411yescharacteristic, complemented
182#390C2×C411yescharacteristic, complemented
183#389—21no—
184#389—21no—
185#389C2×C411yescharacteristic, complemented
186#389C2×C411yescharacteristic, complemented
187#389C2×C411yescharacteristic, complemented
188#389C2×C411yescharacteristic, complemented
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193#388—21no—
194#388—21no—
195#388—21no—
196#388—21no—
197#387—21no—
198#387—21no—
199#387—21no—
200#387—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#386—21no—
205#386—21no—
206#386—21no—
207#385—28no—
208#385—21no—
209#385—21no—
210#385—21no—
211#385—21no—
212#385—21no—
213#385—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×C4⋊C4C2×C411yescharacteristic, complemented
223C4×C4⋊C4C2×C411yescharacteristic, complemented
224C4×C4⋊C4C2×C411yescharacteristic, complemented
225C4×C4⋊C4C2×C411yescharacteristic, complemented
226C4×C22⋊C4—21no—
227C4×C22⋊C4—21no—
228C4×C22⋊C4—21no—
229C4×C22⋊C4—21no—
230C4×C22⋊C4—21no—
231C4×C22⋊C4—21no—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—21no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4C2×C411yescharacteristic
237C4×C22⋊C4C2×C411yescharacteristic
238C4×C22⋊C4C2×C411yescharacteristic
239C4×C22⋊C4C2×C411yescharacteristic
240C4×C22⋊C4D411yescharacteristic
241C4×C22⋊C4D411yescharacteristic
242C4×C22⋊C4D411yescharacteristic
243C4×C22⋊C4D411yescharacteristic
244#376—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95D411yescharacteristic
253C2×#95D411yescharacteristic
254C43—21no—
255#339—22no—
256#339—22no—
257#339—22no—
258#339—22no—
259#339—22no—
260#339—22no—
261#339—22no—
262#339—22no—
263#339—22no—
264#339—41no—
265#339—41no—
266#339D414yescomplemented
267#336—21no—
268#336—21no—
269#336—21no—
270#336—21no—
271C25C2×D411yescharacteristic
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—21no—
276C2×#41—21no—
277C2×#41—21no—
278C2×#41—21no—
279C2×#41—21no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41C2×D412yes—
283C2×#41C2×Q812yes—
284C22×Q8C22×C411yescharacteristic
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C22×C411yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—24no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4C22×C411yescharacteristic
314C23×C4C22×C411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D412yes—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×Q812yes—
324C23×C4#4112yes—
325C23×C4#4112yes—
326C23×C4C2411yescharacteristic
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—28no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—44no—
353C2×M16—44no—
354C2×M16—44no—
355C2×M16—42no—
356C2×M16C2×D412yes—
357C2×M16#4112yes—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—42no—
363C22×C8—42no—
364C22×C8—42no—
365#123—24no—
366#123—24no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8C4⋊C414yescomplemented
370C22⋊Q8C4⋊C414yescomplemented
371#121—22no—
372#121—22no—
373#121C4⋊C414yescomplemented
374#121C4⋊C414yescomplemented
375#120—24no—
376#120—24no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—41no—
380C4×Q8—41no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—24no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—41no—
388C4×D4—41no—
389C4×D4—42no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—44no—
394C4×D4—44no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—22no—
404#117—22no—
405#117—42no—
406#117—42no—
407#117—42no—
408#117—42no—
409#117—42no—
410#117—42no—
411#117—41no—
412#117—41no—
413#117C2×D412yes—
414#117C2×D412yes—
415#117C2×Q812yes—
416#117#4112yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4C22×C411yescharacteristic
438C2×C4⋊C4C22×C411yescharacteristic
439C2×C4⋊C4C22×C411yescharacteristic
440C2×C4⋊C4C22×C411yescharacteristic
441C2×C4⋊C4C22×C411yescharacteristic
442C2×C4⋊C4C22×C411yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4C22⋊C411yescharacteristic
466C2×C22⋊C4C22⋊C411yescharacteristic
467C2×C22⋊C4C22⋊C411yescharacteristic
468C2×C22⋊C4C22⋊C411yescharacteristic
469C2×C22⋊C4C22⋊C411yescharacteristic
470C2×C22⋊C4C22⋊C411yescharacteristic
471C2×C22⋊C4C22⋊C411yescharacteristic
472C2×C22⋊C4C22⋊C411yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—28no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—42no—
516C2×C42—42no—
517C2×C42—42no—
518C2×C42—42no—
519C2×C42—44no—
520C2×C42—44no—
521C2×C42—42no—
522C2×C42—42no—
523C2×C42—44no—
524C2×C42—42no—
525C2×C42C22×C411yescharacteristic
526C2×C42C22×C411yescharacteristic
527C2×C42C22×C411yescharacteristic
528C2×C42C22×C411yescharacteristic
529C2×C42C2×D412yes—
530C2×C42C2×D411yescharacteristic
531C2×C42C2×D411yescharacteristic
532C2×C42C2×D411yescharacteristic
533C2×C42C2×D411yescharacteristic
534C2×C42#4112yes—
535C4⋊C8—42no—
536C4⋊C8—42no—
537C4⋊C8—42no—
538C4⋊C8—42no—
539#104—44no—
540#104—44no—
541#104—44no—
542#104—44no—
543C22⋊C8—42no—
544C22⋊C8—42no—
545#95—24no—
546#95—24no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95C22⋊C411yescharacteristic
565#95C22⋊C411yescharacteristic
566#95C22⋊C411yescharacteristic
567#95C22⋊C411yescharacteristic
568#95C22⋊C411yescharacteristic
569#95C22⋊C411yescharacteristic
570#95C22⋊C411yescharacteristic
571#95C22⋊C411yescharacteristic
572C24—21no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—22no—
577C24—22no—
578C24—21no—
579C24—41no—
580C24—41no—
581C24C2×C22⋊C411yescharacteristic
582C24C2×C22⋊C411yescharacteristic
583C24#12112yes—
584C24C22⋊Q812yes—
585C24C22×D411yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—41no—
601#41—41no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8C2×C4⋊C412yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4C2×C4⋊C412yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—48no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×C22⋊C411yescharacteristic
739C22×C4C2×C22⋊C411yescharacteristic
740C22×C4C2×C22⋊C411yescharacteristic
741C22×C4C2×C22⋊C411yescharacteristic
742C22×C4C2×C22⋊C411yescharacteristic
743C22×C4C2×C22⋊C411yescharacteristic
744C22×C4C2×C22⋊C411yescharacteristic
745C22×C4C2×C22⋊C411yescharacteristic
746C22×C4C2×C22⋊C411yescharacteristic
747C22×C4C2×C22⋊C411yescharacteristic
748C22×C4C2×C4⋊C412yes—
749C22×C4C2×C4⋊C412yes—
750C22×C4#11712yes—
751C22×C4#11712yes—
752C22×C4#12112yes—
753C22×C4#12112yes—
754C22×C4#12112yes—
755C22×C4C22⋊Q812yes—
756C22×C4C22⋊Q812yes—
757C22×C4C22⋊Q812yes—
758C22×C4C23×C411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×Q811yescharacteristic
763C22×C4C2×#4111yescharacteristic
764C22×C4C2×#4111yescharacteristic
765C22×C4C2×#4111yescharacteristic
766C22×C4C2×#4111yescharacteristic
767C22×C4C2×#4111yescharacteristic
768C22×C4H(5,𝔽2)11yescharacteristic
769C22×C4H(5,𝔽2)11yescharacteristic
770C22×C4H(5,𝔽2)11yescharacteristic
771C22×C42−1+411yescharacteristic
772M16—22no—
773M16—22no—
774M16—22no—
775M16—22no—
776M16—48no—
777M16—41no—
778M16—41no—
779M16—41no—
780M16—41no—
781M16—41no—
782M16—41no—
783M16—41no—
784M16—41no—
785M16—41no—
786M16—41no—
787M16—41no—
788M16—41no—
789C2×C8—22no—
790C2×C8—22no—
791C2×C8—48no—
792C2×C8—41no—
793C2×C8—41no—
794C2×C8—41no—
795C2×C8—41no—
796C2×C8—41no—
797C2×C8—41no—
798C2×C8—41no—
799C2×C8—41no—
800C2×C8—41no—
801C2×C8—41no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—48no—
817C4⋊C4—48no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—81no—
821C4⋊C4—81no—
822C4⋊C4C2×C4⋊C412yes—
823C4⋊C4C2×C4⋊C412yes—
824C4⋊C4C4×D412yes—
825C4⋊C4C4×D412yes—
826C22⋊C4—22no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—41no—
840C22⋊C4—41no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—48no—
847C22⋊C4—41no—
848C22⋊C4—41no—
849C22⋊C4—42no—
850C22⋊C4—81no—
851C22⋊C4—81no—
852C22⋊C4#10414yescomplemented
853C42—21no—
854C42—21no—
855C42—21no—
856C42—21no—
857C42—21no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42—22no—
862C42—22no—
863C42—21no—
864C42—21no—
865C42—22no—
866C42—21no—
867C42—21no—
868C42—21no—
869C42—21no—
870C42—22no—
871C42—21no—
872C42—21no—
873C42—22no—
874C42—22no—
875C42—22no—
876C42—22no—
877C42—42no—
878C42—42no—
879C42—42no—
880C42—42no—
881C42—48no—
882C42—42no—
883C42—41no—
884C42—41no—
885C42—41no—
886C42—41no—
887C42—41no—
888C42—41no—
889C42—42no—
890C42—41no—
891C42—41no—
892C42—41no—
893C42—41no—
894C42—41no—
895C42—41no—
896C42—41no—
897C42—41no—
898C42—81no—
899C42—81no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—24no—
909C23—24no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23#38012yes—
938C23#38012yes—
939C23C2×#10412yes—
940C23#42112yes—
941C23C22×C22⋊C411yescharacteristic
942C23C2×#12111yescharacteristic
943C23C2×C22⋊Q811yescharacteristic
944C23D4211yescharacteristic
945C23#54611yescharacteristic
946C23#54611yescharacteristic
947C23#54711yescharacteristic
948Q8—22no—
949Q8—22no—
950Q8—41no—
951Q8—41no—
952D4—22no—
953D4—22no—
954D4—48no—
955D4—42no—
956D4—42no—
957D4—42no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—84no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—432no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—84no—
1059C2×C4—81no—
1060C2×C4—81no—
1061C2×C4—81no—
1062C2×C4—81no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—84no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—81no—
1069C2×C4—81no—
1070C2×C4—81no—
1071C2×C4—81no—
1072C2×C4—81no—
1073C2×C4—81no—
1074C2×C4#38012yes—
1075C2×C4#38012yes—
1076C2×C4C2×#10412yes—
1077C2×C4C2×#10412yes—
1078C2×C4C22×C4⋊C411yescharacteristic
1079C2×C4C2×#11711yescharacteristic
1080C2×C4C2×C4×D411yescharacteristic
1081C2×C4C4×#4111yescharacteristic
1082C2×C4#51811yescharacteristic
1083C2×C4#52011yescharacteristic
1084C2×C4C2×#12111yescharacteristic
1085C2×C4C2×C22⋊Q811yescharacteristic
1086C2×C4#52511yescharacteristic
1087C2×C4#52511yescharacteristic
1088C2×C4#52911yescharacteristic
1089C2×C4#52911yescharacteristic
1090C2×C4#53811yescharacteristic
1091C2×C4#53811yescharacteristic
1092C2×C4#53911yescharacteristic
1093C2×C4#53911yescharacteristic
1094C2×C4D4211yescharacteristic
1095C2×C4D4211yescharacteristic
1096C2×C4#54611yescharacteristic
1097C2×C4#54611yescharacteristic
1098C2×C4#54611yescharacteristic
1099C2×C4#54611yescharacteristic
1100C2×C4#54711yescharacteristic
1101C2×C4#54711yescharacteristic
1102C2×C4D4×Q811yescharacteristic
1103C2×C4#55411yescharacteristic
1104C2×C4#55411yescharacteristic
1105C2×C4#55411yescharacteristic
1106C8—42no—
1107C8—42no—
1108C8—81no—
1109C8—81no—
1110C22—22no—
1111C22—21no—
1112C22—21no—
1113C22—22no—
1114C22—21no—
1115C22—21no—
1116C22—22no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—22no—
1122C22—21no—
1123C22—21no—
1124C22—22no—
1125C22—21no—
1126C22—21no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22#180614yescomplemented
1147C22C2×#38011yescharacteristic
1148C22D4×C22⋊C411yescharacteristic
1149C22#233911yescharacteristic
1150C22#242411yescharacteristic
1151C22#242511yescharacteristic
1152C22#244911yescharacteristic
1153C22#245011yescharacteristic
1154C22C22×#10411yescharacteristic
1155C22C2×#42111yescharacteristic
1156C22#290111yescharacteristic
1157C22#290111yescharacteristic
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—44no—
1163C4—44no—
1164C4—42no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—82no—
1176C4—82no—
1177C4—81no—
1178C4—81no—
1179C4#229011yescharacteristic
1180C4#231811yescharacteristic
1181C4D4×C4⋊C411yescharacteristic
1182C4#234911yescharacteristic
1183C4#242411yescharacteristic
1184C4#242511yescharacteristic
1185C4#244911yescharacteristic
1186C4#245011yescharacteristic
1187C2—21no—
1188C2—21no—
1189C2—24no—
1190C2—21no—
1191C2—21no—
1192C2—42no—
1193C2—82no—
1194C2#1389911yescharacteristic
1195C2C2×#180611yescharacteristic
1196C2#2065511yescharacteristic
1197C2D4×#10411yescharacteristic
1198C2#2243411yescharacteristic
1199C2#2250511yescharacteristic
1200C2#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
4. #20837C2semidirect
5. C2×#1806C2semidirect
6. C22×#339C2semidirect
7. C4×#385C2semidirect
8. #11226C2semidirect
9. #11209C2semidirect
10. #11075C2semidirect
11. #11053C2semidirect
12. #10852C2semidirect
13. #10808C2semidirect
14. #10790C2semidirect
15. #10733C2semidirect
28. #2363C4semidirect
29. #2363C4semidirect
30. #2362C4semidirect
31. #2362C4semidirect
32. #2361C4semidirect
33. #2361C4semidirect
34. #2360C4semidirect
35. #2360C4semidirect
108. C2×C4×Q8C2×C4semidirect
109. C2×C4×Q8C2×C4semidirect
116. C2×C4×D4C2×C4semidirect
117. C2×C4×D4C2×C4semidirect
177. #391C2×C4semidirect
178. #391C2×C4semidirect
181. #390C2×C4semidirect
182. #390C2×C4semidirect
185. #389C2×C4semidirect
186. #389C2×C4semidirect
187. #389C2×C4semidirect
188. #389C2×C4semidirect
222. C4×C4⋊C4C2×C4semidirect
223. C4×C4⋊C4C2×C4semidirect
224. C4×C4⋊C4C2×C4semidirect
225. C4×C4⋊C4C2×C4semidirect
266. #339D4semidirect
369. C22⋊Q8C4⋊C4semidirect
370. C22⋊Q8C4⋊C4semidirect
373. #121C4⋊C4semidirect
374. #121C4⋊C4semidirect
852. C22⋊C4#104semidirect
1146. C22#1806semidirect

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
#208372
C2×#18062
C22×#3392
C4×#3852
#112262
#112092
#110752
#110532
#108522
#108082
#107902
#107332