Finite Group Databasebeta

← #372667

Subgroups — #372667

Order 512.

1754 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2429C211yesmaximal, characteristic
2C2×#1956C211yesmaximal, characteristic, complemented
3C2×#1892C211yesmaximal, characteristic
4C2×#1892C211yesmaximal, characteristic
5C2×C4×#103C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊C4C211yesmaximal, characteristic
7#13876C211yesmaximal, characteristic
8#11207C211yesmaximal, characteristic, complemented
9#11010C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic
11#10970C211yesmaximal, characteristic
12#10932C211yesmaximal, characteristic, complemented
13#10926C211yesmaximal, characteristic, complemented
14#10880C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2429—24no—
33#2429C418yescomplemented
34C2×#398—21no—
35C2×#396—21no—
36C2×#391C2211yescharacteristic
37C2×#389—21no—
38C2×#389C2211yescharacteristic
39C2×#388—21no—
40C2×#388—21no—
41C2×#384C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46#1956—24no—
47#1892—24no—
48#1892—24no—
49C4×#103—24no—
50C8×C22⋊C4—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1442—21no—
62#1439—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×Q8C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—41no—
84C2×C4⋊Q8—41no—
85C2×C4⋊Q8C2×C414yes—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8—22no—
91C2×C22⋊Q8—22no—
92C2×C22⋊Q8—41no—
93C2×C22⋊Q8—41no—
94C2×C22⋊Q8—41no—
95C2×C22⋊Q8—41no—
96C2×C22⋊Q8C2×C414yes—
97C2×C22⋊Q8C2×C414yes—
98C2×C4×Q8—22no—
99C2×C4×Q8—22no—
100C2×C4×Q8—22no—
101C2×C4×Q8—41no—
102C2×C4×Q8—41no—
103C2×C4×Q8C2×C414yes—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4D411yescharacteristic
123C22×C22⋊C4D411yescharacteristic
124C22×C42—21no—
125C22×C42—21no—
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—41no—
146C2×#103—41no—
147C2×#103—41no—
148C2×#103—41no—
149C2×#103—41no—
150C2×#103—41no—
151C2×#103D414yes—
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8—22no—
159C2×C4×C8—41no—
160C2×C4×C8—41no—
161#398—28no—
162#396—28no—
163#391—22no—
164#391C2×C414yes—
165#389—22no—
166#389—28no—
167#389C2×C414yes—
168#388—28no—
169#388—44no—
170#384—22no—
171#384—41no—
172#380—22no—
173#380—22no—
174#380—41no—
175#380—41no—
176C4×C4⋊C4—22no—
177C4×C4⋊C4—41no—
178C4×C22⋊C4C2×C414yes—
179C4×C22⋊C4D414yes—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95D411yescharacteristic
191C2×#95D411yescharacteristic
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—22no—
197#340—41no—
198#340—41no—
199#340D414yes—
200#336—22no—
201#336—22no—
202C25C2×D411yescharacteristic
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—21no—
227C22×Q8C22×C412yes—
228C22×Q8C22×C412yes—
229C22×Q8C2×D412yes—
230C22×Q8#4112yes—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
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×C4C22×C412yes—
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D412yes—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2411yescharacteristic
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—28no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8C2×D412yes—
289C22×C8C2×D412yes—
290C22×C8#4112yes—
291C22×C8#4112yes—
292C22×C8#4112yes—
293C22×C8#4112yes—
294C4⋊Q8—28no—
295C4⋊Q8—44no—
296C4⋊Q8—44no—
297C4⋊Q8—44no—
298C22⋊Q8—28no—
299C22⋊Q8—28no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C22⋊Q8—44no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C4×Q8—28no—
307C4×Q8—44no—
308C4×Q8—44no—
309C4×Q8—44no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—81no—
363C2×C4⋊C4—81no—
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2×D412yes—
369C2×C4⋊C4#4112yes—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—81no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4C22⋊C414yes—
385C2×C22⋊C4C22⋊C414yes—
386C2×C22⋊C4SD1614yes—
387C2×C22⋊C4Q1614yes—
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—24no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—81no—
402C2×C42C22×C412yes—
403C2×C42C22×C412yes—
404C2×C42C2×D412yes—
405C2×C42C2×D412yes—
406#103—28no—
407#103—28no—
408#103—44no—
409#103—44no—
410#103—44no—
411#103—44no—
412#103—44no—
413#103—44no—
414C22⋊C8—28no—
415C4×C8—44no—
416C4×C8—44no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—81no—
427#95C22⋊C414yes—
428#95C22⋊C414yes—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24C2×C22⋊C412yes—
442C24C2×SD1612yes—
443C24C2×Q1612yes—
444C24C22×D411yescharacteristic
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—41no—
473C2×Q8—41no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8C4×D414yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
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—41no—
584C22×C4—41no—
585C22×C4—41no—
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×C4C2×C22⋊C412yes—
610C22×C4C2×C22⋊C412yes—
611C22×C4C2×C22⋊C412yes—
612C22×C4C2×C22⋊C412yes—
613C22×C4C2×C22⋊C412yes—
614C22×C4C2×SD1612yes—
615C22×C4C2×SD1612yes—
616C22×C4C2×Q1612yes—
617C22×C4C2×Q1612yes—
618C22×C4#13512yes—
619C22×C4#13512yes—
620C22×C4C23×C411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C2×#4111yescharacteristic
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×C4H(5,𝔽2)11yescharacteristic
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—416no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8#12114yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—48no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—84no—
693C4⋊C4—84no—
694C4⋊C4C4×D414yes—
695C22⋊C4—28no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—84no—
699C22⋊C4—84no—
700C22⋊C4#103116yescomplemented
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—48no—
710C42—84no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23C2×#10314yes—
746C23C22×C22⋊C411yescharacteristic
747C23#53211yescharacteristic
748C23#53211yescharacteristic
749C23D4211yescharacteristic
750C23D4211yescharacteristic
751C23#54611yescharacteristic
752C23#54611yescharacteristic
753C23C22×SD1611yescharacteristic
754C23C22×Q1611yescharacteristic
755C23C2×#13511yescharacteristic
756C23C2×#13511yescharacteristic
757C23#57711yescharacteristic
758C23#57711yescharacteristic
759C23#57811yescharacteristic
760C23#57811yescharacteristic
761Q8—24no—
762Q8—24no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—42no—
770Q8—42no—
771Q8—42no—
772Q8—42no—
773Q8—81no—
774Q8—81no—
775Q8—81no—
776Q8—81no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4C2×#10314yes—
874C2×C4C2×#10314yes—
875C2×C4#41614yes—
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C2×C4×D411yescharacteristic
878C2×C4C4×#4111yescharacteristic
879C2×C4C4×#4111yescharacteristic
880C2×C4#51811yescharacteristic
881C2×C4#51811yescharacteristic
882C2×C4C2×#12111yescharacteristic
883C2×C4#52511yescharacteristic
884C2×C4#52511yescharacteristic
885C2×C4#52511yescharacteristic
886C2×C4#52911yescharacteristic
887C2×C4#53211yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#53811yescharacteristic
890C2×C4#54011yescharacteristic
891C2×C4#54011yescharacteristic
892C2×C4D4211yescharacteristic
893C2×C4D4211yescharacteristic
894C2×C4#54611yescharacteristic
895C2×C4#54611yescharacteristic
896C2×C4#54611yescharacteristic
897C2×C4#54611yescharacteristic
898C2×C4#54611yescharacteristic
899C2×C4#55011yescharacteristic
900C2×C4#55311yescharacteristic
901C2×C4#55311yescharacteristic
902C2×C4#55311yescharacteristic
903C2×C4#55511yescharacteristic
904C8—24no—
905C8—42no—
906C8—42no—
907C8—42no—
908C22—24no—
909C22—24no—
910C22—24no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22#229711yescharacteristic
924C22D4×C22⋊C411yescharacteristic
925C22D4×C22⋊C411yescharacteristic
926C22#242811yescharacteristic
927C22#246411yescharacteristic
928C22#255511yescharacteristic
929C22#255911yescharacteristic
930C22C22×#10311yescharacteristic
931C22C2×#41611yescharacteristic
932C22#289811yescharacteristic
933C22#289811yescharacteristic
934C22#316711yescharacteristic
935C22#316711yescharacteristic
936C22#317011yescharacteristic
937C22#317011yescharacteristic
938C22#317411yescharacteristic
939C22#317711yescharacteristic
940C22#317811yescharacteristic
941C22#317811yescharacteristic
942C22D4×SD1611yescharacteristic
943C22D4×SD1611yescharacteristic
944C22#328211yescharacteristic
945C22#328311yescharacteristic
946C22#328411yescharacteristic
947C22#328511yescharacteristic
948C22D4×Q1611yescharacteristic
949C22D4×Q1611yescharacteristic
950C22#329811yescharacteristic
951C22#329811yescharacteristic
952C22#329911yescharacteristic
953C22#329911yescharacteristic
954C22#330011yescharacteristic
955C22#330111yescharacteristic
956C22#330211yescharacteristic
957C22#330311yescharacteristic
958C4—24no—
959C4—24no—
960C4—24no—
961C4—42no—
962C4—44no—
963C4—42no—
964C4—44no—
965C4—82no—
966C4—82no—
967C4—82no—
968C4—82no—
969C4—161no—
970C4—161no—
971C4C4×#12111yescharacteristic
972C4#233311yescharacteristic
973C4#236311yescharacteristic
974C4#236411yescharacteristic
975C4#242411yescharacteristic
976C4#245611yescharacteristic
977C4#246411yescharacteristic
978C4#247611yescharacteristic
979C2—44no—
980C2#1410011yescharacteristic
981C2#2140011yescharacteristic
982C2#2141311yescharacteristic
983C2D4×#10311yescharacteristic
984C2D4×#10311yescharacteristic
985C2#2241611yescharacteristic
986C2#2241711yescharacteristic
987C2#2541011yescharacteristic
988C2#2541511yescharacteristic
989C2#2695811yescharacteristic
990C2#2696511yescharacteristic
991C2#2890911yescharacteristic
992C2#2891111yescharacteristic
993C2#2904111yescharacteristic
994C2#2904511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ 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. C2×#1956C2semidirect
5. C2×C4×#103C2semidirect
8. #11207C2semidirect
9. #11010C2semidirect
12. #10932C2semidirect
13. #10926C2semidirect
14. #10880C2semidirect
15. #10789C2semidirect
33. #2429C4semidirect
700. C22⋊C4#103semidirect

Maximal subgroups

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

subgroupindex
C2×#24292
C2×#19562
C2×#18922
C2×C4×#1032
C2×C8×C22⋊C42
#138762
#112072
#110102
#109702
#109322
#109262
#108802
#107892