Finite Group Databasebeta

← #361506

Subgroups — #361506

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 959 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2362C211yesmaximal, characteristic
2C2×#1894C211yesmaximal, characteristic
3C2×#1872C211yesmaximal, characteristic
4C2×#1851C211yesmaximal, characteristic
5C2×#1803C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic
7#13880C211yesmaximal, characteristic
8#11227C211yesmaximal, characteristic, complemented
9#11207C211yesmaximal, characteristic, complemented
10#11077C211yesmaximal, characteristic, complemented
11#11050C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28#2362—24no—
29#2362C418yescomplemented
30C2×#391C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#388—21no—
33C2×#388—21no—
34C2×#387—21no—
35C2×#385—21no—
36C2×#385—21no—
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4—21no—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#1894—24no—
44#1872—24no—
45#1851—24no—
46#1803—24no—
47#1736—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1444—21no—
63#1444—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8C2×C414yes—
84C2×C22⋊Q8D414yes—
85C2×C22⋊Q8Q814yes—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—41no—
90C2×C4×Q8—41no—
91C2×C4×Q8C2×C414yescomplemented
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117C2×C414yes—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—41no—
111C22×C4⋊C4—41no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
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×C42—21no—
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C2×C4⋊C8—22no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8—22no—
132C2×C4⋊C8—22no—
133C2×C4⋊C8—41no—
134C2×C4⋊C8—41no—
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—41no—
144C2×#103—41no—
145C2×#103—41no—
146C2×#103—41no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150#391—22no—
151#391C2×C414yescomplemented
152#389—22no—
153#389C2×C414yescomplemented
154#388—28no—
155#388—28no—
156#387—28no—
157#385—44no—
158#385—44no—
159#384—22no—
160#384—22no—
161#384—41no—
162#384—41no—
163#380—22no—
164#380—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4—28no—
167C4×C4⋊C4C2×C414yescomplemented
168C4×C22⋊C4C2×C414yes—
169C4×C22⋊C4D414yes—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95D411yescharacteristic
180C2×#95D411yescharacteristic
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—22no—
190#340—41no—
191#340—41no—
192#340D414yes—
193#336—22no—
194#336—22no—
195C25C2×D411yescharacteristic
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8C22×C412yes—
208C22×Q8C2×D412yes—
209C22×Q8C2×Q812yes—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4C22×C412yes—
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D412yes—
240C23×C4C2×D412yes—
241C23×C4C2×Q812yes—
242C23×C4#4112yes—
243C23×C4#4112yes—
244C23×C4C2411yescharacteristic
245C2×M16—28no—
246C2×M16—44no—
247C2×M16—44no—
248C2×M16—44no—
249C2×M16—44no—
250C2×M16—44no—
251C2×M16—44no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
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×C8C2×D412yes—
279C22×C8#4112yes—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8—28no—
283C22⋊Q8C4⋊C4116yescomplemented
284C4×Q8—28no—
285C4×Q8—44no—
286C4×Q8—44no—
287C4×Q8—44no—
288#117—28no—
289#117—44no—
290#117—44no—
291#117—44no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
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—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—81no—
350C2×C4⋊C4—81no—
351C2×C4⋊C4—81no—
352C2×C4⋊C4—81no—
353C2×C4⋊C4C22×C412yes—
354C2×C4⋊C4C22×C412yes—
355C2×C4⋊C4C22×C412yes—
356C2×C4⋊C4C2×D412yes—
357C2×C4⋊C4C2×D412yes—
358C2×C4⋊C4C2×D412yes—
359C2×C4⋊C4C2×Q812yes—
360C2×C4⋊C4#4112yes—
361C2×C4⋊C4#4112yes—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C22⋊C414yes—
376C2×C22⋊C4C22⋊C414yes—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42C22×C412yes—
395C2×C42C22×C412yes—
396C2×C42C2×D412yes—
397C2×C42C2×D412yes—
398C4⋊C8—44no—
399C4⋊C8—44no—
400#103—44no—
401#103—44no—
402#103—44no—
403#103—44no—
404C22⋊C8—44no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95C22⋊C414yes—
415#95C22⋊C414yes—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24C2×C22⋊C412yes—
429C24#12112yes—
430C24C22⋊Q812yes—
431C24C22×D411yescharacteristic
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8C2×C4⋊C414yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—48no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
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—84no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4C2×C22⋊C412yes—
572C22×C4C2×C22⋊C412yes—
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C4⋊C414yes—
577C22×C4#11714yes—
578C22×C4#12114yes—
579C22×C4#12112yes—
580C22×C4C22⋊Q814yes—
581C22×C4C22⋊Q812yes—
582C22×C4AGL(1,ℤ/8)12yes—
583C22×C4AGL(1,ℤ/8)12yes—
584C22×C4#13712yes—
585C22×C4#13712yes—
586C22×C4C23×C411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×Q811yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4H(5,𝔽2)11yescharacteristic
597C22×C4H(5,𝔽2)11yescharacteristic
598C22×C4H(5,𝔽2)11yescharacteristic
599C22×C42−1+411yescharacteristic
600M16—416no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—216no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—48no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—84no—
660C4⋊C4—84no—
661C4⋊C4—84no—
662C4⋊C4—84no—
663C4⋊C4C2×C4⋊C414yes—
664C4⋊C4C4×D414yes—
665C22⋊C4—216no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—48no—
679C42—48no—
680C42—48no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23#38014yes—
716C23C22×C22⋊C411yescharacteristic
717C23C2×#12111yescharacteristic
718C23C2×C22⋊Q811yescharacteristic
719C23D4211yescharacteristic
720C23#54611yescharacteristic
721C23#54611yescharacteristic
722C23#54711yescharacteristic
723C23C2×AGL(1,ℤ/8)11yescharacteristic
724C23C2×AGL(1,ℤ/8)11yescharacteristic
725C23C2×#13711yescharacteristic
726C23C2×#13711yescharacteristic
727C23#57711yescharacteristic
728C23#57711yescharacteristic
729C23#57811yescharacteristic
730C23#57811yescharacteristic
731Q8—24no—
732Q8—24no—
733Q8—42no—
734Q8—42no—
735Q8—42no—
736Q8—42no—
737Q8—42no—
738Q8—42no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—816no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4#38014yes—
837C2×C4#41714yes—
838C2×C4#41714yes—
839C2×C4C22×C4⋊C411yescharacteristic
840C2×C4C2×#11711yescharacteristic
841C2×C4C2×C4×D411yescharacteristic
842C2×C4C4×#4111yescharacteristic
843C2×C4#51811yescharacteristic
844C2×C4#52011yescharacteristic
845C2×C4C2×#12111yescharacteristic
846C2×C4C2×C22⋊Q811yescharacteristic
847C2×C4#52511yescharacteristic
848C2×C4#52511yescharacteristic
849C2×C4#52911yescharacteristic
850C2×C4#52911yescharacteristic
851C2×C4#53811yescharacteristic
852C2×C4#53811yescharacteristic
853C2×C4#53911yescharacteristic
854C2×C4#53911yescharacteristic
855C2×C4D4211yescharacteristic
856C2×C4D4211yescharacteristic
857C2×C4#54611yescharacteristic
858C2×C4#54611yescharacteristic
859C2×C4#54611yescharacteristic
860C2×C4#54611yescharacteristic
861C2×C4#54711yescharacteristic
862C2×C4#54711yescharacteristic
863C2×C4D4×Q811yescharacteristic
864C2×C4#55411yescharacteristic
865C2×C4#55411yescharacteristic
866C2×C4#55411yescharacteristic
867C8—42no—
868C8—42no—
869C8—81no—
870C8—81no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22C2×#38011yescharacteristic
887C22D4×C22⋊C411yescharacteristic
888C22#233911yescharacteristic
889C22#242411yescharacteristic
890C22#242511yescharacteristic
891C22#244911yescharacteristic
892C22#245011yescharacteristic
893C22C2×#41711yescharacteristic
894C22C2×#41711yescharacteristic
895C22#289811yescharacteristic
896C22#289811yescharacteristic
897C22#303811yescharacteristic
898C22#303911yescharacteristic
899C22#304311yescharacteristic
900C22#304411yescharacteristic
901C22#307911yescharacteristic
902C22#307911yescharacteristic
903C22#308211yescharacteristic
904C22#308211yescharacteristic
905C22#326511yescharacteristic
906C22#327011yescharacteristic
907C22#327211yescharacteristic
908C22#327611yescharacteristic
909C22#330811yescharacteristic
910C22#331011yescharacteristic
911C22#331211yescharacteristic
912C22#331611yescharacteristic
913C22#332411yescharacteristic
914C22#332811yescharacteristic
915C22#333011yescharacteristic
916C22#333111yescharacteristic
917C22#334311yescharacteristic
918C22#334411yescharacteristic
919C22#335311yescharacteristic
920C22#335611yescharacteristic
921C4—24no—
922C4—24no—
923C4—24no—
924C4—44no—
925C4—42no—
926C4—44no—
927C4—44no—
928C4—42no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—161no—
933C4—161no—
934C4#229011yescharacteristic
935C4#231811yescharacteristic
936C4D4×C4⋊C411yescharacteristic
937C4#234911yescharacteristic
938C4#242411yescharacteristic
939C4#242511yescharacteristic
940C4#244911yescharacteristic
941C4#245011yescharacteristic
942C2—44no—
943C2#1389911yescharacteristic
944C2#2064811yescharacteristic
945C2#2065111yescharacteristic
946C2#2242111yescharacteristic
947C2#2243111yescharacteristic
948C2#2249111yescharacteristic
949C2#2250411yescharacteristic
950C2#2509311yescharacteristic
951C2#2509511yescharacteristic
952C2#2521711yescharacteristic
953C2#2521911yescharacteristic
954C2#2635311yescharacteristic
955C2#2635511yescharacteristic
956C2#2642911yescharacteristic
957C2#2643111yescharacteristic
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
5. C2×#1803C2semidirect
8. #11227C2semidirect
9. #11207C2semidirect
10. #11077C2semidirect
11. #11050C2semidirect
12. #10849C2semidirect
13. #10806C2semidirect
14. #10789C2semidirect
29. #2362C4semidirect
91. C2×C4×Q8C2×C4semidirect
151. #391C2×C4semidirect
153. #389C2×C4semidirect
167. C4×C4⋊C4C2×C4semidirect
283. C22⋊Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23622
C2×#18942
C2×#18722
C2×#18512
C2×#18032
C2×#17362
#138802
#112272
#112072
#110772
#110502
#108492
#108062
#107892
#107312