Finite Group Databasebeta

← #360187

Subgroups — #360187

Order 512.

1964 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#436C211yesmaximal, characteristic
2C22×#428C211yesmaximal, characteristic, complemented
3C2×#1809C211yesmaximal, characteristic, complemented
4C2×#1809C211yesmaximal, characteristic, complemented
5C2×#1809C211yesmaximal, characteristic, complemented
6#13872C211yesmaximal, characteristic
7#13871C211yesmaximal, characteristic
8#11232C211yesmaximal, characteristic, complemented
9#11231C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10862C211yesmaximal, characteristic, complemented
13#10861C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C2×#436—24no—
22C2×#436—24no—
23C2×#436C418yescomplemented
24C2×#428—24no—
25C2×#428—24no—
26C2×#428—24no—
27C22×#107C2211yescharacteristic
28C22×#107C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C2×#386—21no—
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44#1809—24no—
45#1809—24no—
46#1809—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57#1441—21no—
58#1440—21no—
59#1439—21no—
60#1438—21no—
61#1437—21no—
62#1436—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67C22⋊#95—21no—
68C23×D4D411yescharacteristic
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16C2×C414yes—
83C22×M16C2×C414yescomplemented
84C22×M16D414yes—
85C22×M16D414yes—
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4C2×C414yes—
95C2×C4×D4Q814yes—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—41no—
101C2×#117—41no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4D411yescharacteristic
126C22×C22⋊C4D411yescharacteristic
127C22×C42—21no—
128C22×C42C2311yescharacteristic
129#436—232no—
130#428—232no—
131C2×#107—22no—
132C2×#107—22no—
133C2×#107—22no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107—22no—
137C2×#107—22no—
138C2×#107—22no—
139C2×#107D414yescomplemented
140C2×#106—22no—
141C2×#106—22no—
142C2×#106—22no—
143C2×#106—22no—
144C2×#106—22no—
145C2×#106—22no—
146C2×#106—22no—
147C2×#106—22no—
148C2×#106D414yescomplemented
149C2×C4⋊C8—22no—
150C2×C4⋊C8—22no—
151C2×C4⋊C8C2×C414yescomplemented
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8C2×C414yes—
157C2×C22⋊C8C2×C414yescomplemented
158C2×C4×C8—22no—
159C2×C4×C8—22no—
160C2×C4×C8C2×C414yescomplemented
161#386—44no—
162#380—22no—
163#380—22no—
164#380—22no—
165#380—22no—
166#380—22no—
167#380—22no—
168#380—22no—
169#380—22no—
170#380—41no—
171#380—41no—
172#380—41no—
173#380—41no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188#340—22no—
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—41no—
195#340—41no—
196#340—41no—
197#340—41no—
198C25C2×D411yescharacteristic
199C25C2×D411yescharacteristic
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—41no—
205C22×D4—41no—
206C22×D4C4⋊C414yes—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
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—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4C22×C412yes—
243C23×C4C22×C412yes—
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D412yes—
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×Q812yes—
251C23×C4C2×Q812yes—
252C23×C4#4112yes—
253C23×C4#4112yes—
254C23×C4C2411yescharacteristic
255C2×M16—28no—
256C2×M16—28no—
257C2×M16—28no—
258C2×M16—28no—
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—28no—
263C2×M16—28no—
264C2×M16—44no—
265C2×M16—44no—
266C2×M16—44no—
267C2×M16—44no—
268C2×M16C22⋊C4116yescomplemented
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—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8C22×C412yes—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C22×C8#4112yes—
296C22×C8#4112yes—
297C4×D4—28no—
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—28no—
301#117—28no—
302#117—44no—
303#117—44no—
304#117—44no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—28no—
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—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—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
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—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4C4⋊C414yes—
359C2×C4⋊C4C2×D412yes—
360C2×C4⋊C4C2×D412yes—
361C2×C4⋊C4C2×D412yes—
362C2×C4⋊C4C2×D412yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
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⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4—81no—
388C2×C22⋊C4C4⋊C414yes—
389C2×C22⋊C4C4⋊C414yes—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42C22×C412yes—
398C2×C42C2×Q812yes—
399#107—28no—
400#107—28no—
401#107—44no—
402#106—28no—
403#106—28no—
404#106—44no—
405C4⋊C8—28no—
406C22⋊C8—28no—
407C22⋊C8—28no—
408C4×C8—28no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—81no—
420#95—81no—
421#95—81no—
422#95—81no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24C2×C4⋊C412yes—
450C24C2×C4⋊C412yes—
451C24#12112yes—
452C24#12112yes—
453C24C22×D411yescharacteristic
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
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—22no—
470C22×C4—22no—
471C22×C4—22no—
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—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
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—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—48no—
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—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—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4C2×C22⋊C414yes—
597C22×C4C2×C4⋊C412yes—
598C22×C4C2×C4⋊C412yes—
599C22×C4C2×C4⋊C412yes—
600C22×C4C2×C4⋊C412yes—
601C22×C4#11714yes—
602C22×C4#12112yes—
603C22×C4#12112yes—
604C22×C4C22⋊Q814yes—
605C22×C4C22⋊Q814yes—
606C22×C4AGL(1,ℤ/8)12yes—
607C22×C4#13712yes—
608C22×C4C23×C411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×Q811yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4H(5,𝔽2)11yescharacteristic
619C22×C4H(5,𝔽2)11yescharacteristic
620C22×C42−1+411yescharacteristic
621C22×C42−1+411yescharacteristic
622M16—232no—
623M16—416no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8C2×C22⋊C414yes—
645C2×C8C2×C22⋊C414yes—
646C2×C8C4×D414yes—
647C2×C8C4×D414yes—
648C2×C8#12014yes—
649C2×C8#12114yes—
650C2×C8#12114yes—
651C2×C8#12314yes—
652C4⋊C4—28no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—48no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—48no—
689C22⋊C4—84no—
690C22⋊C4—84no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—48no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
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—41no—
726C23—41no—
727C23—41no—
728C23—41no—
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—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23#38014yes—
770C23C22×C4⋊C411yescharacteristic
771C23C2×#12111yescharacteristic
772C23C2×#12111yescharacteristic
773C23D4211yescharacteristic
774C23D4211yescharacteristic
775C23#54711yescharacteristic
776C23#54711yescharacteristic
777C23C2×AGL(1,ℤ/8)11yescharacteristic
778C23C2×#13711yescharacteristic
779C23#57511yescharacteristic
780C23#57511yescharacteristic
781C23#57611yescharacteristic
782C23#57711yescharacteristic
783C23#57711yescharacteristic
784C23#57811yescharacteristic
785D4—416no—
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—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
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—816no—
841C2×C4—81no—
842C2×C4—81no—
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×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4#38014yes—
886C2×C4#42814yescomplemented
887C2×C4C22×C22⋊C411yescharacteristic
888C2×C4C2×#11711yescharacteristic
889C2×C4C2×C4×D411yescharacteristic
890C2×C4C2×C4×D411yescharacteristic
891C2×C4#52011yescharacteristic
892C2×C4#52011yescharacteristic
893C2×C4C2×#12011yescharacteristic
894C2×C4C2×#12111yescharacteristic
895C2×C4C2×#12111yescharacteristic
896C2×C4C2×C22⋊Q811yescharacteristic
897C2×C4C2×C22⋊Q811yescharacteristic
898C2×C4C2×#12311yescharacteristic
899C2×C4#53511yescharacteristic
900C2×C4#53611yescharacteristic
901C2×C4#53711yescharacteristic
902C2×C4#53711yescharacteristic
903C2×C4#54611yescharacteristic
904C2×C4#54611yescharacteristic
905C2×C4#54811yescharacteristic
906C2×C4#54811yescharacteristic
907C2×C4D4×Q811yescharacteristic
908C2×C4D4×Q811yescharacteristic
909C2×C4#55211yescharacteristic
910C2×C4#55211yescharacteristic
911C2×C4#55311yescharacteristic
912C2×C4#55311yescharacteristic
913C2×C4#55411yescharacteristic
914C2×C4#55411yescharacteristic
915C8—24no—
916C8—42no—
917C8—42no—
918C8#38618yescomplemented
919C22—24no—
920C22—24no—
921C22—24no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22C2×#38011yescharacteristic
950C22D4×C4⋊C411yescharacteristic
951C22D4×C4⋊C411yescharacteristic
952C22#240811yescharacteristic
953C22#241611yescharacteristic
954C22#241611yescharacteristic
955C22#248611yescharacteristic
956C22C2×#42811yescharacteristic
957C22#291111yescharacteristic
958C22#291211yescharacteristic
959C22#291311yescharacteristic
960C22#305511yescharacteristic
961C22#305511yescharacteristic
962C22#305611yescharacteristic
963C22#305611yescharacteristic
964C22#306211yescharacteristic
965C22#306211yescharacteristic
966C22#306311yescharacteristic
967C22#306311yescharacteristic
968C22#327211yescharacteristic
969C22#327311yescharacteristic
970C22#327411yescharacteristic
971C22#327511yescharacteristic
972C22#327511yescharacteristic
973C22#327611yescharacteristic
974C22#327711yescharacteristic
975C22#327811yescharacteristic
976C22#335111yescharacteristic
977C22#335111yescharacteristic
978C22#335211yescharacteristic
979C22#335311yescharacteristic
980C22#335411yescharacteristic
981C22#335511yescharacteristic
982C22#335611yescharacteristic
983C22#335711yescharacteristic
984C4—24no—
985C4—24no—
986C4—42no—
987C4—42no—
988C4—82no—
989C4—82no—
990C4—82no—
991C4—82no—
992C4—161no—
993C4—161no—
994C4—161no—
995C4—161no—
996C4C2×#38611yescharacteristic
997C4#231111yescharacteristic
998C4#235211yescharacteristic
999C4#235211yescharacteristic
1000C4#240911yescharacteristic
1001C4#241711yescharacteristic
1002C4#241711yescharacteristic
1003C4#248711yescharacteristic
1004C2—44no—
1005C2—82no—
1006C2#1387211yescharacteristic
1007C2#2066111yescharacteristic
1008C2#2066411yescharacteristic
1009C2#2266311yescharacteristic
1010C2#2266411yescharacteristic
1011C2#2266511yescharacteristic
1012C2#2266611yescharacteristic
1013C2#2427611yescharacteristic
1014C2#2427711yescharacteristic
1015C2#2479211yescharacteristic
1016C2#2479311yescharacteristic
1017C2#2479411yescharacteristic
1018C2#2479511yescharacteristic
1019C2#2767011yescharacteristic
1020C2#2767111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#428C2semidirect
3. C2×#1809C2semidirect
4. C2×#1809C2semidirect
5. C2×#1809C2semidirect
8. #11232C2semidirect
9. #11231C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10862C2semidirect
13. #10861C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
23. C2×#436C4semidirect
83. C22×M16C2×C4semidirect
139. C2×#107D4semidirect
148. C2×#106D4semidirect
151. C2×C4⋊C8C2×C4semidirect
157. C2×C22⋊C8C2×C4semidirect
160. C2×C4×C8C2×C4semidirect
268. C2×M16C22⋊C4semidirect
886. C2×C4#428semidirect
918. C8#386semidirect

Maximal subgroups

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

subgroupindex
C22×#4362
C22×#4282
C2×#18092
#138722
#138712
#112322
#112312
#110962
#110952
#108622
#108612
#107312
#107302