Finite Group Databasebeta

← #418674

Subgroups — #418674

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2584C211yesmaximal, characteristic, complemented
3C2×#2059C211yesmaximal, characteristic, complemented
4C2×#2025C211yesmaximal, characteristic
5C2×#1864C211yesmaximal, characteristic
6C2×#1862C211yesmaximal, characteristic
7#11380C211yesmaximal, characteristic, complemented
8#11328C211yesmaximal, characteristic, complemented
9#11327C211yesmaximal, characteristic, complemented
10#11207C211yesmaximal, characteristic, complemented
11#11207C211yesmaximal, characteristic, complemented
12#11066C211yesmaximal, characteristic
13#11066C211yesmaximal, characteristic
14#10931C211yesmaximal, characteristic
15#10885C211yesmaximal, characteristic, complemented
16C22×#125C2211yescharacteristic
17C22×C22⋊Q8—21no—
18C22×C4×Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26#2584—24no—
27#2584—24no—
28#2538—24no—
29#2538—24no—
30C2×#398—21no—
31C2×#396—21no—
32C2×#396—21no—
33C2×#395—21no—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#389—21no—
37C2×#389—21no—
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#380—21no—
46C2×C4×C4⋊C4C2211yescharacteristic
47#2059—24no—
48#2025—24no—
49#1864—24no—
50#1862—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C23×Q8D411yescharacteristic
68C23×D4C2311yescharacteristic
69C24×C4—21no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#125—22no—
75C2×#125—22no—
76C2×#125—22no—
77C2×#125—22no—
78C2×#125—41no—
79C2×#125—41no—
80C2×C22⋊Q8—28no—
81C2×C22⋊Q8—44no—
82C2×C22⋊Q8—44no—
83C2×C4×Q8—22no—
84C2×C4×Q8—22no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—41no—
88C2×C4×Q8—41no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4—41no—
94C2×C4×D4—41no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4D411yescharacteristic
106C22×C4⋊C4D411yescharacteristic
107C22×C4⋊C4D411yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C42—21no—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C2×#107—22no—
125C2×#107—22no—
126C2×#107—41no—
127C2×#106—22no—
128C2×#106—22no—
129C2×#106—41no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—41no—
139C2×#102—41no—
140C2×#102Q814yescomplemented
141C2×#102Q814yescomplemented
142#398—28no—
143#396—28no—
144#396—28no—
145#395—28no—
146#390—22no—
147#390—22no—
148#390—22no—
149#390D414yes—
150#389—28no—
151#389—28no—
152#389—22no—
153#389—22no—
154#389—22no—
155#389—22no—
156#389—22no—
157#389—22no—
158#389—22no—
159#389—22no—
160#389—22no—
161#389D414yes—
162#389D414yes—
163#389D414yes—
164#384—22no—
165#384—22no—
166#380—28no—
167C4×C4⋊C4—22no—
168C4×C4⋊C4—22no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#336—22no—
187#336—22no—
188#336—22no—
189#336—22no—
190#336—41no—
191#336—41no—
192C25—21no—
193C22×Q8—22no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—41no—
199C22×Q8—41no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C2×D412yes—
212C22×D4C2×Q812yes—
213C22×D4C2×Q812yes—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—24no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
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×C8C2×Q812yes—
262C22×C8C2×Q812yes—
263#125—44no—
264#125—44no—
265#125—44no—
266#125—44no—
267C22⋊Q8—432no—
268C4×Q8—44no—
269C4×Q8—44no—
270C4×Q8—44no—
271C4×Q8—44no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C4×D4—44no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
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—21no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—81no—
341C2×C4⋊C4—81no—
342C2×C4⋊C4—81no—
343C2×C4⋊C4—81no—
344C2×C4⋊C4—81no—
345C2×C4⋊C4—81no—
346C2×C4⋊C4C2×D412yes—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D412yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4C2×Q812yes—
354C2×C4⋊C4C2×Q812yes—
355C2×C4⋊C4#4112yes—
356C2×C4⋊C4#4112yes—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
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—21no—
386C2×C42—24no—
387C2×C42—81no—
388C2×C42—81no—
389C2×C42C2×D412yes—
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393#107—44no—
394#106—44no—
395#102—28no—
396#102—28no—
397#102—44no—
398#102—44no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24C22×D411yescharacteristic
422C2×Q8—28no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4C4⋊Q814yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
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—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
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—41no—
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—84no—
545C22×C4—84no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4#12012yes—
549C22×C4#12012yes—
550C22×C4#12012yes—
551C22×C4#12012yes—
552C22×C4#13512yes—
553C22×C4AGL(1,ℤ/8)12yes—
554C22×C4AGL(1,ℤ/8)12yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×Q811yescharacteristic
560C22×C4C22×Q811yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4H(5,𝔽2)11yescharacteristic
564C22×C4H(5,𝔽2)11yescharacteristic
565C22×C42−1+411yescharacteristic
566C22×C42−1+411yescharacteristic
567C22×C42−1+411yescharacteristic
568C22×C42−1+411yescharacteristic
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—48no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—84no—
636C4⋊C4C22⋊Q814yescomplemented
637C4⋊C4C22⋊Q814yescomplemented
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—84no—
656C23—24no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23C2×#12011yescharacteristic
692C23C2×#12011yescharacteristic
693C23#53411yescharacteristic
694C23#54811yescharacteristic
695C23#54811yescharacteristic
696C23D4×Q811yescharacteristic
697C23D4×Q811yescharacteristic
698C23C2×#13511yescharacteristic
699C23C2×AGL(1,ℤ/8)11yescharacteristic
700C23C2×AGL(1,ℤ/8)11yescharacteristic
701C23#57511yescharacteristic
702C23#57611yescharacteristic
703C23#57711yescharacteristic
704C23#57711yescharacteristic
705C23#57811yescharacteristic
706Q8—416no—
707D4—24no—
708D4—24no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—816no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4#44914yes—
807C2×C4C2×C22⋊Q811yescharacteristic
808C2×C4C2×C22⋊Q811yescharacteristic
809C2×C4C2×C4⋊Q811yescharacteristic
810C2×C4#53211yescharacteristic
811C2×C4#53611yescharacteristic
812C2×C4#53611yescharacteristic
813C2×C4#53611yescharacteristic
814C2×C4#53611yescharacteristic
815C2×C4#54211yescharacteristic
816C2×C4#54211yescharacteristic
817C2×C4#54411yescharacteristic
818C2×C4#54411yescharacteristic
819C2×C4D4211yescharacteristic
820C2×C4D4211yescharacteristic
821C2×C4D4211yescharacteristic
822C2×C4D4211yescharacteristic
823C2×C4#54711yescharacteristic
824C2×C4#54711yescharacteristic
825C2×C4#54811yescharacteristic
826C2×C4#54811yescharacteristic
827C2×C4D4×Q811yescharacteristic
828C2×C4D4×Q811yescharacteristic
829C2×C4D4×Q811yescharacteristic
830C2×C4D4×Q811yescharacteristic
831C2×C4#55411yescharacteristic
832C2×C4#55411yescharacteristic
833C2×C4#56311yescharacteristic
834C2×C4#56311yescharacteristic
835C8—42no—
836C8—42no—
837C8—81no—
838C8—81no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22#240311yescharacteristic
855C22#240911yescharacteristic
856C22#240911yescharacteristic
857C22#243211yescharacteristic
858C22#243411yescharacteristic
859C22#272911yescharacteristic
860C22#272911yescharacteristic
861C22C2×#44911yescharacteristic
862C22#300211yescharacteristic
863C22#300311yescharacteristic
864C22#300611yescharacteristic
865C22#301211yescharacteristic
866C22#301211yescharacteristic
867C22#301311yescharacteristic
868C22#301311yescharacteristic
869C22#318811yescharacteristic
870C22#319411yescharacteristic
871C22#320311yescharacteristic
872C22#320411yescharacteristic
873C22#336011yescharacteristic
874C22#336411yescharacteristic
875C22#336611yescharacteristic
876C22#336611yescharacteristic
877C22#336811yescharacteristic
878C22#336811yescharacteristic
879C22#337611yescharacteristic
880C22#337711yescharacteristic
881C22#338011yescharacteristic
882C22#338111yescharacteristic
883C22#338411yescharacteristic
884C22#338411yescharacteristic
885C22#338611yescharacteristic
886C22#338611yescharacteristic
887C22#338811yescharacteristic
888C22#338911yescharacteristic
889C4—24no—
890C4—44no—
891C4—44no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—82no—
902C4#244011yescharacteristic
903C4#244011yescharacteristic
904C4#245211yescharacteristic
905C4#245211yescharacteristic
906C4#267411yescharacteristic
907C4#267411yescharacteristic
908C4#267711yescharacteristic
909C4#267711yescharacteristic
910C2—84no—
911C2#1526511yescharacteristic
912C2#2392011yescharacteristic
913C2#2392911yescharacteristic
914C2#2432711yescharacteristic
915C2#2432811yescharacteristic
916C2#2434611yescharacteristic
917C2#2434711yescharacteristic
918C2#2565411yescharacteristic
919C2#2565511yescharacteristic
920C2#2584311yescharacteristic
921C2#2584411yescharacteristic
922C2#3257211yescharacteristic
923C2#3257611yescharacteristic
924C2#3258111yescharacteristic
925C2#3258511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2584C2semidirect
3. C2×#2059C2semidirect
7. #11380C2semidirect
8. #11328C2semidirect
9. #11327C2semidirect
10. #11207C2semidirect
11. #11207C2semidirect
15. #10885C2semidirect
140. C2×#102Q8semidirect
141. C2×#102Q8semidirect
636. C4⋊C4C22⋊Q8semidirect
637. C4⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#25842
C2×#20592
C2×#20252
C2×#18642
C2×#18622
#113802
#113282
#113272
#112072
#110662
#109312
#108852