Finite Group Databasebeta

← #674179

Subgroups — #674179

Order 512.

3274 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2580C212yesmaximal
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
4#15406C214yesmaximal, complemented
5#15378C214yesmaximal, complemented
6#15221C212yesmaximal, complemented
7#15202C212yesmaximal, complemented
8#15135C212yesmaximal, complemented
9#15125C212yesmaximal, complemented
10#14712C211yesmaximal, characteristic, complemented
11#14130C212yesmaximal, complemented
12#14018C212yesmaximal
13#13911C211yesmaximal, characteristic, complemented
14#13910C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic
16#13880C212yesmaximal, complemented
17C4×#390C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4×Q8C2212yes—
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#2580—216no—
24C2×#399C2214yes—
25C2×#393C2214yes—
26D4×C4⋊C4—28no—
27C4×C4⋊Q8—28no—
28C2×#391C2212yes—
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2212yes—
34C2×#389C2211yescharacteristic
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#385C2214yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#385C2214yes—
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#384C2212yes—
49C2×#382C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C43C2211yescharacteristic
60#1446C2214yes—
61#1445C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1444C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1437C2212yes—
74#1437C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85C22⋊#95C2214yes—
86C23×Q8C2312yes—
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2314yes—
90C2×C4⋊Q8—24no—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—24no—
93C2×C4×Q8—28no—
94C2×C4×Q8—28no—
95C2×C4×Q8—44no—
96C2×C4×D4—28no—
97C2×C4×D4—24no—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C2×C4×D4—44no—
101C2×C4×D4Q818yescomplemented
102C22×C4⋊C4—28no—
103C22×C4⋊C4—44no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C42C2312yes—
136C22×C42C2312yes—
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145#399—216no—
146#393—216no—
147#391—28no—
148#390—28no—
149#390D418yes—
150#390Q818yescomplemented
151#389—24no—
152#389—24no—
153#389—28no—
154#389—28no—
155#389—28no—
156#389—28no—
157#389—44no—
158#389—44no—
159#389—44no—
160#385—216no—
161#385—216no—
162#385—216no—
163#385—48no—
164#384—24no—
165#384—24no—
166#384—24no—
167#384—44no—
168#382—28no—
169#380—28no—
170#380—28no—
171#380—44no—
172C4×C4⋊C4—28no—
173C4×C4⋊C4—24no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4D418yes—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—44no—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C43—24no—
200C25C2412yes—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—42no—
207C22×Q8—42no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4C2×D414yes—
213C22×D4C2×Q814yes—
214C22×D4C2×Q814yes—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—28no—
222C23×C4—28no—
223C23×C4—44no—
224C23×C4—44no—
225C23×C4—44no—
226C23×C4—44no—
227C23×C4—44no—
228C23×C4C2×Q818yes—
229C23×C4C2412yes—
230C23×C4C2414yes—
231C23×C4C2414yes—
232C23×C4C2411yescharacteristic
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2411yescharacteristic
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242C23×C4C2411yescharacteristic
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C4⋊Q8—232no—
246C4×Q8—432no—
247C4×D4—232no—
248C4×D4—432no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—432no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4C2×D414yes—
313C2×C4⋊C4C2×Q814yes—
314C2×C4⋊C4C2×Q814yes—
315C2×C4⋊C4#4114yes—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4C2×D418yes—
336C2×C22⋊C4C2×D418yes—
337C2×C22⋊C4C2×Q818yes—
338C2×C22⋊C4C2×Q818yes—
339C2×C22⋊C4C2×Q818yes—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—41no—
362C2×C42—41no—
363C2×C42C2×D418yes—
364C2×C42C2×D414yes—
365C2×C42C2×D414yes—
366C2×C42C2×Q814yes—
367C2×C42C2×Q814yes—
368C2×C42#4114yes—
369C2×C42#4114yes—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—44no—
384#95—42no—
385#95—42no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95C2×D418yes—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24C22×D414yes—
404C24C22×Q814yes—
405C24C22×Q814yes—
406C24C2511yescharacteristic
407C2×Q8—216no—
408C2×Q8—48no—
409C2×Q8—48no—
410C2×Q8—48no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—48no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4C4⋊Q8116yescomplemented
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—216no—
482C22×C4—216no—
483C22×C4—216no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—416no—
506C22×C4—416no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—88no—
512C22×C4—88no—
513C22×C4—88no—
514C22×C4—88no—
515C22×C4—88no—
516C22×C4C22×D414yes—
517C22×C4C22×D414yes—
518C22×C4C22×D414yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×Q812yes—
526C22×C4C22×Q814yes—
527C22×C4C22×Q814yes—
528C22×C4C22×Q812yes—
529C22×C4C22×Q812yes—
530C22×C4C22×Q812yes—
531C22×C4C22×Q812yes—
532C22×C4C22×Q812yes—
533C22×C4C2×#4114yes—
534C22×C4C2×#4112yes—
535C22×C4C2×#4112yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C42−1+412yes—
546C22×C42−1+412yes—
547C4⋊C4—216no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—416no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—84no—
566C4⋊C4—88no—
567C4⋊C4—88no—
568C4⋊C4—88no—
569C22⋊C4—216no—
570C22⋊C4—216no—
571C22⋊C4—216no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—416no—
575C22⋊C4—416no—
576C22⋊C4—88no—
577C42—28no—
578C42—216no—
579C42—28no—
580C42—28no—
581C42—44no—
582C42—44no—
583C42—44no—
584C42—48no—
585C42—48no—
586C42C22⋊Q8116yes—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23C2×C4⋊Q818yes—
622C23C23×D411yescharacteristic
623C23C23×D411yescharacteristic
624C23C23×Q811yescharacteristic
625C23C23×Q811yescharacteristic
626C23C22×#4111yescharacteristic
627C23C22×#4111yescharacteristic
628C23C22×#4111yescharacteristic
629C23C2×H(5,𝔽2)11yescharacteristic
630C23C2×H(5,𝔽2)11yescharacteristic
631C23C2×H(5,𝔽2)11yescharacteristic
632C23C2×H(5,𝔽2)11yescharacteristic
633C23C2×2−1+411yescharacteristic
634C23C2×2−1+411yescharacteristic
635C23#58511yescharacteristic
636C23#58511yescharacteristic
637Q8—432no—
638D4—232no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—432no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—832no—
736C2×C4C2×C22⋊Q814yes—
737C2×C4C2×C22⋊Q814yes—
738C2×C4C2×C22⋊Q814yes—
739C2×C4#52514yes—
740C2×C4C2×C4⋊Q814yes—
741C2×C4#53514yes—
742C2×C4#54414yes—
743C2×C4D4214yes—
744C2×C4#54714yes—
745C2×C4#54714yes—
746C2×C4D4×Q814yes—
747C2×C4#55414yes—
748C2×C4#55414yes—
749C2×C4#55414yes—
750C2×C4#55414yes—
751C2×C4#55914yes—
752C2×C4#55914yes—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22C22×C22⋊Q811yescharacteristic
769C22C2×#52511yescharacteristic
770C22C22×C4⋊Q811yescharacteristic
771C22C2×#53511yescharacteristic
772C22C2×#54411yescharacteristic
773C22C2×D4211yescharacteristic
774C22C2×#54711yescharacteristic
775C22C2×#54711yescharacteristic
776C22C2×D4×Q811yescharacteristic
777C22D4×#4111yescharacteristic
778C22C2×#55411yescharacteristic
779C22C2×#55411yescharacteristic
780C22C2×#55411yescharacteristic
781C22C2×#55411yescharacteristic
782C22Q8×#4111yescharacteristic
783C22C2×#55911yescharacteristic
784C22C2×#55911yescharacteristic
785C22#348811yescharacteristic
786C22#348911yescharacteristic
787C22#349611yescharacteristic
788C22#349811yescharacteristic
789C22#350111yescharacteristic
790C22#350311yescharacteristic
791C22#350311yescharacteristic
792C22#350411yescharacteristic
793C22#350611yescharacteristic
794C22#350611yescharacteristic
795C22#350711yescharacteristic
796C22#350711yescharacteristic
797C22#352011yescharacteristic
798C22#352211yescharacteristic
799C22#354611yescharacteristic
800C22#354911yescharacteristic
801C22#355011yescharacteristic
802C22#355411yescharacteristic
803C4—24no—
804C4—24no—
805C4—24no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—82no—
815C4—84no—
816C4—84no—
817C4#244018yes—
818C4#258018yescomplemented
819C2—48no—
820C2C2×#244011yescharacteristic
821C2C2×#258011yescharacteristic
822C2#3551911yescharacteristic
823C2#3610011yescharacteristic
824C2#3618011yescharacteristic
825C2#3626111yescharacteristic
826C2#3654411yescharacteristic
827C2#3896411yescharacteristic
828C2#3934211yescharacteristic
829C2#3949811yescharacteristic
830C2#3959611yescharacteristic
831C2#5964111yescharacteristic
832C2#5964211yescharacteristic
833C2#5982711yescharacteristic
834C2#5986411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊Q8C2semidirect
4. #15406C2semidirect
5. #15378C2semidirect
6. #15221C2semidirect
7. #15202C2semidirect
8. #15135C2semidirect
9. #15125C2semidirect
10. #14712C2semidirect
11. #14130C2semidirect
13. #13911C2semidirect
14. #13910C2semidirect
16. #13880C2semidirect
101. C2×C4×D4Q8semidirect
150. #390Q8semidirect
420. C2×D4C4⋊Q8semidirect
818. C4#2580semidirect

Maximal subgroups

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

subgroupindex
C2×#25802
C2×D4×C4⋊C42
C2×C4×C4⋊Q82
#154062
#153782
#152212
#152022
#151352
#151252
#147122
#141302
#140182
#139112
#139102
#139062
#138802
C4×#3902