Finite Group Databasebeta

← #676290

Subgroups — #676290

Order 512.

2954 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2567C211yesmaximal, characteristic, complemented
3C2×#2369C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic
5#15852C214yesmaximal, complemented
6#15276C214yesmaximal
7#15194C212yesmaximal, complemented
8#15189C212yesmaximal, complemented
9#15131C212yesmaximal
10#15131C212yesmaximal
11#14151C212yesmaximal, complemented
12#14005C212yesmaximal, complemented
13#13997C212yesmaximal
14#13993C212yesmaximal
15#13926C211yesmaximal, characteristic, complemented
16#13910C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2857—28no—
24#2567—28no—
25C2×#396C2214yes—
26C2×#395C2214yes—
27#2369—28no—
28C4×C22⋊Q8—28no—
29C2×#391C2212yes—
30C2×#391C2211yescharacteristic
31C2×#391C2212yes—
32C2×#391C2214yes—
33C2×#391C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2214yes—
44C2×#387C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2212yes—
48C2×#384C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62#1445C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1443C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1437C2214yes—
76#1436C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8D418yes—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—44no—
99C2×C22⋊Q8—44no—
100C2×C22⋊Q8Q818yescomplemented
101C2×C4×Q8—24no—
102C2×C4×Q8—24no—
103C2×C4×Q8—24no—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142#396—48no—
143#395—216no—
144#391—28no—
145#391—28no—
146#391—24no—
147#391—216no—
148#391—44no—
149#389—28no—
150#389—28no—
151#389—28no—
152#389—28no—
153#389—28no—
154#389—24no—
155#389—28no—
156#389—28no—
157#389—48no—
158#389—44no—
159#387—28no—
160#385—28no—
161#384—28no—
162#384—28no—
163#384—24no—
164#380—28no—
165#380—28no—
166#380—24no—
167#380—24no—
168#380Q818yescomplemented
169C4×C4⋊C4—28no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4—24no—
173C4×C4⋊C4—28no—
174C4×C4⋊C4D418yes—
175C4×C22⋊C4—28no—
176C4×C22⋊C4—44no—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C25C2411yescharacteristic
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—24no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—24no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—42no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8C2×D418yes—
216C22×Q8C2×Q814yes—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—41no—
235C23×C4—41no—
236C23×C4C2×Q814yes—
237C23×C4C2×Q814yes—
238C23×C4C2412yes—
239C23×C4C2414yes—
240C23×C4C2412yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C4⋊Q8—232no—
255C22⋊Q8—232no—
256C22⋊Q8—432no—
257C4×Q8—416no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—44no—
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—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4C2×D418yes—
312C2×C4⋊C4C2×D418yes—
313C2×C4⋊C4C2×D414yes—
314C2×C4⋊C4C2×D414yes—
315C2×C4⋊C4C2×Q818yes—
316C2×C4⋊C4C2×Q814yes—
317C2×C4⋊C4C2×Q814yes—
318C2×C4⋊C4C2×Q814yes—
319C2×C4⋊C4#4114yes—
320C2×C4⋊C4#4114yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4C2×Q818yes—
335C2×C22⋊C4C2×Q818yes—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
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—28no—
357C2×C42—416no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42C2×D418yes—
361C2×C42C2×D414yes—
362C2×C42C2×D414yes—
363C2×C42#4114yes—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—28no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—24no—
377#95—28no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D418yes—
388#95C2×Q818yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24C22×Q812yes—
402C24C22×Q812yes—
403C24H(5,𝔽2)12yes—
404C24C2511yescharacteristic
405C2×Q8—216no—
406C2×Q8—28no—
407C2×Q8—28no—
408C2×Q8—28no—
409C2×Q8—48no—
410C2×Q8—48no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—84no—
416C2×Q8—84no—
417C2×Q8—84no—
418C2×Q8—84no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4C22×D414yes—
524C22×C4C22×D418yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D414yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×Q812yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q814yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q812yes—
537C22×C4C22×Q814yes—
538C22×C4C22×Q812yes—
539C22×C4C22×Q812yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C42−1+412yes—
550C22×C42−1+412yes—
551C22×C42−1+412yes—
552C4⋊C4—216no—
553C4⋊C4—216no—
554C4⋊C4—216no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—416no—
560C4⋊C4—48no—
561C4⋊C4—416no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—88no—
569C4⋊C4—88no—
570C4⋊C4—88no—
571C4⋊C4—88no—
572C4⋊C4C22⋊Q8116yescomplemented
573C22⋊C4—216no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—416no—
578C42—216no—
579C42—44no—
580C42—44no—
581C42—44no—
582C42—48no—
583C42—48no—
584C42—48no—
585C42—88no—
586C42#121116yes—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23Q8214yes—
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
632C23C2×2−1+411yescharacteristic
633C23C2×2−1+411yescharacteristic
634C23C2×2−1+411yescharacteristic
635C23#58511yescharacteristic
636C23#58511yescharacteristic
637Q8—416no—
638Q8—816no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4C2×#12114yes—
739C2×C4C2×#12114yes—
740C2×C4C2×#12114yes—
741C2×C4C2×C22⋊Q818yes—
742C2×C4C2×C22⋊Q814yes—
743C2×C4#53314yes—
744C2×C4#53714yes—
745C2×C4#54114yes—
746C2×C4#54714yes—
747C2×C4#54814yes—
748C2×C4D4×Q814yes—
749C2×C4D4×Q814yes—
750C2×C4D4×Q814yes—
751C2×C4#55014yes—
752C2×C4#55414yes—
753C2×C4#55614yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22C22×#12111yescharacteristic
770C22C22×C22⋊Q811yescharacteristic
771C22C2×#53311yescharacteristic
772C22C2×#53711yescharacteristic
773C22C2×#54111yescharacteristic
774C22C2×#54711yescharacteristic
775C22C2×#54811yescharacteristic
776C22C2×D4×Q811yescharacteristic
777C22C2×D4×Q811yescharacteristic
778C22C2×D4×Q811yescharacteristic
779C22C2×#55011yescharacteristic
780C22C2×#55411yescharacteristic
781C22C2×#55611yescharacteristic
782C22C2×Q8211yescharacteristic
783C22Q8×#4111yescharacteristic
784C22Q8×#4111yescharacteristic
785C22#348111yescharacteristic
786C22#348411yescharacteristic
787C22#348511yescharacteristic
788C22#348811yescharacteristic
789C22#348811yescharacteristic
790C22#349411yescharacteristic
791C22#349411yescharacteristic
792C22#350111yescharacteristic
793C22#350211yescharacteristic
794C22#350311yescharacteristic
795C22#350311yescharacteristic
796C22#351511yescharacteristic
797C22#351811yescharacteristic
798C22#351911yescharacteristic
799C22#352211yescharacteristic
800C22#354411yescharacteristic
801C22#354711yescharacteristic
802C22#354811yescharacteristic
803C22#355511yescharacteristic
804C4—28no—
805C4—24no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—42no—
810C4—44no—
811C4—44no—
812C4—44no—
813C4—42no—
814C4—48no—
815C4—82no—
816C4—84no—
817C4—82no—
818C4#242918yes—
819C4#253818yes—
820C2—44no—
821C2C2×#242911yescharacteristic
822C2C2×#253811yescharacteristic
823C2#3551411yescharacteristic
824C2#3627511yescharacteristic
825C2#3648011yescharacteristic
826C2Q8×C22⋊Q811yescharacteristic
827C2#3656411yescharacteristic
828C2#3892211yescharacteristic
829C2#3915711yescharacteristic
830C2#3959811yescharacteristic
831C2#3960711yescharacteristic
832C2#5905211yescharacteristic
833C2#5905711yescharacteristic
834C2#5908111yescharacteristic
835C2#5915111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2567C2semidirect
3. C2×#2369C2semidirect
5. #15852C2semidirect
7. #15194C2semidirect
8. #15189C2semidirect
11. #14151C2semidirect
12. #14005C2semidirect
15. #13926C2semidirect
16. #13910C2semidirect
100. C2×C22⋊Q8Q8semidirect
168. #380Q8semidirect
572. C4⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25672
C2×#23692
C2×C4×C22⋊Q82
#158522
#152762
#151942
#151892
#151312
#141512
#140052
#139972
#139932
#139262
#139102
C4×#3802