Finite Group Databasebeta

← #664150

Subgroups — #664150

Order 512.

3520 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2487C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic
5C2×C4×#123C211yesmaximal, characteristic
6C22×#389C211yesmaximal, characteristic, complemented
7#15804C214yesmaximal, complemented
8#15765C214yesmaximal, complemented
9#15193C212yesmaximal, complemented
10#15135C212yesmaximal, complemented
11#14936C212yesmaximal, complemented
12#14777C212yesmaximal
13#13997C212yesmaximal, complemented
14#13996C212yesmaximal
15#13910C212yesmaximal, complemented
16#13880C212yesmaximal, complemented
17C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
18C22×#123C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26#2855—28no—
27#2502—28no—
28#2487—28no—
29#2417—28no—
30C2×#400C2212yes—
31C2×#399C2212yes—
32C2×#399C2214yes—
33C2×#398C2212yes—
34C2×#398C2214yes—
35C2×#396C2212yes—
36C4×#123—28no—
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2212yes—
40C2×#389—28no—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#389C2214yes—
47C2×#388C2212yes—
48C2×#387C2214yes—
49C2×#387C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2211yescharacteristic
53C2×#385C2212yes—
54C2×#385C2211yescharacteristic
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×#384C2212yes—
59C2×#384C2214yes—
60C2×#381C2212yes—
61C2×#381C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×C4×C4⋊C4C2212yes—
67C2×C4×C4⋊C4C2212yes—
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2212yes—
70C2×C4×C22⋊C4C2211yescharacteristic
71C22×#95C2212yes—
72#1445C2214yes—
73#1445C2214yes—
74#1445C2214yes—
75#1445C2214yes—
76#1445C2214yes—
77#1444C2214yes—
78#1444C2214yes—
79#1444C2214yes—
80#1444C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2214yes—
84#1436C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87C4⋊#95C2214yes—
88C22⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C2×#123—24no—
98C2×#123—24no—
99C2×#123Q818yescomplemented
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C22×C4⋊C4—28no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—48no—
114C22×C4⋊C4D418yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2314yes—
152C22×C42C2312yes—
153#400—28no—
154#399—28no—
155#399—48no—
156#398—28no—
157#398—216no—
158#396—28no—
159#391—28no—
160#391—24no—
161#391—28no—
162#389—28no—
163#389—24no—
164#389—28no—
165#389—28no—
166#389—216no—
167#389—28no—
168#388—28no—
169#387—216no—
170#387—28no—
171#386—28no—
172#386—28no—
173#386—24no—
174#385—28no—
175#385—28no—
176#385—28no—
177#385—28no—
178#385—24no—
179#384—28no—
180#384—48no—
181#381—28no—
182#381—24no—
183#380—28no—
184#380—24no—
185#380—28no—
186#380D418yes—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—28no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4D418yes—
192C2×#95—28no—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2411yescharacteristic
216C25C2411yescharacteristic
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4C2×Q814yes—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—28no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—44no—
253C23×C4—42no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4C2×D418yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×Q814yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2411yescharacteristic
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276#123—232no—
277C22⋊Q8—416no—
278C22⋊Q8—416no—
279C4×D4—416no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—232no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—416no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D418yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×Q818yes—
334C2×C4⋊C4#4118yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×D414yes—
361C2×C22⋊C4C2×D418yes—
362C2×C22⋊C4C2×D414yes—
363C2×C22⋊C4C2×Q818yes—
364C2×C22⋊C4C2×Q814yes—
365C2×C22⋊C4#4114yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—28no—
378C2×C42—28no—
379C2×C42—44no—
380C2×C42—416no—
381C2×C42C2×D418yes—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—44no—
402#95C2×D418yes—
403#95C2×D418yes—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24C22×D412yes—
419C24C22×D412yes—
420C24C22×D412yes—
421C24C22×Q812yes—
422C24C22×Q812yes—
423C24C2×#4112yes—
424C242−1+412yes—
425C242−1+412yes—
426C24C2511yescharacteristic
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—48no—
431C2×Q8—48no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—216no—
451C22×C4—216no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—216no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—216no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—48no—
520C22×C4—416no—
521C22×C4—416no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4#127116yes—
541C22×C4C22×D414yes—
542C22×C4C22×D418yes—
543C22×C4C22×D414yes—
544C22×C4C22×D414yes—
545C22×C4C22×D414yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×Q814yes—
553C22×C4C22×Q812yes—
554C22×C4C22×Q814yes—
555C22×C4C2×#4114yes—
556C22×C4C2×#4118yes—
557C22×C4C2×#4114yes—
558C22×C4H(5,𝔽2)14yes—
559C22×C42−1+414yes—
560C4⋊C4—216no—
561C4⋊C4—216no—
562C4⋊C4—28no—
563C4⋊C4—216no—
564C4⋊C4—48no—
565C4⋊C4—416no—
566C4⋊C4—416no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—84no—
575C4⋊C4—88no—
576C4⋊C4—88no—
577C4⋊C4—88no—
578C4⋊C4#123116yescomplemented
579C22⋊C4—28no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—48no—
583C22⋊C4—44no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—44no—
587C22⋊C4—84no—
588C22⋊C4—88no—
589C22⋊C4C22⋊Q8116yescomplemented
590C42—216no—
591C42—416no—
592C42—48no—
593C42—48no—
594C42—44no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23C2×C22⋊Q814yes—
635C23C2×#12714yes—
636C23#53614yes—
637C23#54714yes—
638C23#54714yes—
639C23D4×Q814yes—
640C23D4×Q814yes—
641C23C23×D411yescharacteristic
642C23C23×D411yescharacteristic
643C23C23×D411yescharacteristic
644C23C23×Q811yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4112yes—
647C23C2×H(5,𝔽2)12yes—
648C23C2×2−1+412yes—
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+411yescharacteristic
651C23#58512yes—
652Q8—88no—
653D4—416no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—28no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—28no—
668C2×C4—232no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—432no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—816no—
740C2×C4—88no—
741C2×C4C2×C22⋊Q818yes—
742C2×C4C2×#12318yes—
743C2×C4C2×#12314yes—
744C2×C4C2×#12714yes—
745C2×C4C2×#12714yes—
746C2×C4#53614yes—
747C2×C4#54718yes—
748C2×C4#54718yes—
749C22—24no—
750C22—24no—
751C22—28no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—24no—
756C22—24no—
757C22—28no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—81no—
765C22—81no—
766C22—82no—
767C22—82no—
768C22—81no—
769C22—81no—
770C22#254218yes—
771C22C22×C22⋊Q811yescharacteristic
772C22C22×#12311yescharacteristic
773C22C22×#12711yescharacteristic
774C22C2×#53611yescharacteristic
775C22C2×#53611yescharacteristic
776C22C2×#54711yescharacteristic
777C22C2×#54711yescharacteristic
778C22C2×#54712yes—
779C22C2×#54712yes—
780C22C2×D4×Q811yescharacteristic
781C22C2×D4×Q811yescharacteristic
782C22Q8×#4112yes—
783C22#348112yes—
784C22#348411yescharacteristic
785C22#348711yescharacteristic
786C22#348812yes—
787C22#348812yes—
788C22#350312yes—
789C22#351512yes—
790C22#351612yes—
791C22#352012yes—
792C22#355212yes—
793C22#356312yes—
794C4—28no—
795C4—28no—
796C4—24no—
797C4—44no—
798C4—42no—
799C4—44no—
800C4—44no—
801C4—48no—
802C4—44no—
803C4—81no—
804C4—82no—
805C4—81no—
806C4—82no—
807C4—84no—
808C4#250118yes—
809C2—28no—
810C2—82no—
811C2C2×#250111yescharacteristic
812C2C2×#254211yescharacteristic
813C2#3556511yescharacteristic
814C2#3623711yescharacteristic
815C2#3627512yes—
816C2Q8×#12311yescharacteristic
817C2#3804012yes—
818C2#3891911yescharacteristic
819C2#3959211yescharacteristic
820C2#5906212yes—
821C2#5911312yes—
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
1. C2×#2855C2semidirect
2. C2×#2502C2semidirect
6. C22×#389C2semidirect
7. #15804C2semidirect
8. #15765C2semidirect
9. #15193C2semidirect
10. #15135C2semidirect
11. #14936C2semidirect
13. #13997C2semidirect
15. #13910C2semidirect
16. #13880C2semidirect
17. C22⋊C4×C4⋊C4C2semidirect
99. C2×#123Q8semidirect
578. C4⋊C4#123semidirect
589. C22⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×#25022
C2×#24872
C2×#24172
C2×C4×#1232
C22×#3892
#158042
#157652
#151932
#151352
#149362
#147772
#139972
#139962
#139102
#138802
C22⋊C4×C4⋊C42