Finite Group Databasebeta

← #917939

Subgroups — #917939

Order 512.

3952 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2417C212yesmaximal, complemented
3C2×#2616C212yesmaximal, complemented
4C2×#2388C211yesmaximal, characteristic
5#17103C214yesmaximal, complemented
6#16522C212yesmaximal, complemented
7#16514C212yesmaximal, complemented
8#16338C212yesmaximal, complemented
9#16303C212yesmaximal, complemented
10#15307C214yesmaximal, complemented
11#15179C212yesmaximal, complemented
12#15178C212yesmaximal, complemented
13#15177C212yesmaximal, complemented
14#13994C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2616—216no—
26#2542—28no—
27#2417—216no—
28C2×#399C2212yes—
29C2×#399C2212yes—
30C2×#398C2214yes—
31C2×#396C2214yes—
32#2388—28no—
33C2×#395C2214yes—
34C2×#395C2211yescharacteristic
35C2×#394C2214yes—
36C2×#394C2214yes—
37C2×#394C2214yes—
38C2×#394C2211yescharacteristic
39C2×#394C2212yes—
40C2×#393C2211yescharacteristic
41C2×#392C2212yes—
42C2×#392C2211yescharacteristic
43C2×#391C2212yes—
44C2×#391C2212yes—
45C2×#390C2212yes—
46C2×#389C2212yes—
47C2×#388C2214yes—
48C2×#386C2214yes—
49C2×#386C2212yes—
50C2×#384C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2214yes—
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59#1444C2214yes—
60#1444C2214yes—
61#1444C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2212yes—
65#1441C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77#1434C2214yes—
78C22⋊#95C2212yes—
79C22×#41—28no—
80C22×#41—24no—
81C22×#41—42no—
82C22×#41—44no—
83C22×#41—42no—
84C23×Q8C2312yes—
85C23×Q8C2311yescharacteristic
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—42no—
96C2×C4⋊Q8—42no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×C22⋊Q8—44no—
108C2×C22⋊Q8—44no—
109C2×C4×D4—28no—
110C2×C4×D4—28no—
111C2×C4×D4—42no—
112C2×C4×D4—42no—
113C2×C4×D4—44no—
114C2×C4×D4D418yes—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148#399—28no—
149#399—28no—
150#398—216no—
151#396—216no—
152#395—24no—
153#395—216no—
154#394—24no—
155#394—216no—
156#394—216no—
157#394—28no—
158#394—216no—
159#393—24no—
160#392—28no—
161#392—24no—
162#391—28no—
163#391—44no—
164#390—28no—
165#389—28no—
166#388—48no—
167#386—216no—
168#386—44no—
169#384—28no—
170#380—28no—
171#380—28no—
172#380—216no—
173#380—42no—
174#380D4116yescomplemented
175C4×C4⋊C4—24no—
176C4×C22⋊C4—24no—
177C4×C22⋊C4—28no—
178C2×#95C2312yes—
179C2×#95C2311yescharacteristic
180C2×#95C2311yescharacteristic
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C25C2411yescharacteristic
197C25C2412yes—
198C25C2411yescharacteristic
199C2×#41—432no—
200C2×#41—416no—
201C2×#41—416no—
202C2×#41—432no—
203C2×#41—416no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—22no—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—41no—
214C22×Q8—42no—
215C22×Q8—41no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—41no—
231C22×D4—41no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4C2×D414yes—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—28no—
258C23×C4—42no—
259C23×C4—44no—
260C23×C4—42no—
261C23×C4C2×D414yes—
262C23×C4C2×D418yes—
263C23×C4C2×D414yes—
264C23×C4C2414yes—
265C23×C4C2414yes—
266C23×C4C2412yes—
267C23×C4C2414yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C4⋊Q8—416no—
277C22⋊Q8—432no—
278C22⋊Q8—432no—
279C22⋊Q8—432no—
280C22⋊Q8—432no—
281C4×D4—416no—
282C4×D4—432no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—416no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C2×D418yes—
320C2×C4⋊C4C2×D418yes—
321C2×C4⋊C4C2×D414yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4C2×D414yes—
365C2×C22⋊C4C2×D414yes—
366C2×C22⋊C4C2×D4116yes—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42C2×D414yes—
376#95—22no—
377#95—24no—
378#95—24no—
379#95—22no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—44no—
389#95—42no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95C2×D4116yes—
394C24—22no—
395C24—21no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24C22×D412yes—
427C24C22×D414yes—
428C24C22×D412yes—
429C242−1+412yes—
430C242−1+412yes—
431C24C2511yescharacteristic
432#41—4128no—
433C2×Q8—48no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—48no—
437C2×Q8—44no—
438C2×Q8—48no—
439C2×Q8—48no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—48no—
445C2×D4—216no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—44no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—44no—
470C2×D4—48no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—48no—
540C22×C4—416no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—88no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4C22×D412yes—
555C22×C4C22×D418yes—
556C22×C4C22×D418yes—
557C22×C4C22×D412yes—
558C22×C4C22×D414yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4H(5,𝔽2)12yes—
564C22×C4H(5,𝔽2)12yes—
565C22×C4H(5,𝔽2)12yes—
566C22×C4H(5,𝔽2)14yes—
567C22×C42−1+414yes—
568C22×C42−1+412yes—
569C4⋊C4—216no—
570C4⋊C4—216no—
571C4⋊C4—44no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—416no—
575C4⋊C4—416no—
576C4⋊C4—416no—
577C4⋊C4—416no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—88no—
582C22⋊C4—416no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—48no—
594C22⋊C4—88no—
595C22⋊C4—88no—
596C22⋊C4—84no—
597C42—28no—
598C42—48no—
599C42—48no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—41no—
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—42no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23#53614yes—
681C23C23×D411yescharacteristic
682C23C23×D412yes—
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)12yes—
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×2−1+411yescharacteristic
688C23C2×2−1+411yescharacteristic
689C23C2×2−1+411yescharacteristic
690C23C2×2−1+412yes—
691C23#58512yes—
692Q8—416no—
693Q8—816no—
694D4—416no—
695D4—432no—
696D4—416no—
697D4—432no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—432no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—816no—
772C2×C4#53414yes—
773C2×C4#53518yes—
774C2×C4#53714yes—
775C2×C4D4218yes—
776C2×C4D4214yes—
777C2×C4#56014yes—
778C22—28no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—82no—
805C22—81no—
806C22—82no—
807C22—82no—
808C22—81no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22C2×#53411yescharacteristic
816C22C2×#53512yes—
817C22C2×#53611yescharacteristic
818C22C2×#53711yescharacteristic
819C22C2×D4211yescharacteristic
820C22C2×D4212yes—
821C22#348612yes—
822C22#348912yes—
823C22#348912yes—
824C22#349612yes—
825C22#349912yes—
826C22C2×#56011yescharacteristic
827C22#353611yescharacteristic
828C22#353611yescharacteristic
829C22#353811yescharacteristic
830C22#353812yes—
831C22#353811yescharacteristic
832C22#354112yes—
833C22#354712yes—
834C22#354712yes—
835C22#354812yes—
836C22#355011yescharacteristic
837C22#355111yescharacteristic
838C4—24no—
839C4—42no—
840C4—44no—
841C4—48no—
842C4—42no—
843C4—42no—
844C4—44no—
845C4—48no—
846C4—84no—
847C4—82no—
848C4—84no—
849C4#266918yes—
850C2—44no—
851C2—82no—
852C2—84no—
853C2#3737611yescharacteristic
854C2#3744211yescharacteristic
855C2#3765112yes—
856C2#3934012yes—
857C2#4243412yes—
858C2#4299412yes—
859C2#4510311yescharacteristic
860C2#4532111yescharacteristic
861C2C2×#266911yescharacteristic
862C2#5300611yescharacteristic
863C2#5300711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2388C2
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×#2542C2semidirect
2. C2×#2417C2semidirect
3. C2×#2616C2semidirect
5. #17103C2semidirect
6. #16522C2semidirect
7. #16514C2semidirect
8. #16338C2semidirect
9. #16303C2semidirect
10. #15307C2semidirect
11. #15179C2semidirect
12. #15178C2semidirect
13. #15177C2semidirect
14. #13994C2semidirect
15. #13872C2semidirect
174. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#24172
C2×#26162
C2×#23882
#171032
#165222
#165142
#163382
#163032
#153072
#151792
#151782
#151772
#139942
#138722