Finite Group Databasebeta

← #711892

Subgroups — #711892

Order 512.

3760 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic
2C2×#2625C211yesmaximal, characteristic, complemented
3C2×#2395C211yesmaximal, characteristic
4C2×#2316C211yesmaximal, characteristic, complemented
5#16674C212yesmaximal, complemented
6#16673C212yesmaximal, complemented
7#15911C214yesmaximal, complemented
8#15311C214yesmaximal
9#15179C212yesmaximal, complemented
10#15128C212yesmaximal, complemented
11#14884C212yesmaximal, complemented
12#14880C212yesmaximal, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14129C212yesmaximal, complemented
15#14017C212yesmaximal, complemented
16#13939C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic
18C2×#556—28no—
19C2×#556—28no—
20C2×#556—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#126C2212yes—
23C22×#126C2212yes—
24C22×#124C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×Q8C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2625—28no—
35#2395—28no—
36C2×#400C2212yes—
37C2×#400C2211yescharacteristic
38C2×#399C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#398C2212yes—
41C2×#397C2211yescharacteristic
42C2×#397C2212yes—
43C2×#397C2214yes—
44C2×#395C2214yes—
45C2×#394C2212yes—
46#2316—28no—
47C2×#391C2212yes—
48C2×#391C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#389C2212yes—
53C2×#389C2212yes—
54C2×#386C2212yes—
55C2×#380C2214yes—
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61#1446C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2214yes—
70#1441C2212yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2212yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1436C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85#1434C2212yes—
86#1434C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2214yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95#556—2128no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—24no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#126—28no—
102C2×#126—28no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#124—28no—
106C2×#124—28no—
107C2×#124—28no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8D418yes—
114C2×C4×Q8—24no—
115C2×C4×Q8—28no—
116C2×C4×Q8—28no—
117C2×C4×Q8—24no—
118C2×C4×Q8—28no—
119C2×C4×Q8—24no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4D418yes—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117—24no—
131C2×#117D418yes—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—28no—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170#400—28no—
171#400—24no—
172#399—24no—
173#398—28no—
174#398—24no—
175#397—216no—
176#397—28no—
177#397—24no—
178#395—48no—
179#394—28no—
180#391—28no—
181#391—28no—
182#389—28no—
183#389—28no—
184#389—28no—
185#389—28no—
186#389—28no—
187#386—44no—
188#380—24no—
189#380—28no—
190#380—216no—
191C4×C4⋊C4—28no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—24no—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C25C2411yescharacteristic
218C25C2411yescharacteristic
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×Q8—24no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—42no—
229C22×Q8—42no—
230C22×Q8C2×D414yes—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4C2×D414yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—28no—
246C23×C4—42no—
247C23×C4—44no—
248C23×C4—42no—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2414yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2414yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C4⋊Q8—232no—
269#126—264no—
270#126—264no—
271#124—264no—
272C22⋊Q8—232no—
273C22⋊Q8—232no—
274C4×Q8—264no—
275C4×Q8—232no—
276C4×D4—232no—
277#117—232no—
278#117—232no—
279#117—416no—
280C2×C4⋊C4—232no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—42no—
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⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D418yes—
333C2×C4⋊C4#4118yes—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4C2×D418yes—
367C2×C22⋊C4C2×D414yes—
368C2×C22⋊C4C2×D414yes—
369C2×C22⋊C4C2×D418yes—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42C2×D418yes—
387C2×C42C2×D414yes—
388#95—24no—
389#95—22no—
390#95—24no—
391#95—22no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—28no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×D412yes—
433C24C2511yescharacteristic
434C2×Q8—216no—
435C2×Q8—28no—
436C2×Q8—216no—
437C2×Q8—48no—
438C2×Q8—48no—
439C2×Q8—48no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—216no—
462C22×C4—216no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—216no—
504C22×C4—28no—
505C22×C4—216no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—88no—
538C22×C4—88no—
539C22×C4—84no—
540C22×C4—84no—
541C22×C4#120116yes—
542C22×C4C22×D412yes—
543C22×C4C22×D414yes—
544C22×C4C22×D414yes—
545C22×C4C22×D414yes—
546C22×C4C22×D414yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C2×#4118yes—
556C22×C4C2×#4114yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C42−1+414yes—
559C22×C42−1+412yes—
560C22×C42−1+414yes—
561C4⋊C4—216no—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—216no—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—216no—
570C4⋊C4—216no—
571C4⋊C4—48no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—88no—
577C4⋊C4—88no—
578C4⋊C4—88no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—28no—
583C22⋊C4—216no—
584C22⋊C4—28no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—88no—
590C22⋊C4—84no—
591C42—216no—
592C42—216no—
593C42—216no—
594C42—28no—
595C42—48no—
596C42—48no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23C2×#12014yes—
643C23C23×D411yescharacteristic
644C23C23×D411yescharacteristic
645C23C23×D411yescharacteristic
646C23C22×#4112yes—
647C23C2×H(5,𝔽2)11yescharacteristic
648C23C2×2−1+412yes—
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+412yes—
651C23#58511yescharacteristic
652C23#58511yescharacteristic
653C23#58512yes—
654Q8—432no—
655Q8—416no—
656D4—416no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—232no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—44no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
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—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—816no—
746C2×C4C2×#12014yes—
747C2×C4C2×#12014yes—
748C2×C4#52514yes—
749C2×C4#53614yes—
750C2×C4#53714yes—
751C2×C4#54718yes—
752C2×C4#54718yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—44no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—82no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—82no—
774C22—81no—
775C22C22×#12011yescharacteristic
776C22C2×#52511yescharacteristic
777C22C2×#53611yescharacteristic
778C22C2×#53711yescharacteristic
779C22#344911yescharacteristic
780C22C2×#54712yes—
781C22C2×#54712yes—
782C22#348811yescharacteristic
783C22#348811yescharacteristic
784C22#348912yes—
785C22#348911yescharacteristic
786C22#348911yescharacteristic
787C22#349712yes—
788C22#349911yescharacteristic
789C22#350011yescharacteristic
790C22#351412yes—
791C22#351812yes—
792C22#352112yes—
793C22#352312yes—
794C22#355212yes—
795C22#355512yes—
796C22#355512yes—
797C22#356512yes—
798C4—24no—
799C4—24no—
800C4—44no—
801C4—44no—
802C4—42no—
803C4—42no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—48no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—84no—
812C4#240618yes—
813C2—44no—
814C2—82no—
815C2C2×#240611yescharacteristic
816C2#3525111yescharacteristic
817C2#3566011yescharacteristic
818C2#3600711yescharacteristic
819C2#3607511yescharacteristic
820C2#3805112yes—
821C2#3892312yes—
822C2#4291511yescharacteristic
823C2#4291811yescharacteristic
824C2#4528712yes—
825C2#4532612yes—
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
2. C2×#2625C2semidirect
4. C2×#2316C2semidirect
5. #16674C2semidirect
6. #16673C2semidirect
7. #15911C2semidirect
9. #15179C2semidirect
10. #15128C2semidirect
11. #14884C2semidirect
12. #14880C2semidirect
13. #14139C2semidirect
14. #14129C2semidirect
15. #14017C2semidirect
16. #13939C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#26252
C2×#23952
C2×#23162
#166742
#166732
#159112
#153112
#151792
#151282
#148842
#148802
#141392
#141292
#140172
#139392
#138722