Finite Group Databasebeta

← #657644

Subgroups — #657644

Order 512.

3470 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×#2419C214yesmaximal
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4#15804C214yesmaximal, complemented
5#15539C214yesmaximal, complemented
6#15153C211yesmaximal, characteristic, complemented
7#15150C211yesmaximal, characteristic, complemented
8#15150C211yesmaximal, characteristic, complemented
9#15145C211yesmaximal, characteristic, complemented
10#14936C214yesmaximal, complemented
11#14686C211yesmaximal, characteristic, complemented
12#14049C211yesmaximal, characteristic, complemented
13#14049C211yesmaximal, characteristic, complemented
14#13904C211yesmaximal, characteristic, complemented
15#13904C211yesmaximal, characteristic, complemented
16#13880C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18C4×#386C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2486—28no—
28#2419—232no—
29C2×#400C2214yes—
30C2×#398C2214yes—
31C2×#398C2212yes—
32C2×#397C2214yes—
33C2×#397C2214yes—
34C2×#397C2212yes—
35D4×C4⋊C4—28no—
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2212yes—
39C2×#387C2214yes—
40C2×#387C2214yes—
41C2×#386C2212yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#381C2214yes—
52C2×#381C2214yes—
53C2×#381C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2214yes—
65#1445C2214yes—
66#1445C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1445C2214yes—
70#1445C2214yes—
71#1445C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1437C2212yes—
76#1436C2212yes—
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2214yes—
90C4⋊#95C2214yes—
91C22⋊#95C2212yes—
92C4×#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C2×#123—216no—
102C2×#123—28no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—28no—
106C2×C4×D4—216no—
107C2×C4×D4D418yes—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—42no—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#400—216no—
158#398—28no—
159#398—216no—
160#397—216no—
161#397—216no—
162#397—28no—
163#389—28no—
164#389—24no—
165#389—24no—
166#387—216no—
167#387—216no—
168#386D4116yes—
169#385—28no—
170#385—28no—
171#385—216no—
172#385—216no—
173#384—24no—
174#384—24no—
175#384—24no—
176#384—42no—
177#384—42no—
178#381—216no—
179#381—216no—
180#381—28no—
181#380—24no—
182#380—24no—
183#380—216no—
184#380—24no—
185#380—24no—
186#380—24no—
187C4×C4⋊C4—24no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—24no—
190C4×C22⋊C4—42no—
191C2×#95—216no—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C25C2411yescharacteristic
220C25C2411yescharacteristic
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4C2×D414yes—
225C22×D4C2×D418yes—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—28no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—28no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—28no—
248C23×C4—28no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4C2×D414yes—
258C23×C4C2×D418yes—
259C23×C4C2×D414yes—
260C23×C4#4114yes—
261C23×C4#4114yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279#123—432no—
280C4×D4—232no—
281C4×D4—432no—
282C2×C4⋊C4—22no—
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—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—416no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—416no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4#4114yes—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4C2×D414yes—
362C2×C22⋊C4C2×D414yes—
363C2×C22⋊C4C2×D418yes—
364C2×C22⋊C4C2×D418yes—
365C2×C22⋊C4C2×D418yes—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—28no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—416no—
384C2×C42—42no—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—42no—
411#95—42no—
412#95C2×D418yes—
413#95C2×D418yes—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24C22×D414yes—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×D414yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C242−1+414yes—
436C24C2511yescharacteristic
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—216no—
440C2×D4—216no—
441C2×D4#127116yes—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—216no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—216no—
495C22×C4—28no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—88no—
552C22×C4—88no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4#123116yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D414yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D414yes—
565C22×C4C22×D412yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4114yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C42−1+414yes—
576C22×C42−1+412yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—416no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—416no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—88no—
595C4⋊C4—88no—
596C4⋊C4—84no—
597C22⋊C4—28no—
598C22⋊C4—216no—
599C22⋊C4—28no—
600C22⋊C4—216no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C42—28no—
608C42—28no—
609C42—48no—
610C42—44no—
611C42—48no—
612C42—44no—
613C42—44no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×#12314yes—
655C23C2×#12714yes—
656C23C2×#12714yes—
657C23#53614yes—
658C23#54718yes—
659C23#54718yes—
660C23C23×D411yescharacteristic
661C23C23×D412yes—
662C23C22×#4111yescharacteristic
663C23C22×#4111yescharacteristic
664C23C22×#4111yescharacteristic
665C23C22×#4111yescharacteristic
666C23C2×H(5,𝔽2)11yescharacteristic
667C23C2×2−1+412yes—
668C23C2×2−1+411yescharacteristic
669C23C2×2−1+412yes—
670C23#58512yes—
671D4—232no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—232no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—432no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—416no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—816no—
765C2×C4—816no—
766C2×C4—816no—
767C2×C4C2×#12314yes—
768C2×C4C2×#12314yes—
769C2×C4#52914yes—
770C2×C4C2×#12714yes—
771C2×C4#53914yes—
772C2×C4#54614yes—
773C2×C4#54718yes—
774C2×C4#54714yes—
775C2×C4#55114yes—
776C2×C4#55214yes—
777C22—28no—
778C22—24no—
779C22—28no—
780C22—24no—
781C22—24no—
782C22—28no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—44no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22#250118yes—
799C22C22×#12311yescharacteristic
800C22C2×#52911yescharacteristic
801C22C22×#12711yescharacteristic
802C22C2×#53611yescharacteristic
803C22C2×#53911yescharacteristic
804C22C2×#54611yescharacteristic
805C22C2×#54712yes—
806C22C2×#54712yes—
807C22C2×#54712yes—
808C22C2×#54711yescharacteristic
809C22D4×#4112yes—
810C22C2×#55111yescharacteristic
811C22C2×#55211yescharacteristic
812C22#349512yes—
813C22#349512yes—
814C22#349612yes—
815C22#349911yescharacteristic
816C22#349912yes—
817C22#350011yescharacteristic
818C22#350712yes—
819C22#352312yes—
820C22#353812yes—
821C22#356312yes—
822C4—28no—
823C4—24no—
824C4—24no—
825C4—44no—
826C4—42no—
827C4—44no—
828C4—42no—
829C4—44no—
830C4—44no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#241918yescomplemented
839C2—28no—
840C2—44no—
841C2C2×#241911yescharacteristic
842C2C2×#250111yescharacteristic
843C2#3561911yescharacteristic
844C2#3611612yes—
845C2#3617911yescharacteristic
846C2#3626011yescharacteristic
847C2#3786511yescharacteristic
848C2#3808111yescharacteristic
849C2#3937612yes—
850C2#5919812yes—
851C2#5929012yes—
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
4. #15804C2semidirect
5. #15539C2semidirect
6. #15153C2semidirect
7. #15150C2semidirect
8. #15150C2semidirect
9. #15145C2semidirect
10. #14936C2semidirect
11. #14686C2semidirect
12. #14049C2semidirect
13. #14049C2semidirect
14. #13904C2semidirect
15. #13904C2semidirect
16. #13880C2semidirect
17. #13880C2semidirect
19. C2×C4⋊#95C2semidirect
838. C4#2419semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24192
C2×D4×C4⋊C42
#158042
#155392
#151532
#151502
#151452
#149362
#146862
#140492
#139042
#138802
C4×#3862
C2×C4⋊#952