Finite Group Databasebeta

← #760389

Subgroups — #760389

Order 512.

3446 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4C2×#2285C211yesmaximal, characteristic, complemented
5#16685C214yesmaximal, complemented
6#15183C212yesmaximal, complemented
7#15177C212yesmaximal, complemented
8#15129C212yesmaximal, complemented
9#15126C212yesmaximal
10#14890C214yesmaximal, complemented
11#14151C211yesmaximal, characteristic, complemented
12#14045C212yesmaximal, complemented
13#14022C212yesmaximal, complemented
14#13997C212yesmaximal, complemented
15#13974C212yesmaximal, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13906C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×#121C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2212yes—
25C23×C42C2211yescharacteristic
26#2538—28no—
27C2×#396C2214yes—
28C2×#394C2214yes—
29C4×C22⋊Q8—28no—
30C4×#121—28no—
31C2×#391C2211yescharacteristic
32C2×#391C2212yes—
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#388C2212yes—
42C2×#388C2214yes—
43C2×#387C2212yes—
44C2×#386C2212yes—
45C2×#385C2212yes—
46#2285—28no—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#382C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64#1445C2214yes—
65#1444C2214yes—
66#1443C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2214yes—
78#1437C2214yes—
79#1436C2214yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C2×C22⋊Q8—24no—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—44no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—24no—
103C2×C4×Q8—24no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×D4—28no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—44no—
111C2×C4×D4—44no—
112C2×#117—28no—
113C2×#117—44no—
114C2×#117—44no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42D418yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2314yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#396—216no—
157#394—48no—
158#391—24no—
159#391—44no—
160#390—28no—
161#390—28no—
162#390—24no—
163#389—28no—
164#389—28no—
165#389—24no—
166#389—24no—
167#389—44no—
168#388—28no—
169#388—48no—
170#387—28no—
171#386—28no—
172#385—28no—
173#384—24no—
174#384D418yescomplemented
175#382—28no—
176#380—24no—
177#380—24no—
178#380—28no—
179#380—28no—
180#380—28no—
181#380—28no—
182#380—44no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—28no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—28no—
187C4×C4⋊C4—24no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25C2412yes—
211C25C2411yescharacteristic
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8#4114yes—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4#4114yes—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2414yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2414yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C22⋊Q8—232no—
277C22⋊Q8—432no—
278#121—232no—
279C4×Q8—416no—
280C4×D4—432no—
281C4×D4—416no—
282#117—432no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4C2×D418yes—
333C2×C4⋊C4C2×D418yes—
334C2×C4⋊C4C2×D418yes—
335C2×C4⋊C4#4114yes—
336C2×C4⋊C4#4114yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—232no—
380C2×C42—28no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—28no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—44no—
392C2×C42C2×D414yes—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397C2×C42#4114yes—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24C22×D412yes—
445C24C2×#4114yes—
446C24H(5,𝔽2)12yes—
447C242−1+412yes—
448C24C2511yescharacteristic
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×D4—216no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4C22×D412yes—
578C22×C4C22×D418yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C42−1+412yes—
601C22×C42−1+412yes—
602C22×C42−1+412yes—
603C4⋊C4—216no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—48no—
609C4⋊C4—416no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—88no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C42—28no—
634C42—28no—
635C42—28no—
636C42—416no—
637C42—48no—
638C42—48no—
639C42—48no—
640C42#121116yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23#53714yes—
711C23C23×D411yescharacteristic
712C23C23×D411yescharacteristic
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4111yescharacteristic
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×2−1+411yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23C2×2−1+411yescharacteristic
725C23C2×2−1+411yescharacteristic
726Q8—416no—
727D4—432no—
728D4—416no—
729C2×C4—232no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—816no—
822C2×C4C2×#12114yes—
823C2×C4C2×#12114yes—
824C2×C4C2×#12114yes—
825C2×C4#52514yes—
826C2×C4#52514yes—
827C2×C4#53514yes—
828C2×C4#53614yes—
829C2×C4#53714yes—
830C2×C4#54614yes—
831C2×C4#54714yes—
832C2×C4#54814yes—
833C2×C4#55014yes—
834C2×C4#55214yes—
835C2×C4#55314yes—
836C2×C4#55514yes—
837C2×C4#55614yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22C22×#12111yescharacteristic
869C22C2×#52511yescharacteristic
870C22C2×#52511yescharacteristic
871C22C2×#53511yescharacteristic
872C22C2×#53611yescharacteristic
873C22C2×#53711yescharacteristic
874C22C2×#53711yescharacteristic
875C22C2×#54611yescharacteristic
876C22C2×#54711yescharacteristic
877C22C2×#54811yescharacteristic
878C22C2×#55011yescharacteristic
879C22C2×#55211yescharacteristic
880C22C2×#55311yescharacteristic
881C22C2×#55511yescharacteristic
882C22C2×#55611yescharacteristic
883C22#348111yescharacteristic
884C22#348211yescharacteristic
885C22#348211yescharacteristic
886C22#348311yescharacteristic
887C22#348411yescharacteristic
888C22#348611yescharacteristic
889C22#349211yescharacteristic
890C22#349211yescharacteristic
891C22#351911yescharacteristic
892C22#351911yescharacteristic
893C22#352011yescharacteristic
894C22#352011yescharacteristic
895C22#352211yescharacteristic
896C22#352211yescharacteristic
897C22#352311yescharacteristic
898C22#352311yescharacteristic
899C22#354811yescharacteristic
900C22#354811yescharacteristic
901C22#355011yescharacteristic
902C22#355011yescharacteristic
903C4—24no—
904C4—24no—
905C4—42no—
906C4—44no—
907C4—42no—
908C4—48no—
909C4—44no—
910C4—44no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—84no—
916C4#241418yes—
917C4#241518yes—
918C2—44no—
919C2—84no—
920C2C2×#241411yescharacteristic
921C2C2×#241511yescharacteristic
922C2#3497611yescharacteristic
923C2#3522311yescharacteristic
924C2#3523611yescharacteristic
925C2#3524711yescharacteristic
926C2#3764011yescharacteristic
927C2#5903911yescharacteristic
928C2#5904211yescharacteristic
929C2#5905511yescharacteristic
930C2#5905711yescharacteristic
931C2#5921811yescharacteristic
932C2#5921911yescharacteristic
933C2#5923411yescharacteristic
934C2#5923511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2538C2semidirect
2. C2×C4×C22⋊Q8C2semidirect
4. C2×#2285C2semidirect
5. #16685C2semidirect
6. #15183C2semidirect
7. #15177C2semidirect
8. #15129C2semidirect
10. #14890C2semidirect
11. #14151C2semidirect
12. #14045C2semidirect
13. #14022C2semidirect
14. #13997C2semidirect
15. #13974C2semidirect
16. #13926C2semidirect
17. #13906C2semidirect
174. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×C4×C22⋊Q82
C2×C4×#1212
C2×#22852
#166852
#151832
#151772
#151292
#151262
#148902
#141512
#140452
#140222
#139972
#139742
#139262
#139062