Finite Group Databasebeta

← #613655

Subgroups — #613655

Order 512.

5038 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#41C211yesmaximal, characteristic
2C2×#2581C211yesmaximal, characteristic, complemented
3C2×#2580C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5#15203C214yesmaximal, complemented
6#14893C212yesmaximal, complemented
7#14887C212yesmaximal, complemented
8#14825C212yesmaximal, complemented
9#14723C212yesmaximal, complemented
10#14695C214yesmaximal, complemented
11#14682C211yesmaximal, characteristic, complemented
12#14129C212yesmaximal, complemented
13#14018C212yesmaximal, complemented
14#14017C212yesmaximal, complemented
15#13942C211yesmaximal, characteristic, complemented
16#13941C211yesmaximal, characteristic, complemented
17#13937C212yesmaximal
18C23×#41C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C2×C4×#41—28no—
21C2×C4×#41—28no—
22C2×C4×#41—28no—
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2212yes—
27C22×C4×D4C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31C22×#117C2211yescharacteristic
32C23×C42C2212yes—
33C23×C42C2211yescharacteristic
34#2581—28no—
35#2580—28no—
36C2×#400C2212yes—
37C2×#399C2212yes—
38C2×#395C2212yes—
39C2×#393C2212yes—
40C4×C22⋊Q8—28no—
41C2×#391C2211yescharacteristic
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#389C2211yescharacteristic
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#387C2214yes—
50C2×#387C2212yes—
51C2×#385C2214yes—
52C2×#385C2212yes—
53C2×#385C2214yes—
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61#1444C2214yes—
62#1442C2214yes—
63#1441C2212yes—
64#1441C2212yes—
65#1439C2214yes—
66#1439C2212yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2214yes—
72#1438C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80#1434C2212yes—
81#1434C2212yes—
82#1434C2214yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—24no—
94C22×#41—24no—
95C22×#41Q818yescomplemented
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—28no—
108C4×#41—2128no—
109C2×C4×Q8—24no—
110C2×C4×Q8—24no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8—24no—
117C2×C4×Q8D418yes—
118C2×C4×D4—24no—
119C2×C4×D4—28no—
120C2×C4×D4—28no—
121C2×C4×D4—28no—
122C2×C4×D4—24no—
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4—28no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4D418yes—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—28no—
133C2×#117—24no—
134C2×#117—28no—
135C2×#117—28no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C42—28no—
161C22×C42—28no—
162C22×C42—28no—
163C22×C42—24no—
164C22×C42—24no—
165C22×C42D418yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2312yes—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#400—28no—
176#399—28no—
177#395—28no—
178#393—28no—
179#391—28no—
180#391—28no—
181#391—24no—
182#390—28no—
183#390—28no—
184#389—28no—
185#389—28no—
186#389—24no—
187#387—216no—
188#387—28no—
189#385—216no—
190#385—28no—
191#385—216no—
192#382—24no—
193#382—24no—
194#380—24no—
195#380—28no—
196C4×C4⋊C4—28no—
197C4×C4⋊C4—24no—
198C4×C22⋊C4—28no—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25C2411yescharacteristic
222C25C2412yes—
223C2×#41—232no—
224C2×#41—232no—
225C2×#41—232no—
226C2×#41—232no—
227C2×#41—232no—
228C2×#41—232no—
229C2×#41—232no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—24no—
238C22×Q8—42no—
239C22×Q8C2×D414yes—
240C22×Q8C2×Q814yes—
241C22×Q8#4114yes—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4C2×D414yes—
253C22×D4C2×Q818yes—
254C22×D4C2×Q814yes—
255C22×D4#4114yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—28no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—42no—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D418yes—
287C23×C4C2×Q818yes—
288C23×C4C2×Q814yes—
289C23×C4#4114yes—
290C23×C4C2412yes—
291C23×C4C2414yes—
292C23×C4C2414yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22⋊Q8—232no—
306C4×Q8—232no—
307C4×Q8—232no—
308C4×Q8—416no—
309C4×D4—264no—
310C4×D4—264no—
311C4×D4—232no—
312C4×D4—232no—
313#117—232no—
314#117—264no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D418yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4#4118yescomplemented
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D418yes—
385C2×C42—264no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—232no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D418yes—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24C22×D412yes—
453C24C22×D414yes—
454C24C22×Q814yes—
455C24C22×Q812yes—
456C24C2×#4114yes—
457C24C2×#4112yes—
458C24C2511yescharacteristic
459#41—2256no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8C22⋊Q8116yescomplemented
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—28no—
479C2×D4—216no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4C22⋊Q8116yescomplemented
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—216no—
490C22×C4—216no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—216no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—416no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—416no—
578C22×C4—416no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—48no—
586C22×C4C22⋊Q8116yes—
587C22×C4C22×D414yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×Q812yes—
603C22×C4C22×Q814yes—
604C22×C4C22×Q812yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C4⋊C4—216no—
614C4⋊C4—28no—
615C4⋊C4—216no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—216no—
619C4⋊C4—416no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—88no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—48no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C42—216no—
638C42—216no—
639C42—28no—
640C42—28no—
641C42—28no—
642C42—216no—
643C42—48no—
644C42—48no—
645C42#120116yes—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—24no—
669C23—28no—
670C23—24no—
671C23—28no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—44no—
681C23—42no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23C2×C22⋊Q818yes—
691C23C2×C22⋊Q814yes—
692C23C23×D411yescharacteristic
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C23×Q811yescharacteristic
696C23C22×#4111yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4112yes—
700C23#58512yes—
701C23#58512yes—
702C23#58512yes—
703Q8—232no—
704Q8—416no—
705D4—264no—
706D4—232no—
707C2×C4—264no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—232no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4C2×#12014yes—
795C2×C4C2×#12014yes—
796C2×C4C2×#12014yes—
797C2×C4C2×C22⋊Q814yes—
798C2×C4C2×C22⋊Q818yes—
799C2×C4C2×C22⋊Q814yes—
800C2×C4C2×C22⋊Q814yes—
801C2×C4C2×C22⋊Q814yes—
802C2×C4#52514yes—
803C2×C4#52514yes—
804C2×C4#52514yes—
805C2×C4#52514yes—
806C22—28no—
807C22—24no—
808C22—24no—
809C22—216no—
810C22—24no—
811C22—44no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—48no—
816C22—48no—
817C22—44no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—48no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—44no—
828C22C22×#12011yescharacteristic
829C22C22×C22⋊Q811yescharacteristic
830C22C22×C22⋊Q811yescharacteristic
831C22C22×C22⋊Q811yescharacteristic
832C22C2×#52511yescharacteristic
833C22C2×#52511yescharacteristic
834C22C2×#52511yescharacteristic
835C22C2×#52511yescharacteristic
836C22#344911yescharacteristic
837C22#344911yescharacteristic
838C22#344911yescharacteristic
839C22D4×#4112yes—
840C22D4×#4112yes—
841C22#347512yes—
842C22Q8×#4112yes—
843C22#348012yes—
844C22#348012yes—
845C22#348512yes—
846C22#348712yes—
847C22#350412yes—
848C22#351012yes—
849C22#352112yes—
850C22#352412yes—
851C4—24no—
852C4—28no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—44no—
858C4—44no—
859C4—44no—
860C4—44no—
861C4—82no—
862C4—84no—
863C4—84no—
864C4—82no—
865C4#284818yes—
866C2—44no—
867C2—48no—
868C2#3473611yescharacteristic
869C2#3490911yescharacteristic
870C2#3495211yescharacteristic
871C2#3514911yescharacteristic
872C2#3521011yescharacteristic
873C2#3533411yescharacteristic
874C2#3621912yes—
875C2#3622912yes—
876C2#3643112yes—
877C2#3643712yes—
878C2C2×#284811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2581C2semidirect
3. C2×#2580C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. #15203C2semidirect
6. #14893C2semidirect
7. #14887C2semidirect
8. #14825C2semidirect
9. #14723C2semidirect
10. #14695C2semidirect
11. #14682C2semidirect
12. #14129C2semidirect
13. #14018C2semidirect
14. #14017C2semidirect
15. #13942C2semidirect
16. #13941C2semidirect
95. C22×#41Q8semidirect
354. C2×C4⋊C4#41semidirect
471. C2×Q8C22⋊Q8semidirect
485. C2×D4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#412
C2×#25812
C2×#25802
C2×C4×C22⋊Q82
#152032
#148932
#148872
#148252
#147232
#146952
#146822
#141292
#140182
#140172
#139422
#139412
#139372