Finite Group Databasebeta

← #648048

Subgroups — #648048

Order 512.

5806 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic
3C2×#2429C212yesmaximal, complemented
4C2×#2434C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
6#15279C214yesmaximal, complemented
7#15276C214yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15178C212yesmaximal, complemented
10#14728C212yesmaximal, complemented
11#14726C212yesmaximal
12#14139C211yesmaximal, characteristic, complemented
13#14130C211yesmaximal, characteristic, complemented
14#14043C212yesmaximal, complemented
15#13971C212yesmaximal
16#13969C212yesmaximal, complemented
17C4×#379C211yesmaximal, characteristic
18C24×Q8C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic, complemented
21C22×C4⋊Q8C2211yescharacteristic, complemented
22C22×C22⋊Q8—28no—
23C22×C22⋊Q8—216no—
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2214yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2212yes—
29C22×C4×Q8C2212yescomplemented
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2212yes—
32C23×C22⋊C4C2212yes—
33#2848—28no—
34#2434—28no—
35#2429—216no—
36C2×#398C2214yescomplemented
37C2×#396C2214yes—
38C2×#395C2212yescomplemented
39C2×#395C2212yescomplemented
40Q8×C22⋊C4—28no—
41C2×#391C2212yescomplemented
42C2×#391C2214yescomplemented
43C2×#391C2212yescomplemented
44C2×#391C2211yescharacteristic, complemented
45C2×#391C2211yescharacteristic, complemented
46C2×#389C2212yescomplemented
47C2×#389C2214yescomplemented
48C2×#388C2214yes—
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#379C2212yes—
58C2×#379C2211yescharacteristic
59C2×#379C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65#1444C2212yescomplemented
66#1444C2214yescomplemented
67#1444C2214yescomplemented
68#1442C2212yescomplemented
69#1442C2214yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1440C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1437C2214yes—
79#1436C2214yescomplemented
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2211yescharacteristic
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2211yescharacteristic
89C26C2311yescharacteristic
90C23×Q8—28no—
91C23×Q8—24no—
92C23×Q8—24no—
93C23×Q8—44no—
94C23×Q8D418yes—
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2312yes—
98C23×Q8C2311yescharacteristic
99C24×C4—28no—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—24no—
103C24×C4—44no—
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C2×C4⋊Q8—28no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—44no—
114C2×C22⋊Q8—2128no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—216no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—28no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—28no—
125C2×C22⋊Q8—216no—
126C2×C22⋊Q8—28no—
127C2×C22⋊Q8—216no—
128C2×C22⋊Q8—44no—
129C2×C22⋊Q8D4116yes—
130C2×C4×Q8—28no—
131C2×C4×Q8—28no—
132C2×C4×Q8—44no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—28no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—216no—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C22⋊C4—28no—
152C22×C22⋊C4—216no—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2314yes—
171#398—216no—
172#396—216no—
173#395—28no—
174#395—28no—
175#391—24no—
176#391—24no—
177#391—28no—
178#391—28no—
179#391—216no—
180#389—216no—
181#389—28no—
182#388—216no—
183#385—28no—
184#385—28no—
185#385—28no—
186#385—28no—
187#385—216no—
188#380—28no—
189#380—28no—
190#380D418yes—
191#379—28no—
192#379—24no—
193#379Q818yescomplemented
194C4×C22⋊C4—24no—
195C4×C22⋊C4—28no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—44no—
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C25—24no—
222C25—22no—
223C25—24no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—42no—
230C25—42no—
231C25C2×Q814yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C22×Q8—232no—
235C22×Q8—232no—
236C22×Q8—22no—
237C22×Q8—28no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—24no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—44no—
252C22×Q8—416no—
253C22×Q8—432no—
254C22×Q8—432no—
255C22×Q8C2×D414yes—
256C22×Q8C2×D418yes—
257C22×Q8C2×D418yes—
258C22×Q8C2×D414yes—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—232no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—28no—
268C23×C4—28no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—432no—
290C23×C4—432no—
291C23×C4—416no—
292C23×C4—416no—
293C23×C4C2×D418yes—
294C23×C4C2×D418yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4#4114yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2414yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C4⋊Q8—416no—
314C4⋊Q8—416no—
315C22⋊Q8—264no—
316C22⋊Q8—2128no—
317C22⋊Q8—264no—
318C22⋊Q8—432no—
319C22⋊Q8—416no—
320C4×Q8—432no—
321C2×C4⋊C4—232no—
322C2×C4⋊C4—264no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C2×D418yes—
358C2×C4⋊C4C2×D4116yes—
359C2×C4⋊C4C2×D418yes—
360C2×C22⋊C4—264no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C2×D4116yes—
397C2×C22⋊C4C2×D418yes—
398C2×C22⋊C4C2×Q814yes—
399C2×C22⋊C4C2×Q814yes—
400C2×C22⋊C4C2×Q818yescomplemented
401C2×C22⋊C4C2×Q818yescomplemented
402C2×C22⋊C4#4114yes—
403C2×C42—28no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—28no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—44no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—42no—
433#95—42no—
434#95C2×D418yes—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—28no—
440C24—28no—
441C24—216no—
442C24—216no—
443C24—28no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—28no—
457C24—28no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—48no—
465C24—48no—
466C24—48no—
467C24—44no—
468C24—44no—
469C24—48no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24C22×D414yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×Q814yes—
478C24C22×Q812yes—
479C24C2×#4112yes—
480C24C2×#4112yes—
481C242−1+414yes—
482C242−1+412yes—
483C242−1+412yes—
484C24C2511yescharacteristic
485C2×Q8—216no—
486C2×Q8—28no—
487C2×Q8—28no—
488C2×Q8—216no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—216no—
493C2×Q8—216no—
494C2×Q8—48no—
495C2×Q8—416no—
496C2×Q8—416no—
497C2×Q8—4128no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—48no—
502C2×Q8—48no—
503C2×Q8—48no—
504C2×Q8—48no—
505C2×Q8#120116yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—28no—
517C22×C4—216no—
518C22×C4—216no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—216no—
564C22×C4—216no—
565C22×C4—216no—
566C22×C4—216no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—416no—
594C22×C4—416no—
595C22×C4—48no—
596C22×C4—4128no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4#121116yes—
607C22×C4C22×D418yes—
608C22×C4C22×D418yes—
609C22×C4C22×D414yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D418yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D414yes—
617C22×C4C22×D412yes—
618C22×C4C22×Q812yes—
619C22×C4C22×Q814yes—
620C22×C4C22×Q812yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4H(5,𝔽2)14yes—
626C4⋊C4—216no—
627C4⋊C4—232no—
628C4⋊C4—216no—
629C4⋊C4—232no—
630C4⋊C4—216no—
631C4⋊C4—416no—
632C4⋊C4—416no—
633C4⋊C4—416no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C22⋊C4—232no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—216no—
646C22⋊C4—232no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—416no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C42—416no—
655C42—44no—
656C42—44no—
657C42—48no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—232no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—432no—
694C23—432no—
695C23—416no—
696C23—432no—
697C23—416no—
698C23—416no—
699C23—432no—
700C23—416no—
701C23—416no—
702C23—42no—
703C23—42no—
704C23—416no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23C2×#12114yes—
720C23#53314yes—
721C23#54114yes—
722C23#54714yes—
723C23#54814yes—
724C23D4×Q818yes—
725C23D4×Q814yes—
726C23D4×Q814yes—
727C23C23×D411yescharacteristic
728C23C23×D412yes—
729C23C23×D411yescharacteristic
730C23C23×Q811yescharacteristic
731C23C22×#4111yescharacteristic
732C23C22×#4111yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23C2×2−1+411yescharacteristic
735C23C2×2−1+411yescharacteristic
736C23C2×2−1+412yes—
737C23#58512yes—
738Q8—232no—
739Q8—432no—
740Q8—416no—
741Q8—88no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—232no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—28no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—432no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—416no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—432no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4C2×#12018yes—
827C2×C4C2×#12014yes—
828C2×C4C2×#12114yes—
829C2×C4C2×#12114yes—
830C2×C4#53414yes—
831C2×C4D4218yes—
832C2×C4#54618yes—
833C22—28no—
834C22—28no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—28no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22#242918yescomplemented
860C22C22×#12011yescharacteristic
861C22C22×#12111yescharacteristic
862C22C2×#53311yescharacteristic
863C22C2×#53411yescharacteristic
864C22C2×#54111yescharacteristic
865C22C2×D4212yes—
866C22C2×#54612yes—
867C22C2×#54711yescharacteristic
868C22C2×#54811yescharacteristic
869C22C2×D4×Q812yes—
870C22C2×D4×Q811yescharacteristic
871C22C2×D4×Q811yescharacteristic
872C22D4×#4112yes—
873C22#348612yes—
874C22#348611yescharacteristic
875C22#348711yescharacteristic
876C22#348912yes—
877C22#348912yes—
878C22#349512yes—
879C22#350112yes—
880C22#352012yes—
881C22#353812yes—
882C22#354112yes—
883C4—24no—
884C4—28no—
885C4—42no—
886C4—48no—
887C4—44no—
888C4—44no—
889C4—44no—
890C4—48no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4#241018yes—
898C2—28no—
899C2—48no—
900C2C2×#241011yescharacteristic
901C2C2×#242911yescharacteristic
902C2#3566111yescharacteristic
903C2#3613012yes—
904C2#3642811yescharacteristic
905C2Q8×#12011yescharacteristic
906C2#3766312yes—
907C2#3912111yescharacteristic
908C2#3959511yescharacteristic
909C2#5899812yes—
910C2#5900212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#2429C2semidirect
4. C2×#2434C2semidirect
5. C2×Q8×C22⋊C4C2semidirect
6. #15279C2semidirect
7. #15276C2semidirect
8. #15179C2semidirect
9. #15178C2semidirect
10. #14728C2semidirect
12. #14139C2semidirect
13. #14130C2semidirect
14. #14043C2semidirect
16. #13969C2semidirect
20. C22×C4⋊Q8C22semidirect
21. C22×C4⋊Q8C22semidirect
29. C22×C4×Q8C22semidirect
36. C2×#398C22semidirect
38. C2×#395C22semidirect
39. C2×#395C22semidirect
41. C2×#391C22semidirect
42. C2×#391C22semidirect
43. C2×#391C22semidirect
44. C2×#391C22semidirect
45. C2×#391C22semidirect
46. C2×#389C22semidirect
47. C2×#389C22semidirect
65. #1444C22semidirect
66. #1444C22semidirect
67. #1444C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
79. #1436C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
193. #379Q8semidirect
400. C2×C22⋊C4C2×Q8semidirect
401. C2×C22⋊C4C2×Q8semidirect
859. C22#2429semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C2×#28482
C2×#24292
C2×#24342
C2×Q8×C22⋊C42
#152792
#152762
#151792
#151782
#147282
#147262
#141392
#141302
#140432
#139712
#139692
C4×#3792