Finite Group Databasebeta

← #873752

Subgroups — #873752

Order 512.

3686 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2868C211yesmaximal, characteristic, complemented
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2429C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5C2×#2434C211yesmaximal, characteristic
6C2×#2434C211yesmaximal, characteristic
7#16522C214yesmaximal, complemented
8#15625C214yesmaximal, complemented
9#15392C214yesmaximal
10#15190C211yesmaximal, characteristic, complemented
11#15190C211yesmaximal, characteristic, complemented
12#15188C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic
15#15178C211yesmaximal, characteristic
16#14703C211yesmaximal, characteristic, complemented
17#14405C214yesmaximal
18#14024C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34#2868—28no—
35#2546—28no—
36#2434—28no—
37#2434—28no—
38#2434—28no—
39#2429—28no—
40C2×#398C2214yes—
41C2×#398C2212yes—
42C2×#396C2212yes—
43C2×#395C2212yes—
44C2×#395C2214yes—
45C2×#395C2214yes—
46C2×#395C2212yes—
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#389C2212yes—
59C2×#389C2214yes—
60C2×#389C2211yescharacteristic
61C2×#388C2212yes—
62C2×#388C2212yes—
63C2×#385C2212yes—
64C2×#385C2214yes—
65C2×#385C2214yes—
66C2×#385C2212yes—
67C2×#384C2214yes—
68C2×#384C2214yes—
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C43C2211yescharacteristic
74#1444C2214yes—
75#1444C2214yes—
76#1444C2214yes—
77#1444C2214yes—
78#1444C2214yes—
79#1444C2214yes—
80#1442C2214yes—
81#1442C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1437C2212yes—
88#1436C2212yes—
89#1436C2214yes—
90#1436C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94#1434C2212yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8—42no—
103C23×Q8—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×Q8C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×Q8C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8—24no—
124C2×C4⋊Q8—24no—
125C2×C4⋊Q8—24no—
126C2×C4⋊Q8—42no—
127C2×C4⋊Q8—42no—
128C2×C4⋊Q8—42no—
129C2×C4⋊Q8—42no—
130C2×C4⋊Q8—42no—
131C2×C4⋊Q8—42no—
132C2×C4⋊Q8—42no—
133C2×C4⋊Q8—42no—
134C2×C4⋊Q8—42no—
135C2×C4⋊Q8—42no—
136C2×C4⋊Q8—42no—
137C2×C4⋊Q8—42no—
138C2×C4⋊Q8D418yes—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—42no—
145C2×C22⋊Q8—42no—
146C2×C22⋊Q8—42no—
147C2×C22⋊Q8—42no—
148C2×C4×Q8—24no—
149C2×C4×Q8—24no—
150C2×C4×Q8—42no—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2314yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2314yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2314yes—
170C22×C4⋊C4C2314yes—
171C22×C4⋊C4C2314yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2312yes—
182C22×C42C2312yes—
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186C22×C42C2311yescharacteristic
187C22×C42C2312yes—
188#398—28no—
189#398—216no—
190#396—28no—
191#395—216no—
192#395—216no—
193#395—28no—
194#395—28no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—24no—
199#391—24no—
200#391—24no—
201#391—24no—
202#391—42no—
203#391—42no—
204#391—42no—
205#391D418yes—
206#389—24no—
207#389—28no—
208#389—216no—
209#388—28no—
210#388Q8116yescomplemented
211#385—216no—
212#385—28no—
213#385—28no—
214#385—216no—
215#384—216no—
216#384—216no—
217C4×C4⋊C4—24no—
218C4×C22⋊C4—24no—
219C4×C22⋊C4—24no—
220C4×C22⋊C4D418yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2312yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2314yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C43—24no—
248C25C2411yescharacteristic
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—24no—
262C22×Q8—24no—
263C22×Q8—24no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—42no—
285C22×Q8—42no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8—416no—
289C22×Q8—416no—
290C22×Q8—416no—
291C22×Q8—416no—
292C22×Q8—416no—
293C22×Q8—416no—
294C22×Q8—416no—
295C22×Q8C2×D414yes—
296C22×Q8C2×D414yes—
297C22×Q8C2×D414yes—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—24no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4C2×D414yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C4⋊Q8—416no—
331C4⋊Q8—416no—
332C4⋊Q8—416no—
333C4⋊Q8—416no—
334C4⋊Q8—416no—
335C4⋊Q8—416no—
336C4⋊Q8—416no—
337C4⋊Q8—416no—
338C4⋊Q8—416no—
339C22⋊Q8—416no—
340C22⋊Q8—416no—
341C22⋊Q8—416no—
342C4×Q8—416no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4C2×D414yes—
403C2×C4⋊C4C2×D4116yes—
404C2×C4⋊C4C2×Q818yescomplemented
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4C2×D414yes—
420C2×C22⋊C4C2×D414yes—
421C2×C22⋊C4C2×Q818yes—
422C2×C22⋊C4C2×Q818yes—
423C2×C22⋊C4C2×Q818yes—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—24no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—42no—
446C2×C42C2×D414yes—
447C2×C42C2×D414yes—
448C2×C42C2×D414yes—
449C2×C42C2×D414yes—
450C2×C42C2×Q818yescomplemented
451#95—24no—
452#95—24no—
453#95—24no—
454#95—28no—
455#95—28no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—28no—
461#95—24no—
462#95—24no—
463#95—28no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—28no—
468#95—28no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95C2×D414yes—
473#95C2×D414yes—
474#95C2×D4116yes—
475#95C2×Q818yescomplemented
476#95C2×Q818yescomplemented
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24C22×D412yes—
487C24C22×Q814yes—
488C24C2511yescharacteristic
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—28no—
498C2×Q8—48no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—48no—
502C2×Q8—48no—
503C2×Q8—48no—
504C2×Q8—4128no—
505C2×Q8—48no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8—44no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4C22×D414yes—
632C22×C4C22×D412yes—
633C22×C4C22×D414yes—
634C22×C4C22×D414yes—
635C22×C4C22×D412yes—
636C22×C4C22×D414yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×Q814yes—
646C22×C4C22×Q814yes—
647C22×C4C22×Q814yes—
648C22×C4C22×Q814yes—
649C22×C4C22×Q814yes—
650C22×C4C22×Q814yes—
651C22×C4H(5,𝔽2)12yes—
652C22×C4H(5,𝔽2)12yes—
653C22×C4H(5,𝔽2)12yes—
654C22×C4H(5,𝔽2)12yes—
655C22×C42−1+414yes—
656C22×C42−1+414yes—
657C22×C42−1+414yes—
658C4⋊C4—28no—
659C4⋊C4—216no—
660C4⋊C4—416no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—416no—
671C4⋊C4—48no—
672C4⋊C4—416no—
673C4⋊C4—48no—
674C4⋊C4—416no—
675C4⋊C4—416no—
676C4⋊C4—44no—
677C4⋊C4—48no—
678C4⋊C4—44no—
679C22⋊C4—28no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4C4⋊Q8116yescomplemented
686C42—216no—
687C42—28no—
688C42—28no—
689C42—28no—
690C42—28no—
691C42—216no—
692C42—48no—
693C42—44no—
694C42—44no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23C2×C4⋊Q814yes—
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C23×D411yescharacteristic
721C23C23×Q812yes—
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×2−1+412yes—
727C23C2×2−1+412yes—
728C23C2×2−1+412yes—
729Q8—432no—
730Q8—416no—
731Q8—416no—
732Q8—416no—
733Q8—88no—
734Q8—88no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—432no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
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—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—416no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4C2×C4⋊Q814yes—
838C2×C4C2×C4⋊Q814yes—
839C2×C4#53414yes—
840C2×C4#53514yes—
841C2×C4#53514yes—
842C2×C4#53614yes—
843C2×C4D4214yes—
844C2×C4D4214yes—
845C2×C4D4214yes—
846C2×C4D4×Q818yes—
847C2×C4D4×Q818yes—
848C2×C4#56014yes—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—42no—
858C22—44no—
859C22—44no—
860C22C22×C4⋊Q811yescharacteristic
861C22C2×#53411yescharacteristic
862C22C2×#53511yescharacteristic
863C22C2×#53511yescharacteristic
864C22C2×#53611yescharacteristic
865C22C2×D4211yescharacteristic
866C22C2×D4211yescharacteristic
867C22C2×D4211yescharacteristic
868C22C2×D4×Q812yes—
869C22C2×D4×Q812yes—
870C22#348612yes—
871C22#349911yescharacteristic
872C22#349911yescharacteristic
873C22#349912yes—
874C22#350312yes—
875C22#350312yes—
876C22#350312yes—
877C22#350312yes—
878C22C2×#56011yescharacteristic
879C22#355212yes—
880C22#355212yes—
881C22#355212yes—
882C22#355212yes—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—28no—
887C4—28no—
888C4—44no—
889C4—42no—
890C4—44no—
891C4—44no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4#266918yes—
901C2—44no—
902C2#3528111yescharacteristic
903C2D4×C4⋊Q811yescharacteristic
904C2D4×C4⋊Q811yescharacteristic
905C2#3739011yescharacteristic
906C2#3767511yescharacteristic
907C2#3936011yescharacteristic
908C2#3959312yes—
909C2#3961612yes—
910C2#4600212yes—
911C2C2×#266911yescharacteristic
912C2#5912712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2868C2semidirect
2. C2×#2546C2semidirect
7. #16522C2semidirect
8. #15625C2semidirect
10. #15190C2semidirect
11. #15190C2semidirect
12. #15188C2semidirect
13. #15180C2semidirect
16. #14703C2semidirect
18. #14024C2semidirect
210. #388Q8semidirect
404. C2×C4⋊C4C2×Q8semidirect
450. C2×C42C2×Q8semidirect
475. #95C2×Q8semidirect
476. #95C2×Q8semidirect
685. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28682
C2×#25462
C2×#24292
C2×#24342
#165222
#156252
#153922
#151902
#151882
#151802
#151782
#147032
#144052
#140242
C4×#3882