Finite Group Databasebeta

← #530380

Subgroups — #530380

Order 512.

4102 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C212yesmaximal, complemented
2C2×#2325C212yesmaximal
3C2×C4×#121C211yesmaximal, characteristic
4#14686C211yesmaximal, characteristic, complemented
5#14442C214yesmaximal, complemented
6#14441C212yesmaximal, complemented
7#14440C212yesmaximal, complemented
8#14275C212yesmaximal, complemented
9#13975C214yesmaximal, complemented
10#13884C212yesmaximal, complemented
11#13880C212yesmaximal, complemented
12#13876C212yesmaximal, complemented
13#13872C212yesmaximal, complemented
14#13872C212yesmaximal, complemented
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2214yes—
18C22×C4×D4C2212yes—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24D4×C4⋊C4—216no—
25#2325—216no—
26C4×#121C4116yescomplemented
27C2×#390C2211yescharacteristic
28C2×#389C2214yes—
29C2×#389C2211yescharacteristic
30C2×#388C2214yes—
31C2×#388C2212yes—
32C2×#387C2214yes—
33C2×#386C2214yes—
34C2×#386C2214yes—
35C2×#386C2212yes—
36C2×#385C2214yes—
37C2×#385C2214yes—
38C2×#385C2214yes—
39C2×#385C2214yes—
40C2×#384C2212yes—
41C2×#384C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2212yes—
53C22×#95C2212yes—
54C22×#95C2212yes—
55#1444C2214yes—
56#1444C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1441C2214yes—
60#1441C2214yes—
61#1441C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1436C2214yes—
66#1436C2214yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C22⋊#95C2214yes—
77C22⋊#95C2214yes—
78C23×D4C2312yes—
79C23×D4C2311yescharacteristic
80C24×C4C2312yes—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2312yes—
84C24×C4C2314yes—
85C24×C4C2312yes—
86C24×C4C2311yescharacteristic
87C2×#121C2×C418yes—
88C2×#121D418yes—
89C2×#121Q818yes—
90C2×C4×D4—28no—
91C2×C4×D4—28no—
92C2×C4×D4—216no—
93C2×C4×D4—216no—
94C2×C4×D4—42no—
95C2×C4×D4—42no—
96C2×C4×D4—48no—
97C2×C4×D4C2×C4116yescomplemented
98C2×C4×D4C2×C418yescomplemented
99C22×C4⋊C4—24no—
100C22×C4⋊C4—28no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—44no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4D418yescomplemented
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C42—42no—
135C22×C42—42no—
136C22×C42C2×C418yescomplemented
137C22×C42C2314yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143#390C2×C418yescomplemented
144#389—216no—
145#389C2×C418yescomplemented
146#388—216no—
147#388C2×C4116yescomplemented
148#387—216no—
149#386—216no—
150#386—216no—
151#386C2×C4116yescomplemented
152#385—216no—
153#385—216no—
154#385—216no—
155#385—48no—
156#384—28no—
157#384—42no—
158#384—42no—
159#380—28no—
160#380—28no—
161#380—28no—
162#380—44no—
163#380—44no—
164#380—44no—
165#380C2×C418yescomplemented
166C4×C4⋊C4—28no—
167C4×C4⋊C4C2×C418yescomplemented
168C4×C22⋊C4C2×C4116yescomplemented
169C2×#95—28no—
170C2×#95—44no—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C25C2412yes—
190C25C2411yescharacteristic
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—24no—
195C22×D4—41no—
196C22×D4—41no—
197C22×D4—41no—
198C22×D4—41no—
199C22×D4C22×C418yes—
200C22×D4C22×C414yes—
201C22×D4C2×D418yes—
202C22×D4C2×D414yes—
203C22×D4C2×Q818yes—
204C22×D4C2×Q814yes—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—28no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—28no—
226C23×C4—41no—
227C23×C4—41no—
228C23×C4—41no—
229C23×C4—41no—
230C23×C4—41no—
231C23×C4—41no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—44no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4C22×C418yes—
246C23×C4C22×C414yes—
247C23×C4C22×C414yes—
248C23×C4C22×C414yes—
249C23×C4C2×D414yes—
250C23×C4C2×D418yes—
251C23×C4C2×D414yes—
252C23×C4C2×Q814yes—
253C23×C4#4114yes—
254C23×C4C2414yes—
255C23×C4C2414yes—
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2414yes—
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267#121C4⋊C4164yescomplemented
268C4×D4—264no—
269C4×D4—416no—
270C4×D4—464no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—416no—
294C2×C4⋊C4—432no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—416no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4C22×C418yes—
318C2×C4⋊C4C22×C414yes—
319C2×C4⋊C4C22×C414yes—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C2×D418yes—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×Q814yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4C22×C418yes—
346C2×C22⋊C4C22×C418yes—
347C2×C22⋊C4C22×C418yes—
348C2×C22⋊C4C22×C418yes—
349C2×C22⋊C4C22×C418yes—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×Q818yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—28no—
359C2×C42—28no—
360C2×C42—416no—
361C2×C42—44no—
362C2×C42—41no—
363C2×C42—41no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42C22×C418yes—
367C2×C42C22×C414yes—
368C2×C42C22×C414yes—
369C2×C42C22×C414yes—
370C2×C42C22×C414yes—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C22×C418yes—
387#95C22×C418yes—
388#95C22×C418yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C23×C414yes—
410C24C23×C412yes—
411C24C22×D414yes—
412C24C22×D412yes—
413C24C22×D412yes—
414C24C22×Q814yes—
415C24C22×Q812yes—
416C24C2×#4112yes—
417C24H(5,𝔽2)12yes—
418C242−1+412yes—
419C24C2511yescharacteristic
420C2×D4—216no—
421C2×D4—216no—
422C2×D4—216no—
423C2×D4—216no—
424C2×D4—216no—
425C2×D4—216no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4C2×C4⋊C4132yescomplemented
433C2×D4C2×C4⋊C4116yescomplemented
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—28no—
489C22×C4—216no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—88no—
534C22×C4—84no—
535C22×C4—88no—
536C22×C4—84no—
537C22×C4—88no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4—84no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—88no—
545C22×C4—88no—
546C22×C4C2×C4⋊C4116yescomplemented
547C22×C4C4×D4116yes—
548C22×C4C23×C412yes—
549C22×C4C23×C414yes—
550C22×C4C23×C414yes—
551C22×C4C23×C412yes—
552C22×C4C23×C414yes—
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C412yes—
556C22×C4C23×C412yes—
557C22×C4C22×D418yes—
558C22×C4C22×D412yes—
559C22×C4C22×D414yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×Q812yes—
564C22×C4C22×Q814yes—
565C22×C4C22×Q812yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C42−1+412yes—
573C22×C42−1+412yes—
574C4⋊C4—216no—
575C4⋊C4—216no—
576C4⋊C4—48no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—416no—
580C4⋊C4—48no—
581C4⋊C4—416no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C4⋊C4—88no—
590C4⋊C4C2×C4⋊C4116yescomplemented
591C22⋊C4—216no—
592C22⋊C4—216no—
593C22⋊C4—216no—
594C22⋊C4—48no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C22⋊C4C2×C4⋊C4132yescomplemented
600C42—216no—
601C42—28no—
602C42—28no—
603C42—44no—
604C42—44no—
605C42—416no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23C22×C4⋊C418yes—
669C23C22×C4⋊C414yes—
670C23C2×C4×D414yes—
671C23#52014yes—
672C23D4214yes—
673C23#54714yes—
674C23D4×Q814yes—
675C23#55414yes—
676C23C24×C411yescharacteristic
677C23C23×D411yescharacteristic
678C23C23×D411yescharacteristic
679C23C23×Q811yescharacteristic
680C23C22×#4111yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×2−1+411yescharacteristic
687C23C2×2−1+411yescharacteristic
688C23C2×2−1+411yescharacteristic
689C23#58511yescharacteristic
690C23#58511yescharacteristic
691D4—264no—
692D4—416no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—41no—
753C2×C4—44no—
754C2×C4—432no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—816no—
777C2×C4—832no—
778C2×C4—816no—
779C2×C4C22×C4⋊C414yes—
780C2×C4C22×C4⋊C418yes—
781C2×C4C22×C4⋊C414yes—
782C2×C4C2×C4×D414yes—
783C2×C4C2×C4×D414yes—
784C2×C4#51814yes—
785C2×C4#52014yes—
786C2×C4#52014yes—
787C2×C4#53414yes—
788C2×C4#53714yes—
789C2×C4#53814yes—
790C2×C4#53914yes—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—28no—
806C22—28no—
807C22—28no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22D4×C4⋊C418yes—
821C22C23×C4⋊C411yescharacteristic
822C22C22×C4×D411yescharacteristic
823C22C2×#51811yescharacteristic
824C22C2×#52011yescharacteristic
825C22C2×#52011yescharacteristic
826C22C2×#52011yescharacteristic
827C22#342811yescharacteristic
828C22C2×#53411yescharacteristic
829C22C2×#53711yescharacteristic
830C22C2×#53811yescharacteristic
831C22C2×#53911yescharacteristic
832C22C2×D4211yescharacteristic
833C22C2×#54711yescharacteristic
834C22C2×D4×Q811yescharacteristic
835C22C2×#55411yescharacteristic
836C22#349611yescharacteristic
837C22#349611yescharacteristic
838C22#349611yescharacteristic
839C22#349711yescharacteristic
840C22#349811yescharacteristic
841C22#349911yescharacteristic
842C22#350111yescharacteristic
843C22#350111yescharacteristic
844C22#350311yescharacteristic
845C22#350311yescharacteristic
846C22#350611yescharacteristic
847C22#350711yescharacteristic
848C22#353611yescharacteristic
849C22#353611yescharacteristic
850C22#353711yescharacteristic
851C22#353811yescharacteristic
852C22#355811yescharacteristic
853C22#355911yescharacteristic
854C22#356111yescharacteristic
855C22#356311yescharacteristic
856C4—24no—
857C4—24no—
858C4—28no—
859C4—24no—
860C4—24no—
861C4—44no—
862C4—42no—
863C4—44no—
864C4—48no—
865C4—84no—
866C4—84no—
867C4—84no—
868C4#232518yescomplemented
869C2—28no—
870C2—48no—
871C2C2×#232511yescharacteristic
872C2C2×D4×C4⋊C411yescharacteristic
873C2#3418111yescharacteristic
874C2#3418311yescharacteristic
875C2#3420611yescharacteristic
876C2#3436011yescharacteristic
877C2#3438211yescharacteristic
878C2#3935811yescharacteristic
879C2#3935911yescharacteristic
880C2#3937511yescharacteristic
881C2#3937611yescharacteristic
882C2#3961411yescharacteristic
883C2#3961511yescharacteristic
884C2#3963111yescharacteristic
885C2#3963211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×D4×C4⋊C4C2semidirect
4. #14686C2semidirect
5. #14442C2semidirect
6. #14441C2semidirect
7. #14440C2semidirect
8. #14275C2semidirect
9. #13975C2semidirect
10. #13884C2semidirect
11. #13880C2semidirect
12. #13876C2semidirect
13. #13872C2semidirect
14. #13872C2semidirect
15. C2×C4⋊#95C2semidirect
26. C4×#121C4semidirect
97. C2×C4×D4C2×C4semidirect
98. C2×C4×D4C2×C4semidirect
107. C22×C4⋊C4D4semidirect
136. C22×C42C2×C4semidirect
143. #390C2×C4semidirect
145. #389C2×C4semidirect
147. #388C2×C4semidirect
151. #386C2×C4semidirect
165. #380C2×C4semidirect
167. C4×C4⋊C4C2×C4semidirect
168. C4×C22⋊C4C2×C4semidirect
267. #121C4⋊C4semidirect
432. C2×D4C2×C4⋊C4semidirect
433. C2×D4C2×C4⋊C4semidirect
546. C22×C4C2×C4⋊C4semidirect
590. C4⋊C4C2×C4⋊C4semidirect
599. C22⋊C4C2×C4⋊C4semidirect
868. C4#2325semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×#23252
C2×C4×#1212
#146862
#144422
#144412
#144402
#142752
#139752
#138842
#138802
#138762
#138722
C2×C4⋊#952