Finite Group Databasebeta

← #524515

Subgroups — #524515

Order 512.

3562 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×#2316C212yesmaximal, complemented
4C2×#2293C211yesmaximal, characteristic
5#14712C211yesmaximal, characteristic, complemented
6#14408C214yesmaximal, complemented
7#14402C214yesmaximal, complemented
8#14264C212yesmaximal, complemented
9#14151C211yesmaximal, characteristic, complemented
10#14129C212yesmaximal, complemented
11#14046C212yesmaximal, complemented
12#14005C212yesmaximal, complemented
13#13920C212yesmaximal
14#13910C211yesmaximal, characteristic, complemented
15#13907C212yesmaximal, complemented
16#13906C212yesmaximal
17C4×#389C211yesmaximal, characteristic, complemented
18C22×C4×D4C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2212yes—
21C22×#117C2212yes—
22C23×C4⋊C4C2212yes—
23#2354—28no—
24D4×C4⋊C4C4116yescomplemented
25#2316—216no—
26#2293—28no—
27C2×#390C2212yes—
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#389C2212yes—
31C2×#389C2214yes—
32C2×#389C2214yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#388C2212yes—
45C2×#388C2214yes—
46C2×#388C2212yes—
47C2×#385C2214yes—
48C2×#384C2211yescharacteristic
49C2×#384C2212yes—
50C2×#384C2211yescharacteristic
51C2×#380C2214yes—
52C2×#380C2214yes—
53C2×#380C2212yes—
54C2×#380C2214yes—
55C2×#380C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C43C2211yescharacteristic
63#1444C2214yes—
64#1444C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2212yes—
76#1436C2212yes—
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85C22⋊#95C2214yes—
86C4×#95C2212yes—
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2314yes—
90C2×C4×D4—44no—
91C2×C4×D4—44no—
92C2×C4×D4C2×C4116yes—
93C2×C4×D4C2×C418yes—
94C2×C4×D4D418yes—
95C2×C4×D4Q818yes—
96C2×#117—28no—
97C2×#117—28no—
98C2×#117—28no—
99C2×#117—28no—
100C2×#117—44no—
101C2×#117—44no—
102C22×C4⋊C4—28no—
103C22×C4⋊C4—28no—
104C22×C4⋊C4C2×C4116yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C42C2312yes—
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#390—28no—
147#390—24no—
148#390—24no—
149#389—216no—
150#389—28no—
151#389—28no—
152#389—24no—
153#389—24no—
154#389—24no—
155#389—28no—
156#389—216no—
157#389—44no—
158#389—44no—
159#389—44no—
160#389—44no—
161#389C2×C4116yes—
162#389D418yescomplemented
163#388—216no—
164#388—28no—
165#388—28no—
166#385C2×C4132yes—
167#384—24no—
168#384—44no—
169#384C2×C418yes—
170#380—28no—
171#380—216no—
172#380—216no—
173#380—48no—
174#380C2×C4116yes—
175C4×C4⋊C4—28no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—24no—
178C4×C4⋊C4—44no—
179C4×C4⋊C4C2×C418yes—
180C4×C22⋊C4—28no—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C43—24no—
203C25C2412yes—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4C22×C414yes—
209C22×D4C2×D414yes—
210C22×D4C2×Q814yes—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—28no—
216C23×C4—28no—
217C23×C4—44no—
218C23×C4—44no—
219C23×C4—44no—
220C23×C4—44no—
221C23×C4C22×C418yes—
222C23×C4C22×C4116yes—
223C23×C4C2×D418yes—
224C23×C4C2×Q818yes—
225C23×C4C2412yes—
226C23×C4C2414yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2414yes—
231C23×C4C2411yescharacteristic
232C23×C4C2412yes—
233C23×C4C2411yescharacteristic
234C23×C4C2411yescharacteristic
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C4×D4—432no—
242C4×D4C4⋊C4164yescomplemented
243#117—432no—
244#117—432no—
245C2×C4⋊C4—28no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—28no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—264no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4C22×C418yes—
300C2×C4⋊C4C22×C4116yes—
301C2×C4⋊C4C22×C418yes—
302C2×C4⋊C4C22×C414yes—
303C2×C4⋊C4C22×C418yes—
304C2×C4⋊C4C22×C414yes—
305C2×C4⋊C4C22×C414yes—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D418yes—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D414yes—
310C2×C4⋊C4C2×Q814yes—
311C2×C4⋊C4#4114yes—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4C22×C4116yes—
333C2×C22⋊C4C22×C418yes—
334C2×C22⋊C4C2×D418yes—
335C2×C22⋊C4C2×Q818yes—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—28no—
342C2×C42—28no—
343C2×C42—24no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—44no—
362C2×C42—41no—
363C2×C42—41no—
364C2×C42C22×C418yes—
365C2×C42C22×C414yes—
366C2×C42C2×D414yes—
367C2×C42C2×D414yes—
368C2×C42C2×Q814yes—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—28no—
379#95—24no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C22×C418yes—
388#95C22×C4116yes—
389#95C2×D418yes—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24C23×C414yes—
403C24C22×D414yes—
404C24C22×Q814yes—
405C24C2511yescharacteristic
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4C2×C4⋊C4116yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—216no—
426C22×C4—216no—
427C22×C4—216no—
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—232no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—416no—
503C22×C4—416no—
504C22×C4—88no—
505C22×C4—88no—
506C22×C4—88no—
507C22×C4—88no—
508C22×C4C2×C4⋊C4132yes—
509C22×C4C23×C414yes—
510C22×C4C23×C418yes—
511C22×C4C23×C412yes—
512C22×C4C23×C414yes—
513C22×C4C23×C414yes—
514C22×C4C23×C412yes—
515C22×C4C23×C412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D414yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D414yes—
521C22×C4C22×D414yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×Q812yes—
526C22×C4C22×Q814yes—
527C22×C4C22×Q812yes—
528C22×C4C22×Q812yes—
529C22×C4C2×#4114yes—
530C22×C4C2×#4112yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C4H(5,𝔽2)12yes—
535C22×C42−1+412yes—
536C22×C42−1+412yes—
537C22×C42−1+412yes—
538C22×C42−1+412yes—
539C4⋊C4—232no—
540C4⋊C4—216no—
541C4⋊C4—216no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—44no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—84no—
555C4⋊C4—88no—
556C4⋊C4—88no—
557C4⋊C4—88no—
558C4⋊C4—88no—
559C4⋊C4C2×C4⋊C4116yes—
560C4⋊C4C4×D4116yes—
561C22⋊C4—416no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—416no—
567C22⋊C4—88no—
568C22⋊C4C2×C4⋊C4132yes—
569C42—216no—
570C42—28no—
571C42—44no—
572C42—44no—
573C42—416no—
574C42—44no—
575C42—44no—
576C42—48no—
577C42—48no—
578C42—44no—
579C42C2×C4⋊C4116yes—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23C22×C4⋊C418yes—
615C23C24×C411yescharacteristic
616C23C23×D411yescharacteristic
617C23C23×D411yescharacteristic
618C23C23×Q811yescharacteristic
619C23C22×#4111yescharacteristic
620C23C2×H(5,𝔽2)11yescharacteristic
621C23C2×H(5,𝔽2)11yescharacteristic
622C23C2×H(5,𝔽2)11yescharacteristic
623C23C2×H(5,𝔽2)11yescharacteristic
624C23C2×2−1+411yescharacteristic
625C23C2×2−1+411yescharacteristic
626C23C2×2−1+411yescharacteristic
627C23C2×2−1+411yescharacteristic
628C23#58511yescharacteristic
629C23#58511yescharacteristic
630D4—232no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—264no—
650C2×C4—28no—
651C2×C4—24no—
652C2×C4—28no—
653C2×C4—24no—
654C2×C4—28no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—41no—
684C2×C4—44no—
685C2×C4—41no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—832no—
728C2×C4C22×C4⋊C414yes—
729C2×C4C22×C4⋊C418yes—
730C2×C4C22×C4⋊C414yes—
731C2×C4C22×C4⋊C414yes—
732C2×C4C2×C4×D418yes—
733C2×C4C2×C4×D414yes—
734C2×C4#51814yes—
735C2×C4#51914yes—
736C2×C4#52014yes—
737C2×C4#53714yes—
738C2×C4#53714yes—
739C2×C4#54414yes—
740C2×C4#54414yes—
741C2×C4D4214yes—
742C2×C4#54714yes—
743C2×C4D4×Q814yes—
744C2×C4#55414yes—
745C22—28no—
746C22—28no—
747C22—28no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22C23×C4⋊C411yescharacteristic
761C22C22×C4×D411yescharacteristic
762C22C2×#51811yescharacteristic
763C22C2×#51911yescharacteristic
764C22C2×#52011yescharacteristic
765C22C4×H(5,𝔽2)11yescharacteristic
766C22C4×2−1+411yescharacteristic
767C22C2×#53711yescharacteristic
768C22C2×#53711yescharacteristic
769C22C2×#54411yescharacteristic
770C22C2×#54411yescharacteristic
771C22C2×D4211yescharacteristic
772C22C2×#54711yescharacteristic
773C22C2×D4×Q811yescharacteristic
774C22C2×#55411yescharacteristic
775C22#348811yescharacteristic
776C22#348911yescharacteristic
777C22#349611yescharacteristic
778C22#349711yescharacteristic
779C22#349811yescharacteristic
780C22#349911yescharacteristic
781C22#350311yescharacteristic
782C22#350411yescharacteristic
783C22#351411yescharacteristic
784C22#351811yescharacteristic
785C22#351911yescharacteristic
786C22#352311yescharacteristic
787C22#354411yescharacteristic
788C22#354611yescharacteristic
789C22#354711yescharacteristic
790C22#354711yescharacteristic
791C22#354811yescharacteristic
792C22#354811yescharacteristic
793C22#355211yescharacteristic
794C22#355511yescharacteristic
795C4—28no—
796C4—28no—
797C4—24no—
798C4—48no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—42no—
804C4—44no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—84no—
809C4#231618yescomplemented
810C4D4×C4⋊C418yes—
811C2—48no—
812C2C2×#231611yescharacteristic
813C2C2×D4×C4⋊C411yescharacteristic
814C2#3425011yescharacteristic
815C2#3431011yescharacteristic
816C2#3431111yescharacteristic
817C2#3448011yescharacteristic
818C2#3448411yescharacteristic
819C2#3892211yescharacteristic
820C2#3892311yescharacteristic
821C2#3896511yescharacteristic
822C2#3896711yescharacteristic
823C2#3934011yescharacteristic
824C2#3934111yescharacteristic
825C2#3936911yescharacteristic
826C2#3937011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2316C2semidirect
5. #14712C2semidirect
6. #14408C2semidirect
7. #14402C2semidirect
8. #14264C2semidirect
9. #14151C2semidirect
10. #14129C2semidirect
11. #14046C2semidirect
12. #14005C2semidirect
14. #13910C2semidirect
15. #13907C2semidirect
17. C4×#389C2semidirect
24. D4×C4⋊C4C4semidirect
162. #389D4semidirect
242. C4×D4C4⋊C4semidirect
809. C4#2316semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×D4×C4⋊C42
C2×#23162
C2×#22932
#147122
#144082
#144022
#142642
#141512
#141292
#140462
#140052
#139202
#139102
#139072
#139062
C4×#3892