Finite Group Databasebeta

← #525267

Subgroups — #525267

Order 512.

3294 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#2323C212yesmaximal, complemented
4C2×#2293C211yesmaximal, characteristic
5#14712C211yesmaximal, characteristic, complemented
6#14562C214yesmaximal, complemented
7#14556C214yesmaximal, complemented
8#14264C212yesmaximal, complemented
9#14141C212yesmaximal
10#14133C212yesmaximal, complemented
11#14005C212yesmaximal, complemented
12#14001C212yesmaximal
13#13974C212yesmaximal, complemented
14#13969C212yesmaximal, complemented
15#13906C211yesmaximal, characteristic
16C4⋊C42C211yesmaximal, characteristic, complemented
17C4×#391C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2212yes—
19C22×C4×Q8C2212yes—
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2212yes—
23#2538C4116yescomplemented
24C2×#396C2214yes—
25Q8×C4⋊C4—28no—
26#2323—216no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29#2293—28no—
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#390C2212yes—
33C2×#390C2212yes—
34C2×#389C2212yes—
35C2×#389C2214yes—
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2214yes—
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#388C2214yes—
44C2×#388C2214yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2214yes—
48C2×#387C2214yes—
49C2×#384C2211yescharacteristic
50C2×#384C2212yes—
51C2×#384C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C43C2211yescharacteristic
62#1444C2214yes—
63#1443C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1437C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2212yes—
75#1436C2212yes—
76#1436C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4×#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C24×C4C2312yes—
90C2×C22⋊Q8—28no—
91C2×C22⋊Q8—28no—
92C2×C22⋊Q8C2×C4116yes—
93C2×C4×Q8—28no—
94C2×C4×Q8—24no—
95C2×C4×Q8—28no—
96C2×C4×Q8—24no—
97C2×C4×Q8—44no—
98C2×C4×Q8C2×C418yes—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4C2×C418yes—
102C2×#117—28no—
103C2×#117—28no—
104C2×#117—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C42C2311yescharacteristic
134C22×C42C2312yes—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2314yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2312yes—
143C22×C42C2314yes—
144C22×C42C2311yescharacteristic
145#396C2×C4132yes—
146#391—24no—
147#391D418yescomplemented
148#390—24no—
149#390—24no—
150#390—44no—
151#390C2×C4116yes—
152#389—24no—
153#389—24no—
154#389—28no—
155#389—28no—
156#389—216no—
157#389—216no—
158#389—44no—
159#389—44no—
160#389C2×C4116yes—
161#388—216no—
162#388—216no—
163#388—28no—
164#388—28no—
165#388—48no—
166#387—216no—
167#384—28no—
168#384—24no—
169#384C2×C418yes—
170#380—28no—
171#380—44no—
172#380C2×C4116yes—
173C4×C4⋊C4—28no—
174C4×C4⋊C4—28no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—44no—
177C4×C4⋊C4D418yes—
178C4×C22⋊C4—28no—
179C2×#95C2312yes—
180C2×#95C2312yes—
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×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C43—24no—
202C25C2412yes—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8C22×C414yes—
208C22×Q8C2×D414yes—
209C22×Q8#4114yes—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4C22×C414yes—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4C22×C418yes—
224C23×C4C2414yes—
225C23×C4C2412yes—
226C23×C4C2414yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2411yescharacteristic
230C23×C4C2412yes—
231C23×C4C2412yes—
232C23×C4C2411yescharacteristic
233C23×C4C2412yes—
234C23×C4C2411yescharacteristic
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C23×C4C2412yes—
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C22⋊Q8—264no—
241C4×Q8—232no—
242C4×Q8—432no—
243C4×D4—232no—
244#117—432no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4C22×C414yes—
293C2×C4⋊C4C22×C414yes—
294C2×C4⋊C4C22×C418yes—
295C2×C4⋊C4C22×C418yes—
296C2×C4⋊C4C22×C4116yes—
297C2×C4⋊C4C22×C418yes—
298C2×C4⋊C4C22×C418yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×D414yes—
301C2×C4⋊C4C2×D414yes—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4C22×C418yes—
327C2×C22⋊C4C22×C4116yes—
328C2×C22⋊C4C22×C4116yes—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—28no—
336C2×C42—28no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—22no—
344C2×C42—24no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—28no—
354C2×C42—44no—
355C2×C42—41no—
356C2×C42—41no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42C22×C418yes—
360C2×C42C22×C414yes—
361C2×C42C2×D414yes—
362C2×C42C2×D418yes—
363C2×C42C2×D414yes—
364C2×C42#4114yes—
365#95—24no—
366#95—24no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—24no—
377#95—42no—
378#95—42no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95C22×C4116yes—
384#95C2×D418yes—
385#95C2×D418yes—
386#95C2×D418yes—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24C23×C414yes—
402C24C2511yescharacteristic
403C2×Q8—28no—
404C2×Q8—28no—
405C2×Q8—28no—
406C2×Q8—28no—
407C2×Q8—28no—
408C2×Q8—28no—
409C2×Q8C4×D4116yes—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4C23×C414yes—
507C22×C4C23×C414yes—
508C22×C4C23×C418yes—
509C22×C4C23×C412yes—
510C22×C4C23×C414yes—
511C22×C4C23×C412yes—
512C22×C4C23×C412yes—
513C22×C4C22×D414yes—
514C22×C4C22×D412yes—
515C22×C4C22×D414yes—
516C22×C4C22×D414yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D414yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4114yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C4H(5,𝔽2)12yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C42−1+412yes—
532C22×C42−1+412yes—
533C22×C42−1+412yes—
534C22×C42−1+412yes—
535C22×C42−1+412yes—
536C4⋊C4—28no—
537C4⋊C4—216no—
538C4⋊C4—28no—
539C4⋊C4—216no—
540C4⋊C4—232no—
541C4⋊C4—216no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—416no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—44no—
552C4⋊C4—84no—
553C4⋊C4—88no—
554C4⋊C4—88no—
555C22⋊C4—216no—
556C22⋊C4—232no—
557C22⋊C4—416no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—88no—
563C22⋊C4—88no—
564C42—216no—
565C42—28no—
566C42—216no—
567C42—44no—
568C42—44no—
569C42—416no—
570C42—44no—
571C42—44no—
572C42—48no—
573C42—44no—
574C42—88no—
575C42C4×D4116yes—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
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—
611C23C24×C411yescharacteristic
612C23C23×D411yescharacteristic
613C23C23×D411yescharacteristic
614C23C22×#4111yescharacteristic
615C23C22×#4111yescharacteristic
616C23C2×H(5,𝔽2)11yescharacteristic
617C23C2×H(5,𝔽2)11yescharacteristic
618C23C2×H(5,𝔽2)11yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23C2×2−1+411yescharacteristic
621C23C2×2−1+411yescharacteristic
622C23C2×2−1+411yescharacteristic
623C23C2×2−1+411yescharacteristic
624C23#58511yescharacteristic
625C23#58511yescharacteristic
626Q8—232no—
627D4—416no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—28no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
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—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—432no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4C2×C4×D414yes—
726C2×C4C2×C4×D418yes—
727C2×C4C2×C4×D414yes—
728C2×C4C2×C4×D414yes—
729C2×C4C2×C4×D414yes—
730C2×C4#51914yes—
731C2×C4#52014yes—
732C2×C4#52014yes—
733C2×C4#53614yes—
734C2×C4#53714yes—
735C2×C4#54114yes—
736C2×C4#54214yes—
737C2×C4D4214yes—
738C2×C4#54714yes—
739C2×C4#54814yes—
740C2×C4#55314yes—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22C22×C4×D411yescharacteristic
757C22C22×C4×D411yescharacteristic
758C22C2×#51911yescharacteristic
759C22C2×#52011yescharacteristic
760C22C2×#52011yescharacteristic
761C22C4×H(5,𝔽2)11yescharacteristic
762C22C4×2−1+411yescharacteristic
763C22C2×#53611yescharacteristic
764C22C2×#53711yescharacteristic
765C22C2×#54111yescharacteristic
766C22C2×#54211yescharacteristic
767C22C2×D4211yescharacteristic
768C22C2×#54711yescharacteristic
769C22C2×#54811yescharacteristic
770C22C2×#55311yescharacteristic
771C22#348811yescharacteristic
772C22#348911yescharacteristic
773C22#349711yescharacteristic
774C22#349711yescharacteristic
775C22#349811yescharacteristic
776C22#349911yescharacteristic
777C22#351111yescharacteristic
778C22#351211yescharacteristic
779C22#351711yescharacteristic
780C22#351811yescharacteristic
781C22#352211yescharacteristic
782C22#352311yescharacteristic
783C22#354411yescharacteristic
784C22#354611yescharacteristic
785C22#354711yescharacteristic
786C22#354811yescharacteristic
787C22#355011yescharacteristic
788C22#355211yescharacteristic
789C22#355511yescharacteristic
790C22#355511yescharacteristic
791C4—28no—
792C4—24no—
793C4—48no—
794C4—44no—
795C4—44no—
796C4—42no—
797C4—44no—
798C4—42no—
799C4—44no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—82no—
804C4—84no—
805C4#232318yescomplemented
806C4#236118yes—
807C2—84no—
808C2C2×#232311yescharacteristic
809C2C2×#236111yescharacteristic
810C2#3426711yescharacteristic
811C2#3431111yescharacteristic
812C2#3431311yescharacteristic
813C2#3448111yescharacteristic
814C2#3448411yescharacteristic
815C2#3912511yescharacteristic
816C2#3912711yescharacteristic
817C2#3919211yescharacteristic
818C2#3919411yescharacteristic
819C2#3934111yescharacteristic
820C2#3934311yescharacteristic
821C2#3937711yescharacteristic
822C2#3937911yescharacteristic
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
2. C2×Q8×C4⋊C4C2semidirect
3. C2×#2323C2semidirect
5. #14712C2semidirect
6. #14562C2semidirect
7. #14556C2semidirect
8. #14264C2semidirect
10. #14133C2semidirect
11. #14005C2semidirect
13. #13974C2semidirect
14. #13969C2semidirect
16. C4⋊C42C2semidirect
17. C4×#391C2semidirect
23. #2538C4semidirect
147. #391D4semidirect
805. C4#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×Q8×C4⋊C42
C2×#23232
C2×#22932
#147122
#145622
#145562
#142642
#141412
#141332
#140052
#140012
#139742
#139692
#139062
C4⋊C422
C4×#3912