Finite Group Databasebeta

← #522237

Subgroups — #522237

Order 512.

2770 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2369C211yesmaximal, characteristic, complemented
3C2×#2283C211yesmaximal, characteristic
4#14380C214yesmaximal, complemented
5#14364C214yesmaximal
6#14266C212yesmaximal, complemented
7#14161C211yesmaximal, characteristic, complemented
8#14151C211yesmaximal, characteristic, complemented
9#14006C212yesmaximal, complemented
10#13994C212yesmaximal
11#13994C212yesmaximal
12#13982C212yesmaximal, complemented
13#13974C212yesmaximal
14#13974C212yesmaximal
15C4⋊C42C211yesmaximal, characteristic, complemented
16#13783C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C23×C42C2211yescharacteristic
21#2857C4116yescomplemented
22#2369—28no—
23C2×#391C2214yes—
24C2×#391C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#389C2212yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#388C2214yes—
32C2×#388C2214yes—
33C2×#384C2211yescharacteristic
34#2283—28no—
35C2×#383C2212yes—
36C2×#382C2211yescharacteristic
37C2×#382C2211yescharacteristic
38C2×#381C2212yes—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×#376C2212yes—
56#1446C2214yes—
57#1445C2214yes—
58#1443C2214yes—
59#1443C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1440C2214yes—
65#1440C2214yes—
66#1436C2214yes—
67#1436C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70C4⋊#95C2214yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81#1434C2212yes—
82#1434C2214yes—
83#1434C2214yes—
84C22⋊#95C2212yes—
85C4×#95C2212yes—
86C23×Q8C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×C4⋊Q8—24no—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8C2×C418yes—
93C2×C22⋊Q8—44no—
94C2×C22⋊Q8—44no—
95C2×C22⋊Q8C2×C4116yes—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C22⋊C4C2312yes—
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2314yes—
117C22×C42—24no—
118C22×C42—24no—
119C22×C42C2×C418yes—
120C22×C42C2312yes—
121C22×C42C2312yes—
122C22×C42C2312yes—
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126C22×C42C2312yes—
127C22×C42C2314yes—
128C22×C42C2314yes—
129C22×C42C2311yescharacteristic
130#391—216no—
131#391C2×C4116yes—
132#389—28no—
133#389—28no—
134#389—28no—
135#389—44no—
136#389C2×C4116yes—
137#389C2×C4116yes—
138#388—48no—
139#388—48no—
140#384C2×C418yes—
141#383—28no—
142#382—24no—
143#382—24no—
144#381—28no—
145#380—24no—
146#380—24no—
147#380—24no—
148#380—24no—
149#380C2×C4116yes—
150#380C2×C4116yes—
151C4×C4⋊C4—28no—
152C4×C4⋊C4—28no—
153C4×C4⋊C4—28no—
154C4×C4⋊C4—24no—
155C4×C4⋊C4—24no—
156C4×C4⋊C4—24no—
157C4×C4⋊C4—44no—
158C4×C4⋊C4D418yes—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—44no—
161#376—28no—
162C2×#95C2312yes—
163C2×#95C2312yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C25C2411yescharacteristic
193C22×Q8—24no—
194C22×Q8—24no—
195C22×Q8—42no—
196C22×Q8—42no—
197C22×Q8—42no—
198C22×Q8—42no—
199C22×Q8C22×C418yes—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—41no—
217C23×C4—41no—
218C23×C4C22×C414yes—
219C23×C4C22×C414yes—
220C23×C4C22×C414yes—
221C23×C4C2412yes—
222C23×C4C2412yes—
223C23×C4C2412yes—
224C23×C4C2412yes—
225C23×C4C2414yes—
226C23×C4C2414yes—
227C23×C4C2411yescharacteristic
228C23×C4C2411yescharacteristic
229C23×C4C2411yescharacteristic
230C23×C4C2412yes—
231C23×C4C2412yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2411yescharacteristic
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C4⋊Q8—232no—
238C22⋊Q8—432no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4C22×C418yes—
278C2×C4⋊C4C22×C418yes—
279C2×C4⋊C4C22×C418yes—
280C2×C4⋊C4C22×C418yes—
281C2×C4⋊C4C22×C418yes—
282C2×C4⋊C4C22×C4116yes—
283C2×C4⋊C4C2×D414yes—
284C2×C4⋊C4C2×D414yes—
285C2×C4⋊C4#4114yes—
286C2×C4⋊C4#4114yes—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4C22×C4116yes—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—24no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—24no—
310C2×C42—232no—
311C2×C42—24no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—28no—
321C2×C42—28no—
322C2×C42—44no—
323C2×C42—44no—
324C2×C42—44no—
325C2×C42—44no—
326C2×C42C22×C414yes—
327C2×C42C22×C414yes—
328C2×C42C22×C414yes—
329C2×C42C22×C414yes—
330C2×C42C2×D418yes—
331C2×C42C2×D414yes—
332C2×C42#4114yes—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—28no—
341#95—28no—
342#95—24no—
343#95—28no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—28no—
348#95—42no—
349#95—44no—
350#95—42no—
351#95—44no—
352#95—42no—
353#95—42no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—44no—
360#95C22×C4116yes—
361#95C22×C4116yes—
362#95C2×D418yes—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24C23×C412yes—
376C24H(5,𝔽2)12yes—
377C24H(5,𝔽2)12yes—
378C24C2511yescharacteristic
379C2×Q8—216no—
380C2×Q8—48no—
381C2×Q8—48no—
382C2×Q8—84no—
383C2×Q8—84no—
384C2×Q8—84no—
385C2×Q8—84no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—28no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4C23×C412yes—
494C22×C4C23×C412yes—
495C22×C4C23×C418yes—
496C22×C4C23×C418yes—
497C22×C4C23×C412yes—
498C22×C4C23×C412yes—
499C22×C4C23×C412yes—
500C22×C4C23×C412yes—
501C22×C4C22×D414yes—
502C22×C4C22×D414yes—
503C22×C4C22×D412yes—
504C22×C4C22×D412yes—
505C22×C4C22×D412yes—
506C22×C4C2×#4114yes—
507C22×C4C2×#4114yes—
508C22×C4C2×#4112yes—
509C22×C4C2×#4112yes—
510C22×C4C2×#4112yes—
511C22×C4C2×#4112yes—
512C22×C4C2×#4112yes—
513C22×C4H(5,𝔽2)12yes—
514C22×C42−1+412yes—
515C22×C42−1+412yes—
516C22×C42−1+412yes—
517C22×C42−1+412yes—
518C22×C42−1+412yes—
519C4⋊C4—216no—
520C4⋊C4—216no—
521C4⋊C4—216no—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—416no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C4⋊C4—44no—
533C4⋊C4—88no—
534C4⋊C4—88no—
535C22⋊C4—232no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—48no—
539C22⋊C4—48no—
540C42—28no—
541C42—28no—
542C42—28no—
543C42—216no—
544C42—48no—
545C42—48no—
546C42—48no—
547C42—88no—
548C42—88no—
549C42C4×D4116yes—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23#51814yes—
585C23C24×C411yescharacteristic
586C23C23×D411yescharacteristic
587C23C22×#4111yescharacteristic
588C23C22×#4111yescharacteristic
589C23C22×#4111yescharacteristic
590C23C2×H(5,𝔽2)11yescharacteristic
591C23C2×H(5,𝔽2)11yescharacteristic
592C23C2×H(5,𝔽2)11yescharacteristic
593C23C2×2−1+411yescharacteristic
594C23C2×2−1+411yescharacteristic
595C23C2×2−1+411yescharacteristic
596C23C2×2−1+411yescharacteristic
597C23C2×2−1+411yescharacteristic
598C23#58511yescharacteristic
599C23#58511yescharacteristic
600Q8—816no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—28no—
611C2×C4—28no—
612C2×C4—22no—
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—416no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—416no—
672C2×C4—416no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4C2×C4×D414yes—
702C2×C4C2×C4×D414yes—
703C2×C4C2×C4×D414yes—
704C2×C4C4×#4114yes—
705C2×C4#51914yes—
706C2×C4#51914yes—
707C2×C4#52014yes—
708C2×C4#53614yes—
709C2×C4#53714yes—
710C2×C4#54114yes—
711C2×C4#54214yes—
712C2×C4#54714yes—
713C2×C4#54814yes—
714C2×C4#55214yes—
715C2×C4#55614yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22C22×C4×D411yescharacteristic
732C22C2×C4×#4111yescharacteristic
733C22C2×#51811yescharacteristic
734C22C2×#51911yescharacteristic
735C22C2×#51911yescharacteristic
736C22C2×#52011yescharacteristic
737C22#342811yescharacteristic
738C22C2×#53611yescharacteristic
739C22C2×#53711yescharacteristic
740C22C2×#54111yescharacteristic
741C22C2×#54211yescharacteristic
742C22C2×#54711yescharacteristic
743C22C2×#54811yescharacteristic
744C22C2×#55211yescharacteristic
745C22C2×#55611yescharacteristic
746C22#348811yescharacteristic
747C22#348811yescharacteristic
748C22#349411yescharacteristic
749C22#349411yescharacteristic
750C22#351511yescharacteristic
751C22#351511yescharacteristic
752C22#351811yescharacteristic
753C22#351811yescharacteristic
754C22#351911yescharacteristic
755C22#351911yescharacteristic
756C22#352211yescharacteristic
757C22#352211yescharacteristic
758C22#354411yescharacteristic
759C22#354411yescharacteristic
760C22#354411yescharacteristic
761C22#354411yescharacteristic
762C22#354711yescharacteristic
763C22#354711yescharacteristic
764C22#355511yescharacteristic
765C22#355511yescharacteristic
766C4—24no—
767C4—44no—
768C4—44no—
769C4—42no—
770C4—44no—
771C4—42no—
772C4—42no—
773C4—48no—
774C4—48no—
775C4—44no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4#232318yes—
781C4#236218yes—
782C2—44no—
783C2C2×#232311yescharacteristic
784C2C2×#236211yescharacteristic
785C2#3420411yescharacteristic
786C2#3423111yescharacteristic
787C2#3423611yescharacteristic
788C2#3436511yescharacteristic
789C2#3439411yescharacteristic
790C2#3892111yescharacteristic
791C2#3892211yescharacteristic
792C2#3893111yescharacteristic
793C2#3893211yescharacteristic
794C2#3912511yescharacteristic
795C2#3912611yescharacteristic
796C2#3915711yescharacteristic
797C2#3915811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
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×#2369C2semidirect
4. #14380C2semidirect
6. #14266C2semidirect
7. #14161C2semidirect
8. #14151C2semidirect
9. #14006C2semidirect
12. #13982C2semidirect
15. C4⋊C42C2semidirect
16. #13783C2semidirect
21. #2857C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#23692
C2×#22832
#143802
#143642
#142662
#141612
#141512
#140062
#139942
#139822
#139742
C4⋊C422
#137832
C4×#3802