Finite Group Databasebeta

← #530442

Subgroups — #530442

Order 512.

3474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2352C212yesmaximal, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#14686C211yesmaximal, characteristic, complemented
4#14447C214yesmaximal, complemented
5#14446C212yesmaximal, complemented
6#14445C212yesmaximal, complemented
7#14271C212yesmaximal
8#13999C214yesmaximal, complemented
9#13885C212yesmaximal, complemented
10#13879C212yesmaximal, complemented
11#13876C212yesmaximal, complemented
12#13872C212yesmaximal, complemented
13#13871C212yesmaximal, complemented
14#13778C212yesmaximal, complemented
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2212yes—
18C22×C4×D4C2211yescharacteristic
19C22×#117C2212yes—
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2352—216no—
24C4×#121C4116yescomplemented
25C2×#390C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#388C2214yes—
28C2×#388C2214yes—
29C2×#388C2212yes—
30C2×#387C2214yes—
31C2×#386C2214yes—
32C2×#386C2214yes—
33C2×#386C2212yes—
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#382C2212yes—
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4C2212yes—
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2214yes—
47C2×C4×C22⋊C4C2212yes—
48C22×#95C2212yes—
49C22×#95C2212yes—
50#1445C2214yes—
51#1443C2214yes—
52#1442C2214yes—
53#1441C2214yes—
54#1440C2214yes—
55#1439C2214yes—
56#1439C2214yes—
57#1439C2214yes—
58#1439C2214yes—
59#1438C2214yes—
60#1437C2214yes—
61#1436C2214yes—
62#1436C2214yes—
63#1436C2214yes—
64#1436C2214yes—
65#1436C2214yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75#1434C2214yes—
76C22⋊#95C2214yes—
77C23×D4C2312yes—
78C23×D4C2311yescharacteristic
79C24×C4C2312yes—
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2312yes—
83C24×C4C2312yes—
84C24×C4C2311yescharacteristic
85C2×#121—24no—
86C2×#121—24no—
87C2×#121C2×C418yes—
88C2×C4×D4—28no—
89C2×C4×D4—28no—
90C2×C4×D4—42no—
91C2×C4×D4—42no—
92C2×C4×D4C2×C4116yes—
93C2×C4×D4C2×C418yescomplemented
94C2×#117—28no—
95C2×#117—44no—
96C2×#117—44no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4D418yescomplemented
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C42—42no—
128C22×C42—42no—
129C22×C42C2×C418yes—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2312yes—
133C22×C42C2314yes—
134C22×C42C2314yes—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137#390C2×C418yescomplemented
138#389C2×C418yescomplemented
139#388—216no—
140#388—48no—
141#388C2×C4116yescomplemented
142#387—216no—
143#386—216no—
144#386—48no—
145#386C2×C4116yes—
146#384—42no—
147#384—42no—
148#382—28no—
149#380—28no—
150#380—28no—
151#380—28no—
152#380—44no—
153#380—44no—
154#380—44no—
155#380C2×C418yes—
156C4×C4⋊C4—28no—
157C4×C4⋊C4C2×C418yescomplemented
158C4×C22⋊C4—216no—
159C4×C22⋊C4C2×C4116yescomplemented
160C2×#95—28no—
161C2×#95—44no—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C25C2412yes—
183C25C2411yescharacteristic
184C22×D4—24no—
185C22×D4—24no—
186C22×D4—24no—
187C22×D4—24no—
188C22×D4—24no—
189C22×D4—24no—
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—41no—
193C22×D4—41no—
194C22×D4—41no—
195C22×D4—41no—
196C22×D4C22×C418yes—
197C22×D4C22×C414yes—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—41no—
218C23×C4—41no—
219C23×C4—41no—
220C23×C4—41no—
221C23×C4—41no—
222C23×C4—41no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4C22×C418yes—
232C23×C4C22×C414yes—
233C23×C4C22×C414yes—
234C23×C4C22×C414yes—
235C23×C4C2×D414yes—
236C23×C4C2×D418yes—
237C23×C4#4114yes—
238C23×C4#4114yes—
239C23×C4#4114yes—
240C23×C4C2414yes—
241C23×C4C2414yes—
242C23×C4C2414yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2414yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253#121—232no—
254C4×D4—264no—
255C4×D4—416no—
256#117—432no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—416no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—416no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4C22×C418yes—
296C2×C4⋊C4C22×C414yes—
297C2×C4⋊C4C22×C414yes—
298C2×C4⋊C4C22×C414yes—
299C2×C4⋊C4C2×D418yes—
300C2×C4⋊C4C2×D418yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
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×C418yes—
328C2×C22⋊C4C22×C418yes—
329C2×C22⋊C4C22×C418yes—
330C2×C22⋊C4C22×C418yes—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—28no—
338C2×C42—28no—
339C2×C42—416no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—41no—
343C2×C42—41no—
344C2×C42—41no—
345C2×C42—41no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42C22×C418yes—
349C2×C42C22×C414yes—
350C2×C42C22×C414yes—
351C2×C42C22×C414yes—
352C2×C42C22×C414yes—
353#95—28no—
354#95—28no—
355#95—28no—
356#95—28no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95C22×C418yes—
371#95C22×C418yes—
372#95C22×C418yes—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24C23×C414yes—
396C24C23×C412yes—
397C24C22×D412yes—
398C24C2×#4112yes—
399C24C2×#4112yes—
400C24C2×#4112yes—
401C24H(5,𝔽2)12yes—
402C242−1+412yes—
403C24C2511yescharacteristic
404C2×D4—216no—
405C2×D4—216no—
406C2×D4—216no—
407C2×D4—28no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—216no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—84no—
518C22×C4—84no—
519C22×C4—84no—
520C22×C4—84no—
521C22×C4—84no—
522C22×C4—84no—
523C22×C4—84no—
524C22×C4—84no—
525C22×C4#117116yescomplemented
526C22×C4C4×D4116yes—
527C22×C4C23×C412yes—
528C22×C4C23×C414yes—
529C22×C4C23×C414yes—
530C22×C4C23×C414yes—
531C22×C4C23×C412yes—
532C22×C4C23×C412yes—
533C22×C4C23×C412yes—
534C22×C4C23×C412yes—
535C22×C4C23×C412yes—
536C22×C4C22×D418yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C42−1+412yes—
550C22×C42−1+412yes—
551C4⋊C4—28no—
552C4⋊C4—216no—
553C4⋊C4—216no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—84no—
562C4⋊C4—84no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C22⋊C4—216no—
566C22⋊C4—216no—
567C22⋊C4—216no—
568C22⋊C4—216no—
569C22⋊C4—48no—
570C22⋊C4—416no—
571C22⋊C4—416no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C42—216no—
576C42—28no—
577C42—28no—
578C42—44no—
579C42—44no—
580C42—416no—
581C42—88no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C2×#11714yes—
646C23C2×C4×D414yes—
647C23#52014yes—
648C23#54714yes—
649C23#55014yes—
650C23#55514yes—
651C23#55614yes—
652C23C24×C411yescharacteristic
653C23C23×D411yescharacteristic
654C23C22×#4111yescharacteristic
655C23C22×#4111yescharacteristic
656C23C22×#4111yescharacteristic
657C23C2×H(5,𝔽2)11yescharacteristic
658C23C2×H(5,𝔽2)11yescharacteristic
659C23C2×H(5,𝔽2)11yescharacteristic
660C23C2×H(5,𝔽2)11yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×2−1+411yescharacteristic
663C23C2×2−1+411yescharacteristic
664C23C2×2−1+411yescharacteristic
665C23#58511yescharacteristic
666C23#58511yescharacteristic
667D4—416no—
668D4—432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—232no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—416no—
710C2×C4—416no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
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—44no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—432no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—816no—
754C2×C4—816no—
755C2×C4C2×#11714yes—
756C2×C4C2×#11714yes—
757C2×C4C2×C4×D414yes—
758C2×C4C2×C4×D414yes—
759C2×C4#51814yes—
760C2×C4#52014yes—
761C2×C4#52014yes—
762C2×C4#53414yes—
763C2×C4#53714yes—
764C2×C4#53814yes—
765C2×C4#53914yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22#235418yes—
796C22C22×#11711yescharacteristic
797C22C22×C4×D411yescharacteristic
798C22C2×#51811yescharacteristic
799C22C2×#52011yescharacteristic
800C22C2×#52011yescharacteristic
801C22C2×#52011yescharacteristic
802C22#342811yescharacteristic
803C22C2×#53411yescharacteristic
804C22C2×#53711yescharacteristic
805C22C2×#53811yescharacteristic
806C22C2×#53911yescharacteristic
807C22C2×#54711yescharacteristic
808C22C2×#55011yescharacteristic
809C22C2×#55511yescharacteristic
810C22C2×#55611yescharacteristic
811C22#349611yescharacteristic
812C22#349711yescharacteristic
813C22#350511yescharacteristic
814C22#350511yescharacteristic
815C22#350511yescharacteristic
816C22#350511yescharacteristic
817C22#350611yescharacteristic
818C22#350711yescharacteristic
819C22#350811yescharacteristic
820C22#350911yescharacteristic
821C22#351111yescharacteristic
822C22#351111yescharacteristic
823C22#353611yescharacteristic
824C22#353611yescharacteristic
825C22#353711yescharacteristic
826C22#353811yescharacteristic
827C22#355811yescharacteristic
828C22#355911yescharacteristic
829C22#356111yescharacteristic
830C22#356311yescharacteristic
831C4—24no—
832C4—24no—
833C4—24no—
834C4—24no—
835C4—44no—
836C4—42no—
837C4—48no—
838C4—44no—
839C4—44no—
840C4—84no—
841C4—84no—
842C4—84no—
843C4#232518yes—
844C2—28no—
845C2—84no—
846C2C2×#232511yescharacteristic
847C2C2×#235411yescharacteristic
848C2#3418511yescharacteristic
849C2#3418811yescharacteristic
850C2#3420611yescharacteristic
851C2#3436011yescharacteristic
852C2#3438211yescharacteristic
853C2#3948611yescharacteristic
854C2#3948711yescharacteristic
855C2#3950311yescharacteristic
856C2#3950411yescharacteristic
857C2#3974211yescharacteristic
858C2#3974311yescharacteristic
859C2#3975911yescharacteristic
860C2#3976011yescharacteristic
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×#2352C2semidirect
3. #14686C2semidirect
4. #14447C2semidirect
5. #14446C2semidirect
6. #14445C2semidirect
8. #13999C2semidirect
9. #13885C2semidirect
10. #13879C2semidirect
11. #13876C2semidirect
12. #13872C2semidirect
13. #13871C2semidirect
14. #13778C2semidirect
15. C2×C4⋊#95C2semidirect
24. C4×#121C4semidirect
93. C2×C4×D4C2×C4semidirect
102. C22×C4⋊C4D4semidirect
137. #390C2×C4semidirect
138. #389C2×C4semidirect
141. #388C2×C4semidirect
157. C4×C4⋊C4C2×C4semidirect
159. C4×C22⋊C4C2×C4semidirect
525. C22×C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23522
C2×C4×#1212
#146862
#144472
#144462
#144452
#142712
#139992
#138852
#138792
#138762
#138722
#138712
#137782
C2×C4⋊#952