Finite Group Databasebeta

← #216008

Subgroups — #216008

Order 512.

959 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
1#35079C211yesmaximal, characteristic
2#21904C211yesmaximal, characteristic
3#13788C211yesmaximal, characteristic
4#9910C211yesmaximal, characteristic, complemented
5#9910C211yesmaximal, characteristic, complemented
6#9909C211yesmaximal, characteristic, complemented
7#9908C211yesmaximal, characteristic, complemented
8#9888C211yesmaximal, characteristic, complemented
9#9887C211yesmaximal, characteristic, complemented
10#9886C211yesmaximal, characteristic, complemented
11#9885C211yesmaximal, characteristic, complemented
12#8715C211yesmaximal, characteristic
13#8715C211yesmaximal, characteristic
14#8713C211yesmaximal, characteristic
15#8712C211yesmaximal, characteristic
16#2857C2211yescharacteristic
17#2857C2211yescharacteristic
18#2851C2211yescharacteristic
19#2851C2211yescharacteristic
20#2667—21no—
21#2665—21no—
22#2569—21no—
23#2549—21no—
24#2442C411yescharacteristic, complemented
25#2442C411yescharacteristic, complemented
26#2441C411yescharacteristic, complemented
27#2441C411yescharacteristic, complemented
28#2440C411yescharacteristic, complemented
29#2440C411yescharacteristic, complemented
30#2439C411yescharacteristic, complemented
31#2439C411yescharacteristic, complemented
32#2437—21no—
33#2437—21no—
34#2329—21no—
35#2329—21no—
36C2×#388—21no—
37#2280C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40#1924—21no—
41#1924—21no—
42#1923—21no—
43#1923—21no—
44#1797C2211yescharacteristic
45#1797C2211yescharacteristic
46#1779C2211yescharacteristic
47#1779C2211yescharacteristic
48#1749C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50#1437—21no—
51#1436—21no—
52C4⋊#95C2211yescharacteristic
53#1434—21no—
54#1434C2211yescharacteristic
55C22⋊#95C2211yescharacteristic
56C22⋊#95C2211yescharacteristic
57C4×#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59#1294C2211yescharacteristic
60#1294C2211yescharacteristic
61#1294C2211yescharacteristic
62#1294C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4C2311yescharacteristic
76C2×C4⋊Q8C2×C411yescharacteristic
77C2×C4⋊Q8C2×C411yescharacteristic
78C2×#125C2×C411yescharacteristic
79C2×#125C2×C411yescharacteristic
80C2×C22⋊Q8—21no—
81C2×C22⋊Q8—21no—
82C2×C22⋊Q8—21no—
83C2×C22⋊Q8—21no—
84C2×#117C2×C411yescharacteristic
85C2×#117C2×C411yescharacteristic
86C22×C4⋊C4—21no—
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4D411yescharacteristic
93C22×C22⋊C4D411yescharacteristic
94C22×C42—21no—
95C22×C42—21no—
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C22⋊C8—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×#97—21no—
109C2×C4×C8—21no—
110#400—21no—
111#400—21no—
112#399—21no—
113#399—21no—
114#398—21no—
115#398—21no—
116#398—21no—
117#398—21no—
118#396—21no—
119#396—21no—
120#396—21no—
121#396—21no—
122#395—21no—
123#395—21no—
124#393—21no—
125#393—21no—
126#391—21no—
127#391—21no—
128#391—21no—
129#391—21no—
130#389—21no—
131#389—21no—
132#389—21no—
133#389—21no—
134#389C2×C411yescharacteristic
135#389C2×C411yescharacteristic
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#389C2×C411yescharacteristic
141#389C2×C411yescharacteristic
142#388—28no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#385—21no—
152#385—21no—
153#385—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#384C2×C411yescharacteristic
160#384C2×C411yescharacteristic
161#382C2×C411yescharacteristic
162#382C2×C411yescharacteristic
163#381—21no—
164#380—21no—
165#380—21no—
166#380—21no—
167#380—21no—
168#380—21no—
169#380—21no—
170#380C2×C411yescharacteristic
171#380C2×C411yescharacteristic
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2311yescharacteristic
175#380C2311yescharacteristic
176#380C2311yescharacteristic
177#380C2311yescharacteristic
178#379—21no—
179C4×C22⋊C4—21no—
180C4×C22⋊C4—21no—
181C4×C22⋊C4C2×C411yescharacteristic
182C4×C22⋊C4C2×C411yescharacteristic
183C4×C22⋊C4C2×C411yescharacteristic
184C4×C22⋊C4C2×C411yescharacteristic
185C4×C22⋊C4D411yescharacteristic
186C4×C22⋊C4D411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95D411yescharacteristic
198C2×#95D411yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207C25C2×D411yescharacteristic
208C22×Q8—21no—
209C22×Q8—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—81no—
221C23×C4—81no—
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2411yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C4⋊Q8—81no—
237C4⋊Q8—81no—
238#125—81no—
239#125—81no—
240C22⋊Q8—44no—
241C22⋊Q8—44no—
242C22⋊Q8—81no—
243C22⋊Q8—81no—
244C22⋊Q8—81no—
245C22⋊Q8—81no—
246#117—81no—
247#117—81no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—81no—
270C2×C4⋊C4—81no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4C22×C411yescharacteristic
274C2×C4⋊C4C22×C411yescharacteristic
275C2×C4⋊C4C22×C411yescharacteristic
276C2×C4⋊C4C22×C411yescharacteristic
277C2×C4⋊C4C22×C411yescharacteristic
278C2×C4⋊C4C22×C411yescharacteristic
279C2×C4⋊C4C22×C411yescharacteristic
280C2×C4⋊C4C22×C411yescharacteristic
281C2×C22⋊C4—24no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—81no—
296C2×C22⋊C4—81no—
297C2×C22⋊C4—81no—
298C2×C22⋊C4—81no—
299C2×C22⋊C4—81no—
300C2×C22⋊C4—81no—
301C2×C22⋊C4C22⋊C411yescharacteristic
302C2×C22⋊C4C22⋊C411yescharacteristic
303C2×C22⋊C4C22⋊C411yescharacteristic
304C2×C22⋊C4C22⋊C411yescharacteristic
305C2×C22⋊C4C22⋊C411yescharacteristic
306C2×C22⋊C4C22⋊C411yescharacteristic
307C2×C22⋊C4C22⋊C411yescharacteristic
308C2×C22⋊C4C22⋊C411yescharacteristic
309C2×C42—24no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—42no—
313C2×C42—81no—
314C2×C42—81no—
315C2×C42—81no—
316C2×C42—81no—
317C2×C42—81no—
318C2×C42—81no—
319C2×C42C22×C411yescharacteristic
320C2×C42C22×C411yescharacteristic
321C2×C42C22×C411yescharacteristic
322C2×C42C22×C411yescharacteristic
323C2×C42C2×D411yescharacteristic
324C2×C42C2×D411yescharacteristic
325C2×C42C2×D411yescharacteristic
326C2×C42C2×D411yescharacteristic
327C4⋊C8—81no—
328C4⋊C8—81no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—81no—
338C22⋊C8—81no—
339C22⋊C8—81no—
340C22⋊C8—81no—
341#97—81no—
342C4×C8—81no—
343#95—24no—
344#95—24no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—42no—
374#95—81no—
375#95—81no—
376#95—81no—
377#95—81no—
378#95C22⋊C411yescharacteristic
379#95C22⋊C411yescharacteristic
380#95C22⋊C411yescharacteristic
381#95C22⋊C411yescharacteristic
382#95C22⋊C411yescharacteristic
383#95C22⋊C411yescharacteristic
384#95C22⋊C411yescharacteristic
385#95C22⋊C411yescharacteristic
386C24—22no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24C2×C22⋊C411yescharacteristic
397C24C2×C22⋊C411yescharacteristic
398C24C22×D411yescharacteristic
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8—81no—
402C2×Q8—81no—
403C2×Q8—81no—
404C2×Q8—81no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—82no—
482C22×C4—82no—
483C22×C4—82no—
484C22×C4—82no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C42−1+411yescharacteristic
502C22×C42−1+411yescharacteristic
503C22×C42−1+411yescharacteristic
504C22×C42−1+411yescharacteristic
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4—84no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—42no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C22⋊C4—84no—
568C22⋊C4—84no—
569C22⋊C4#10414yes—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—81no—
579C42—81no—
580C42—84no—
581C42—84no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23C2×#10412yes—
616C23C22×C22⋊C411yescharacteristic
617C23#53611yescharacteristic
618C23#53611yescharacteristic
619C23#57611yescharacteristic
620C23#57711yescharacteristic
621C23#57711yescharacteristic
622C23#57811yescharacteristic
623Q8—162no—
624Q8—162no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
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—42no—
672C2×C4—42no—
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—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—162no—
731C2×C4—162no—
732C2×C4C2×#10412yes—
733C2×C4C2×#10412yes—
734C2×C4#42112yes—
735C2×C4#51911yescharacteristic
736C2×C4#51911yescharacteristic
737C2×C4#53611yescharacteristic
738C2×C4#53611yescharacteristic
739C8—81no—
740C8—81no—
741C8—81no—
742C8—81no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22#231011yescharacteristic
774C22#288311yescharacteristic
775C22#288311yescharacteristic
776C22#289711yescharacteristic
777C22#289811yescharacteristic
778C22C22×#10411yescharacteristic
779C22C2×#42111yescharacteristic
780C22#324111yescharacteristic
781C22#324211yescharacteristic
782C22#324311yescharacteristic
783C22#324411yescharacteristic
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—42no—
815C2—81no—
816C2#1754711yescharacteristic
817C2#1754811yescharacteristic
818C2#1759711yescharacteristic
819C2#1760011yescharacteristic
820C2#2182711yescharacteristic
821C2#2184311yescharacteristic
822C2#2184411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9910C2semidirect
5. #9910C2semidirect
6. #9909C2semidirect
7. #9908C2semidirect
8. #9888C2semidirect
9. #9887C2semidirect
10. #9886C2semidirect
11. #9885C2semidirect
24. #2442C4semidirect
25. #2442C4semidirect
26. #2441C4semidirect
27. #2441C4semidirect
28. #2440C4semidirect
29. #2440C4semidirect
30. #2439C4semidirect
31. #2439C4semidirect

Maximal subgroups

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

subgroupindex
#350792
#219042
#137882
#99102
#99092
#99082
#98882
#98872
#98862
#98852
#87152
#87132
#87122