Finite Group Databasebeta

← #224151

Subgroups — #224151

Order 512.

1047 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36561C211yesmaximal, characteristic
2#22627C211yesmaximal, characteristic, complemented
3#13819C211yesmaximal, characteristic, complemented
4#9909C211yesmaximal, characteristic, complemented
5#9908C211yesmaximal, characteristic, complemented
6#9908C211yesmaximal, characteristic, complemented
7#9889C211yesmaximal, characteristic, complemented
8#9888C211yesmaximal, characteristic, complemented
9#9884C211yesmaximal, characteristic, complemented
10#8577C211yesmaximal, characteristic
11#8575C211yesmaximal, characteristic
12#8573C211yesmaximal, characteristic
13#8218C211yesmaximal, characteristic
14#8218C211yesmaximal, characteristic
15C4×#327C211yesmaximal, characteristic
16C2×#554—21no—
17#2857C2211yescharacteristic
18#2857C2211yescharacteristic
19#2857C2211yescharacteristic
20#2564—21no—
21#2564—21no—
22#2556—21no—
23#2556—21no—
24#2551C411yescharacteristic, complemented
25#2542C411yescharacteristic, complemented
26#2506C411yescharacteristic, complemented
27#2506C411yescharacteristic, complemented
28#2492—21no—
29#2452C411yescharacteristic, complemented
30#2452C411yescharacteristic, complemented
31#2417—21no—
32#2365C411yescharacteristic, complemented
33#2360—21no—
34D4×C4⋊C4C411yescharacteristic, complemented
35C4×#121C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C2×#387—21no—
39C2×C4×C4⋊C4C2211yescharacteristic
40#1940—21no—
41#1917—21no—
42#1916—21no—
43#1797C2211yescharacteristic
44#1797C2211yescharacteristic
45#1797C2211yescharacteristic
46#1771—21no—
47#1749C2211yescharacteristic
48#1749C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50C2×#327C2211yescharacteristic
51C2×#327C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54#1436—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57#1434C2211yescharacteristic
58#1434C2211yescharacteristic
59C4×#95—21no—
60C4×#95C2211yescharacteristic
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#554—44no—
76#554—44no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8C2×C411yescharacteristic
79C2×C4⋊Q8C2×C411yescharacteristic
80C2×C4⋊Q8C2×C411yescharacteristic
81C2×#125—21no—
82C2×#125—21no—
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×#121C2311yescharacteristic
91C2×C4×Q8—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4C2×C411yescharacteristic
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2×C411yescharacteristic
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4D411yescharacteristic
101C22×C4⋊C4D411yescharacteristic
102C22×C42—21no—
103C22×C42—21no—
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C22⋊C8C2311yescharacteristic
112C2×C22⋊C8C2311yescharacteristic
113C2×C22⋊C8C2311yescharacteristic
114C2×C22⋊C8C2311yescharacteristic
115C2×#97—21no—
116C2×#97—21no—
117C2×C4×C8—21no—
118#400—21no—
119#400—21no—
120#399—21no—
121#399—21no—
122#398—21no—
123#398—21no—
124#396—21no—
125#396—21no—
126#395—21no—
127#395—21no—
128#393—21no—
129#393—21no—
130#391—21no—
131#391—21no—
132#391—21no—
133#391—21no—
134#390C2×C411yescharacteristic
135#390C2×C411yescharacteristic
136#390C2×C411yescharacteristic
137#389—21no—
138#389—21no—
139#389—21no—
140#389—21no—
141#389C2×C411yescharacteristic
142#389C2×C411yescharacteristic
143#389C2×C411yescharacteristic
144#389C2×C411yescharacteristic
145#389C2×C411yescharacteristic
146#389C2×C411yescharacteristic
147#389C2×C411yescharacteristic
148#389C2×C411yescharacteristic
149#389C2×C411yescharacteristic
150#388—21no—
151#388—21no—
152#388—21no—
153#387—28no—
154#387—21no—
155#387—21no—
156#387—21no—
157#387—21no—
158#386—21no—
159#386—21no—
160#386—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—21no—
165#384C2×C411yescharacteristic
166#384C2×C411yescharacteristic
167#384C2×C411yescharacteristic
168#380—21no—
169#380—21no—
170#380—21no—
171#380—21no—
172#380C2311yescharacteristic
173#380C2311yescharacteristic
174#380C2311yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C4⋊C4D411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
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—
207#336—21no—
208#336—21no—
209#327—22no—
210#327—22no—
211#327—22no—
212#327Q814yescomplemented
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×D4—21no—
217C22×D4C22×C411yescharacteristic
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
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—42no—
237C4⋊Q8—44no—
238C4⋊Q8—81no—
239C4⋊Q8—81no—
240#125—44no—
241#125—44no—
242C22⋊Q8—44no—
243C22⋊Q8—44no—
244C22⋊Q8—44no—
245C22⋊Q8—42no—
246C22⋊Q8—42no—
247C22⋊Q8—42no—
248C22⋊Q8—42no—
249C22⋊Q8—42no—
250C22⋊Q8—42no—
251C22⋊Q8—44no—
252#121—21no—
253#121—21no—
254#121C2×Q812yes—
255#121#4112yes—
256C4×Q8—44no—
257C4×D4—42no—
258C4×D4—42no—
259C4×D4—42no—
260C4×D4—42no—
261C4×D4—42no—
262C4×D4—42no—
263C4×D4—42no—
264C4×D4—81no—
265C4×D4—81no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4C22⋊C411yescharacteristic
292C2×C4⋊C4C22⋊C411yescharacteristic
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22⋊C411yescharacteristic
297C2×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22⋊C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—24no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—81no—
329C2×C42—81no—
330C2×C42—81no—
331C2×C42—81no—
332C2×C42—81no—
333C2×C42—81no—
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C22×C411yescharacteristic
338C2×C42C22×C411yescharacteristic
339C2×C42C22×C411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C4⋊C8—42no—
347C4⋊C8—81no—
348C4⋊C8—81no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8C2×Q812yes—
357#97—42no—
358#97—81no—
359C4×C8—81no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
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—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—81no—
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C2×Q812yes—
399C24—21no—
400C24C22×D411yescharacteristic
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8—81no—
407C2×Q8—81no—
408C2×Q8—81no—
409C2×Q8—81no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4C4×Q812yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
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—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
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—42no—
458C22×C4—42no—
459C22×C4—42no—
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—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4C2×C22⋊C411yescharacteristic
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×C4C2×C22⋊C411yescharacteristic
500C22×C4AGL(1,ℤ/8)12yes—
501C22×C4AGL(1,ℤ/8)12yes—
502C22×C4C23×C411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C22×Q811yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C42−1+411yescharacteristic
507C22×C42−1+411yescharacteristic
508C2×C8—22no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—84no—
553C4⋊C4#10414yes—
554C4⋊C4C4×Q812yes—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—22no—
573C42—22no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—42no—
585C42—42no—
586C42—42no—
587C42—84no—
588C42—84no—
589C42—84no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C22×C22⋊C411yescharacteristic
602C23#54811yescharacteristic
603C23D4×Q811yescharacteristic
604C23C2×AGL(1,ℤ/8)11yescharacteristic
605C23C2×AGL(1,ℤ/8)11yescharacteristic
606C23#57711yescharacteristic
607C23#57811yescharacteristic
608Q8—84no—
609Q8—162no—
610Q8—162no—
611D4—42no—
612D4—42no—
613D4—42no—
614D4—42no—
615D4—42no—
616D4—42no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
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—24no—
634C2×C4—22no—
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—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
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—41no—
674C2×C4—41no—
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—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—84no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
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—162no—
718C2×C4—162no—
719C2×C4#41012yes—
720C2×C4#41812yes—
721C2×C4#41812yes—
722C2×C4C2×#10412yes—
723C2×C4C2×#10412yes—
724C2×C4C2×#10412yes—
725C2×C4C2×C4×Q811yescharacteristic
726C2×C4#51911yescharacteristic
727C2×C4#54811yescharacteristic
728C2×C4D4×Q811yescharacteristic
729C8—42no—
730C8—81no—
731C8—81no—
732C8—81no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22Q8×C22⋊C411yescharacteristic
753C22C2×#41011yescharacteristic
754C22#288311yescharacteristic
755C22C2×#41811yescharacteristic
756C22#289811yescharacteristic
757C22C22×#10411yescharacteristic
758C22#290111yescharacteristic
759C22#336711yescharacteristic
760C22#337311yescharacteristic
761C22#338411yescharacteristic
762C22#338611yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—44no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4—81no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—82no—
795C2#1754411yescharacteristic
796C2#1754811yescharacteristic
797C2#1760911yescharacteristic
798C2#1762011yescharacteristic
799C2#2251311yescharacteristic
800C2#2252311yescharacteristic
801C2Q8×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22627C2semidirect
3. #13819C2semidirect
4. #9909C2semidirect
5. #9908C2semidirect
6. #9908C2semidirect
7. #9889C2semidirect
8. #9888C2semidirect
9. #9884C2semidirect
24. #2551C4semidirect
25. #2542C4semidirect
26. #2506C4semidirect
27. #2506C4semidirect
29. #2452C4semidirect
30. #2452C4semidirect
32. #2365C4semidirect
34. D4×C4⋊C4C4semidirect
212. #327Q8semidirect

Maximal subgroups

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

subgroupindex
#365612
#226272
#138192
#99092
#99082
#98892
#98882
#98842
#85772
#85752
#85732
#82182
C4×#3272