Finite Group Databasebeta

← #190894

Subgroups — #190894

Order 512.

1100 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34126C211yesmaximal, characteristic
2#21924C211yesmaximal, characteristic, complemented
3#20782C211yesmaximal, characteristic, complemented
4#8711C211yesmaximal, characteristic, complemented
5#8711C211yesmaximal, characteristic, complemented
6#8569C211yesmaximal, characteristic, complemented
7#8567C211yesmaximal, characteristic, complemented
8#8565C211yesmaximal, characteristic, complemented
9#8563C211yesmaximal, characteristic, complemented
10#8310C211yesmaximal, characteristic
11#8310C211yesmaximal, characteristic
12#8183C211yesmaximal, characteristic, complemented
13#8179C211yesmaximal, characteristic, complemented
14#8174C211yesmaximal, characteristic, complemented
15#8170C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17#2357C411yescharacteristic
18#2357C411yescharacteristic
19#2353—21no—
20#2353—21no—
21#2349C411yescharacteristic
22#2349C411yescharacteristic
23#2345C411yescharacteristic
24#2345C411yescharacteristic
25#2342—21no—
26#2342—21no—
27D4×C22⋊C4C411yescharacteristic
28D4×C22⋊C4C411yescharacteristic
29#2293C2211yescharacteristic
30#2293C2211yescharacteristic
31#2290—21no—
32#2290—21no—
33#2283C2211yescharacteristic
34#2280—21no—
35C42×D4C2211yescharacteristic
36C42×D4C2211yescharacteristic
37C4×#117C2211yescharacteristic
38C2×C4×C22⋊C4—21no—
39#1924—21no—
40#1923—21no—
41#1917—21no—
42#1916—21no—
43#1842C2211yescharacteristic, complemented
44#1840—21no—
45#1832—21no—
46#1831C2211yescharacteristic, complemented
47#1818—21no—
48#1798—21no—
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1767C2211yescharacteristic, complemented
52C4×C4⋊C8C2211yescharacteristic, complemented
53C4×C4⋊C8C2211yescharacteristic, complemented
54C4×C4⋊C8C2211yescharacteristic, complemented
55C4×C22⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57#1744C2211yescharacteristic, complemented
58#1744C2211yescharacteristic, complemented
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67#1279C2211yescharacteristic, complemented
68#1279C2211yescharacteristic, complemented
69#1279C2211yescharacteristic, complemented
70#1279C2211yescharacteristic, complemented
71#1279C2211yescharacteristic, complemented
72#1279C2211yescharacteristic, complemented
73#1279C2211yescharacteristic, complemented
74#1279C2211yescharacteristic, complemented
75C23×D4C2×C411yescharacteristic
76C24×C4—21no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—21no—
82C2×C4×D4—21no—
83C2×C4×D4C2×C411yescharacteristic
84C2×C4×D4C2×C411yescharacteristic
85C2×C4×D4C2×C411yescharacteristic
86C2×C4×D4C2×C411yescharacteristic
87C2×C4×D4C2×C411yescharacteristic
88C2×C4×D4C2×C411yescharacteristic
89C2×C4×D4C2311yescharacteristic
90C2×C4×D4C2311yescharacteristic
91C2×#117—21no—
92C2×#117—21no—
93C2×#117D411yescharacteristic
94C2×#117D411yescharacteristic
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C42—21no—
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8C2311yescharacteristic
107C2×C4⋊C8C2311yescharacteristic
108C2×C4⋊C8C2311yescharacteristic
109C2×C4⋊C8C2311yescharacteristic
110C2×C22⋊C8—21no—
111C2×C22⋊C8—21no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—21no—
114C2×#97—21no—
115C2×C4×C8—21no—
116C2×C4×C8C2311yescharacteristic
117C2×C4×C8C2311yescharacteristic
118C2×C4×C8C2311yescharacteristic
119C2×C4×C8C2311yescharacteristic
120#390C2×C411yescharacteristic
121#390C2×C411yescharacteristic
122#390C2×C411yescharacteristic
123#390C2×C411yescharacteristic
124#389C2×C411yescharacteristic
125#389C2×C411yescharacteristic
126#389C2×C411yescharacteristic
127#389C2×C411yescharacteristic
128#388—21no—
129#388—21no—
130#388—21no—
131#388—21no—
132#388—21no—
133#388—21no—
134#388—21no—
135#388—21no—
136#387—21no—
137#387—21no—
138#387—21no—
139#387—21no—
140#386—21no—
141#386—21no—
142#386—21no—
143#386—21no—
144#385—21no—
145#385—21no—
146#385—21no—
147#385—21no—
148#383—21no—
149#382C2×C411yescharacteristic
150#382C2×C411yescharacteristic
151#381—21no—
152#381—21no—
153#381—21no—
154#380—21no—
155#380—21no—
156#380—21no—
157#380—21no—
158#380C2×C411yescharacteristic
159#380C2×C411yescharacteristic
160#379—21no—
161#379—21no—
162C4×C4⋊C4C2×C411yescharacteristic
163C4×C4⋊C4C2×C411yescharacteristic
164C4×C4⋊C4C2×C411yescharacteristic
165C4×C4⋊C4C2×C411yescharacteristic
166C4×C4⋊C4C2×C411yescharacteristic
167C4×C4⋊C4C2×C411yescharacteristic
168C4×C4⋊C4D411yescharacteristic
169C4×C4⋊C4D411yescharacteristic
170C4×C4⋊C4C2311yescharacteristic
171C4×C4⋊C4C2311yescharacteristic
172C4×C22⋊C4—21no—
173C4×C22⋊C4—21no—
174C4×C22⋊C4—21no—
175C4×C22⋊C4—21no—
176C4×C22⋊C4—21no—
177C4×C22⋊C4—21no—
178C4×C22⋊C4—21no—
179C4×C22⋊C4—21no—
180C4×C22⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189#376—21no—
190#376D411yescharacteristic
191#376D411yescharacteristic
192C2×#95—21no—
193C2×#95—21no—
194C43C2311yescharacteristic
195C43C2311yescharacteristic
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210D4⋊C8—22no—
211D4⋊C8—22no—
212D4⋊C8—22no—
213D4⋊C8—22no—
214D4⋊C8—22no—
215D4⋊C8—22no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218C25—21no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—21no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4C22×C411yescharacteristic
227C22×D4C22×C411yescharacteristic
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—81no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4C22×C411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C4×D4—24no—
255C4×D4—24no—
256C4×D4—24no—
257C4×D4—24no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—41no—
271C4×D4—41no—
272C4×D4—41no—
273C4×D4—41no—
274C4×D4#4112yes—
275C4×D4#4112yes—
276C4×D4#4112yes—
277C4×D4#4112yes—
278#117—42no—
279#117—42no—
280#117—81no—
281#117—81no—
282#117—81no—
283#117—81no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
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×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
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×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—81no—
338C2×C42—81no—
339C2×C42—81no—
340C2×C42—81no—
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2411yescharacteristic
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—42no—
366C4⋊C8—42no—
367C4⋊C8—81no—
368C4⋊C8—81no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—81no—
372C22⋊C8—81no—
373#97—81no—
374C4×C8—21no—
375C4×C8—21no—
376C4×C8—21no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—81no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407C24—21no—
408C24—24no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—81no—
415C24—81no—
416C24C2×C22⋊C411yescharacteristic
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4#11712yes—
433C2×D4#11712yes—
434C2×D4#13112yes—
435C2×D4#13112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
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—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—84no—
490C22×C4—84no—
491C22×C4—84no—
492C22×C4—84no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C2×C22⋊C411yescharacteristic
501C22×C4C2×C22⋊C411yescharacteristic
502C22×C4C2×C22⋊C411yescharacteristic
503C22×C4C2×C22⋊C411yescharacteristic
504C22×C4C2×C22⋊C411yescharacteristic
505C22×C4C2×C22⋊C411yescharacteristic
506C22×C4C23×C411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
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—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4#11712yes—
553C4⋊C4#11712yes—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—22no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—81no—
609C42—81no—
610C42—81no—
611C42—81no—
612C42C2×#4111yescharacteristic
613C42C2×#4111yescharacteristic
614C42C2×#4111yescharacteristic
615C42C2×#4111yescharacteristic
616C23—22no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—21no—
625C23—22no—
626C23—48no—
627C23—48no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23#42112yes—
644C23C22×C22⋊C411yescharacteristic
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—48no—
651D4—41no—
652D4—41no—
653D4#43314yes—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#42112yes—
732C2×C4C2×#11711yescharacteristic
733C2×C4C2×#11711yescharacteristic
734C2×C4#52511yescharacteristic
735C2×C4#52511yescharacteristic
736C2×C4#52511yescharacteristic
737C2×C4#52511yescharacteristic
738C2×C4C2×#13111yescharacteristic
739C2×C4C2×#13111yescharacteristic
740C2×C4#56811yescharacteristic
741C2×C4#56811yescharacteristic
742C2×C4#57611yescharacteristic
743C2×C4#57611yescharacteristic
744C2×C4#57711yescharacteristic
745C2×C4#57711yescharacteristic
746C8—81no—
747C8—81no—
748C8—81no—
749C8—81no—
750C8—81no—
751C8—81no—
752C8—81no—
753C8—81no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—24no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—816no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22#228011yescharacteristic
777C22#288011yescharacteristic
778C22#288011yescharacteristic
779C22#289711yescharacteristic
780C22#289711yescharacteristic
781C22C2×#42111yescharacteristic
782C22C2×#42111yescharacteristic
783C4—21no—
784C4—21no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#43311yescharacteristic
803C4#292111yescharacteristic
804C4#292411yescharacteristic
805C4#292411yescharacteristic
806C4#311811yescharacteristic
807C4#311811yescharacteristic
808C4#312211yescharacteristic
809C4#312311yescharacteristic
810C2—42no—
811C2—44no—
812C2—82no—
813C2#1752111yescharacteristic
814C2#1752111yescharacteristic
815C2#1752111yescharacteristic
816C2#1752211yescharacteristic
817C2#2071611yescharacteristic
818C2#2074411yescharacteristic
819C2#2074811yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21924C2semidirect
3. #20782C2semidirect
4. #8711C2semidirect
5. #8711C2semidirect
6. #8569C2semidirect
7. #8567C2semidirect
8. #8565C2semidirect
9. #8563C2semidirect
12. #8183C2semidirect
13. #8179C2semidirect
14. #8174C2semidirect
15. #8170C2semidirect
43. #1842C22semidirect
46. #1831C22semidirect
51. #1767C22semidirect
52. C4×C4⋊C8C22semidirect
53. C4×C4⋊C8C22semidirect
54. C4×C4⋊C8C22semidirect
57. #1744C22semidirect
58. #1744C22semidirect
67. #1279C22semidirect
68. #1279C22semidirect
69. #1279C22semidirect
70. #1279C22semidirect
71. #1279C22semidirect
72. #1279C22semidirect
73. #1279C22semidirect
74. #1279C22semidirect

Maximal subgroups

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

subgroupindex
#341262
#219242
#207822
#87112
#85692
#85672
#85652
#85632
#83102
#81832
#81792
#81742
#81702