Finite Group Databasebeta

← #222008

Subgroups — #222008

Order 512.

1211 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊Q8C211yesmaximal, characteristic
2#22748C211yesmaximal, characteristic
3#22648C211yesmaximal, characteristic
4C2×#1549C211yesmaximal, characteristic, complemented
5C22×#332C211yesmaximal, characteristic, complemented
6#9703C211yesmaximal, characteristic, complemented
7#9694C211yesmaximal, characteristic, complemented
8#9137C211yesmaximal, characteristic, complemented
9#9132C211yesmaximal, characteristic, complemented
10#9131C211yesmaximal, characteristic, complemented
11#9129C211yesmaximal, characteristic, complemented
12#8591C211yesmaximal, characteristic, complemented
13#8340C211yesmaximal, characteristic, complemented
14#8340C211yesmaximal, characteristic, complemented
15#8237C211yesmaximal, characteristic, complemented
16C2×D4×Q8—21no—
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C2×#435—21no—
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24#2868C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2551—21no—
28#2551C412yes—
29#2546—21no—
30#2440—21no—
31#2440—21no—
32#2440C412yes—
33#2440C412yes—
34#2434—21no—
35#2434—21no—
36D4×C4⋊C4—21no—
37D4×C4⋊C4C412yes—
38C4×C4⋊Q8C2211yescharacteristic
39C42×D4C2211yescharacteristic
40#1940—21no—
41#1923—21no—
42#1916—21no—
43#1869—21no—
44#1851—21no—
45#1850—21no—
46#1842C2211yescharacteristic
47#1831C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52#1767C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C8×C22⋊C4—21no—
55#1549—24no—
56C2×#332—24no—
57C2×#332C2211yescharacteristic
58C2×#332C2211yescharacteristic
59C2×#332C2211yescharacteristic
60C2×#332C2211yescharacteristic
61C2×#332C2211yescharacteristic
62C2×#332C2211yescharacteristic
63C2×#332C2211yescharacteristic
64C2×#332C2211yescharacteristic
65C2×#332C2211yescharacteristic
66C2×#332C2211yescharacteristic
67C2×#332C2211yescharacteristic
68C2×#332C2211yescharacteristic
69#1296C2211yescharacteristic
70#1296C2211yescharacteristic
71#1296C2211yescharacteristic
72#1296C2211yescharacteristic
73C23×Q8—21no—
74C23×Q8—21no—
75C22×M16—21no—
76C23×C8—21no—
77C23×C8—21no—
78D4×Q8—44no—
79D4×Q8—44no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8—22no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8—21no—
88C2×C4⋊Q8—21no—
89C2×C4⋊Q8—21no—
90C2×C4⋊Q8—21no—
91C2×C4⋊Q8—41no—
92C2×C4⋊Q8—41no—
93C2×C4⋊Q8—41no—
94C2×C4⋊Q8—41no—
95C2×C4⋊Q8C2×C412yes—
96C2×C4⋊Q8C2×C412yes—
97C2×C4⋊Q8C2311yescharacteristic
98C2×C4⋊Q8C2311yescharacteristic
99C2×C4⋊Q8C2311yescharacteristic
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C4×Q8—21no—
105C2×C4×D4—22no—
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×C4×D4D411yescharacteristic
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4C2×C412yes—
112C22×C4⋊C4C2×C412yes—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115#435—44no—
116#431—22no—
117#431—41no—
118#423—22no—
119#423—41no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8—41no—
129C2×C4⋊C8C2311yescharacteristic
130C2×C4⋊C8C2311yescharacteristic
131C2×C4⋊C8C2311yescharacteristic
132C2×C4⋊C8C2311yescharacteristic
133C2×C4⋊C8C2311yescharacteristic
134C2×C4⋊C8C2311yescharacteristic
135C2×C4⋊C8C2311yescharacteristic
136C2×C4⋊C8C2311yescharacteristic
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×#97—21no—
143C2×C4×C8—21no—
144C2×C4×C8—21no—
145#398—22no—
146#398—22no—
147#395—22no—
148#395—22no—
149#395—22no—
150#395—22no—
151#391—21no—
152#391—21no—
153#391—21no—
154#389—22no—
155#389—22no—
156#389—21no—
157#389—21no—
158#389—21no—
159#389C2×C412yes—
160#389C2×C412yes—
161#389C2×C412yes—
162#385—22no—
163#385—22no—
164#385—22no—
165#385—22no—
166#384—21no—
167#384—21no—
168#384C2×C412yes—
169#384C2×C412yes—
170#384C2311yescharacteristic
171#380—21no—
172#380—21no—
173#380C2×C412yes—
174#380C2×C412yes—
175C4×C4⋊C4—21no—
176C4×C4⋊C4C2×C412yes—
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4D411yescharacteristic
179C4×C4⋊C4D411yescharacteristic
180C4×C22⋊C4C2×C411yescharacteristic
181C4×C22⋊C4C2×C411yescharacteristic
182C4×C22⋊C4D411yescharacteristic
183C4×C22⋊C4D411yescharacteristic
184C4×C22⋊C4D411yescharacteristic
185C4×C22⋊C4D411yescharacteristic
186C43C2311yescharacteristic
187#336—21no—
188#336—21no—
189#336—21no—
190#336—21no—
191#336—21no—
192#336—21no—
193#336—21no—
194#336—21no—
195#332—22no—
196#332—22no—
197#332—22no—
198#332—22no—
199#332—22no—
200#332—22no—
201#332—22no—
202#332—41no—
203#332—41no—
204#332—41no—
205#332—41no—
206#332D414yescomplemented
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8—42no—
216C22×Q8—42no—
217C22×Q8—42no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8—81no—
221C22×Q8—81no—
222C22×Q8—81no—
223C22×Q8—81no—
224C22×D4C22⋊C411yescharacteristic
225C23×C4—22no—
226C23×C4—22no—
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C2×M16—42no—
234C2×M16—42no—
235C2×M16—81no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—42no—
245C22×C8—42no—
246C22×C8—42no—
247C22×C8—42no—
248C22×C8—81no—
249C22×C8—81no—
250C4⋊Q8—24no—
251C4⋊Q8—24no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—42no—
263C4⋊Q8—42no—
264C4⋊Q8—42no—
265C4⋊Q8—42no—
266C4⋊Q8—42no—
267C4⋊Q8—42no—
268C4⋊Q8—42no—
269C4⋊Q8—42no—
270C4⋊Q8—42no—
271C4⋊Q8—42no—
272C4⋊Q8—42no—
273C4⋊Q8—42no—
274C4⋊Q8—48no—
275C4⋊Q8—81no—
276C4⋊Q8—81no—
277C4⋊Q8C2×D412yes—
278C4⋊Q8#4112yes—
279C22⋊Q8—48no—
280C22⋊Q8—48no—
281C22⋊Q8—42no—
282C22⋊Q8—42no—
283C22⋊Q8—42no—
284C22⋊Q8—42no—
285C4×Q8—42no—
286C4×Q8—42no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—24no—
290C4×D4—48no—
291C4×D4SD1614yes—
292C4×D4Q1614yes—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22⋊C411yescharacteristic
319C2×C4⋊C4C22⋊C411yescharacteristic
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C22×C412yes—
323C2×C4⋊C4C22×C412yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—22no—
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2411yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
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—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—42no—
369C4⋊C8—42no—
370C4⋊C8—42no—
371C4⋊C8—42no—
372C4⋊C8—81no—
373C4⋊C8C2×D412yes—
374C4⋊C8C2×D412yes—
375C22⋊C8—42no—
376C22⋊C8—42no—
377C22⋊C8—42no—
378C22⋊C8—42no—
379C22⋊C8—81no—
380#97—42no—
381C4×C8—42no—
382C4×C8—81no—
383#95—22no—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395C24C2×C22⋊C411yescharacteristic
396C24C2×C22⋊C411yescharacteristic
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—44no—
419C2×Q8—82no—
420C2×Q8—82no—
421C2×Q8—84no—
422C2×Q8—84no—
423C2×Q8—84no—
424C2×Q8—84no—
425C2×Q8—84no—
426C2×Q8—84no—
427C2×Q8—84no—
428C2×Q8—84no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4#10314yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—82no—
467C22×C4—82no—
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×SD1612yes—
479C22×C4C2×SD1612yes—
480C22×C4C2×Q1612yes—
481C22×C4C2×Q1612yes—
482C22×C4AGL(1,ℤ/8)12yes—
483C22×C4AGL(1,ℤ/8)12yes—
484C22×C4C23×C411yescharacteristic
485C22×C4C22×D411yescharacteristic
486C22×C4C22×D411yescharacteristic
487M16—84no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—84no—
513C2×C8—84no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C4⋊C4—42no—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—44no—
541C4⋊C4—82no—
542C4⋊C4—82no—
543C4⋊C4#10314yes—
544C4⋊C4C4×D414yes—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—44no—
549C22⋊C4—44no—
550C22⋊C4#10114yes—
551C22⋊C4#10314yes—
552C22⋊C4#10314yes—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—22no—
572C42—41no—
573C42—44no—
574C42C2×SD1612yes—
575C42C2×Q1612yes—
576C42C22×D411yescharacteristic
577C42C2×#4111yescharacteristic
578C42H(5,𝔽2)11yescharacteristic
579C42H(5,𝔽2)11yescharacteristic
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23C2×#10112yes—
591C23C2×#10312yes—
592C23C2×#10312yes—
593C23#41812yes—
594C23C22×C22⋊C411yescharacteristic
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—42no—
599Q8—88no—
600Q8—88no—
601Q8—81no—
602Q8—81no—
603Q8—81no—
604Q8—81no—
605Q8—81no—
606Q8—81no—
607Q8—81no—
608Q8—81no—
609D4—28no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
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—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
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—88no—
668C2×C4—88no—
669C2×C4C2×#10112yes—
670C2×C4C2×#10112yes—
671C2×C4C2×#10312yes—
672C2×C4C2×#10312yes—
673C2×C4C2×#10312yes—
674C2×C4C2×#10312yes—
675C2×C4#41812yes—
676C2×C4C2×C4×D411yescharacteristic
677C2×C4#51811yescharacteristic
678C2×C4D4211yescharacteristic
679C2×C4D4211yescharacteristic
680C2×C4#54611yescharacteristic
681C2×C4#54611yescharacteristic
682C2×C4C22×SD1611yescharacteristic
683C2×C4C22×Q1611yescharacteristic
684C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
685C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
686C2×C4#57611yescharacteristic
687C2×C4#57711yescharacteristic
688C2×C4#57711yescharacteristic
689C2×C4#57811yescharacteristic
690C8—42no—
691C8—42no—
692C8—81no—
693C8—81no—
694C8—81no—
695C8—81no—
696C8—81no—
697C8—81no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22#154914yescomplemented
712C22D4×C22⋊C411yescharacteristic
713C22C22×#10111yescharacteristic
714C22#288911yescharacteristic
715C22C22×#10311yescharacteristic
716C22C2×#41811yescharacteristic
717C22#289711yescharacteristic
718C22#289811yescharacteristic
719C4—22no—
720C4—22no—
721C4—22no—
722C4—21no—
723C4—21no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—44no—
732C4—82no—
733C4—82no—
734C4—82no—
735C4#326411yescharacteristic
736C4#326511yescharacteristic
737C4D4×SD1611yescharacteristic
738C4D4×Q1611yescharacteristic
739C4#329811yescharacteristic
740C4#329911yescharacteristic
741C4#331011yescharacteristic
742C4#331811yescharacteristic
743C2—24no—
744C2—42no—
745C2C2×#154911yescharacteristic
746C2#1772311yescharacteristic
747C2#1775911yescharacteristic
748C2#1777411yescharacteristic
749C2D4×#10111yescharacteristic
750C2D4×#10311yescharacteristic
751C2#2242311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC22×D4C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1549C2semidirect
5. C22×#332C2semidirect
6. #9703C2semidirect
7. #9694C2semidirect
8. #9137C2semidirect
9. #9132C2semidirect
10. #9131C2semidirect
11. #9129C2semidirect
12. #8591C2semidirect
13. #8340C2semidirect
14. #8340C2semidirect
15. #8237C2semidirect
206. #332D4semidirect
711. C22#1549semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Q82
#227482
#226482
C2×#15492
C22×#3322
#97032
#96942
#91372
#91322
#91312
#91292
#85912
#83402
#82372