Finite Group Databasebeta

← #363881

Subgroups — #363881

Order 512.

3440 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
1C22×#551C211yesmaximal, characteristic
2C2×#1898C212yesmaximal
3C2×#1819C211yesmaximal, characteristic, complemented
4C22×#342C211yesmaximal, characteristic, complemented
5#13869C212yesmaximal, complemented
6#11381C212yesmaximal, complemented
7#10966C212yesmaximal, complemented
8#10761C212yesmaximal, complemented
9#10726C212yesmaximal, complemented
10C2×#551—28no—
11C2×#551—24no—
12C2×#551—24no—
13C2×#551—24no—
14C2×#551—24no—
15C22×#126C411yescharacteristic, complemented
16C22×#126C411yescharacteristic, complemented
17C22×#124C411yescharacteristic, complemented
18C22×#123C411yescharacteristic, complemented
19C22×#123C411yescharacteristic, complemented
20C22×#123C2211yescharacteristic
21C22×C22⋊Q8C411yescharacteristic, complemented
22C22×C22⋊Q8C2211yescharacteristic
23C22×#120C2211yescharacteristic
24C22×C4×D4C411yescharacteristic, complemented
25C22×C4×D4C2211yescharacteristic
26C22×#117C411yescharacteristic, complemented
27C22×#117C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C22×#99C2214yes—
32C2×#381C2214yes—
33C2×#379C2212yes—
34#1898—28no—
35#1819—24no—
36C2×#342—24no—
37C2×#342C2212yes—
38C2×#342C2212yes—
39C2×#342C2212yes—
40C2×#342C2212yes—
41C2×#342C2214yes—
42#1440—24no—
43C22⋊#95—24no—
44C22⋊#95C2214yes—
45C26C2311yescharacteristic
46C23×Q8C2×C411yescharacteristic, complemented
47C23×D4C2×C411yescharacteristic
48C23×D4C2×C411yescharacteristic
49C23×D4C2311yescharacteristic
50C24×C4—22no—
51C24×C4C2×C411yescharacteristic
52C24×C4C2×C411yescharacteristic
53C24×C4C2×C411yescharacteristic, complemented
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56#551—232no—
57#551—232no—
58#551—232no—
59#551—232no—
60C2×#126—24no—
61C2×#126—24no—
62C2×#126—24no—
63C2×#126—24no—
64C2×#126—24no—
65C2×#126—24no—
66C2×#124—24no—
67C2×#124—24no—
68C2×#124—24no—
69C2×#123—24no—
70C2×#123—24no—
71C2×#123—24no—
72C2×#123—24no—
73C2×#123—24no—
74C2×#123—24no—
75C2×#123—24no—
76C2×#123—22no—
77C2×#123—22no—
78C2×#123—22no—
79C2×#123—22no—
80C2×C22⋊Q8—24no—
81C2×C22⋊Q8—24no—
82C2×C22⋊Q8—24no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8—22no—
85C2×C22⋊Q8—24no—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×#120—22no—
89C2×#120—22no—
90C2×#120—22no—
91C2×#120—22no—
92C2×#120D418yes—
93C2×C4×D4—24no—
94C2×C4×D4—24no—
95C2×C4×D4—24no—
96C2×C4×D4—24no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×#117—24no—
102C2×#117—24no—
103C2×#117—24no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—24no—
107C2×#117—22no—
108C2×#117—22no—
109C22×C4⋊C4C2×C411yescharacteristic, complemented
110C22×C4⋊C4C2×C411yescharacteristic, complemented
111C22×C4⋊C4C2×C411yescharacteristic, complemented
112C22×C4⋊C4C2×C411yescharacteristic, complemented
113C22×C4⋊C4C2×C411yescharacteristic, complemented
114C22×C4⋊C4C2×C411yescharacteristic, complemented
115C22×C4⋊C4C2×C411yescharacteristic, complemented
116C22×C4⋊C4C2×C411yescharacteristic, complemented
117C22×C22⋊C4—22no—
118C22×C22⋊C4—22no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—22no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—22no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—28no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—22no—
127C22×C22⋊C4—22no—
128C22×C22⋊C4—22no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4C2×C411yescharacteristic
131C22×C22⋊C4C2×C411yescharacteristic
132C22×C22⋊C4C2×C411yescharacteristic
133C22×C22⋊C4C2×C411yescharacteristic
134C22×C22⋊C4C2×C411yescharacteristic
135C22×C22⋊C4C2×C411yescharacteristic
136C22×C22⋊C4C2×C411yescharacteristic
137C22×C22⋊C4C2×C411yescharacteristic
138C22×C22⋊C4C2×C411yescharacteristic, complemented
139C22×C22⋊C4C2×C411yescharacteristic, complemented
140C22×C22⋊C4C2×C411yescharacteristic, complemented
141C22×C22⋊C4D414yes—
142C22×C22⋊C4D414yes—
143C22×C22⋊C4D414yes—
144C22×C22⋊C4D414yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C42C2×C411yescharacteristic, complemented
151C22×C42C2×C411yescharacteristic, complemented
152C22×C42C2×C411yescharacteristic, complemented
153C2×#99—28no—
154C2×#99—28no—
155C2×#99—44no—
156#381—28no—
157#381—44no—
158#379—24no—
159#379—24no—
160C2×#95—28no—
161C2×#95—28no—
162#342—24no—
163#342—24no—
164#342—28no—
165#342—24no—
166#342—24no—
167C25—24no—
168C25—22no—
169C25—22no—
170C25—44no—
171C25—82no—
172C25C22×C411yescharacteristic
173C25C22×C411yescharacteristic
174C25C22×C411yescharacteristic
175C25C2×D412yes—
176C25C2×D412yes—
177C25C2×D412yes—
178C25C2×D414yes—
179C25C2×D412yes—
180C25C2411yescharacteristic
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—22no—
184C22×Q8—82no—
185C22×D4—22no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—22no—
191C22×D4—24no—
192C22×D4—22no—
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—22no—
196C22×D4—44no—
197C22×D4—82no—
198C22×D4C22⋊C414yes—
199C22×D4C22⋊C414yes—
200C22×D4C2×D414yes—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—24no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—48no—
222C23×C4—44no—
223C23×C4—44no—
224C23×C4—48no—
225C23×C4—82no—
226C23×C4—84no—
227C23×C4—82no—
228C23×C4—82no—
229C23×C4C22⋊C414yes—
230C23×C4C22⋊C414yes—
231C23×C4C22×C411yescharacteristic
232C23×C4C22×C411yescharacteristic
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C411yescharacteristic
235C23×C4C22×C411yescharacteristic
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C2×D414yes—
243C23×C4C2×D414yes—
244#126—232no—
245#126—232no—
246#124—232no—
247#123—216no—
248#123—216no—
249#123—216no—
250#123—216no—
251#123—232no—
252C22⋊Q8—216no—
253C22⋊Q8—216no—
254C22⋊Q8—216no—
255C22⋊Q8—216no—
256#120—28no—
257#120—28no—
258#120—28no—
259#120—28no—
260C4×D4—216no—
261C4×D4—216no—
262C4×D4—216no—
263C4×D4—216no—
264#117—216no—
265#117—216no—
266#117—216no—
267#117—216no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—416no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4—48no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—48no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—84no—
353C2×C22⋊C4C22⋊C412yes—
354C2×C22⋊C4C22⋊C412yes—
355C2×C22⋊C4C22⋊C412yes—
356C2×C22⋊C4C22⋊C412yes—
357C2×C22⋊C4C22⋊C414yes—
358C2×C22⋊C4C22⋊C414yes—
359C2×C22⋊C4C22⋊C414yes—
360C2×C22⋊C4C22⋊C414yes—
361C2×C22⋊C4C22⋊C414yes—
362C2×C22⋊C4C22⋊C414yes—
363C2×C22⋊C4C2×D412yes—
364C2×C22⋊C4C2×D412yes—
365C2×C22⋊C4C2×D412yes—
366C2×C22⋊C4C2×D412yes—
367C2×C22⋊C4C2×D414yes—
368C2×C22⋊C4#4118yes—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378#99—416no—
379#95—416no—
380#95—88no—
381C24—22no—
382C24—22no—
383C24—24no—
384C24—24no—
385C24—28no—
386C24—24no—
387C24—22no—
388C24—22no—
389C24—24no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—24no—
394C24—24no—
395C24—28no—
396C24—24no—
397C24—28no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—42no—
403C24—44no—
404C24—42no—
405C24—42no—
406C24—44no—
407C24—42no—
408C24—42no—
409C24—44no—
410C24—44no—
411C24—48no—
412C24—44no—
413C24—42no—
414C24—42no—
415C24—82no—
416C24—84no—
417C24—82no—
418C24—816no—
419C24—88no—
420C24—88no—
421C24C2×C22⋊C412yes—
422C24C2×C22⋊C411yescharacteristic
423C24C2×C22⋊C412yes—
424C24C2×C22⋊C412yes—
425C24C2×C22⋊C411yescharacteristic
426C24C2×C22⋊C412yes—
427C24C2×C22⋊C412yes—
428C24C2×C22⋊C412yes—
429C24#12014yes—
430C24#12014yes—
431C24#12014yes—
432C24#12014yes—
433C24C23×C411yescharacteristic
434C24C22×D412yes—
435C24C22×D411yescharacteristic
436C24C22×D411yescharacteristic
437C24C22×D412yes—
438C24C2×#4114yes—
439C24H(5,𝔽2)12yes—
440C242−1+412yes—
441C2×Q8—28no—
442C2×Q8—84no—
443C2×Q8—84no—
444C2×Q8—84no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—28no—
452C2×D4—48no—
453C2×D4—44no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—48no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—84no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—28no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—48no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—48no—
527C22×C4—416no—
528C22×C4—48no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—84no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—84no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4—832no—
547C22×C4—88no—
548C22×C4—88no—
549C22×C4C2×C22⋊C412yes—
550C22×C4C2×C22⋊C412yes—
551C22×C4C2×C22⋊C412yes—
552C22×C4C2×C22⋊C412yes—
553C22×C4C2×C22⋊C412yes—
554C22×C4C2×C22⋊C412yes—
555C22×C4C2×C22⋊C412yes—
556C22×C4C2×C22⋊C412yes—
557C22×C4C2×C22⋊C412yes—
558C22×C4C2×C22⋊C412yes—
559C22×C4C2×C22⋊C412yes—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—416no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C42—28no—
600C42—28no—
601C42—28no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—28no—
619C23—28no—
620C23—24no—
621C23—24no—
622C23—28no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—44no—
642C23—48no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—416no—
654C23—416no—
655C23—48no—
656C23—48no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—88no—
667C23—88no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—88no—
673C23—88no—
674C23—84no—
675C23—84no—
676C23—88no—
677C23—816no—
678C23—816no—
679C23#37914yes—
680C23#37912yes—
681C23#37912yes—
682C23#41014yes—
683C23C22×C22⋊C411yescharacteristic
684C23C22×C22⋊C411yescharacteristic
685C23C22×C22⋊C411yescharacteristic
686C23C4×#4112yes—
687C23#52012yes—
688C23C2×#12012yes—
689C23C2×#12012yes—
690C23#52512yes—
691C23#53212yes—
692C23#53511yescharacteristic
693C23#53611yescharacteristic
694C23#53712yes—
695C23#54614yes—
696C23#54614yes—
697C23#54714yes—
698C23#54714yes—
699Q8—88no—
700D4—48no—
701D4—44no—
702D4—44no—
703D4—48no—
704D4—48no—
705D4—88no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—416no—
759C2×C4—48no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—88no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—88no—
768C2×C4—832no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4—88no—
772C2×C4—88no—
773C2×C4—84no—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—22no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—24no—
793C22—22no—
794C22—24no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—416no—
804C22—44no—
805C22—48no—
806C22—44no—
807C22—48no—
808C22—44no—
809C22—48no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22—88no—
815C22—82no—
816C22—84no—
817C22—82no—
818C22—84no—
819C22—84no—
820C22—82no—
821C22—82no—
822C22—84no—
823C22#178214yes—
824C22C2×#37911yescharacteristic
825C22#229711yescharacteristic
826C22#231111yescharacteristic
827C22#233912yes—
828C22#233912yes—
829C22#240412yes—
830C22#240612yes—
831C22#243014yes—
832C22C2×#41012yes—
833C22#288312yes—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—88no—
846C4—164no—
847C2—22no—
848C2—24no—
849C2—24no—
850C2—21no—
851C2—22no—
852C2—21no—
853C2—22no—
854C2—42no—
855C2—44no—
856C2—82no—
857C2#1395611yescharacteristic
858C2C2×#178211yescharacteristic
859C2#2058511yescharacteristic
860C2#2247714yes—
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC25C24
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C22⋊C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1819C2semidirect
4. C22×#342C2semidirect
5. #13869C2semidirect
6. #11381C2semidirect
7. #10966C2semidirect
8. #10761C2semidirect
9. #10726C2semidirect
15. C22×#126C4semidirect
16. C22×#126C4semidirect
17. C22×#124C4semidirect
18. C22×#123C4semidirect
19. C22×#123C4semidirect
21. C22×C22⋊Q8C4semidirect
24. C22×C4×D4C4semidirect
26. C22×#117C4semidirect
46. C23×Q8C2×C4semidirect
53. C24×C4C2×C4semidirect
109. C22×C4⋊C4C2×C4semidirect
110. C22×C4⋊C4C2×C4semidirect
111. C22×C4⋊C4C2×C4semidirect
112. C22×C4⋊C4C2×C4semidirect
113. C22×C4⋊C4C2×C4semidirect
114. C22×C4⋊C4C2×C4semidirect
115. C22×C4⋊C4C2×C4semidirect
116. C22×C4⋊C4C2×C4semidirect
138. C22×C22⋊C4C2×C4semidirect
139. C22×C22⋊C4C2×C4semidirect
140. C22×C22⋊C4C2×C4semidirect
150. C22×C42C2×C4semidirect
151. C22×C42C2×C4semidirect
152. C22×C42C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5512
C2×#18982
C2×#18192
C22×#3422
#138692
#113812
#109662
#107612
#107262