Finite Group Databasebeta

← #372389

Subgroups — #372389

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2422C211yesmaximal, characteristic
2C2×#1924C211yesmaximal, characteristic, complemented
3C2×#1875C211yesmaximal, characteristic
4C2×#1762C211yesmaximal, characteristic, complemented
5#13801C211yesmaximal, characteristic, complemented
6#11373C211yesmaximal, characteristic, complemented
7#11200C211yesmaximal, characteristic, complemented
8#11076C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10885C211yesmaximal, characteristic, complemented
12#10881C211yesmaximal, characteristic, complemented
13#10849C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic, complemented
16C22×#123—21no—
17C22×#121C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28#2422—24no—
29#2422C418yescomplemented
30C2×#397—21no—
31C2×#394—21no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#385—21no—
35C2×#384C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1924—24no—
42#1875—24no—
43#1762—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1437—21no—
59#1437—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63C4×#95—21no—
64C23×D4—21no—
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×#123—28no—
73C2×#123—44no—
74C2×#123—44no—
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—41no—
79C2×#121—41no—
80C2×#121C2×C414yes—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4C2×C414yes—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—41no—
92C2×#117—41no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4D411yescharacteristic
111C22×C22⋊C4D411yescharacteristic
112C22×C42—21no—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—41no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—41no—
130C2×#102—41no—
131C2×#102D414yes—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8—41no—
138C2×#97—22no—
139C2×#97—22no—
140C2×#97—41no—
141#397—28no—
142#394—28no—
143#390—22no—
144#390C2×C414yes—
145#389—22no—
146#389C2×C414yes—
147#385—28no—
148#384—22no—
149#384C2×C414yes—
150#380—22no—
151#380—22no—
152#380—22no—
153#380C2×C414yes—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—41no—
157C4×C4⋊C4—41no—
158C4×C22⋊C4C2×C414yes—
159C4×C22⋊C4D414yes—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95D411yescharacteristic
170C2×#95D411yescharacteristic
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340—41no—
183#336—22no—
184#336—22no—
185C25—21no—
186C25C2×D411yescharacteristic
187C22×D4—24no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4—42no—
202C22×D4—42no—
203C22×D4—81no—
204C22×D4—81no—
205C22×D4C22×C412yes—
206C22×D4C2×D412yes—
207C22×D4#4112yes—
208C23×C4—21no—
209C23×C4—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—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—24no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—81no—
233C23×C4—81no—
234C23×C4C22×C412yes—
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D412yes—
240C23×C4C2×D411yescharacteristic
241C23×C4C2411yescharacteristic
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8C2×D412yes—
269C22×C8#4112yes—
270#123—432no—
271#121—28no—
272#121—44no—
273#121—44no—
274#121—44no—
275C4×D4—28no—
276C4×D4—44no—
277C4×D4—44no—
278C4×D4—44no—
279#117—44no—
280#117—44no—
281#117—44no—
282#117—44no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4C22×C412yes—
326C2×C4⋊C4C22×C412yes—
327C2×C4⋊C4C22×C412yes—
328C2×C4⋊C4C2×D412yes—
329C2×C4⋊C4#4112yes—
330C2×C4⋊C4#4112yes—
331C2×C4⋊C4#4112yes—
332C2×C4⋊C4#4112yes—
333C2×C4⋊C4#4112yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
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—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4—81no—
359C2×C22⋊C4C22⋊C414yes—
360C2×C22⋊C4C22⋊C414yes—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—81no—
377C2×C42—81no—
378C2×C42C22×C412yes—
379C2×C42C22×C412yes—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C4⋊C8—44no—
383#102—28no—
384#102—28no—
385#102—44no—
386#102—44no—
387C22⋊C8—44no—
388C22⋊C8—44no—
389#97—44no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—81no—
398#95—81no—
399#95C22⋊C414yes—
400#95C22⋊C414yes—
401C24—22no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24C2×C22⋊C412yes—
431C24C22×D411yescharacteristic
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—84no—
462C2×D4—84no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4C4×D414yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
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—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
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—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C412yes—
582C22×C4C2×C22⋊C412yes—
583C22×C4C2×C22⋊C412yes—
584C22×C4AGL(1,ℤ/8)12yes—
585C22×C4AGL(1,ℤ/8)12yes—
586C22×C4C23×C411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4H(5,𝔽2)11yescharacteristic
597C22×C4H(5,𝔽2)11yescharacteristic
598C22×C4H(5,𝔽2)11yescharacteristic
599C22×C42−1+411yescharacteristic
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—48no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—48no—
657C4⋊C4—84no—
658C4⋊C4#12314yescomplemented
659C22⋊C4—28no—
660C22⋊C4—44no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—84no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—48no—
677C42—84no—
678C42—84no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23—41no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23C22×C22⋊C411yescharacteristic
750C23#52511yescharacteristic
751C23#52511yescharacteristic
752C23D4211yescharacteristic
753C23#54611yescharacteristic
754C23#54611yescharacteristic
755C23#54711yescharacteristic
756C23C2×AGL(1,ℤ/8)11yescharacteristic
757C23C2×AGL(1,ℤ/8)11yescharacteristic
758C23#57511yescharacteristic
759C23#57511yescharacteristic
760C23#57611yescharacteristic
761C23#57711yescharacteristic
762C23#57711yescharacteristic
763C23#57811yescharacteristic
764D4—24no—
765D4—24no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—816no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—816no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4#41814yes—
866C2×C4C2×C4×D411yescharacteristic
867C2×C4C4×#4111yescharacteristic
868C2×C4C4×#4111yescharacteristic
869C2×C4C4×#4111yescharacteristic
870C2×C4#51811yescharacteristic
871C2×C4#52011yescharacteristic
872C2×C4C2×#12311yescharacteristic
873C2×C4#52511yescharacteristic
874C2×C4#52911yescharacteristic
875C2×C4#52911yescharacteristic
876C2×C4#53211yescharacteristic
877C2×C4#53211yescharacteristic
878C2×C4#53811yescharacteristic
879C2×C4#53911yescharacteristic
880C2×C4#54011yescharacteristic
881C2×C4#54211yescharacteristic
882C2×C4D4211yescharacteristic
883C2×C4#54611yescharacteristic
884C2×C4#54611yescharacteristic
885C2×C4#54611yescharacteristic
886C2×C4#54711yescharacteristic
887C2×C4#54711yescharacteristic
888C2×C4#55111yescharacteristic
889C2×C4#55111yescharacteristic
890C2×C4#55211yescharacteristic
891C2×C4#55311yescharacteristic
892C2×C4#55311yescharacteristic
893C2×C4#55911yescharacteristic
894C8—42no—
895C8—42no—
896C8—81no—
897C8—81no—
898C22—42no—
899C22—44no—
900C22—42no—
901C22—42no—
902C22—44no—
903C22—42no—
904C22—44no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—81no—
909C22—82no—
910C22—81no—
911C22—82no—
912C22—81no—
913C22—82no—
914C22—81no—
915C22—82no—
916C22—81no—
917C22—82no—
918C22—81no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—81no—
923C22—82no—
924C22—81no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22#229711yescharacteristic
929C22D4×C22⋊C411yescharacteristic
930C22#233911yescharacteristic
931C22#241811yescharacteristic
932C22#245511yescharacteristic
933C22#245711yescharacteristic
934C22#247011yescharacteristic
935C22C2×#41811yescharacteristic
936C22#289611yescharacteristic
937C22#289711yescharacteristic
938C22#289811yescharacteristic
939C22#311511yescharacteristic
940C22#311511yescharacteristic
941C22#311511yescharacteristic
942C22#311511yescharacteristic
943C22#311811yescharacteristic
944C22#312111yescharacteristic
945C22#312411yescharacteristic
946C22#312511yescharacteristic
947C22#326711yescharacteristic
948C22#326911yescharacteristic
949C22#327211yescharacteristic
950C22#327411yescharacteristic
951C22#330611yescharacteristic
952C22#330711yescharacteristic
953C22#330711yescharacteristic
954C22#330811yescharacteristic
955C22#330911yescharacteristic
956C22#331511yescharacteristic
957C22#332411yescharacteristic
958C22#332511yescharacteristic
959C22#334311yescharacteristic
960C22#334511yescharacteristic
961C22#334711yescharacteristic
962C22#335011yescharacteristic
963C4—24no—
964C4—42no—
965C4—44no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—82no—
974C4—82no—
975C4C4×#12311yescharacteristic
976C4#233511yescharacteristic
977C4#235911yescharacteristic
978C4#237411yescharacteristic
979C4#242211yescharacteristic
980C4#246411yescharacteristic
981C4#255311yescharacteristic
982C4#255711yescharacteristic
983C2—82no—
984C2—84no—
985C2#1409611yescharacteristic
986C2#2139311yescharacteristic
987C2#2139711yescharacteristic
988C2#2242011yescharacteristic
989C2#2242811yescharacteristic
990C2#2249511yescharacteristic
991C2#2249811yescharacteristic
992C2#2491111yescharacteristic
993C2#2491611yescharacteristic
994C2#2656411yescharacteristic
995C2#2656911yescharacteristic
996C2#2668011yescharacteristic
997C2#2668411yescharacteristic
998C2#2718211yescharacteristic
999C2#2718611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1924C2semidirect
4. C2×#1762C2semidirect
5. #13801C2semidirect
6. #11373C2semidirect
7. #11200C2semidirect
8. #11076C2semidirect
10. #10931C2semidirect
11. #10885C2semidirect
12. #10881C2semidirect
13. #10849C2semidirect
14. #10788C2semidirect
15. #10731C2semidirect
29. #2422C4semidirect
658. C4⋊C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24222
C2×#19242
C2×#18752
C2×#17622
#138012
#113732
#112002
#110762
#109692
#109312
#108852
#108812
#108492
#107882
#107312