Finite Group Databasebeta

← #357192

Subgroups — #357192

Order 512.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1972C211yesmaximal, characteristic
2C2×#1879C211yesmaximal, characteristic
3C2×#1879C211yesmaximal, characteristic
4C2×#1762C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6#13820C211yesmaximal, characteristic, complemented
7#13820C211yesmaximal, characteristic, complemented
8#10931C211yesmaximal, characteristic, complemented
9#10931C211yesmaximal, characteristic, complemented
10#10927C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10703C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×D8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4—21no—
38C2×C4×C22⋊C4—21no—
39#1972C418yescomplemented
40#1879C418yescomplemented
41#1879C418yescomplemented
42#1762—24no—
43C4×#102—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1437—21no—
56#1437—21no—
57#1437—21no—
58#1437—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C22⋊#95—21no—
62C22⋊#95—21no—
63C4×#95C2211yescharacteristic
64C23×D4C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C22×D8—41no—
69C22×D8—41no—
70C22×D8—41no—
71C22×D8—41no—
72C22×D8C2×C414yes—
73C22×D8C2×C414yes—
74C22×D8C2×C414yes—
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4C2×C414yescomplemented
90C2×C4×D4C2×C414yescomplemented
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C42—21no—
108C22×C42—21no—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C2×#106—41no—
115C2×#106—41no—
116C2×#106C2×C414yescomplemented
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—41no—
126C2×#102—41no—
127C2×#102—41no—
128C2×#102—41no—
129C2×#102C2×C414yes—
130C2×#102C2×C414yes—
131C2×#102C2×C414yescomplemented
132C2×#102C2×C414yescomplemented
133C2×#102C2×C414yescomplemented
134C2×#102C2×C414yescomplemented
135C2×#97—22no—
136C2×#97—22no—
137C2×#97—41no—
138C2×#97—41no—
139C2×#97—41no—
140C2×#97C2×C414yescomplemented
141C2×C4×C8—22no—
142C2×C4×C8—22no—
143C2×C4×C8—41no—
144#390—22no—
145#390—22no—
146#390—22no—
147#390—22no—
148#390C2×C414yes—
149#390C2×C414yes—
150#390C2×C414yescomplemented
151#390C2×C414yescomplemented
152C4×C4⋊C4—22no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—41no—
157C4×C4⋊C4—41no—
158C4×C4⋊C4—41no—
159C4×C4⋊C4—41no—
160C4×C22⋊C4—44no—
161C4×C22⋊C4—44no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95D411yescharacteristic
171C2×#95D411yescharacteristic
172C2×#95D411yescharacteristic
173C2×#95D411yescharacteristic
174#340—22no—
175#340—22no—
176#340—22no—
177#340—41no—
178#340—41no—
179#340C2×C414yescomplemented
180#340C2×C414yescomplemented
181#340D414yes—
182#336—22no—
183#336C2×C414yescomplemented
184#336C2×C414yescomplemented
185C25—21no—
186C25—21no—
187C22×D4—21no—
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—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C22×C412yes—
210C22×D4C22×C412yes—
211C22×D4C22×C412yes—
212C22×D4C22×C412yes—
213C22×D4C22×C412yes—
214C22×D4C22×C412yes—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4—81no—
234C23×C4—81no—
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2411yescharacteristic
242C2×D8—44no—
243C2×D8—44no—
244C2×D8—44no—
245C2×D8—44no—
246C2×D8—44no—
247C2×D8—44no—
248C2×D8C42116yescomplemented
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×C8—21no—
269C22×C8C22×C412yes—
270C22×C8C22×C412yes—
271C22×C8C22×C412yes—
272C22×C8C22×C412yes—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C2×D412yes—
276C22×C8#4112yes—
277C4×D4—28no—
278C4×D4—28no—
279C4×D4—44no—
280C4×D4—44no—
281C4×D4—44no—
282C4×D4—44no—
283C4×D4—44no—
284C4×D4—44no—
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—21no—
311C2×C4⋊C4C22×C412yes—
312C2×C4⋊C4C22×C412yes—
313C2×C4⋊C4C22×C412yes—
314C2×C4⋊C4C22×C412yes—
315C2×C4⋊C4C22×C412yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C2×D412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4#4112yes—
320C2×C4⋊C4#4112yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—81no—
344C2×C22⋊C4—81no—
345C2×C22⋊C4—81no—
346C2×C22⋊C4—81no—
347C2×C22⋊C4—81no—
348C2×C22⋊C4—81no—
349C2×C22⋊C4—81no—
350C2×C22⋊C4—81no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—81no—
372C2×C42—81no—
373C2×C42—81no—
374C2×C42—81no—
375C2×C42C22×C412yes—
376C2×C42C22×C412yes—
377C2×C42C22×C412yes—
378C2×C42#4112yes—
379C2×C42#4112yes—
380C2×C42#4112yes—
381#106—44no—
382#102—28no—
383#102—28no—
384#102—28no—
385#102—28no—
386#102—44no—
387#102—44no—
388#97—44no—
389#97—44no—
390C4×C8—44no—
391#95—22no—
392#95—22no—
393#95—41no—
394#95—41no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—81no—
402#95—81no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24C22×D411yescharacteristic
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—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4C2×C4214yes—
489C2×D4C2×C4214yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
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—48no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4C4×D412yes—
581C22×C4C4×D412yes—
582C22×C4C4×D412yes—
583C22×C4C4×D412yes—
584C22×C4C4×D412yes—
585C22×C4C4×D412yes—
586C22×C4AGL(1,ℤ/8)12yes—
587C22×C4AGL(1,ℤ/8)12yes—
588C22×C4C23×C411yescharacteristic
589C22×C4C23×C411yescharacteristic
590C22×C4C23×C411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4H(5,𝔽2)11yescharacteristic
599C22×C4H(5,𝔽2)11yescharacteristic
600C22×C4H(5,𝔽2)11yescharacteristic
601C22×C4H(5,𝔽2)11yescharacteristic
602D8—416no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8C2×C4214yes—
630C2×C8C4×D414yes—
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—22no—
644C4⋊C4—22no—
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⋊C4C4×D414yes—
654C4⋊C4C4×D414yes—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C22⋊C4—84no—
664C22⋊C4—84no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—84no—
678C42—84no—
679C42—84no—
680C42—84no—
681C23—24no—
682C23—24no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—81no—
731C23—81no—
732C23—81no—
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—
749C23—81no—
750C23—81no—
751C23C2×C4×D411yescharacteristic
752C23C2×C4×D411yescharacteristic
753C23C2×C4×D411yescharacteristic
754C23D4211yescharacteristic
755C23#54611yescharacteristic
756C23#54611yescharacteristic
757C23#55011yescharacteristic
758C23C2×AGL(1,ℤ/8)11yescharacteristic
759C23C2×AGL(1,ℤ/8)11yescharacteristic
760C23#57511yescharacteristic
761C23#57511yescharacteristic
762C23#57611yescharacteristic
763C23#57611yescharacteristic
764C23#57711yescharacteristic
765C23#57711yescharacteristic
766D4—24no—
767D4—24no—
768D4—24no—
769D4—24no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—42no—
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—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—816no—
850C2×C4—816no—
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—81no—
866C2×C4—81no—
867C2×C4#44214yes—
868C2×C4C22×C4211yescharacteristic
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C2×C4×D411yescharacteristic
872C2×C4C4×#4111yescharacteristic
873C2×C4C4×#4111yescharacteristic
874C2×C4C4×#4111yescharacteristic
875C2×C4C4×#4111yescharacteristic
876C2×C4C4×#4111yescharacteristic
877C2×C4C4×#4111yescharacteristic
878C2×C4#51811yescharacteristic
879C2×C4#51811yescharacteristic
880C2×C4#51811yescharacteristic
881C2×C4#51811yescharacteristic
882C2×C4#51811yescharacteristic
883C2×C4#51811yescharacteristic
884C2×C4#54611yescharacteristic
885C2×C4#54611yescharacteristic
886C2×C4#55011yescharacteristic
887C2×C4#55111yescharacteristic
888C2×C4#55111yescharacteristic
889C2×C4#55311yescharacteristic
890C2×C4#55311yescharacteristic
891C2×C4#55311yescharacteristic
892C2×C4#55311yescharacteristic
893C2×C4#55511yescharacteristic
894C2×C4#55511yescharacteristic
895C2×C4#55911yescharacteristic
896C8—24no—
897C8—24no—
898C8—42no—
899C8—42no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—82no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22C42×D411yescharacteristic
931C22#235811yescharacteristic
932C22#235811yescharacteristic
933C22#236311yescharacteristic
934C22#236311yescharacteristic
935C22#236411yescharacteristic
936C22#236611yescharacteristic
937C22C2×#44211yescharacteristic
938C22#294311yescharacteristic
939C22C4×AGL(1,ℤ/8)11yescharacteristic
940C22C4×AGL(1,ℤ/8)11yescharacteristic
941C22C4×AGL(1,ℤ/8)11yescharacteristic
942C22C4×AGL(1,ℤ/8)11yescharacteristic
943C22#294611yescharacteristic
944C22#294611yescharacteristic
945C22#294611yescharacteristic
946C22#294611yescharacteristic
947C22#294811yescharacteristic
948C22#295211yescharacteristic
949C22#326411yescharacteristic
950C22#326511yescharacteristic
951C22#326811yescharacteristic
952C22#327111yescharacteristic
953C22#330611yescharacteristic
954C22#330911yescharacteristic
955C22#331811yescharacteristic
956C22#332111yescharacteristic
957C22#332211yescharacteristic
958C22#332511yescharacteristic
959C22#332611yescharacteristic
960C22#333211yescharacteristic
961C22#339711yescharacteristic
962C22#339911yescharacteristic
963C22#340111yescharacteristic
964C22#340311yescharacteristic
965C4—24no—
966C4—42no—
967C4—44no—
968C4—42no—
969C4—44no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4C42×D411yescharacteristic
978C4#227311yescharacteristic
979C4#236311yescharacteristic
980C4#236311yescharacteristic
981C4#236411yescharacteristic
982C4#237211yescharacteristic
983C4#237411yescharacteristic
984C4#237411yescharacteristic
985C2—84no—
986C2—84no—
987C2#1382411yescharacteristic
988C2C4×#44211yescharacteristic
989C2#2050311yescharacteristic
990C2#2285711yescharacteristic
991C2#2285811yescharacteristic
992C2#2288011yescharacteristic
993C2#2288311yescharacteristic
994C2#2309911yescharacteristic
995C2#2310411yescharacteristic
996C2#2310811yescharacteristic
997C2#2310911yescharacteristic
998C2#2314011yescharacteristic
999C2#2314311yescharacteristic
1000C2#2319311yescharacteristic
1001C2#2319511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1762C2semidirect
5. C2×C4×#102C2semidirect
6. #13820C2semidirect
7. #13820C2semidirect
8. #10931C2semidirect
9. #10931C2semidirect
10. #10927C2semidirect
11. #10925C2semidirect
12. #10908C2semidirect
13. #10908C2semidirect
14. #10703C2semidirect
15. #10696C2semidirect
39. #1972C4semidirect
40. #1879C4semidirect
41. #1879C4semidirect
89. C2×C4×D4C2×C4semidirect
90. C2×C4×D4C2×C4semidirect
116. C2×#106C2×C4semidirect
131. C2×#102C2×C4semidirect
132. C2×#102C2×C4semidirect
133. C2×#102C2×C4semidirect
134. C2×#102C2×C4semidirect
140. C2×#97C2×C4semidirect
150. #390C2×C4semidirect
151. #390C2×C4semidirect
179. #340C2×C4semidirect
180. #340C2×C4semidirect
183. #336C2×C4semidirect
184. #336C2×C4semidirect
248. C2×D8C42semidirect

Maximal subgroups

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

subgroupindex
C2×#19722
C2×#18792
C2×#17622
C2×C4×#1022
#138202
#109312
#109272
#109252
#109082
#107032
#106962