Finite Group Databasebeta

← #376499

Subgroups — #376499

Order 512.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2033C211yesmaximal, characteristic
2C2×#1925C211yesmaximal, characteristic, complemented
3C2×#1874C211yesmaximal, characteristic
4C2×#1852C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6#13970C211yesmaximal, characteristic
7C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
8#11315C211yesmaximal, characteristic, complemented
9#11199C211yesmaximal, characteristic, complemented
10#11123C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10907C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10862C211yesmaximal, characteristic, complemented
15#10788C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#386—21no—
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4—21no—
36C2×C4×C22⋊C4C2211yescharacteristic
37#2033C418yescomplemented
38#1925—24no—
39#1874—24no—
40#1852—24no—
41C4×#102—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1440—21no—
55#1438—21no—
56#1436—21no—
57#1436—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—21no—
63C22⋊#95—21no—
64C23×D4—21no—
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C2×#121—22no—
74C2×#121—22no—
75C2×#121—22no—
76C2×#121—41no—
77C2×#121—41no—
78C2×#121C2×C414yes—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
106C22×C22⋊C4D411yescharacteristic
107C22×C42—21no—
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—41no—
117C2×#107—41no—
118C2×#107—41no—
119C2×#107C2×C414yescomplemented
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—41no—
129C2×#102C2×C414yescomplemented
130C2×#102C2×C414yescomplemented
131C2×#102D414yes—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8C2×C414yescomplemented
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141#390—22no—
142#390—41no—
143#386—44no—
144#380—22no—
145#380—22no—
146#380—41no—
147#380C2×C414yescomplemented
148C4×C4⋊C4—22no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—41no—
151C4×C4⋊C4—41no—
152C4×C22⋊C4—22no—
153C4×C22⋊C4—22no—
154C4×C22⋊C4—44no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95D411yescharacteristic
168C2×#95D411yescharacteristic
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—41no—
175#340—41no—
176#340C2×C414yescomplemented
177#340D414yescomplemented
178#336—22no—
179#336—22no—
180#336—22no—
181C25—21no—
182C25C2×D411yescharacteristic
183C22×D4—24no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—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—42no—
196C22×D4—42no—
197C22×D4—42no—
198C22×D4—42no—
199C22×D4—81no—
200C22×D4—81no—
201C22×D4C22×C412yes—
202C22×D4C2×D412yes—
203C22×D4#4112yes—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
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—24no—
223C23×C4—21no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—81no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4C22×C412yes—
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4#4112yes—
244C23×C4C2411yescharacteristic
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×C8C22×C412yes—
269C22×C8C22×C412yes—
270C22×C8C2×D412yes—
271C22×C8C2×D412yes—
272C22×C8#4112yes—
273#121—28no—
274#121—44no—
275#121—44no—
276#121—44no—
277C4×D4—28no—
278C4×D4—44no—
279C4×D4—44no—
280C4×D4—44no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
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—24no—
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⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C22×C412yes—
323C2×C4⋊C4C22×C412yes—
324C2×C4⋊C4C22×C412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4C2×D412yes—
327C2×C4⋊C4C2×D412yes—
328C2×C4⋊C4#4112yes—
329C2×C4⋊C4#4112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—41no—
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—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—81no—
351C2×C22⋊C4—81no—
352C2×C22⋊C4—81no—
353C2×C22⋊C4D814yes—
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—21no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—81no—
369C2×C42—81no—
370C2×C42#4112yes—
371C2×C42#4112yes—
372#107—44no—
373#107—44no—
374#107—44no—
375#102—28no—
376#102—28no—
377#102—28no—
378#102—44no—
379C22⋊C8—28no—
380C22⋊C8—44no—
381C4×C8—44no—
382#95—24no—
383#95—22no—
384#95—22no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—81no—
393#95—81no—
394#95—81no—
395#95—81no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24C4×D412yes—
424C24C2×D812yes—
425C24#13512yes—
426C24C22×D411yescharacteristic
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
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—48no—
443C2×D4—48no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—84no—
457C2×D4—84no—
458C2×D4—84no—
459C2×D4—84no—
460C2×D4—84no—
461C2×D4C4×D414yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
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—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
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—48no—
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—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×C4—84no—
581C22×C4—84no—
582C22×C4C4×D412yes—
583C22×C4#12312yes—
584C22×C4#12312yes—
585C22×C4C2×D812yes—
586C22×C4C2×D812yes—
587C22×C4#13712yes—
588C22×C4C23×C411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C2×#4111yescharacteristic
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×C42−1+411yescharacteristic
602C2×C8—22no—
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—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—
628C2×C8—41no—
629C2×C8C4×D414yes—
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—41no—
657C4⋊C4—41no—
658C4⋊C4#12114yes—
659C22⋊C4—28no—
660C22⋊C4—44no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C22⋊C4—84no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—41no—
672C42—41no—
673C42—41no—
674C42—41no—
675C42—84no—
676C42—84no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
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—
746C23C4×D814yes—
747C23C2×C4×D411yescharacteristic
748C23C2×#12311yescharacteristic
749C23#52511yescharacteristic
750C23D4211yescharacteristic
751C23D4211yescharacteristic
752C23#54611yescharacteristic
753C23#54711yescharacteristic
754C23C22×D811yescharacteristic
755C23C2×#13511yescharacteristic
756C23C2×#13711yescharacteristic
757C23#57511yescharacteristic
758C23#57611yescharacteristic
759C23#57611yescharacteristic
760C23#57711yescharacteristic
761C23#57811yescharacteristic
762D4—24no—
763D4—24no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—816no—
771C2×C4—22no—
772C2×C4—22no—
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—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
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—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—816no—
836C2×C4—816no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
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#48014yes—
865C2×C4C2×C4×D411yescharacteristic
866C2×C4C2×C4×D411yescharacteristic
867C2×C4C4×#4111yescharacteristic
868C2×C4C4×#4111yescharacteristic
869C2×C4#51811yescharacteristic
870C2×C4#52011yescharacteristic
871C2×C4C2×#12111yescharacteristic
872C2×C4#52511yescharacteristic
873C2×C4#52911yescharacteristic
874C2×C4#52911yescharacteristic
875C2×C4#52911yescharacteristic
876C2×C4#53211yescharacteristic
877C2×C4#53811yescharacteristic
878C2×C4#53811yescharacteristic
879C2×C4#54211yescharacteristic
880C2×C4#54211yescharacteristic
881C2×C4#54611yescharacteristic
882C2×C4#54611yescharacteristic
883C2×C4#54611yescharacteristic
884C2×C4#54611yescharacteristic
885C2×C4#54711yescharacteristic
886C2×C4#54811yescharacteristic
887C2×C4#55111yescharacteristic
888C2×C4#55111yescharacteristic
889C2×C4#55211yescharacteristic
890C2×C4#55311yescharacteristic
891C2×C4#55311yescharacteristic
892C2×C4#55311yescharacteristic
893C8—24no—
894C8—42no—
895C8—42no—
896C8—81no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22C4×#12311yescharacteristic
928C22#235811yescharacteristic
929C22#236111yescharacteristic
930C22#241811yescharacteristic
931C22#242211yescharacteristic
932C22#242411yescharacteristic
933C22#247011yescharacteristic
934C22C2×C4×D811yescharacteristic
935C22C4×#13711yescharacteristic
936C22#294611yescharacteristic
937C22#295111yescharacteristic
938C22C2×#48011yescharacteristic
939C22#309111yescharacteristic
940C22#309611yescharacteristic
941C22#309811yescharacteristic
942C22#310011yescharacteristic
943C22#310811yescharacteristic
944C22#312111yescharacteristic
945C22#312211yescharacteristic
946C22#326611yescharacteristic
947C22#326811yescharacteristic
948C22#327311yescharacteristic
949C22#327611yescharacteristic
950C22D4×D811yescharacteristic
951C22D4×D811yescharacteristic
952C22#328211yescharacteristic
953C22#328511yescharacteristic
954C22#329411yescharacteristic
955C22#329711yescharacteristic
956C22#331411yescharacteristic
957C22#331511yescharacteristic
958C22#333411yescharacteristic
959C22#333911yescharacteristic
960C22#335111yescharacteristic
961C22#335711yescharacteristic
962C4—24no—
963C4—42no—
964C4—44no—
965C4—42no—
966C4—42no—
967C4—82no—
968C4—82no—
969C4—82no—
970C4—82no—
971C4—81no—
972C4—82no—
973C4—161no—
974C4C4×#12111yescharacteristic
975C4#233711yescharacteristic
976C4#235911yescharacteristic
977C4#236411yescharacteristic
978C4#242711yescharacteristic
979C4#247711yescharacteristic
980C4#255911yescharacteristic
981C4#257611yescharacteristic
982C2—44no—
983C2—84no—
984C2#1418211yescharacteristic
985C2C4×#48011yescharacteristic
986C2#2159011yescharacteristic
987C2#2286211yescharacteristic
988C2#2287011yescharacteristic
989C2#2302511yescharacteristic
990C2#2303511yescharacteristic
991C2#2486111yescharacteristic
992C2#2486411yescharacteristic
993C2#2501011yescharacteristic
994C2#2501811yescharacteristic
995C2#2514811yescharacteristic
996C2#2515711yescharacteristic
997C2#2715811yescharacteristic
998C2#2715911yescharacteristic
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×#1925C2semidirect
4. C2×#1852C2semidirect
5. C2×C4×#102C2semidirect
7. C22⋊C4×C4⋊C4C2semidirect
8. #11315C2semidirect
9. #11199C2semidirect
10. #11123C2semidirect
11. #10921C2semidirect
12. #10907C2semidirect
13. #10907C2semidirect
14. #10862C2semidirect
15. #10788C2semidirect
37. #2033C4semidirect
119. C2×#107C2×C4semidirect
129. C2×#102C2×C4semidirect
130. C2×#102C2×C4semidirect
137. C2×C22⋊C8C2×C4semidirect
147. #380C2×C4semidirect
176. #340C2×C4semidirect
177. #340D4semidirect

Maximal subgroups

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

subgroupindex
C2×#20332
C2×#19252
C2×#18742
C2×#18522
C2×C4×#1022
#139702
C22⋊C4×C4⋊C42
#113152
#111992
#111232
#109212
#109072
#108622
#107882