Finite Group Databasebeta

← #370132

Subgroups — #370132

Order 512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2349C211yesmaximal, characteristic
2C2×#1941C211yesmaximal, characteristic, complemented
3C2×#1864C211yesmaximal, characteristic
4C2×#1864C211yesmaximal, characteristic
5C2×#1862C211yesmaximal, characteristic
6C2×C4×#102C211yesmaximal, characteristic
7#14046C211yesmaximal, characteristic, complemented
8#11328C211yesmaximal, characteristic, complemented
9#11325C211yesmaximal, characteristic, complemented
10#11220C211yesmaximal, characteristic, complemented
11#11208C211yesmaximal, characteristic, complemented
12#10885C211yesmaximal, characteristic, complemented
13#10874C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2349—24no—
28#2349—24no—
29C2×#389—21no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#385—21no—
36C2×#385—21no—
37C2×#382C2211yescharacteristic
38C2×#380—21no—
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C22×#95—21no—
42#1941—24no—
43#1864—24no—
44#1864C418yescomplemented
45#1862—24no—
46C4×#102—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1442—21no—
62#1441—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×D4C2311yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4—21no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
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—22no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C2×C4×D4C2×C414yes—
91C2×C4×D4D414yes—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4D411yescharacteristic
98C22×C4⋊C4D411yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×#107—22no—
114C2×#107—41no—
115C2×#107—41no—
116C2×#106—22no—
117C2×#106—22no—
118C2×#106—22no—
119C2×#106—22no—
120C2×#106—41no—
121C2×#106C2×C414yescomplemented
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102C2×C414yes—
130C2×#102C2×C414yes—
131C2×#102D414yes—
132C2×#102Q814yes—
133C2×#102Q814yes—
134C2×C4×C8—22no—
135C2×C4×C8—22no—
136C2×C4×C8—41no—
137#389—22no—
138#389—22no—
139#389—22no—
140#389—22no—
141#389—22no—
142#389—22no—
143#389—22no—
144#389—41no—
145#389—44no—
146#389C2×C414yescomplemented
147#389D414yes—
148#385—28no—
149#385—28no—
150#382—22no—
151#382—22no—
152#380—28no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—41no—
157C2×#95—28no—
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×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95D411yescharacteristic
171C2×#95D411yescharacteristic
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#340C2×C414yescomplemented
181#336—22no—
182#336—22no—
183#336—22no—
184#336—41no—
185#336C2×C414yescomplemented
186C25—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4C22×C412yes—
195C22×D4C2×D412yes—
196C22×D4C2×D412yes—
197C22×D4C2×Q812yes—
198C22×D4C2×Q812yes—
199C22×D4#4112yes—
200C22×D4#4112yes—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—21no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—81no—
222C23×C4—81no—
223C23×C4—81no—
224C23×C4—81no—
225C23×C4—81no—
226C23×C4—81no—
227C23×C4—81no—
228C23×C4—81no—
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2411yescharacteristic
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—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×C8C22×C412yes—
260C22×C8C22×C412yes—
261C22×C8C2×D412yes—
262C22×C8C2×Q812yes—
263C22×C8C2×Q812yes—
264C4×D4—28no—
265C4×D4—28no—
266C4×D4—28no—
267C4×D4—28no—
268C4×D4—28no—
269C4×D4—44no—
270C4×D4—44no—
271C4×D4—44no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C4×D4—44no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
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—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
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⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4—81no—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C2×D412yes—
333C2×C4⋊C4C2×D412yes—
334C2×C4⋊C4C2×D412yes—
335C2×C4⋊C4C2×D412yes—
336C2×C4⋊C4C2×Q812yes—
337C2×C4⋊C4C2×Q812yes—
338C2×C4⋊C4#4112yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
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—42no—
363C2×C42—42no—
364C2×C42—81no—
365C2×C42C22×C412yes—
366C2×C42C2×D412yes—
367C2×C42C2×D412yes—
368C2×C42#4112yes—
369#107—44no—
370#106—28no—
371#106—44no—
372#102—28no—
373#102—28no—
374#102—44no—
375#102C4⋊C4116yescomplemented
376C4×C8—44no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—22no—
382#95—24no—
383#95—22no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—81no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24C22×D411yescharacteristic
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4C2×C4⋊C414yes—
429C2×D4C4×D414yes—
430C2×D4C4×Q814yes—
431C2×D4#12114yes—
432C2×D4C22⋊Q814yes—
433C2×D4#12514yes—
434C2×D4C4⋊Q814yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—216no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—48no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—48no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—84no—
525C22×C4—84no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4#12012yes—
543C22×C4#12012yes—
544C22×C4#13512yes—
545C22×C4#13512yes—
546C22×C4AGL(1,ℤ/8)12yes—
547C22×C4C23×C411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×Q811yescharacteristic
552C22×C4C22×Q811yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4H(5,𝔽2)11yescharacteristic
558C22×C4H(5,𝔽2)11yescharacteristic
559C22×C42−1+411yescharacteristic
560C22×C42−1+411yescharacteristic
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8C2×C4⋊C414yes—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—44no—
604C4⋊C4—48no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—44no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C4⋊C4C2×C4⋊C414yes—
623C4⋊C4C4×D414yes—
624C22⋊C4—216no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—84no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×C4×D411yescharacteristic
676C23C2×#12011yescharacteristic
677C23#52511yescharacteristic
678C23D4211yescharacteristic
679C23#54611yescharacteristic
680C23D4×Q811yescharacteristic
681C23D4×Q811yescharacteristic
682C23C2×#13511yescharacteristic
683C23C2×#13511yescharacteristic
684C23C2×AGL(1,ℤ/8)11yescharacteristic
685C23#57511yescharacteristic
686C23#57611yescharacteristic
687C23#57711yescharacteristic
688C23#57711yescharacteristic
689C23#57711yescharacteristic
690D4—24no—
691D4—24no—
692D4—24no—
693D4—24no—
694D4—24no—
695D4—24no—
696D4—24no—
697D4#38918yescomplemented
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—816no—
766C2×C4—816no—
767C2×C4—816no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4#44914yes—
792C2×C4C22×C4⋊C411yescharacteristic
793C2×C4C2×C4×D411yescharacteristic
794C2×C4C2×C4×D411yescharacteristic
795C2×C4C2×C4×Q811yescharacteristic
796C2×C4#52011yescharacteristic
797C2×C4#52011yescharacteristic
798C2×C4C2×#12111yescharacteristic
799C2×C4C2×C22⋊Q811yescharacteristic
800C2×C4#52511yescharacteristic
801C2×C4#52511yescharacteristic
802C2×C4C2×#12511yescharacteristic
803C2×C4C2×C4⋊Q811yescharacteristic
804C2×C4#53411yescharacteristic
805C2×C4#53611yescharacteristic
806C2×C4#53911yescharacteristic
807C2×C4#53911yescharacteristic
808C2×C4D4211yescharacteristic
809C2×C4#54611yescharacteristic
810C2×C4#54711yescharacteristic
811C2×C4#54711yescharacteristic
812C2×C4D4×Q811yescharacteristic
813C2×C4D4×Q811yescharacteristic
814C2×C4#55211yescharacteristic
815C2×C4#55211yescharacteristic
816C2×C4#55411yescharacteristic
817C2×C4#55411yescharacteristic
818C2×C4#55411yescharacteristic
819C2×C4#55411yescharacteristic
820C8—24no—
821C8—42no—
822C8—42no—
823C8—81no—
824C22—28no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22C4×#12011yescharacteristic
840C22D4×C4⋊C411yescharacteristic
841C22#236011yescharacteristic
842C22#241011yescharacteristic
843C22#243411yescharacteristic
844C22#244911yescharacteristic
845C22#247311yescharacteristic
846C22C4×#13511yescharacteristic
847C22C4×AGL(1,ℤ/8)11yescharacteristic
848C22#294611yescharacteristic
849C22#294911yescharacteristic
850C22C2×#44911yescharacteristic
851C22#300211yescharacteristic
852C22#300911yescharacteristic
853C22#301211yescharacteristic
854C22#310211yescharacteristic
855C22#310611yescharacteristic
856C22#311811yescharacteristic
857C22#312311yescharacteristic
858C22#326411yescharacteristic
859C22#326711yescharacteristic
860C22#328211yescharacteristic
861C22#328211yescharacteristic
862C22#329611yescharacteristic
863C22#329711yescharacteristic
864C22#330611yescharacteristic
865C22#331111yescharacteristic
866C22#338011yescharacteristic
867C22#338111yescharacteristic
868C22#338111yescharacteristic
869C22#338111yescharacteristic
870C22#338411yescharacteristic
871C22#338411yescharacteristic
872C22#338811yescharacteristic
873C22#338911yescharacteristic
874C4—24no—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—44no—
881C4—82no—
882C4—81no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—161no—
887C4C2×#38911yescharacteristic
888C4#232211yescharacteristic
889C4D4×C4⋊C411yescharacteristic
890C4#236011yescharacteristic
891C4#241311yescharacteristic
892C4#244911yescharacteristic
893C4#247311yescharacteristic
894C4#258311yescharacteristic
895C2—48no—
896C2#1404311yescharacteristic
897C2C4×#44911yescharacteristic
898C2#2145911yescharacteristic
899C2#2267611yescharacteristic
900C2#2268311yescharacteristic
901C2#2296611yescharacteristic
902C2#2297511yescharacteristic
903C2#2443411yescharacteristic
904C2#2443611yescharacteristic
905C2#2583511yescharacteristic
906C2#2584311yescharacteristic
907C2#2637811yescharacteristic
908C2#2638011yescharacteristic
909C2#2730411yescharacteristic
910C2#2730711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1941C2semidirect
7. #14046C2semidirect
8. #11328C2semidirect
9. #11325C2semidirect
10. #11220C2semidirect
11. #11208C2semidirect
12. #10885C2semidirect
13. #10874C2semidirect
44. #1864C4semidirect
121. C2×#106C2×C4semidirect
146. #389C2×C4semidirect
180. #340C2×C4semidirect
185. #336C2×C4semidirect
375. #102C4⋊C4semidirect
697. D4#389semidirect

Maximal subgroups

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

subgroupindex
C2×#23492
C2×#19412
C2×#18642
C2×#18622
C2×C4×#1022
#140462
#113282
#113252
#112202
#112082
#108852
#108742
#107882