Finite Group Databasebeta

← #375158

Subgroups — #375158

Order 512.

1902 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C2×#1875C211yesmaximal, characteristic
3C2×#1872C211yesmaximal, characteristic, complemented
4C2×#1753C211yesmaximal, characteristic, complemented
5C2×#1736C211yesmaximal, characteristic, complemented
6#14138C211yesmaximal, characteristic, complemented
7#14137C211yesmaximal, characteristic
8#11379C211yesmaximal, characteristic, complemented
9#11377C211yesmaximal, characteristic, complemented
10#11023C211yesmaximal, characteristic, complemented
11#11023C211yesmaximal, characteristic, complemented
12#10928C211yesmaximal, characteristic, complemented
13#10927C211yesmaximal, characteristic, complemented
14#10926C211yesmaximal, characteristic, complemented
15#10925C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C2×#468—24no—
23C2×#468—24no—
24C2×#468C418yescomplemented
25C22×#107C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#386—22no—
40C2×C4×C22⋊C4C2211yescharacteristic
41#1875—24no—
42#1872—24no—
43#1753—24no—
44#1736—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1440—22no—
56#1439—22no—
57#1436—22no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C23×D4—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—41no—
70C22×SD16—41no—
71C22×SD16—41no—
72C22×SD16—41no—
73C22×SD16C2×C414yescomplemented
74C22×M16—41no—
75C22×M16—41no—
76C22×M16—41no—
77C22×M16—41no—
78C22×M16C2×C414yes—
79C22×M16D414yes—
80C22×M16D414yes—
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C2×C22⋊Q8—22no—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8C2×C414yes—
91C2×#121—22no—
92C2×#121—22no—
93C2×#121—22no—
94C2×#121—22no—
95C2×#121—22no—
96C2×#121C2×C414yes—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—41no—
102C2×#117—41no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4—41no—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—22no—
121C22×C22⋊C4—22no—
122C22×C22⋊C4D412yes—
123C22×C42—21no—
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126#468—232no—
127C2×#107—22no—
128C2×#107—22no—
129C2×#107C2×C414yescomplemented
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—41no—
137C2×#103—41no—
138C2×#103C2×C414yescomplemented
139C2×#102—22no—
140C2×#102—22no—
141C2×#102—22no—
142C2×#102—22no—
143C2×#102—22no—
144C2×#102—22no—
145C2×#102—41no—
146C2×#102—41no—
147C2×#102C2×C414yescomplemented
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8D414yes—
151C2×#97—22no—
152C2×#97—41no—
153C2×#97—41no—
154C2×C4×C8—22no—
155C2×C4×C8—41no—
156C2×C4×C8—41no—
157#391—22no—
158#391—22no—
159#391—41no—
160#391—41no—
161#390—22no—
162#390—22no—
163#390—41no—
164#390—41no—
165#386—48no—
166C4×C22⋊C4—22no—
167C4×C22⋊C4—22no—
168C2×#95—22no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—22no—
174C2×#95D412yes—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#336—22no—
184#336—22no—
185C25—21no—
186C25C2×D411yescharacteristic
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8C22×C412yes—
201C22×D4—24no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—44no—
216C22×D4—44no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4C22×C412yes—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—44no—
239C23×C4—82no—
240C23×C4C22×C412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4C2411yescharacteristic
250C2×SD16—28no—
251C2×SD16—44no—
252C2×SD16—44no—
253C2×SD16—44no—
254C2×SD16—44no—
255C2×SD16—44no—
256C2×SD16—44no—
257C2×M16—44no—
258C2×M16—44no—
259C2×M16—44no—
260C2×M16—44no—
261C2×M16—44no—
262C2×M16—44no—
263C2×M16C22⋊C4116yescomplemented
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8C22×C412yes—
285C22×C8C22×C412yes—
286C22×C8C2×D412yes—
287C22×C8C2×D412yes—
288C22×C8C2×D412yes—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22⋊Q8—28no—
293C22⋊Q8—28no—
294C22⋊Q8—44no—
295C22⋊Q8—44no—
296#121—28no—
297#121—28no—
298#121—44no—
299#121—44no—
300#117—28no—
301#117—44no—
302#117—44no—
303#117—44no—
304C2×C4⋊C4—28no—
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—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C22×C412yes—
345C2×C4⋊C4C22×C412yes—
346C2×C4⋊C4#4112yes—
347C2×C4⋊C4#4112yes—
348C2×C4⋊C4#4112yes—
349C2×C4⋊C4#4112yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—82no—
367C2×C22⋊C4—82no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383#107—28no—
384#103—28no—
385#103—44no—
386#103—44no—
387#102—28no—
388#102—44no—
389#102—44no—
390C22⋊C8—28no—
391#97—44no—
392C4×C8—44no—
393#95—24no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24C4×D412yes—
420C24#12112yes—
421C24#12712yes—
422C24C22×D411yescharacteristic
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—416no—
458C2×D4—48no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
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—84no—
482C2×D4—84no—
483C2×D4—88no—
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—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
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—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—48no—
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—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—88no—
564C22×C4—88no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4C2×C22⋊C414yes—
568C22×C4C4×D414yes—
569C22×C4C4×D412yes—
570C22×C4#12114yes—
571C22×C4#12112yes—
572C22×C4#12414yes—
573C22×C4#12712yes—
574C22×C4AGL(1,ℤ/8)14yes—
575C22×C4C23×C411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583C22×C4C2×#4111yescharacteristic
584C22×C4C2×#4111yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C22×C4H(5,𝔽2)11yescharacteristic
588C22×C4H(5,𝔽2)11yescharacteristic
589SD16—416no—
590M16—416no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
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×C8C2×C22⋊C414yes—
618C2×C8C2×C22⋊C414yes—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—48no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—88no—
650C22⋊C4—88no—
651C42—48no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—44no—
686C23—42no—
687C23—82no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23—82no—
697C23—81no—
698C23—81no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23—82no—
703C23—82no—
704C23—82no—
705C23#39014yes—
706C23C2×C4×D411yescharacteristic
707C23C2×#12111yescharacteristic
708C23C2×#12711yescharacteristic
709C23#54611yescharacteristic
710C23#54611yescharacteristic
711C23#54611yescharacteristic
712C23#54611yescharacteristic
713C23C2×AGL(1,ℤ/8)12yes—
714C23#57512yes—
715C23#57712yes—
716C23#57812yes—
717Q8—42no—
718Q8—42no—
719Q8—42no—
720Q8—42no—
721Q8—81no—
722Q8—81no—
723Q8—81no—
724Q8—81no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—816no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—816no—
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—81no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—82no—
800C2×C4#39014yes—
801C2×C4C22×C22⋊C411yescharacteristic
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C4×#4111yescharacteristic
804C2×C4C4×#4111yescharacteristic
805C2×C4#51811yescharacteristic
806C2×C4#51811yescharacteristic
807C2×C4C2×#12111yescharacteristic
808C2×C4#52511yescharacteristic
809C2×C4#52511yescharacteristic
810C2×C4C2×#12411yescharacteristic
811C2×C4#53211yescharacteristic
812C2×C4#53211yescharacteristic
813C2×C4#53411yescharacteristic
814C2×C4#53411yescharacteristic
815C2×C4#53411yescharacteristic
816C2×C4#53411yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54611yescharacteristic
819C2×C4#54611yescharacteristic
820C2×C4#54611yescharacteristic
821C2×C4#55311yescharacteristic
822C2×C4#55311yescharacteristic
823C2×C4#55311yescharacteristic
824C2×C4#55311yescharacteristic
825C2×C4#55311yescharacteristic
826C2×C4#55311yescharacteristic
827C2×C4#55311yescharacteristic
828C2×C4#55311yescharacteristic
829C8—24no—
830C8—24no—
831C8—42no—
832C8—42no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—82no—
848C22—82no—
849C22—162no—
850C22—162no—
851C22—161no—
852C22—161no—
853C22—161no—
854C22—161no—
855C22C2×#39011yescharacteristic
856C22#236411yescharacteristic
857C22#236411yescharacteristic
858C22#253911yescharacteristic
859C22#253911yescharacteristic
860C22#254311yescharacteristic
861C22#254311yescharacteristic
862C22C4×AGL(1,ℤ/8)12yes—
863C22#294712yes—
864C22#305512yes—
865C22#306312yes—
866C22#315111yescharacteristic
867C22#315311yescharacteristic
868C22#315411yescharacteristic
869C22#315611yescharacteristic
870C22#330712yes—
871C22#330812yes—
872C22#331012yes—
873C22#331312yes—
874C22#332412yes—
875C22#332612yes—
876C22#332712yes—
877C22#333012yes—
878C4—24no—
879C4—44no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4#229711yescharacteristic
889C4#230811yescharacteristic
890C4#236411yescharacteristic
891C4#236411yescharacteristic
892C4#254311yescharacteristic
893C4#254311yescharacteristic
894C4#259111yescharacteristic
895C4#259111yescharacteristic
896C2—44no—
897C2—162no—
898C2#1415211yescharacteristic
899C2#2123411yescharacteristic
900C2#2123611yescharacteristic
901C2#2313812yes—
902C2#2314112yes—
903C2#2835811yescharacteristic
904C2#2835911yescharacteristic
905C2#2836511yescharacteristic
906C2#2836811yescharacteristic
907C2#2855912yes—
908C2#2856912yes—
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
3. C2×#1872C2semidirect
4. C2×#1753C2semidirect
5. C2×#1736C2semidirect
6. #14138C2semidirect
8. #11379C2semidirect
9. #11377C2semidirect
10. #11023C2semidirect
11. #11023C2semidirect
12. #10928C2semidirect
13. #10927C2semidirect
14. #10926C2semidirect
15. #10925C2semidirect
24. C2×#468C4semidirect
73. C22×SD16C2×C4semidirect
129. C2×#107C2×C4semidirect
138. C2×#103C2×C4semidirect
147. C2×#102C2×C4semidirect
263. C2×M16C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4682
C2×#18752
C2×#18722
C2×#17532
C2×#17362
#141382
#141372
#113792
#113772
#110232
#109282
#109272
#109262
#109252