Finite Group Databasebeta

← C2×#31024 #7503170

Subgroups — C2×#31024 #7503170

Order 512.

3778 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#481C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4C2×#2408C211yesmaximal, characteristic
5#31024C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2065C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic, complemented
14C2×#1934C211yesmaximal, characteristic, complemented
15C2×#1874C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic, complemented
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#120—21no—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic, complemented
27C2×#481—28no—
28C2×#481C2218yescomplemented
29C2×#450—28no—
30C2×#450C2218yescomplemented
31C22×#106C2211yescharacteristic, complemented
32C22×#106C2211yescharacteristic, complemented
33C22×C4⋊C8C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C22×#103C2211yescharacteristic, complemented
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic, complemented
45C22×C22⋊C8C2211yescharacteristic, complemented
46C22×C4×C8C2211yescharacteristic, complemented
47#2417—24no—
48#2417C2218yescomplemented
49#2408—24no—
50#2408C2218yes—
51C2×#398—21no—
52C2×#396—21no—
53C2×#394—21no—
54C2×#392—21no—
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic, complemented
59C2×#386—21no—
60C2×#380—21no—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#379—21no—
64#2077C2218yescomplemented
65#2065C2218yescomplemented
66#2055C2218yescomplemented
67#2035C2218yescomplemented
68#2000C2218yescomplemented
69#2000C2218yescomplemented
70#1968C2218yescomplemented
71#1954C2218yescomplemented
72#1934C2218yescomplemented
73#1874C2218yescomplemented
74#1786C2218yescomplemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C26—21no—
80C23×Q8C2311yescharacteristic
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—21no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4—22no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4D411yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2314yes—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8C2314yes—
117C2×C22⋊Q8C2314yescomplemented
118C2×#121—22no—
119C2×#121—22no—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121—42no—
123C2×#121—42no—
124C2×#121C2314yes—
125C2×#121C2314yes—
126C2×#120—28no—
127C2×#120—48no—
128C2×C4×D4—42no—
129C2×C4×D4—42no—
130C2×C4×D4D414yes—
131C2×C4×D4C2314yes—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—42no—
139C22×C4⋊C4D411yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2314yescomplemented
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4D411yescharacteristic
157C22×C22⋊C4D411yescharacteristic
158C22×C42C2311yescharacteristic
159#481—232no—
160#450—232no—
161C2×#106—24no—
162C2×#106—24no—
163C2×#106C2314yescomplemented
164C2×#106C2314yescomplemented
165C2×C4⋊C8—42no—
166C2×C4⋊C8C2314yescomplemented
167C2×#103—42no—
168C2×#103—42no—
169C2×#103C2314yescomplemented
170C2×#103C2314yescomplemented
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102—42no—
176C2×#102D418yescomplemented
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8—24no—
184C2×C22⋊C8—24no—
185C2×C22⋊C8—42no—
186C2×C22⋊C8—42no—
187C2×C22⋊C8C2314yes—
188C2×C22⋊C8C2314yes—
189C2×C22⋊C8C2314yescomplemented
190C2×C22⋊C8C2314yescomplemented
191C2×C4×C8—42no—
192C2×C4×C8C2314yescomplemented
193#398—28no—
194#396—28no—
195#394—28no—
196#392—28no—
197#391—22no—
198#391C2314yescomplemented
199#390—22no—
200#390—22no—
201#390C2314yes—
202#390C2314yes—
203#389—22no—
204#389C2314yescomplemented
205#386—28no—
206#380—22no—
207#380—22no—
208#380—28no—
209#380C2314yes—
210#380C2314yes—
211#379—28no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217#340C2314yescomplemented
218#340C2314yescomplemented
219#340C2314yescomplemented
220#340C2314yescomplemented
221C25—21no—
222C25—21no—
223C25—24no—
224C25—44no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—44no—
229C25—82no—
230C25—82no—
231C25C2×D411yescharacteristic
232C25C2×D411yescharacteristic
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8C2412yes—
241C22×D4—28no—
242C22×D4—28no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—48no—
263C22×D4—48no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—48no—
270C22×D4—416no—
271C22×D4—416no—
272C22×D4—416no—
273C22×D4—416no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4—82no—
279C22×D4—82no—
280C22×D4SD1618yescomplemented
281C22×D4C2×D414yes—
282C22×D4C2×D414yes—
283C22×D4#4114yes—
284C22×D4C2412yes—
285C22×D4C2412yes—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—24no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—82no—
308C23×C4C2×D412yes—
309C23×C4C2×D412yes—
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C2×SD16—28no—
318C2×SD16—28no—
319C2×SD16—28no—
320C2×SD16—44no—
321C2×SD16—44no—
322C2×SD16—44no—
323C2×SD16—416no—
324C2×SD16—416no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8C2×D414yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22⋊Q8—28no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—48no—
346C22⋊Q8—48no—
347#121—28no—
348#121—28no—
349#121—44no—
350#121—44no—
351#121—48no—
352#121—48no—
353#120—432no—
354C4×D4—48no—
355C4×D4—44no—
356C4×D4—44no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—48no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—82no—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—82no—
410C2×C22⋊C4—82no—
411C2×C22⋊C4—82no—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4C2×D414yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42C2×D412yes—
417C2×C42C2412yes—
418#106—28no—
419#106—28no—
420C4⋊C8—44no—
421#103—44no—
422#103—44no—
423#102—28no—
424#102—28no—
425#102—44no—
426#102—44no—
427#102—44no—
428#102C2×D4116yescomplemented
429C22⋊C8—28no—
430C22⋊C8—28no—
431C22⋊C8—44no—
432C22⋊C8—44no—
433C4×C8—44no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—24no—
453C24—22no—
454C24—22no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—432no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—48no—
473C24—84no—
474C24—84no—
475C24—816no—
476C24—816no—
477C24—816no—
478C24—816no—
479C24—816no—
480C24—816no—
481C24C2×SD1614yes—
482C24C2×SD1614yes—
483C24C22×D412yes—
484C24C22×D412yes—
485C24C22×D411yescharacteristic
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—24no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—44no—
516C2×D4—416no—
517C2×D4—44no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—416no—
522C2×D4—416no—
523C2×D4—416no—
524C2×D4—432no—
525C2×D4—464no—
526C2×D4—416no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—84no—
540C2×D4—84no—
541C2×D4—816no—
542C2×D4—816no—
543C2×D4C2×SD16116yescomplemented
544C2×D4C22×D414yes—
545C2×D4C2×#4114yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—48no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—84no—
610C22×C4—816no—
611C22×C4C2×SD1614yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C2×#4112yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C4H(5,𝔽2)12yes—
623C22×C4C2511yescharacteristic
624SD16—416no—
625SD16—416no—
626C2×C8—28no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—44no—
639C2×C8—44no—
640C2×C8—44no—
641C2×C8C22×D414yes—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—84no—
661C4⋊C4C22×D414yes—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C42—24no—
675C42—22no—
676C42—22no—
677C23—28no—
678C23—28no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—432no—
706C23—42no—
707C23—42no—
708C23—48no—
709C23—48no—
710C23—42no—
711C23—42no—
712C23—48no—
713C23—48no—
714C23—48no—
715C23—42no—
716C23—42no—
717C23—48no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—816no—
725C23—816no—
726C23—816no—
727C23—816no—
728C23—816no—
729C23—8128no—
730C23—816no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#53412yes—
740C23D4212yes—
741C23#54612yes—
742C23C22×SD1614yes—
743C23C22×SD1614yes—
744C23C22×SD1612yes—
745C23#57512yes—
746C23#57612yes—
747C23#57712yes—
748C23C23×D411yescharacteristic
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—42no—
753Q8—84no—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—416no—
759D4—432no—
760D4—48no—
761D4—48no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—816no—
767D4—816no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—48no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—816no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4#53412yes—
819C2×C4#53514yes—
820C2×C4#53814yes—
821C2×C4D4212yes—
822C2×C4#54612yes—
823C2×C4#54614yes—
824C2×C4#56014yes—
825C2×C4C22×SD1614yes—
826C2×C4C23×D411yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C2×H(5,𝔽2)11yescharacteristic
829C2×C4C2×H(5,𝔽2)11yescharacteristic
830C2×C4C2×H(5,𝔽2)11yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C8—24no—
833C8—42no—
834C8—42no—
835C8—42no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—416no—
843C22—416no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—864no—
859C22—816no—
860C22—816no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22#267814yes—
870C22#318714yes—
871C22#319814yes—
872C22#327314yes—
873C22D4×SD1614yes—
874C22#329514yes—
875C22#332314yes—
876C22C2×#53411yescharacteristic
877C22C2×D4211yescharacteristic
878C22C2×#54611yescharacteristic
879C22C23×SD1611yescharacteristic
880C22C2×#57511yescharacteristic
881C22C2×#57611yescharacteristic
882C22C2×#57711yescharacteristic
883C4—24no—
884C4—42no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4#267814yes—
894C4C2×#53511yescharacteristic
895C4C2×#53811yescharacteristic
896C4C2×#54611yescharacteristic
897C4C2×#56011yescharacteristic
898C2—44no—
899C2—44no—
900C2—84no—
901C2—84no—
902C2#3102418yesdirect product factor
903C2C2×#267811yescharacteristic
904C2C2×#318711yescharacteristic
905C2C2×#319811yescharacteristic
906C2C2×#327311yescharacteristic
907C2C2×D4×SD1611yescharacteristic
908C2C2×#329511yescharacteristic
909C2C2×#332311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#481C2semidirect
2. C22×#450C2semidirect
3. C2×#2417C2semidirect
5. #31024C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2065C2semidirect
8. C2×#2055C2semidirect
9. C2×#2035C2semidirect
10. C2×#2000C2semidirect
11. C2×#2000C2semidirect
12. C2×#1968C2semidirect
13. C2×#1954C2semidirect
14. C2×#1934C2semidirect
15. C2×#1874C2semidirect
16. C2×#1786C2semidirect
21. C22×C22⋊Q8C22semidirect
26. C23×C4⋊C4C22semidirect
28. C2×#481C22semidirect
30. C2×#450C22semidirect
31. C22×#106C22semidirect
32. C22×#106C22semidirect
33. C22×C4⋊C8C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×C22⋊C8C22semidirect
45. C22×C22⋊C8C22semidirect
46. C22×C4×C8C22semidirect
48. #2417C22semidirect
55. C2×#391C22semidirect
58. C2×#389C22semidirect
64. #2077C22semidirect
65. #2065C22semidirect
66. #2055C22semidirect
67. #2035C22semidirect
68. #2000C22semidirect
69. #2000C22semidirect
70. #1968C22semidirect
71. #1954C22semidirect
72. #1934C22semidirect
73. #1874C22semidirect
74. #1786C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
117. C2×C22⋊Q8C23semidirect
145. C22×C4⋊C4C23semidirect
163. C2×#106C23semidirect
164. C2×#106C23semidirect
166. C2×C4⋊C8C23semidirect
169. C2×#103C23semidirect
170. C2×#103C23semidirect
176. C2×#102D4semidirect
189. C2×C22⋊C8C23semidirect
190. C2×C22⋊C8C23semidirect
192. C2×C4×C8C23semidirect
198. #391C23semidirect
204. #389C23semidirect
217. #340C23semidirect
218. #340C23semidirect
219. #340C23semidirect
220. #340C23semidirect
280. C22×D4SD16semidirect
428. #102C2×D4semidirect
543. C2×D4C2×SD16semidirect
902. C2#31024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4812
C22×#4502
C2×#24172
C2×#24082
#310242
C2×#20772
C2×#20652
C2×#20552
C2×#20352
C2×#20002
C2×#19682
C2×#19542
C2×#19342
C2×#18742
C2×#17862