Finite Group Databasebeta

← C2×#30404 #7500628

Subgroups — C2×#30404 #7500628

Order 512.

3794 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×#465C211yesmaximal, characteristic, complemented
2C22×#450C211yesmaximal, characteristic, complemented
3C2×#2538C211yesmaximal, characteristic, complemented
4C2×#2408C211yesmaximal, characteristic
5#30404C2116yesmaximal, direct product factor
6C2×#2094C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2071C211yesmaximal, characteristic, complemented
9C2×#2034C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1880C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1869C211yesmaximal, characteristic, complemented
16C2×#1786C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C24×C8C2211yescharacteristic, complemented
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic, complemented
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#120—21no—
26C22×C4×Q8C2211yescharacteristic, complemented
27C22×C4×D4C2211yescharacteristic
28C2×#465—28no—
29C2×#465C2218yescomplemented
30C2×#450—28no—
31C2×#450C2218yescomplemented
32C22×#106C2211yescharacteristic, complemented
33C22×#106C2211yescharacteristic, 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
45#2538—24no—
46#2538C2218yescomplemented
47#2408—24no—
48#2408C2218yes—
49C2×#396—21no—
50C2×#396—21no—
51C2×#394—21no—
52C2×#392—21no—
53C2×#390—21no—
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389—21no—
57C2×#384C2211yescharacteristic, complemented
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic, complemented
61C2×#379—21no—
62#2094C2218yescomplemented
63#2077C2218yescomplemented
64#2071C2218yescomplemented
65#2035C2218yescomplemented
66#2034C2218yescomplemented
67#2000C2218yescomplemented
68#1893C2218yescomplemented
69#1880C2218yescomplemented
70#1880C2218yescomplemented
71#1869C2218yescomplemented
72#1786C2218yescomplemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#336C2211yescharacteristic, complemented
78C2×#336C2211yescharacteristic, 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×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16D418yescomplemented
103C22×SD16C2314yes—
104C22×SD16C2314yes—
105C23×C8—24no—
106C23×C8—42no—
107C23×C8—42no—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C23×C8C2314yescomplemented
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8C2314yes—
120C2×C22⋊Q8C2314yescomplemented
121C2×#121—22no—
122C2×#121—22no—
123C2×#121—24no—
124C2×#121—24no—
125C2×#121—42no—
126C2×#121—42no—
127C2×#121C2314yes—
128C2×#121C2314yes—
129C2×#120—28no—
130C2×#120—48no—
131C2×C4×Q8—22no—
132C2×C4×Q8—42no—
133C2×C4×Q8—42no—
134C2×C4×Q8C2314yescomplemented
135C2×C4×D4—42no—
136C2×C4×D4—42no—
137C2×C4×D4D414yes—
138C2×C4×D4C2314yes—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4D411yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4D411yescharacteristic
162C22×C22⋊C4D411yescharacteristic
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165#465—232no—
166#450—232no—
167C2×#106—24no—
168C2×#106—42no—
169C2×#106C2314yescomplemented
170C2×#106C2314yescomplemented
171C2×#103—24no—
172C2×#103—42no—
173C2×#103C2314yescomplemented
174C2×#103C2314yescomplemented
175C2×#102—24no—
176C2×#102—24no—
177C2×#102—24no—
178C2×#102—42no—
179C2×#102—42no—
180C2×#102—42no—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×C22⋊C8—24no—
188C2×C22⋊C8—42no—
189C2×C22⋊C8—42no—
190C2×C22⋊C8C2314yes—
191C2×C22⋊C8C2314yes—
192C2×C22⋊C8C2314yescomplemented
193#396—28no—
194#396—28no—
195#394—28no—
196#392—28no—
197#390—28no—
198#390—22no—
199#390—22no—
200#390C2314yes—
201#390C2314yes—
202#389—28no—
203#384—22no—
204#384C2314yescomplemented
205#380—22no—
206#380—22no—
207#380—22no—
208#380C2314yes—
209#380C2314yes—
210#380C2314yescomplemented
211#379—28no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215#340C2314yescomplemented
216#340C2314yescomplemented
217#340C2314yescomplemented
218#340C2314yescomplemented
219#336C2314yescomplemented
220#336C2314yescomplemented
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×Q8C2×D414yes—
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×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—416no—
316C2×SD16—44no—
317C2×SD16—44no—
318C2×SD16—44no—
319C2×SD16—416no—
320C2×SD16C2×D4116yescomplemented
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—28no—
333C22×C8—44no—
334C22×C8—44no—
335C22×C8—416no—
336C22×C8C2×D414yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22⋊Q8—28no—
342C22⋊Q8—28no—
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×Q8—44no—
355C4×Q8—44no—
356C4×Q8—48no—
357C4×D4—48no—
358C4×D4—44no—
359C4×D4—44no—
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—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—82no—
386C2×C4⋊C4C2×D414yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
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—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—82no—
413C2×C22⋊C4—82no—
414C2×C22⋊C4—82no—
415C2×C22⋊C4—82no—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4C2×D414yes—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—44no—
422C2×C42C2×D412yes—
423C2×C42C2412yes—
424#106—28no—
425#106—44no—
426#103—28no—
427#103—44no—
428#102—28no—
429#102—28no—
430#102—28no—
431#102—44no—
432#102—44no—
433#102—44no—
434C22⋊C8—28no—
435C22⋊C8—44no—
436C22⋊C8—44no—
437#95—24no—
438#95—24no—
439#95—24no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—24no—
453C24—24no—
454C24—22no—
455C24—22no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—432no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—48no—
474C24—84no—
475C24—84no—
476C24—816no—
477C24—816no—
478C24—816no—
479C24—816no—
480C24—816no—
481C24—816no—
482C24C2×SD1614yes—
483C24C2×SD1614yes—
484C24C22×D412yes—
485C24C22×D412yes—
486C24C22×D411yescharacteristic
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—42no—
496C2×Q8—44no—
497C2×Q8—42no—
498C2×Q8—44no—
499C2×Q8C22×D414yes—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—24no—
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—22no—
516C2×D4—44no—
517C2×D4—416no—
518C2×D4—44no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—416no—
523C2×D4—416no—
524C2×D4—416no—
525C2×D4—432no—
526C2×D4—464no—
527C2×D4—416no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—84no—
541C2×D4—84no—
542C2×D4—816no—
543C2×D4—816no—
544C2×D4C2×SD16116yescomplemented
545C2×D4C22×D414yes—
546C2×D4C2×#4114yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
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—22no—
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—42no—
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×C4C2×SD1614yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C2×#4112yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4C2511yescharacteristic
621SD16—416no—
622SD16—416no—
623C2×C8—28no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
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—416no—
636C2×C8—44no—
637C2×C8—44no—
638C2×C8—44no—
639C2×C8C22×D414yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—84no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—84no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C42—24no—
675C42—22no—
676C42—22no—
677C42—48no—
678C23—28no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—432no—
707C23—48no—
708C23—48no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—48no—
714C23—48no—
715C23—48no—
716C23—48no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—816no—
726C23—816no—
727C23—816no—
728C23—816no—
729C23—816no—
730C23—816no—
731C23—8128no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23#53412yes—
741C23D4212yes—
742C23#54612yes—
743C23C22×SD1614yes—
744C23C22×SD1614yes—
745C23C22×SD1612yes—
746C23#57512yes—
747C23#57612yes—
748C23#57712yes—
749C23C23×D411yescharacteristic
750Q8—24no—
751Q8—24no—
752Q8—48no—
753Q8—42no—
754Q8—42no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—24no—
759D4—416no—
760D4—432no—
761D4—48no—
762D4—48no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—816no—
768D4—816no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—48no—
789C2×C4—48no—
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—42no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4#53412yes—
819C2×C4#53414yes—
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—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—864no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—816no—
867C22—816no—
868C22—82no—
869C22#266814yes—
870C22#318714yes—
871C22#319814yes—
872C22#326814yes—
873C22D4×SD1614yes—
874C22#329514yes—
875C22#331114yes—
876C22C2×#53411yescharacteristic
877C22C2×D4211yescharacteristic
878C22C2×#54611yescharacteristic
879C22C23×SD1611yescharacteristic
880C22C2×#57511yescharacteristic
881C22C2×#57611yescharacteristic
882C22C2×#57711yescharacteristic
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4#266814yes—
894C4C2×#53411yescharacteristic
895C4C2×#53811yescharacteristic
896C4C2×#54611yescharacteristic
897C4C2×#56011yescharacteristic
898C2—44no—
899C2—44no—
900C2—84no—
901C2—84no—
902C2#3040418yesdirect product factor
903C2C2×#266811yescharacteristic
904C2C2×#318711yescharacteristic
905C2C2×#319811yescharacteristic
906C2C2×#326811yescharacteristic
907C2C2×D4×SD1611yescharacteristic
908C2C2×#329511yescharacteristic
909C2C2×#331111yescharacteristic
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×#465C2semidirect
2. C22×#450C2semidirect
3. C2×#2538C2semidirect
5. #30404C2direct (N × H)
6. C2×#2094C2semidirect
7. C2×#2077C2semidirect
8. C2×#2071C2semidirect
9. C2×#2034C2semidirect
10. C2×#2035C2semidirect
11. C2×#2000C2semidirect
12. C2×#1893C2semidirect
13. C2×#1880C2semidirect
14. C2×#1880C2semidirect
15. C2×#1869C2semidirect
16. C2×#1786C2semidirect
20. C24×C8C22semidirect
22. C22×C22⋊Q8C22semidirect
26. C22×C4×Q8C22semidirect
29. C2×#465C22semidirect
31. C2×#450C22semidirect
32. C22×#106C22semidirect
33. C22×#106C22semidirect
34. C22×#103C22semidirect
35. C22×#103C22semidirect
44. C22×C22⋊C8C22semidirect
46. #2538C22semidirect
57. C2×#384C22semidirect
60. C2×#380C22semidirect
62. #2094C22semidirect
63. #2077C22semidirect
64. #2071C22semidirect
65. #2035C22semidirect
66. #2034C22semidirect
67. #2000C22semidirect
68. #1893C22semidirect
69. #1880C22semidirect
70. #1880C22semidirect
71. #1869C22semidirect
72. #1786C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#336C22semidirect
78. C2×#336C22semidirect
102. C22×SD16D4semidirect
112. C23×C8C23semidirect
120. C2×C22⋊Q8C23semidirect
134. C2×C4×Q8C23semidirect
169. C2×#106C23semidirect
170. C2×#106C23semidirect
173. C2×#103C23semidirect
174. C2×#103C23semidirect
192. C2×C22⋊C8C23semidirect
204. #384C23semidirect
210. #380C23semidirect
215. #340C23semidirect
216. #340C23semidirect
217. #340C23semidirect
218. #340C23semidirect
219. #336C23semidirect
220. #336C23semidirect
280. C22×D4SD16semidirect
320. C2×SD16C2×D4semidirect
544. C2×D4C2×SD16semidirect
902. C2#30404direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×#4502
C2×#25382
C2×#24082
#304042
C2×#20942
C2×#20772
C2×#20712
C2×#20342
C2×#20352
C2×#20002
C2×#18932
C2×#18802
C2×#18692
C2×#17862