Finite Group Databasebeta

← C2×#31386 #7504590

Subgroups — C2×#31386 #7504590

Order 512.

2584 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3#31386C2116yesmaximal, direct product factor
4C2×#2100C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2071C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1872C211yesmaximal, characteristic, complemented
14C2×#1869C211yesmaximal, characteristic, complemented
15C2×#1865C211yesmaximal, characteristic, complemented
16C2×#1823C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121—21no—
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37#2538—24no—
38#2538C2218yescomplemented
39#2416—24no—
40#2416C2218yes—
41C2×#396—21no—
42C2×#396—21no—
43C2×#396—21no—
44C2×#394—21no—
45C2×#390—21no—
46C2×#390C2211yescharacteristic
47C2×#389—21no—
48C2×#389C2211yescharacteristic
49C2×#386—21no—
50C2×#384C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54#2100C2218yescomplemented
55#2077C2218yescomplemented
56#2071C2218yescomplemented
57#2034C2218yescomplemented
58#2000C2218yescomplemented
59#2000C2218yescomplemented
60#1893C2218yescomplemented
61#1892C2218yescomplemented
62#1880C2218yescomplemented
63#1872C2218yescomplemented
64#1869C2218yescomplemented
65#1865C2218yescomplemented
66#1823C2218yescomplemented
67C2×#340C2211yescharacteristic
68C2×#340C2211yescharacteristic
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×Q8C2311yescharacteristic
78C23×D4—21no—
79C23×D4—21no—
80C23×D4D411yescharacteristic
81C23×D4C2311yescharacteristic
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×SD16—24no—
86C22×SD16—42no—
87C22×SD16—42no—
88C22×SD16C2314yes—
89C23×C8—42no—
90C23×C8—42no—
91C23×C8—42no—
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2314yes—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—42no—
102C2×C22⋊Q8—42no—
103C2×C22⋊Q8C2314yes—
104C2×C22⋊Q8C2314yes—
105C2×#121—28no—
106C2×#121—22no—
107C2×#121—22no—
108C2×#121—24no—
109C2×#121—42no—
110C2×#121—42no—
111C2×#121—42no—
112C2×#121—48no—
113C2×#121C2314yes—
114C2×#121C2314yes—
115C2×C4×Q8—22no—
116C2×C4×Q8—42no—
117C2×C4×Q8—42no—
118C2×C4×Q8C2314yes—
119C2×C4×D4—42no—
120C2×C4×D4—42no—
121C2×C4×D4D414yes—
122C2×C4×D4C2314yes—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—22no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4D411yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4D411yescharacteristic
151C22×C22⋊C4D411yescharacteristic
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154C2×#106—42no—
155C2×#106C2314yes—
156C2×#103—24no—
157C2×#103—42no—
158C2×#103—42no—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#102—42no—
163C2×#102—42no—
164C2×#102—42no—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8—42no—
169C2×C22⋊C8—42no—
170C2×C22⋊C8—42no—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C2×C22⋊C8C2314yes—
174#396—28no—
175#396—28no—
176#396—28no—
177#394—28no—
178#390—28no—
179#390—22no—
180#390C2314yes—
181#389—28no—
182#389—22no—
183#389C2314yes—
184#386—28no—
185#384—22no—
186#384C2314yes—
187#380—22no—
188#380—22no—
189#380—22no—
190#380C2314yes—
191#380C2314yes—
192#380C2314yes—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197#340C2314yes—
198#340C2314yes—
199#340C2314yes—
200#340C2314yes—
201#340C2314yes—
202#340C2314yes—
203#340C2314yes—
204#340C2314yes—
205#336C2314yes—
206#336C2314yes—
207C25—21no—
208C25C2×D411yescharacteristic
209C25C2×D411yescharacteristic
210C22×Q8—21no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8#4114yes—
217C22×Q8C2412yes—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—21no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—44no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—82no—
235C22×D4SD1618yescomplemented
236C22×D4C2×D414yes—
237C22×D4C2412yes—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—24no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—82no—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C2×SD16—28no—
271C2×SD16—44no—
272C2×SD16—44no—
273C2×SD16—416no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8—416no—
290C22×C8C2412yes—
291C22×C8C2412yes—
292C22×C8C2412yes—
293C22×C8C2412yes—
294C22⋊Q8—28no—
295C22⋊Q8—28no—
296C22⋊Q8—44no—
297C22⋊Q8—44no—
298C22⋊Q8—48no—
299C22⋊Q8—48no—
300#121—28no—
301#121—44no—
302#121—44no—
303#121—44no—
304#121—48no—
305#121—48no—
306#121—432no—
307C4×Q8—44no—
308C4×Q8—44no—
309C4×Q8—48no—
310C4×D4—48no—
311C4×D4—44no—
312C4×D4—44no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—48no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—82no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4#4114yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—44no—
382C2×C42C2×D412yes—
383C2×C42C2412yes—
384#106—44no—
385#103—28no—
386#103—44no—
387#103—44no—
388#102—44no—
389#102—44no—
390#102—44no—
391C22⋊C8—44no—
392C22⋊C8—44no—
393C22⋊C8—44no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24C2×SD1614yes—
419C24C2×SD1614yes—
420C24C22×D412yes—
421C24C22×D412yes—
422C24C22×D411yescharacteristic
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—28no—
426C2×Q8—28no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—42no—
432C2×Q8—44no—
433C2×Q8—42no—
434C2×Q8—44no—
435C2×Q8C2×#4114yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—44no—
443C2×D4—416no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—42no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—84no—
458C2×D4—816no—
459C2×D4—816no—
460C2×D4C2×SD16116yescomplemented
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
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—48no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—48no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—84no—
529C22×C4—816no—
530C22×C4C2×SD1614yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4C2511yescharacteristic
543SD16—416no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—416no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8—44no—
560C2×C8—44no—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—48no—
585C4⋊C4—84no—
586C4⋊C4C2×#4114yes—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C22⋊C4—84no—
598C42—24no—
599C42—22no—
600C42—22no—
601C42—48no—
602C23—28no—
603C23—28no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—28no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23#53412yes—
643C23#54612yes—
644C23#54612yes—
645C23C22×SD1614yes—
646C23C22×SD1614yes—
647C23C22×SD1612yes—
648C23#57512yes—
649C23#57612yes—
650C23#57812yes—
651C23C23×D411yescharacteristic
652Q8—24no—
653Q8—24no—
654Q8—42no—
655Q8—48no—
656Q8—42no—
657D4—416no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—816no—
663D4—816no—
664D4—84no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—48no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—48no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—816no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4#53412yes—
720C2×C4#53814yes—
721C2×C4#54014yes—
722C2×C4#54612yes—
723C2×C4#54612yes—
724C2×C4#55314yes—
725C2×C4#56014yes—
726C2×C4C22×SD1614yes—
727C2×C4C22×#4111yescharacteristic
728C2×C4C22×#4111yescharacteristic
729C2×C4C2×H(5,𝔽2)11yescharacteristic
730C2×C4C2×H(5,𝔽2)11yescharacteristic
731C2×C4C2×H(5,𝔽2)11yescharacteristic
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C8—42no—
734C8—42no—
735C8—42no—
736C8—42no—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—416no—
748C22—416no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—168no—
761C22#268814yes—
762C22#318714yes—
763C22#320314yes—
764C22#329514yes—
765C22#329814yes—
766C22#330914yes—
767C22#331314yes—
768C22C2×#53411yescharacteristic
769C22C2×#54611yescharacteristic
770C22C2×#54611yescharacteristic
771C22C23×SD1611yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57611yescharacteristic
774C22C2×#57811yescharacteristic
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—44no—
780C4—44no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4#268814yes—
787C4C2×#53811yescharacteristic
788C4C2×#54011yescharacteristic
789C4C2×#55311yescharacteristic
790C4C2×#56011yescharacteristic
791C2—44no—
792C2—44no—
793C2—162no—
794C2#3138618yesdirect product factor
795C2C2×#268811yescharacteristic
796C2C2×#318711yescharacteristic
797C2C2×#320311yescharacteristic
798C2C2×#329511yescharacteristic
799C2C2×#329811yescharacteristic
800C2C2×#330911yescharacteristic
801C2C2×#331311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2416C2
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. C2×#2538C2semidirect
3. #31386C2direct (N × H)
4. C2×#2100C2semidirect
5. C2×#2077C2semidirect
6. C2×#2071C2semidirect
7. C2×#2034C2semidirect
8. C2×#2000C2semidirect
9. C2×#2000C2semidirect
10. C2×#1893C2semidirect
11. C2×#1892C2semidirect
12. C2×#1880C2semidirect
13. C2×#1872C2semidirect
14. C2×#1869C2semidirect
15. C2×#1865C2semidirect
16. C2×#1823C2semidirect
38. #2538C22semidirect
54. #2100C22semidirect
55. #2077C22semidirect
56. #2071C22semidirect
57. #2034C22semidirect
58. #2000C22semidirect
59. #2000C22semidirect
60. #1893C22semidirect
61. #1892C22semidirect
62. #1880C22semidirect
63. #1872C22semidirect
64. #1869C22semidirect
65. #1865C22semidirect
66. #1823C22semidirect
235. C22×D4SD16semidirect
460. C2×D4C2×SD16semidirect
794. C2#31386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24162
#313862
C2×#21002
C2×#20772
C2×#20712
C2×#20342
C2×#20002
C2×#18932
C2×#18922
C2×#18802
C2×#18722
C2×#18692
C2×#18652
C2×#18232