Finite Group Databasebeta

← C2×#29897 #6433139

Subgroups — C2×#29897 #6433139

Order 512.

3114 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic
3#29897C2116yesmaximal, direct product factor
4C2×#2076C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2075C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#2035C211yesmaximal, characteristic, complemented
12C2×#1873C211yesmaximal, characteristic, complemented
13C2×#1873C211yesmaximal, characteristic, complemented
14C2×#1854C211yesmaximal, characteristic, complemented
15C2×#1854C211yesmaximal, characteristic, complemented
16C2×#1779C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#107C2211yescharacteristic, complemented
24C22×#107C2211yescharacteristic, complemented
25C22×#106C2211yescharacteristic, complemented
26C22×#106C2211yescharacteristic, complemented
27C22×#103C2211yescharacteristic, complemented
28C22×#103C2211yescharacteristic, complemented
29C22×#103C2211yescharacteristic, complemented
30C22×#103C2211yescharacteristic, complemented
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37#2848—24no—
38#2848C2218yes—
39C2×#385—21no—
40C2×#385—21no—
41C2×#385—21no—
42#2280—24no—
43#2280C2218yes—
44C2×#381—21no—
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#379—21no—
53C2×#379—21no—
54C2×C4×C22⋊C4—21no—
55C2×C4×C22⋊C4—21no—
56#2077C2218yescomplemented
57#2077C2218yescomplemented
58#2076C2218yescomplemented
59#2075C2218yescomplemented
60#2036C2218yescomplemented
61#2036C2218yescomplemented
62#2035C2218yescomplemented
63#2035C2218yescomplemented
64#1873C2218yescomplemented
65#1873C2218yescomplemented
66#1854C2218yescomplemented
67#1854C2218yescomplemented
68#1779C2218yes—
69C2×#340C2211yescharacteristic, complemented
70C2×#340C2211yescharacteristic, complemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C26D411yescharacteristic
78C23×Q8C2311yescharacteristic
79C24×C4—24no—
80C24×C4—24no—
81C24×C4—42no—
82C24×C4—42no—
83C24×C4—42no—
84C24×C4—42no—
85C24×C4D414yes—
86C24×C4D411yescharacteristic
87C24×C4D411yescharacteristic
88C24×C4D411yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—42no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8C2314yes—
107C2×C22⋊Q8C2314yes—
108C2×C22⋊Q8C2314yes—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—42no—
112C2×#117—42no—
113C2×#117—42no—
114C2×#117—42no—
115C2×#117C2314yes—
116C2×#117C2314yes—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—21no—
140C22×C42—21no—
141C2×#107—42no—
142C2×#107—42no—
143C2×#107C2314yescomplemented
144C2×#107C2314yescomplemented
145C2×#106—42no—
146C2×#106—42no—
147C2×#106C2314yescomplemented
148C2×#106C2314yescomplemented
149C2×#103—42no—
150C2×#103—42no—
151C2×#103—42no—
152C2×#103—42no—
153C2×#103C2314yescomplemented
154C2×#103C2314yescomplemented
155C2×#103C2314yescomplemented
156C2×#103C2314yescomplemented
157C2×C22⋊C8—24no—
158C2×C22⋊C8—24no—
159C2×C22⋊C8—42no—
160C2×C22⋊C8—42no—
161C2×C22⋊C8—42no—
162C2×C22⋊C8—42no—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169#385—28no—
170#385—28no—
171#385—28no—
172#381—28no—
173#380—22no—
174#380—22no—
175#380—22no—
176#380—22no—
177#380—22no—
178#380—22no—
179#380—22no—
180#380C2314yes—
181#380C2314yes—
182#380C2314yes—
183#380C2314yes—
184#380C2314yes—
185#380C2314yes—
186#380C2314yes—
187#379—28no—
188#379—28no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198#340C2314yescomplemented
199#340C2314yescomplemented
200#340C2314yescomplemented
201#340C2314yescomplemented
202#340C2314yescomplemented
203#340C2314yescomplemented
204#340C2314yescomplemented
205#340C2314yescomplemented
206C25—24no—
207C25—24no—
208C25—24no—
209C25—42no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25C2×D411yescharacteristic
214C25C2×D411yescharacteristic
215C25C2×D411yescharacteristic
216C25C2×D414yes—
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2412yes—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—216no—
233C23×C4—28no—
234C23×C4—28no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—48no—
256C23×C4—48no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—416no—
268C23×C4—416no—
269C23×C4—416no—
270C23×C4—416no—
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4#4114yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—44no—
307C22⋊Q8—44no—
308C22⋊Q8—48no—
309C22⋊Q8—48no—
310C22⋊Q8—48no—
311#117—44no—
312#117—44no—
313#117—44no—
314#117—44no—
315#117—48no—
316#117—48no—
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—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
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—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
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—44no—
374C2×C22⋊C4—44no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—44no—
378C2×C42—44no—
379#107—44no—
380#107—44no—
381#106—44no—
382#106—44no—
383#103—44no—
384#103—44no—
385#103—44no—
386#103—44no—
387C22⋊C8—28no—
388C22⋊C8—28no—
389C22⋊C8—44no—
390C22⋊C8—44no—
391C22⋊C8—44no—
392C22⋊C8—44no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—28no—
419C24—28no—
420C24—28no—
421C24—44no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—416no—
426C24—416no—
427C24—416no—
428C24—416no—
429C24—416no—
430C24—416no—
431C24—416no—
432C24#12314yes—
433C24#13514yes—
434C24#13714yes—
435C24C22×D412yes—
436C24C22×D412yes—
437C24C22×D412yes—
438C24C22×D411yescharacteristic
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
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—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—416no—
506C22×C4—416no—
507C22×C4—464no—
508C22×C4—416no—
509C22×C4—416no—
510C22×C4—416no—
511C22×C4—416no—
512C22×C4—416no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4#12314yes—
546C22×C4#12318yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C2×#4114yes—
552C22×C4C2×#4114yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4C2511yescharacteristic
560C2×C8—22no—
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—44no—
573C2×C8—44no—
574C2×C8—44no—
575C2×C8—44no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—42no—
593C4⋊C4—48no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C42—48no—
613C42—48no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—416no—
642C23—416no—
643C23—416no—
644C23—416no—
645C23—416no—
646C23—416no—
647C23—416no—
648C23—4128no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23C2×#12314yes—
662C23C2×#12312yes—
663C23#53412yes—
664C23#53412yes—
665C23C2×#13514yes—
666C23C2×#13512yes—
667C23C2×#13714yes—
668C23C2×#13712yes—
669C23#57512yes—
670C23#57512yes—
671C23C23×D411yescharacteristic
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—84no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—216no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—416no—
692C2×C4—416no—
693C2×C4—416no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—48no—
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—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4C2×#12314yes—
739C2×C4C2×#12312yes—
740C2×C4#53412yes—
741C2×C4#53412yes—
742C2×C4#53814yes—
743C2×C4#53814yes—
744C2×C4#53814yes—
745C2×C4#53814yes—
746C2×C4C22×#4111yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C8—42no—
753C8—42no—
754C8—42no—
755C8—42no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—464no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—416no—
778C22—416no—
779C22—42no—
780C22—42no—
781C22#262214yes—
782C22#309114yes—
783C22#309514yes—
784C22#319014yes—
785C22#319114yes—
786C22#319614yes—
787C22#319714yes—
788C22C22×#12311yescharacteristic
789C22C2×#53411yescharacteristic
790C22C2×#53411yescharacteristic
791C22C22×#13511yescharacteristic
792C22C22×#13711yescharacteristic
793C22C2×#57511yescharacteristic
794C22C2×#57511yescharacteristic
795C4—24no—
796C4—42no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4#262214yes—
807C4C2×#53811yescharacteristic
808C4C2×#53811yescharacteristic
809C4C2×#53811yescharacteristic
810C4C2×#53811yescharacteristic
811C2—44no—
812C2—44no—
813C2—44no—
814C2#2989718yesdirect product factor
815C2C2×#262211yescharacteristic
816C2C2×#309111yescharacteristic
817C2C2×#309511yescharacteristic
818C2C2×#319011yescharacteristic
819C2C2×#319111yescharacteristic
820C2C2×#319611yescharacteristic
821C2C2×#319711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29897C2direct (N × H)
4. C2×#2076C2semidirect
5. C2×#2077C2semidirect
6. C2×#2077C2semidirect
7. C2×#2075C2semidirect
8. C2×#2036C2semidirect
9. C2×#2036C2semidirect
10. C2×#2035C2semidirect
11. C2×#2035C2semidirect
12. C2×#1873C2semidirect
13. C2×#1873C2semidirect
14. C2×#1854C2semidirect
15. C2×#1854C2semidirect
23. C22×#107C22semidirect
24. C22×#107C22semidirect
25. C22×#106C22semidirect
26. C22×#106C22semidirect
27. C22×#103C22semidirect
28. C22×#103C22semidirect
29. C22×#103C22semidirect
30. C22×#103C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2076C22semidirect
59. #2075C22semidirect
60. #2036C22semidirect
61. #2036C22semidirect
62. #2035C22semidirect
63. #2035C22semidirect
64. #1873C22semidirect
65. #1873C22semidirect
66. #1854C22semidirect
67. #1854C22semidirect
69. C2×#340C22semidirect
70. C2×#340C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
143. C2×#107C23semidirect
144. C2×#107C23semidirect
147. C2×#106C23semidirect
148. C2×#106C23semidirect
153. C2×#103C23semidirect
154. C2×#103C23semidirect
155. C2×#103C23semidirect
156. C2×#103C23semidirect
198. #340C23semidirect
199. #340C23semidirect
200. #340C23semidirect
201. #340C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #340C23semidirect
205. #340C23semidirect
814. C2#29897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#22802
#298972
C2×#20762
C2×#20772
C2×#20752
C2×#20362
C2×#20352
C2×#18732
C2×#18542
C2×#17792