Finite Group Databasebeta

← C2×#26624 #6439496

Subgroups — C2×#26624 #6439496

Order 512.

2846 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#483C211yesmaximal, characteristic, complemented
2C22×C4×SD16C211yesmaximal, characteristic, complemented
3C2×#2429C211yesmaximal, characteristic, complemented
4C2×#2361C211yesmaximal, characteristic
5#26624C2116yesmaximal, direct product factor
6C2×#2065C211yesmaximal, characteristic, complemented
7C2×#2013C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic
9C2×#2000C211yesmaximal, characteristic
10C2×#1981C211yesmaximal, characteristic, complemented
11C2×#1933C211yesmaximal, characteristic, complemented
12C2×#1923C211yesmaximal, characteristic, complemented
13C2×#1920C211yesmaximal, characteristic, complemented
14C2×#1877C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C2×#1865C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×D4—21no—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#483—28no—
28C2×#483C2218yescomplemented
29C2×C4×SD16—28no—
30C2×C4×SD16C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2429—24no—
46#2429C2218yescomplemented
47C2×#398—21no—
48C2×#396—21no—
49#2361—24no—
50#2361C2218yes—
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389—21no—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#388—21no—
58C2×#386—21no—
59C2×#385—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2065C2218yescomplemented
63#2013C2218yescomplemented
64#2000C2218yes—
65#2000C2218yes—
66#1981C2218yescomplemented
67#1933C2218yescomplemented
68#1923C2218yescomplemented
69#1920C2218yescomplemented
70#1877C2218yescomplemented
71#1872C2218yescomplemented
72#1865C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4—21no—
85C24×C4C2311yescharacteristic
86C22×SD16—24no—
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16C2314yes—
93C22×SD16C2314yes—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—22no—
100C2×C4⋊Q8—42no—
101C2×C4⋊Q8C2314yes—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8C2314yes—
109C2×C22⋊Q8C2314yes—
110C2×#121—24no—
111C2×#121—22no—
112C2×#121—24no—
113C2×#121C2314yes—
114C2×C4×Q8—22no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C2×C4×Q8C2314yes—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C2×C4×D4—22no—
121C2×C4×D4—42no—
122C2×C4×D4—48no—
123C2×C4×D4C2314yes—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—22no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#483—232no—
154C4×SD16—232no—
155C2×#106—24no—
156C2×#106D418yescomplemented
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8—42no—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102—24no—
174C2×#102—42no—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—42no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C4×C8—24no—
182C2×C4×C8C2314yes—
183#398—28no—
184#396—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389—28no—
192#389C2314yes—
193#389C2314yes—
194#388—28no—
195#388—28no—
196#386—28no—
197#385—28no—
198C4×C4⋊C4—22no—
199C4×C4⋊C4C2314yes—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8#4114yes—
231C22×Q8C2412yes—
232C22×Q8C2412yes—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—21no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4#4114yes—
244C22×D4C2412yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—82no—
265C23×C4—82no—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C2×SD16—232no—
275C2×SD16—28no—
276C2×SD16—28no—
277C2×SD16—28no—
278C2×SD16—28no—
279C2×SD16—44no—
280C2×SD16—44no—
281C2×SD16—416no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8C2×D414yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C4⋊Q8—28no—
299C4⋊Q8—44no—
300C4⋊Q8—48no—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—48no—
306C22⋊Q8—48no—
307#121—216no—
308#121—28no—
309#121—28no—
310C4×Q8—28no—
311C4×Q8—44no—
312C4×Q8—48no—
313C4×D4—28no—
314C4×D4—44no—
315C4×D4—48no—
316C4×D4—432no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
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—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—48no—
340C2×C4⋊C4—44no—
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—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4#4114yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—28no—
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—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—82no—
369C2×C22⋊C4SD1618yescomplemented
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C2×C42C2412yes—
383C2×C42C2412yes—
384#106—28no—
385#106C2×D4116yescomplemented
386C4⋊C8—44no—
387#103—28no—
388#103—28no—
389#103—28no—
390#103—28no—
391#103—28no—
392#103—44no—
393#102—28no—
394#102—44no—
395C22⋊C8—28no—
396C22⋊C8—44no—
397C4×C8—28no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95C2×D414yes—
404#95C2×D414yes—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24C2×SD1614yes—
420C24C22×D412yes—
421C24C22×D411yescharacteristic
422C2×Q8—24no—
423C2×Q8—22no—
424C2×Q8—28no—
425C2×Q8—28no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8C2×#4114yes—
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—432no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4C2×#4114yes—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
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—48no—
499C22×C4—48no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
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—48no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—48no—
523C22×C4—84no—
524C22×C4—816no—
525C22×C4—84no—
526C22×C4—816no—
527C22×C4C2×SD1614yes—
528C22×C4C2×SD1614yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D412yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4C2511yescharacteristic
542SD16—232no—
543SD16—416no—
544C2×C8—28no—
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—44no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8C22×D414yes—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—48no—
580C4⋊C4C22×D414yes—
581C4⋊C4C22×D414yes—
582C4⋊C4C2×#4114yes—
583C22⋊C4—216no—
584C22⋊C4—44no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—84no—
590C22⋊C4C2×SD16116yescomplemented
591C42—24no—
592C42—24no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—48no—
598C42—48no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—48no—
614C23—48no—
615C23—42no—
616C23—42no—
617C23—48no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23#52512yes—
627C23D4212yes—
628C23#54612yes—
629C23C22×SD1614yes—
630C23C22×SD1612yes—
631C23#57512yes—
632C23#57712yes—
633C23#57812yes—
634C23C23×D411yescharacteristic
635Q8—24no—
636Q8—24no—
637Q8—42no—
638Q8—42no—
639Q8—48no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—84no—
645D4—24no—
646D4—24no—
647D4—432no—
648D4—42no—
649D4—42no—
650D4—48no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—44no—
674C2×C4—48no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—48no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—816no—
700C2×C4—816no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4#52514yes—
705C2×C4#52512yes—
706C2×C4#53814yes—
707C2×C4D4212yes—
708C2×C4#54612yes—
709C2×C4#55014yes—
710C2×C4#55314yes—
711C2×C4C22×SD1614yes—
712C2×C4C22×SD1614yes—
713C2×C4C23×D411yescharacteristic
714C2×C4C22×#4111yescharacteristic
715C2×C4C22×#4111yescharacteristic
716C2×C4C22×#4111yescharacteristic
717C2×C4C2×H(5,𝔽2)11yescharacteristic
718C2×C4C2×H(5,𝔽2)11yescharacteristic
719C8—24no—
720C8—42no—
721C8—42no—
722C8—42no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—416no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—816no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22#245614yes—
740C22#310114yes—
741C22#312014yes—
742C22#326914yes—
743C22D4×SD1614yes—
744C22#329814yes—
745C22#332614yes—
746C22C2×#52511yescharacteristic
747C22C2×D4211yescharacteristic
748C22C2×#54611yescharacteristic
749C22C23×SD1611yescharacteristic
750C22C2×#57511yescharacteristic
751C22C2×#57711yescharacteristic
752C22C2×#57811yescharacteristic
753C4—24no—
754C4—24no—
755C4—42no—
756C4—44no—
757C4—42no—
758C4—44no—
759C4—44no—
760C4—44no—
761C4—42no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4#245614yes—
766C4C2×#52511yescharacteristic
767C4C2×#53811yescharacteristic
768C4C2×#55011yescharacteristic
769C4C2×#55311yescharacteristic
770C2—44no—
771C2—84no—
772C2#2662418yesdirect product factor
773C2C2×#245611yescharacteristic
774C2C2×#310111yescharacteristic
775C2C2×#312011yescharacteristic
776C2C2×#326911yescharacteristic
777C2C2×D4×SD1611yescharacteristic
778C2C2×#329811yescharacteristic
779C2C2×#332611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#483C2semidirect
2. C22×C4×SD16C2semidirect
3. C2×#2429C2semidirect
5. #26624C2direct (N × H)
6. C2×#2065C2semidirect
7. C2×#2013C2semidirect
10. C2×#1981C2semidirect
11. C2×#1933C2semidirect
12. C2×#1923C2semidirect
13. C2×#1920C2semidirect
14. C2×#1877C2semidirect
15. C2×#1872C2semidirect
16. C2×#1865C2semidirect
28. C2×#483C22semidirect
30. C2×C4×SD16C22semidirect
46. #2429C22semidirect
62. #2065C22semidirect
63. #2013C22semidirect
66. #1981C22semidirect
67. #1933C22semidirect
68. #1923C22semidirect
69. #1920C22semidirect
70. #1877C22semidirect
71. #1872C22semidirect
72. #1865C22semidirect
156. C2×#106D4semidirect
369. C2×C22⋊C4SD16semidirect
385. #106C2×D4semidirect
590. C22⋊C4C2×SD16semidirect
772. C2#26624direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4832
C22×C4×SD162
C2×#24292
C2×#23612
#266242
C2×#20652
C2×#20132
C2×#20002
C2×#19812
C2×#19332
C2×#19232
C2×#19202
C2×#18772
C2×#18722
C2×#18652