Finite Group Databasebeta

← C2×#30592 #7501247

Subgroups — C2×#30592 #7501247

Order 512.

2844 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#460C211yesmaximal, characteristic, complemented
3C2×#2423C211yesmaximal, characteristic, complemented
4C2×#2428C211yesmaximal, characteristic
5#30592C2116yesmaximal, direct product factor
6C2×#2094C211yesmaximal, characteristic, complemented
7C2×#2088C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2041C211yesmaximal, characteristic, complemented
10C2×#2034C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1850C211yesmaximal, characteristic, complemented
16C2×#1802C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×#127C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121—21no—
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#465—28no—
28C2×#465C2218yescomplemented
29C2×#460—28no—
30C2×#460C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2428—24no—
45#2428C2218yes—
46#2423—24no—
47#2423C2218yescomplemented
48C2×#399—21no—
49C2×#398—21no—
50C2×#394—21no—
51C2×#392—21no—
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#387—21no—
58C2×#386—21no—
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2094C2218yescomplemented
63#2088C2218yescomplemented
64#2055C2218yescomplemented
65#2041C2218yescomplemented
66#2034C2218yescomplemented
67#2000C2218yescomplemented
68#1893C2218yescomplemented
69#1877C2218yescomplemented
70#1865C2218yescomplemented
71#1850C2218yescomplemented
72#1802C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16—42no—
93C22×SD16D418yescomplemented
94C22×SD16C2314yes—
95C22×SD16C2314yes—
96C23×C8—24no—
97C23×C8—42no—
98C23×C8—42no—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C2×#127—24no—
105C2×#127—22no—
106C2×#127—42no—
107C2×#127C2314yes—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8C2314yes—
112C2×#121—22no—
113C2×#121—22no—
114C2×#121—28no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—42no—
118C2×#121—42no—
119C2×#121—48no—
120C2×#121C2314yes—
121C2×#121C2314yes—
122C2×C4×Q8—22no—
123C2×C4×Q8—24no—
124C2×C4×Q8—42no—
125C2×C4×Q8C2314yes—
126C2×C4×D4—24no—
127C2×C4×D4—22no—
128C2×C4×D4—42no—
129C2×C4×D4C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
148C22×C22⋊C4D411yescharacteristic
149C22×C22⋊C4D411yescharacteristic
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#465—232no—
154#460—232no—
155C2×#106—24no—
156C2×#106—42no—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8—42no—
161C2×C4⋊C8C2314yes—
162C2×C4⋊C8C2314yes—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102—24no—
168C2×#102—24no—
169C2×#102—24no—
170C2×#102—42no—
171C2×#102—42no—
172C2×#102—42no—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181#399—28no—
182#398—28no—
183#394—28no—
184#392—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389C2314yes—
192#389C2314yes—
193#388—28no—
194#387—28no—
195#386—28no—
196#384—22no—
197#384C2314yes—
198#380—22no—
199#380C2314yes—
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—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2×D414yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4—82no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4C2×D414yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—82no—
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—416no—
284C2×SD16—44no—
285C2×SD16—44no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—416no—
289C2×SD16C2×D4116yescomplemented
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×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—28no—
302C22×C8—44no—
303C22×C8—44no—
304C22×C8—416no—
305C22×C8C2×D414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310#127—28no—
311#127—44no—
312#127—48no—
313C22⋊Q8—28no—
314C22⋊Q8—44no—
315C22⋊Q8—48no—
316#121—28no—
317#121—28no—
318#121—44no—
319#121—44no—
320#121—48no—
321#121—48no—
322#121—432no—
323C4×Q8—28no—
324C4×Q8—44no—
325C4×Q8—48no—
326C4×D4—28no—
327C4×D4—44no—
328C4×D4—48no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—82no—
354C2×C4⋊C4—82no—
355C2×C4⋊C4#4114yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4SD1618yescomplemented
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—44no—
385C2×C42C2×D412yes—
386C2×C42C2×D412yes—
387C2×C42C2412yes—
388C2×C42C2412yes—
389#106—28no—
390#106—44no—
391C4⋊C8—28no—
392C4⋊C8—44no—
393#103—28no—
394#103—28no—
395#102—28no—
396#102—28no—
397#102—28no—
398#102—44no—
399#102—44no—
400#102—44no—
401C22⋊C8—44no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95C2×D414yes—
408#95C2×D414yes—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—22no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24C2×SD1614yes—
432C24C22×D412yes—
433C24C22×D411yescharacteristic
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8—42no—
445C2×Q8—44no—
446C2×Q8C22×D414yes—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—28no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—816no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—816no—
486C2×D4—816no—
487C2×D4—816no—
488C2×D4C22×D414yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—48no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
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—48no—
541C22×C4—84no—
542C22×C4—816no—
543C22×C4C2×SD1614yes—
544C22×C4C2×SD1614yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C2×#4112yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C42−1+412yes—
557C22×C4C2511yescharacteristic
558SD16—416no—
559SD16—416no—
560C2×C8—28no—
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—416no—
573C2×C8—44no—
574C2×C8—44no—
575C2×C8—44no—
576C2×C8C22×D414yes—
577C4⋊C4—24no—
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—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—48no—
595C4⋊C4—84no—
596C4⋊C4—84no—
597C4⋊C4C2×#4114yes—
598C22⋊C4—44no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4C2×SD16116yescomplemented
607C42—24no—
608C42—24no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—48no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—28no—
618C23—28no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—48no—
629C23—42no—
630C23—42no—
631C23—48no—
632C23—48no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#53712yes—
656C23D4212yes—
657C23#54612yes—
658C23C22×SD1614yes—
659C23C22×SD1612yes—
660C23#57512yes—
661C23#57612yes—
662C23#57712yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—24no—
666Q8—48no—
667Q8—42no—
668Q8—42no—
669D4—24no—
670D4—24no—
671D4—48no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—816no—
679D4—816no—
680D4—816no—
681D4—816no—
682D4—84no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—48no—
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—816no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#53414yes—
732C2×C4#53712yes—
733C2×C4#54014yes—
734C2×C4D4212yes—
735C2×C4#54612yes—
736C2×C4#54714yes—
737C2×C4#56214yes—
738C2×C4C22×SD1614yes—
739C2×C4C22×SD1614yes—
740C2×C4C23×D411yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×2−1+411yescharacteristic
746C8—24no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—416no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—816no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—168no—
774C22#267114yes—
775C22#324614yes—
776C22#325714yes—
777C22#326814yes—
778C22D4×SD1614yes—
779C22#329514yes—
780C22#331714yes—
781C22C2×#53711yescharacteristic
782C22C2×D4211yescharacteristic
783C22C2×#54611yescharacteristic
784C22C23×SD1611yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57611yescharacteristic
787C22C2×#57711yescharacteristic
788C4—24no—
789C4—24no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—44no—
794C4—42no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4#267114yes—
800C4C2×#53411yescharacteristic
801C4C2×#54011yescharacteristic
802C4C2×#54711yescharacteristic
803C4C2×#56211yescharacteristic
804C2—44no—
805C2—84no—
806C2—162no—
807C2#3059218yesdirect product factor
808C2C2×#267111yescharacteristic
809C2C2×#324611yescharacteristic
810C2C2×#325711yescharacteristic
811C2C2×#326811yescharacteristic
812C2C2×D4×SD1611yescharacteristic
813C2C2×#329511yescharacteristic
814C2C2×#331711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
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×#465C2semidirect
2. C22×#460C2semidirect
3. C2×#2423C2semidirect
5. #30592C2direct (N × H)
6. C2×#2094C2semidirect
7. C2×#2088C2semidirect
8. C2×#2055C2semidirect
9. C2×#2041C2semidirect
10. C2×#2034C2semidirect
11. C2×#2000C2semidirect
12. C2×#1893C2semidirect
13. C2×#1877C2semidirect
14. C2×#1865C2semidirect
15. C2×#1850C2semidirect
16. C2×#1802C2semidirect
28. C2×#465C22semidirect
30. C2×#460C22semidirect
47. #2423C22semidirect
62. #2094C22semidirect
63. #2088C22semidirect
64. #2055C22semidirect
65. #2041C22semidirect
66. #2034C22semidirect
67. #2000C22semidirect
68. #1893C22semidirect
69. #1877C22semidirect
70. #1865C22semidirect
71. #1850C22semidirect
72. #1802C22semidirect
93. C22×SD16D4semidirect
289. C2×SD16C2×D4semidirect
376. C2×C22⋊C4SD16semidirect
606. C22⋊C4C2×SD16semidirect
807. C2#30592direct (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×#4602
C2×#24232
C2×#24282
#305922
C2×#20942
C2×#20882
C2×#20552
C2×#20412
C2×#20342
C2×#20002
C2×#18932
C2×#18772
C2×#18652
C2×#18502
C2×#18022