Finite Group Databasebeta

← C2×#25169 #6438645

Subgroups — C2×#25169 #6438645

Order 512.

3378 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#464C211yesmaximal, characteristic, complemented
2C22×#451C211yesmaximal, characteristic, complemented
3C22×#448C211yesmaximal, characteristic
4C22×#441C211yesmaximal, characteristic, complemented
5C2×#2426C211yesmaximal, characteristic
6C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7#25169C2116yesmaximal, direct product factor
8C2×#2066C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2034C211yesmaximal, characteristic
11C2×#2015C211yesmaximal, characteristic, complemented
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1924C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1878C211yesmaximal, characteristic, complemented
16C2×#1863C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C2×#464—28no—
29C2×#464C2218yescomplemented
30C2×#451—28no—
31C2×#451C2218yescomplemented
32C2×#448—28no—
33C2×#448C2218yes—
34C2×#441—28no—
35C2×#441C2218yescomplemented
36C22×#107C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×C22⋊C8C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×#97C2211yescharacteristic
50#2426—24no—
51#2426C2218yes—
52C2×#396—21no—
53C2×#394—21no—
54Q8×C22⋊C4—24no—
55Q8×C22⋊C4C2218yescomplemented
56C2×#391—21no—
57C2×#391—21no—
58C2×#391C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#390—21no—
61C2×#390C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#388—21no—
64C2×#380—21no—
65C2×#380C2211yescharacteristic
66C2×C4×C22⋊C4—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2066C2218yescomplemented
69#2036C2218yescomplemented
70#2034C2218yes—
71#2015C2218yescomplemented
72#1973C2218yescomplemented
73#1924C2218yescomplemented
74#1880C2218yescomplemented
75#1878C2218yescomplemented
76#1863C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—22no—
84C23×Q8—21no—
85C23×Q8—24no—
86C23×Q8—24no—
87C23×Q8—42no—
88C23×Q8—42no—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2314yes—
92C23×Q8C2311yescharacteristic
93C23×D4—21no—
94C23×D4C2311yescharacteristic
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C22×Q16—24no—
98C22×Q16—24no—
99C22×Q16—24no—
100C22×Q16—24no—
101C22×Q16—42no—
102C22×Q16D418yescomplemented
103C22×Q16C2314yes—
104C22×Q16C2314yes—
105C22×SD16—24no—
106C22×SD16—24no—
107C22×SD16—24no—
108C22×SD16—24no—
109C22×SD16—24no—
110C22×SD16—42no—
111C22×SD16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C23×C8C2311yescharacteristic
116C23×C8C2311yescharacteristic
117C2×#124—24no—
118C2×#124—22no—
119C2×#124—42no—
120C2×#124C2314yes—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8C2314yes—
125C2×#121—22no—
126C2×#121—24no—
127C2×#121—42no—
128C2×#121C2314yes—
129C2×C4×Q8—22no—
130C2×C4×Q8—22no—
131C2×C4×Q8—22no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—42no—
136C2×C4×Q8—42no—
137C2×C4×Q8—42no—
138C2×C4×Q8C2314yes—
139C2×C4×Q8C2314yes—
140C2×C4×Q8C2314yes—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
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⋊C4D411yescharacteristic
158C22×C22⋊C4D411yescharacteristic
159C22×C42—21no—
160C22×C42—21no—
161C22×C42—21no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#464—232no—
165#451—232no—
166#448—232no—
167#441—232no—
168C2×#107—42no—
169C2×#107C2314yes—
170C2×#106—24no—
171C2×#106C2314yes—
172C2×C4⋊C8—24no—
173C2×C4⋊C8C2314yes—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—24no—
178C2×#103—24no—
179C2×#103D418yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#102—24no—
187C2×#102—42no—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×C22⋊C8—24no—
191C2×C22⋊C8—24no—
192C2×C22⋊C8C2314yes—
193C2×C22⋊C8C2314yes—
194C2×#97—24no—
195C2×#97C2314yes—
196#396—28no—
197#394—28no—
198#391—22no—
199#391—22no—
200#391—28no—
201#391—28no—
202#391C2314yes—
203#391C2314yes—
204#390—28no—
205#390—22no—
206#390C2314yes—
207#389—22no—
208#389C2314yes—
209#388—28no—
210#380—22no—
211#380—28no—
212#380C2314yes—
213C4×C22⋊C4—28no—
214C4×C22⋊C4D414yes—
215C4×C22⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C22×Q8—28no—
231C22×Q8—216no—
232C22×Q8—28no—
233C22×Q8—28no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8—24no—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—28no—
244C22×Q8—28no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×Q8—48no—
258C22×Q8—48no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8C2×D414yes—
264C22×Q8C2×D414yes—
265C22×Q8C2×D414yes—
266C22×Q8#4114yes—
267C22×Q8#4114yes—
268C22×Q8C2412yes—
269C22×Q8C2412yes—
270C22×Q8C2412yes—
271C22×D4—24no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4—82no—
282C22×D4C2412yes—
283C23×C4—21no—
284C23×C4—28no—
285C23×C4—24no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4C2×D412yes—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C2×Q16—232no—
309C2×Q16—28no—
310C2×Q16—28no—
311C2×Q16—28no—
312C2×Q16—28no—
313C2×Q16—44no—
314C2×Q16—416no—
315C2×Q16C2×D4116yescomplemented
316C2×SD16—28no—
317C2×SD16—28no—
318C2×SD16—28no—
319C2×SD16—28no—
320C2×SD16—28no—
321C2×SD16—44no—
322C2×SD16—416no—
323C2×SD16—416no—
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—22no—
333C22×C8—22no—
334C22×C8C2×D414yes—
335C22×C8C2×D414yes—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340#124—28no—
341#124—44no—
342#124—48no—
343C22⋊Q8—28no—
344C22⋊Q8—44no—
345C22⋊Q8—48no—
346#121—28no—
347#121—44no—
348#121—48no—
349C4×Q8—28no—
350C4×Q8—28no—
351C4×Q8—28no—
352C4×Q8—44no—
353C4×Q8—44no—
354C4×Q8—44no—
355C4×Q8—48no—
356C4×Q8—48no—
357C4×Q8—48no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
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—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—82no—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—82no—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4C2×D414yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—44no—
410C2×C42—44no—
411C2×C42—44no—
412C2×C42C2×D412yes—
413C2×C42C2×D412yes—
414C2×C42C2412yes—
415C2×C42C2412yes—
416#107—44no—
417#106—28no—
418C4⋊C8—28no—
419#103—28no—
420#103—28no—
421#103—28no—
422#103—28no—
423#103—28no—
424#103C2×D4116yes—
425#102—28no—
426#102—44no—
427C22⋊C8—28no—
428C22⋊C8—28no—
429#97—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95C2×D414yes—
437#95C2×D414yes—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24#13714yes—
453C24C22×D412yes—
454C24C22×D411yescharacteristic
455C2×Q8—216no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—28no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—24no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—432no—
484C2×Q8—416no—
485C2×Q8—416no—
486C2×Q8—464no—
487C2×Q8—416no—
488C2×Q8—416no—
489C2×Q8—44no—
490C2×Q8—42no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—44no—
497C2×Q8#121116yes—
498C2×Q8C22×D414yes—
499C2×Q8C22×D414yes—
500C2×Q8C22×D414yes—
501C2×Q8C2×#4114yes—
502C2×Q8C2×#4114yes—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—84no—
519C2×D4—816no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—216no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—432no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D411yescharacteristic
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C4C2511yescharacteristic
593Q16—232no—
594Q16—416no—
595SD16—416no—
596SD16—416no—
597C2×C8—28no—
598C2×C8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—44no—
610C2×C8—44no—
611C2×C8C22×D414yes—
612C2×C8C22×D414yes—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—84no—
629C4⋊C4C22×D414yes—
630C22⋊C4—28no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—48no—
646C42—48no—
647C42—48no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23#52512yes—
676C23D4212yes—
677C23D4212yes—
678C23C2×#13714yes—
679C23C2×#13712yes—
680C23#57512yes—
681C23#57712yes—
682C23#57812yes—
683C23C23×D411yescharacteristic
684Q8—216no—
685Q8—24no—
686Q8—24no—
687Q8—24no—
688Q8—24no—
689Q8—24no—
690Q8—24no—
691Q8—24no—
692Q8—432no—
693Q8—42no—
694Q8—48no—
695Q8—48no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699Q8C2×#12118yes—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—816no—
705D4—84no—
706C2×C4—24no—
707C2×C4—216no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—432no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4C2×#12114yes—
761C2×C4#52512yes—
762C2×C4#53814yes—
763C2×C4D4212yes—
764C2×C4D4212yes—
765C2×C4#54614yes—
766C2×C4#54614yes—
767C2×C4C23×D411yescharacteristic
768C2×C4C23×D411yescharacteristic
769C2×C4C22×#4111yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C2×H(5,𝔽2)11yescharacteristic
772C2×C4C2×H(5,𝔽2)11yescharacteristic
773C8—24no—
774C8—24no—
775C8—42no—
776C8—42no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—416no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—168no—
793C22#242414yes—
794C22#311714yes—
795C22#312114yes—
796C22#326614yes—
797C22#327014yes—
798C22#327114yes—
799C22#327714yes—
800C22C2×#52511yescharacteristic
801C22C2×D4211yescharacteristic
802C22C2×D4211yescharacteristic
803C22C22×#13711yescharacteristic
804C22C2×#57511yescharacteristic
805C22C2×#57711yescharacteristic
806C22C2×#57811yescharacteristic
807C4—28no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—44no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#242414yes—
820C4C22×#12111yescharacteristic
821C4C2×#53811yescharacteristic
822C4C2×#54611yescharacteristic
823C4C2×#54611yescharacteristic
824C2—44no—
825C2—162no—
826C2#2516918yesdirect product factor
827C2C2×#242411yescharacteristic
828C2C2×#311711yescharacteristic
829C2C2×#312111yescharacteristic
830C2C2×#326611yescharacteristic
831C2C2×#327011yescharacteristic
832C2C2×#327111yescharacteristic
833C2C2×#327711yescharacteristic
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×#464C2semidirect
2. C22×#451C2semidirect
4. C22×#441C2semidirect
6. C2×Q8×C22⋊C4C2semidirect
7. #25169C2direct (N × H)
8. C2×#2066C2semidirect
9. C2×#2036C2semidirect
11. C2×#2015C2semidirect
12. C2×#1973C2semidirect
13. C2×#1924C2semidirect
14. C2×#1880C2semidirect
15. C2×#1878C2semidirect
16. C2×#1863C2semidirect
29. C2×#464C22semidirect
31. C2×#451C22semidirect
35. C2×#441C22semidirect
55. Q8×C22⋊C4C22semidirect
68. #2066C22semidirect
69. #2036C22semidirect
71. #2015C22semidirect
72. #1973C22semidirect
73. #1924C22semidirect
74. #1880C22semidirect
75. #1878C22semidirect
76. #1863C22semidirect
102. C22×Q16D4semidirect
315. C2×Q16C2×D4semidirect
826. C2#25169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4642
C22×#4512
C22×#4482
C22×#4412
C2×#24262
C2×Q8×C22⋊C42
#251692
C2×#20662
C2×#20362
C2×#20342
C2×#20152
C2×#19732
C2×#19242
C2×#18802
C2×#18782
C2×#18632