Finite Group Databasebeta

← C2×#31202 #7503735

Subgroups — C2×#31202 #7503735

Order 512.

2748 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#484C211yesmaximal, characteristic, complemented
2C22×#480C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#31202C2116yesmaximal, direct product factor
6C2×#2068C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2000C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1955C211yesmaximal, characteristic, complemented
14C2×#1943C211yesmaximal, characteristic, complemented
15C2×#1852C211yesmaximal, characteristic, complemented
16C2×#1852C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121—21no—
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C2×#484—28no—
27C2×#484C2218yescomplemented
28C2×#480—28no—
29C2×#480C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#107C2211yescharacteristic
33C22×#107C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×C4⋊C8C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46C22×#97C2211yescharacteristic
47#2417—24no—
48#2417C2218yescomplemented
49#2416—24no—
50#2416C2218yes—
51C2×#398—21no—
52C2×#396—21no—
53C2×#396—21no—
54C2×#394—21no—
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#386—21no—
60C2×#386—21no—
61C2×#380—21no—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64#2068C2218yescomplemented
65#2067C2218yescomplemented
66#2035C2218yescomplemented
67#2034C2218yescomplemented
68#2000C2218yescomplemented
69#2000C2218yescomplemented
70#1973C2218yescomplemented
71#1955C2218yescomplemented
72#1943C2218yescomplemented
73#1852C2218yescomplemented
74#1852C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—42no—
100C2×C22⋊Q8—42no—
101C2×C22⋊Q8—42no—
102C2×C22⋊Q8C2314yes—
103C2×C22⋊Q8C2314yes—
104C2×#121—28no—
105C2×#121—22no—
106C2×#121—22no—
107C2×#121—24no—
108C2×#121—42no—
109C2×#121—42no—
110C2×#121—42no—
111C2×#121—48no—
112C2×#121C2314yes—
113C2×#121C2314yes—
114C2×C4×D4—42no—
115C2×C4×D4—42no—
116C2×C4×D4D414yes—
117C2×C4×D4C2314yes—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—22no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4—42no—
130C22×C4⋊C4D411yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
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×C42C2311yescharacteristic
150#484—232no—
151#480—232no—
152C2×#107—24no—
153C2×#107—24no—
154C2×#107—42no—
155C2×#107D418yescomplemented
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106—42no—
161C2×#106C2314yes—
162C2×C4⋊C8—42no—
163C2×C4⋊C8C2314yes—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—42no—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8—24no—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—24no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×#97—42no—
185C2×#97C2314yes—
186#398—28no—
187#396—28no—
188#396—28no—
189#394—28no—
190#391—22no—
191#391C2314yes—
192#390—22no—
193#390C2314yes—
194#389—22no—
195#389—22no—
196#389C2314yes—
197#389C2314yes—
198#386—28no—
199#386—28no—
200#380—22no—
201#380—22no—
202#380—28no—
203#380C2314yes—
204#380C2314yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—21no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—42no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—82no—
244C22×D4C2×D414yes—
245C22×D4C2412yes—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—82no—
272C23×C4—82no—
273C23×C4C2×D412yes—
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—44no—
284C2×SD16—44no—
285C2×SD16—416no—
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×C8C2×D414yes—
297C22×C8#4114yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22⋊Q8—28no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—48no—
307C22⋊Q8—48no—
308#121—28no—
309#121—44no—
310#121—44no—
311#121—44no—
312#121—48no—
313#121—48no—
314#121—432no—
315C4×D4—48no—
316C4×D4—44no—
317C4×D4—44no—
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—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—48no—
345C2×C4⋊C4—48no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—82no—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
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—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—82no—
379C2×C22⋊C4—82no—
380C2×C22⋊C4C2×D414yes—
381C2×C22⋊C4C2×D414yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42C2×D412yes—
385C2×C42C2412yes—
386#107—28no—
387#107—28no—
388#107—44no—
389#107C2×D4116yescomplemented
390#106—44no—
391C4⋊C8—44no—
392#103—28no—
393#103—28no—
394#103—44no—
395#102—28no—
396#102—28no—
397#102—44no—
398C22⋊C8—28no—
399C22⋊C8—28no—
400C22⋊C8—28no—
401C22⋊C8—28no—
402#97—44no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24AGL(1,ℤ/8)14yes—
430C24#13714yes—
431C24C22×D412yes—
432C24C22×D412yes—
433C24C22×D411yescharacteristic
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—44no—
456C2×D4—48no—
457C2×D4—416no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—84no—
470C2×D4—816no—
471C2×D4—816no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
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—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
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—48no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—816no—
545C22×C4—816no—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D412yes—
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—
559C2×C8—28no—
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—44no—
572C2×C8—44no—
573C2×C8C22×D414yes—
574C2×C8C2×#4114yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
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—44no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—84no—
598C4⋊C4C22×D414yes—
599C4⋊C4C22×D414yes—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C42—24no—
611C42—22no—
612C42—22no—
613C23—28no—
614C23—28no—
615C23—22no—
616C23—22no—
617C23—28no—
618C23—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#53412yes—
654C23D4212yes—
655C23#54712yes—
656C23C2×AGL(1,ℤ/8)14yes—
657C23C2×AGL(1,ℤ/8)12yes—
658C23C2×#13714yes—
659C23C2×#13712yes—
660C23#57612yes—
661C23#57812yes—
662C23C23×D411yescharacteristic
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—42no—
667Q8—84no—
668D4—416no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—816no—
674D4—816no—
675D4—84no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—48no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—48no—
703C2×C4—48no—
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—816no—
726C2×C4—816no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4#53412yes—
733C2×C4#53714yes—
734C2×C4#53814yes—
735C2×C4D4212yes—
736C2×C4#54712yes—
737C2×C4#55014yes—
738C2×C4#56214yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×2−1+411yescharacteristic
745C8—24no—
746C8—24no—
747C8—42no—
748C8—42no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—416no—
764C22—416no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—168no—
773C22#268214yes—
774C22#319314yes—
775C22#320314yes—
776C22#326414yes—
777C22#327014yes—
778C22#334314yes—
779C22#334614yes—
780C22C2×#53411yescharacteristic
781C22C2×D4211yescharacteristic
782C22C2×#54711yescharacteristic
783C22C22×AGL(1,ℤ/8)11yescharacteristic
784C22C22×#13711yescharacteristic
785C22C2×#57611yescharacteristic
786C22C2×#57811yescharacteristic
787C4—42no—
788C4—42no—
789C4—44no—
790C4—44no—
791C4—42no—
792C4—42no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4#268214yes—
799C4C2×#53711yescharacteristic
800C4C2×#53811yescharacteristic
801C4C2×#55011yescharacteristic
802C4C2×#56211yescharacteristic
803C2—44no—
804C2—44no—
805C2—162no—
806C2#3120218yesdirect product factor
807C2C2×#268211yescharacteristic
808C2C2×#319311yescharacteristic
809C2C2×#320311yescharacteristic
810C2C2×#326411yescharacteristic
811C2C2×#327011yescharacteristic
812C2C2×#334311yescharacteristic
813C2C2×#334611yescharacteristic
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. C22×#484C2semidirect
2. C22×#480C2semidirect
3. C2×#2417C2semidirect
5. #31202C2direct (N × H)
6. C2×#2068C2semidirect
7. C2×#2067C2semidirect
8. C2×#2034C2semidirect
9. C2×#2035C2semidirect
10. C2×#2000C2semidirect
11. C2×#2000C2semidirect
12. C2×#1973C2semidirect
13. C2×#1955C2semidirect
14. C2×#1943C2semidirect
15. C2×#1852C2semidirect
16. C2×#1852C2semidirect
27. C2×#484C22semidirect
29. C2×#480C22semidirect
48. #2417C22semidirect
64. #2068C22semidirect
65. #2067C22semidirect
66. #2035C22semidirect
67. #2034C22semidirect
68. #2000C22semidirect
69. #2000C22semidirect
70. #1973C22semidirect
71. #1955C22semidirect
72. #1943C22semidirect
73. #1852C22semidirect
74. #1852C22semidirect
155. C2×#107D4semidirect
389. #107C2×D4semidirect
806. C2#31202direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4842
C22×#4802
C2×#24172
C2×#24162
#312022
C2×#20682
C2×#20672
C2×#20342
C2×#20352
C2×#20002
C2×#19732
C2×#19552
C2×#19432
C2×#18522