Finite Group Databasebeta

← C2×#30741 #7501686

Subgroups — C2×#30741 #7501686

Order 512.

2848 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#492C211yesmaximal, characteristic
2C22×#461C211yesmaximal, characteristic, complemented
3C2×#2546C211yesmaximal, characteristic, complemented
4C2×#2445C211yesmaximal, characteristic
5#30741C2116yesmaximal, direct product factor
6C2×#2055C211yesmaximal, characteristic, complemented
7C2×#2043C211yesmaximal, characteristic, complemented
8C2×#2013C211yesmaximal, characteristic, complemented
9C2×#2013C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2014C211yesmaximal, characteristic
12C2×#1933C211yesmaximal, characteristic, complemented
13C2×#1916C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1880C211yesmaximal, characteristic, complemented
16C2×#1877C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×SD16C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#123—21no—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C2×#492—28no—
31C2×#492C2218yes—
32C2×#461—28no—
33C2×#461C2218yescomplemented
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C4×C8C2211yescharacteristic
44#2546—24no—
45#2546C2218yescomplemented
46#2445—24no—
47#2445C2218yes—
48C2×#398—21no—
49C2×#398—21no—
50C2×#394—21no—
51C2×#394—21no—
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389—21no—
58C2×#389—21no—
59C2×#389C2211yescharacteristic
60C2×#386—21no—
61C2×C4×C4⋊C4C2211yescharacteristic
62#2055C2218yescomplemented
63#2043C2218yescomplemented
64#2014C2218yes—
65#2013C2218yescomplemented
66#2013C2218yescomplemented
67#2013C2218yescomplemented
68#1933C2218yescomplemented
69#1916C2218yescomplemented
70#1880C2218yescomplemented
71#1880C2218yescomplemented
72#1877C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16—42no—
94C22×SD16—42no—
95C22×SD16—42no—
96C22×SD16—42no—
97C22×SD16—42no—
98C22×SD16—42no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16D418yes—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C22×SD16C2314yes—
110C22×SD16C2314yes—
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113C23×C8C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—22no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8C2314yes—
125C2×C4⋊Q8C2314yes—
126C2×C4⋊Q8C2314yes—
127C2×#127—24no—
128C2×#127—22no—
129C2×#127—42no—
130C2×#127C2314yes—
131C2×#123—28no—
132C2×#123—48no—
133C2×C4×Q8—22no—
134C2×C4×Q8—42no—
135C2×C4×Q8—42no—
136C2×C4×Q8C2314yes—
137C2×C4×D4—24no—
138C2×C4×D4—22no—
139C2×C4×D4—42no—
140C2×C4×D4C2314yes—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4D411yescharacteristic
150C22×C4⋊C4D411yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C42—21no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#492—232no—
166#461—232no—
167C2×C4⋊C8—24no—
168C2×C4⋊C8C2314yes—
169C2×#103—24no—
170C2×#103—24no—
171C2×#103—24no—
172C2×#103—42no—
173C2×#103—42no—
174C2×#103—42no—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102—42no—
182C2×#102—42no—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×C4×C8—24no—
186C2×C4×C8C2314yes—
187#398—28no—
188#398—28no—
189#394—28no—
190#394—28no—
191#391—22no—
192#391—22no—
193#391C2314yes—
194#391C2314yes—
195#390—22no—
196#390—22no—
197#390—22no—
198#390C2314yes—
199#390C2314yes—
200#390C2314yes—
201#389—28no—
202#389—28no—
203#389—22no—
204#389C2314yes—
205#386—28no—
206C4×C4⋊C4D414yes—
207C4×C4⋊C4C2314yes—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95D411yescharacteristic
214C2×#95D411yescharacteristic
215#340C2314yes—
216#340C2314yes—
217#336C2314yes—
218#336C2314yes—
219#336C2314yes—
220#336C2314yes—
221C25—21no—
222C25—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8C2×D414yes—
244C22×Q8C2412yes—
245C22×Q8C2412yes—
246C22×Q8C2412yes—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—82no—
267C22×D4—82no—
268C22×D4C2×D414yes—
269C22×D4C2412yes—
270C22×D4C2412yes—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—82no—
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2411yescharacteristic
288C2×SD16—28no—
289C2×SD16—28no—
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—28no—
293C2×SD16—28no—
294C2×SD16—416no—
295C2×SD16—44no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—44no—
302C2×SD16—44no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—44no—
306C2×SD16—416no—
307C2×SD16—416no—
308C2×SD16—416no—
309C2×SD16—416no—
310C2×SD16—416no—
311C2×SD16C2×D4116yes—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8C2×D414yes—
323C22×C8#4114yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—44no—
331C4⋊Q8—44no—
332C4⋊Q8—44no—
333C4⋊Q8—44no—
334C4⋊Q8—48no—
335C4⋊Q8—48no—
336C4⋊Q8—48no—
337#127—28no—
338#127—44no—
339#127—48no—
340#123—432no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×Q8—48no—
344C4×D4—28no—
345C4×D4—44no—
346C4×D4—48no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4SD1618yescomplemented
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—82no—
391C2×C22⋊C4—82no—
392C2×C22⋊C4—82no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—44no—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2×D412yes—
404C2×C42C2412yes—
405C2×C42C2412yes—
406C2×C42C2412yes—
407C4⋊C8—28no—
408#103—28no—
409#103—28no—
410#103—28no—
411#103—44no—
412#103—44no—
413#103—44no—
414#102—44no—
415#102—44no—
416C4×C8—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95C2×D414yes—
423#95C2×D414yes—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24C22×D411yescharacteristic
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—44no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8C22×D414yes—
480C2×D4—28no—
481C2×D4—24no—
482C2×D4—28no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—816no—
512C2×D4—816no—
513C2×D4C22×D414yes—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—48no—
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—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—48no—
554C22×C4—84no—
555C22×C4—816no—
556C22×C4C2×SD1614yes—
557C22×C4C2×SD1614yes—
558C22×C4C2×SD1614yes—
559C22×C4#13714yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4C2511yescharacteristic
574SD16—416no—
575SD16—416no—
576SD16—416no—
577SD16—416no—
578SD16—416no—
579SD16—416no—
580C2×C8—28no—
581C2×C8—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—44no—
594C2×C8C22×D414yes—
595C2×C8C2×#4114yes—
596C4⋊C4—28no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—48no—
614C4⋊C4C2×SD16116yescomplemented
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C42—24no—
623C42—24no—
624C42—24no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—48no—
632C23—24no—
633C23—48no—
634C23—42no—
635C23—42no—
636C23—48no—
637C23—48no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23#53512yes—
661C23D4212yes—
662C23#55012yes—
663C23C22×SD1612yes—
664C23C2×#13712yes—
665C23#57712yes—
666C23#57712yes—
667C23C23×D411yescharacteristic
668Q8—24no—
669Q8—24no—
670Q8—48no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—84no—
682Q8—84no—
683D4—24no—
684D4—24no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—816no—
693D4—816no—
694D4—84no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
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—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—816no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4#53414yes—
741C2×C4#53512yes—
742C2×C4#54014yes—
743C2×C4D4212yes—
744C2×C4#54614yes—
745C2×C4#55012yes—
746C2×C4#56014yes—
747C2×C4C22×SD1614yes—
748C2×C4C22×SD1614yes—
749C2×C4C22×SD1614yes—
750C2×C4C2×#13714yes—
751C2×C4C23×D411yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C8—24no—
758C8—24no—
759C8—42no—
760C8—42no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—816no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—168no—
777C22#267314yes—
778C22#320614yes—
779C22#322114yes—
780C22#326614yes—
781C22D4×SD1614yes—
782C22#339214yes—
783C22#340014yes—
784C22C2×#53511yescharacteristic
785C22C2×D4211yescharacteristic
786C22C2×#55011yescharacteristic
787C22C23×SD1611yescharacteristic
788C22C22×#13711yescharacteristic
789C22C2×#57711yescharacteristic
790C22C2×#57711yescharacteristic
791C4—24no—
792C4—24no—
793C4—24no—
794C4—24no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#267314yes—
804C4C2×#53411yescharacteristic
805C4C2×#54011yescharacteristic
806C4C2×#54611yescharacteristic
807C4C2×#56011yescharacteristic
808C2—84no—
809C2—162no—
810C2#3074118yesdirect product factor
811C2C2×#267311yescharacteristic
812C2C2×#320611yescharacteristic
813C2C2×#322111yescharacteristic
814C2C2×#326611yescharacteristic
815C2C2×D4×SD1611yescharacteristic
816C2C2×#339211yescharacteristic
817C2C2×#340011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#461C2semidirect
3. C2×#2546C2semidirect
5. #30741C2direct (N × H)
6. C2×#2055C2semidirect
7. C2×#2043C2semidirect
8. C2×#2013C2semidirect
9. C2×#2013C2semidirect
10. C2×#2013C2semidirect
12. C2×#1933C2semidirect
13. C2×#1916C2semidirect
14. C2×#1880C2semidirect
15. C2×#1880C2semidirect
16. C2×#1877C2semidirect
33. C2×#461C22semidirect
45. #2546C22semidirect
62. #2055C22semidirect
63. #2043C22semidirect
65. #2013C22semidirect
66. #2013C22semidirect
67. #2013C22semidirect
68. #1933C22semidirect
69. #1916C22semidirect
70. #1880C22semidirect
71. #1880C22semidirect
72. #1877C22semidirect
373. C2×C4⋊C4SD16semidirect
614. C4⋊C4C2×SD16semidirect
810. C2#30741direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4922
C22×#4612
C2×#25462
C2×#24452
#307412
C2×#20552
C2×#20432
C2×#20132
C2×#20142
C2×#19332
C2×#19162
C2×#18802
C2×#18772