Finite Group Databasebeta

← C2×#25558 #6452142

Subgroups — C2×#25558 #6452142

Order 512.

3564 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic
2C22×#485C211yesmaximal, characteristic, complemented
3C22×#470C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic
5#25558C2116yesmaximal, direct product factor
6C2×#2058C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2024C211yesmaximal, characteristic, complemented
9C2×#2001C211yesmaximal, characteristic, complemented
10C2×#1878C211yesmaximal, characteristic, complemented
11C2×#1873C211yesmaximal, characteristic, complemented
12C2×#1872C211yesmaximal, characteristic, complemented
13C2×#1870C211yesmaximal, characteristic
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1854C211yesmaximal, characteristic, complemented
16C2×#1736C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C2×#556—28no—
20C2×#556—24no—
21C2×#556—28no—
22C2×#556C2218yes—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126—21no—
25C22×#126—21no—
26C22×#124—21no—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C4×Q8—21no—
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C2×#485—28no—
38C2×#485C2218yescomplemented
39C2×#470—28no—
40C2×#470C2218yescomplemented
41C22×#107C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C22×#106C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#103C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53#2417—24no—
54#2417C2218yes—
55C2×#398—21no—
56C2×#396—21no—
57C2×#391C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#386—21no—
60C2×#380—21no—
61C2×#380C2211yescharacteristic
62#2058C2218yescomplemented
63#2035C2218yescomplemented
64#2024C2218yescomplemented
65#2001C2218yescomplemented
66#1878C2218yescomplemented
67#1873C2218yescomplemented
68#1872C2218yescomplemented
69#1870C2218yes—
70#1863C2218yescomplemented
71#1854C2218yescomplemented
72#1736C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4D411yescharacteristic
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—42no—
91C22×Q16C2314yes—
92C22×M16—24no—
93C22×M16—24no—
94C22×M16—42no—
95C22×M16C2314yes—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100#556—264no—
101#556—232no—
102#556—232no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—22no—
106C2×C4⋊Q8C2314yes—
107C2×#126—216no—
108C2×#126—216no—
109C2×#126—28no—
110C2×#126—28no—
111C2×#124—216no—
112C2×#124—28no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—22no—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8D418yes—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2314yes—
127C2×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2314yes—
129C2×C4×Q8—216no—
130C2×C4×Q8—24no—
131C2×C4×Q8—28no—
132C2×C4×Q8—24no—
133C2×C4×Q8—22no—
134C2×C4×Q8C2314yes—
135C2×C4×D4—24no—
136C2×C4×D4—24no—
137C2×C4×D4D414yes—
138C2×C4×D4C2314yes—
139C2×#117—24no—
140C2×#117—22no—
141C2×#117—22no—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117D418yes—
145C2×#117C2314yes—
146C2×#117C2314yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—24no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—22no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—42no—
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2314yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4D411yescharacteristic
174C22×C22⋊C4D411yescharacteristic
175C22×C42—21no—
176C22×C42—21no—
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179#485—232no—
180#470—232no—
181C2×#107—24no—
182C2×#107C2314yes—
183C2×#106—24no—
184C2×#106—24no—
185C2×#106C2314yes—
186C2×#106C2314yes—
187C2×#103—24no—
188C2×#103—24no—
189C2×#103—24no—
190C2×#103—24no—
191C2×#103—24no—
192C2×#103—42no—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×C22⋊C8—24no—
200C2×C22⋊C8—24no—
201C2×C22⋊C8—42no—
202C2×C22⋊C8C2314yes—
203C2×C22⋊C8C2314yes—
204C2×C22⋊C8C2314yes—
205#398—28no—
206#396—28no—
207#391—22no—
208#391C2314yes—
209#389—22no—
210#389C2314yes—
211#386—28no—
212#380—22no—
213#380—28no—
214#380C2314yes—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25C2×D411yescharacteristic
228C25C2×D411yescharacteristic
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—21no—
232C22×Q8—24no—
233C22×Q8—21no—
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×Q8—22no—
244C22×Q8—44no—
245C22×Q8—44no—
246C22×Q8C2×D414yes—
247C22×Q8C2412yes—
248C22×Q8C2412yes—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—42no—
252C22×D4C2×D414yes—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—24no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—82no—
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×Q16—28no—
287C2×Q16—28no—
288C2×Q16—44no—
289C2×Q16—416no—
290C2×M16—28no—
291C2×M16—28no—
292C2×M16—44no—
293C2×M16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8#4114yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—216no—
311C4⋊Q8—28no—
312C4⋊Q8—28no—
313#126—264no—
314#126—264no—
315#124—264no—
316C22⋊Q8—216no—
317C22⋊Q8—28no—
318C22⋊Q8—216no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—28no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—44no—
325C22⋊Q8—48no—
326C22⋊Q8—48no—
327C22⋊Q8C2×D4116yes—
328C4×Q8—264no—
329C4×Q8—216no—
330C4×Q8—28no—
331C4×Q8—28no—
332C4×D4—216no—
333C4×D4—28no—
334C4×D4—28no—
335#117—216no—
336#117—216no—
337#117—28no—
338#117—28no—
339#117—28no—
340#117C2×D4116yes—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—48no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4#4114yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—82no—
402C2×C22⋊C4C2×D414yes—
403C2×C22⋊C4C2×D414yes—
404C2×C42—28no—
405C2×C42—28no—
406C2×C42—28no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42C2×D412yes—
413C2×C42C2412yes—
414#107—28no—
415#106—28no—
416#106—28no—
417#103—28no—
418#103—28no—
419#103—28no—
420#103—28no—
421#103—28no—
422#103—44no—
423C22⋊C8—28no—
424C22⋊C8—28no—
425C22⋊C8—44no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24#12014yes—
444C24C22×D412yes—
445C24C22×D412yes—
446C24C22×D411yescharacteristic
447C2×Q8—216no—
448C2×Q8—24no—
449C2×Q8—22no—
450C2×Q8—28no—
451C2×Q8—28no—
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—22no—
462C2×Q8—432no—
463C2×Q8—48no—
464C2×Q8—42no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—48no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8C22×D414yes—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—44no—
480C2×D4—416no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—24no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—24no—
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—24no—
500C22×C4—24no—
501C22×C4—24no—
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—24no—
512C22×C4—24no—
513C22×C4—24no—
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—48no—
524C22×C4—42no—
525C22×C4—42no—
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—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—48no—
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—84no—
549C22×C4—816no—
550C22×C4#12014yes—
551C22×C4#12018yes—
552C22×C4#13714yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D412yes—
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4H(5,𝔽2)12yes—
565C22×C42−1+412yes—
566C22×C4C2511yescharacteristic
567Q16—416no—
568M16—416no—
569C2×C8—28no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—44no—
582C2×C8—44no—
583C2×C8—44no—
584C2×C8C2×#4114yes—
585C4⋊C4—216no—
586C4⋊C4—216no—
587C4⋊C4—216no—
588C4⋊C4—216no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—28no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—42no—
605C4⋊C4—48no—
606C4⋊C4—42no—
607C4⋊C4—84no—
608C4⋊C4C22×D414yes—
609C4⋊C4C22×D414yes—
610C4⋊C4C22×D414yes—
611C4⋊C4C2×#4114yes—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—84no—
621C42—216no—
622C42—216no—
623C42—216no—
624C42—24no—
625C42—22no—
626C42—22no—
627C23—28no—
628C23—22no—
629C23—22no—
630C23—28no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23C2×#12014yes—
655C23C2×#12012yes—
656C23#54612yes—
657C23#54712yes—
658C23C2×#13712yes—
659C23#57512yes—
660C23#57712yes—
661C23#57812yes—
662C23C23×D411yescharacteristic
663Q8—24no—
664Q8—24no—
665Q8—432no—
666Q8—42no—
667Q8—42no—
668Q8—48no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—84no—
674D4—416no—
675C2×C4—22no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—216no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—44no—
698C2×C4—48no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—48no—
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—48no—
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—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4C2×#12014yes—
733C2×C4C2×#12012yes—
734C2×C4#53214yes—
735C2×C4#53714yes—
736C2×C4#54612yes—
737C2×C4#54614yes—
738C2×C4#54712yes—
739C2×C4#54714yes—
740C2×C4C2×#13714yes—
741C2×C4C23×D411yescharacteristic
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C2×C4C2×2−1+411yescharacteristic
747C8—24no—
748C8—42no—
749C8—42no—
750C8—42no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—88no—
767C22#243014yes—
768C22#300714yes—
769C22#301314yes—
770C22#331114yes—
771C22#332814yes—
772C22#334914yes—
773C22#335614yes—
774C22C22×#12011yescharacteristic
775C22C2×#54611yescharacteristic
776C22C2×#54711yescharacteristic
777C22C22×#13711yescharacteristic
778C22C2×#57511yescharacteristic
779C22C2×#57711yescharacteristic
780C22C2×#57811yescharacteristic
781C4—24no—
782C4—24no—
783C4—42no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—44no—
789C4—44no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4#243014yes—
794C4C2×#53211yescharacteristic
795C4C2×#53711yescharacteristic
796C4C2×#54611yescharacteristic
797C4C2×#54711yescharacteristic
798C2—44no—
799C2—82no—
800C2#2555818yesdirect product factor
801C2C2×#243011yescharacteristic
802C2C2×#300711yescharacteristic
803C2C2×#301311yescharacteristic
804C2C2×#331111yescharacteristic
805C2C2×#332811yescharacteristic
806C2C2×#334911yescharacteristic
807C2C2×#335611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
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
2. C22×#485C2semidirect
3. C22×#470C2semidirect
5. #25558C2direct (N × H)
6. C2×#2058C2semidirect
7. C2×#2035C2semidirect
8. C2×#2024C2semidirect
9. C2×#2001C2semidirect
10. C2×#1878C2semidirect
11. C2×#1873C2semidirect
12. C2×#1872C2semidirect
14. C2×#1863C2semidirect
15. C2×#1854C2semidirect
16. C2×#1736C2semidirect
38. C2×#485C22semidirect
40. C2×#470C22semidirect
62. #2058C22semidirect
63. #2035C22semidirect
64. #2024C22semidirect
65. #2001C22semidirect
66. #1878C22semidirect
67. #1873C22semidirect
68. #1872C22semidirect
70. #1863C22semidirect
71. #1854C22semidirect
72. #1736C22semidirect
800. C2#25558direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5562
C22×#4852
C22×#4702
C2×#24172
#255582
C2×#20582
C2×#20352
C2×#20242
C2×#20012
C2×#18782
C2×#18732
C2×#18722
C2×#18702
C2×#18632
C2×#18542
C2×#17362