Finite Group Databasebeta

← C2×#17622 #6343464

Subgroups — C2×#17622 #6343464

Order 512.

3500 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#2973C211yesmaximal, characteristic, complemented
3C2×#2349C211yesmaximal, characteristic, complemented
4#17622C2116yesmaximal, direct product factor
5C2×#1520C211yesmaximal, characteristic, complemented
6C2×#1519C211yesmaximal, characteristic, complemented
7C2×#1513C212yesmaximal, complemented
8C2×#1512C212yesmaximal, complemented
9C2×#1504C212yesmaximal, complemented
10C2×#1509C212yesmaximal, complemented
11C22×#328C211yesmaximal, characteristic, complemented
12C22×#327C211yesmaximal, characteristic, complemented
13#3505—24no—
14#3505—24no—
15#3505C418yescomplemented
16#3505C2218yes—
17C2×#553—22no—
18C2×#553C412yescomplemented
19C2×#552C412yescomplemented
20C2×#551—22no—
21C2×#548C412yescomplemented
22C2×#546C412yescomplemented
23C2×#539—21no—
24C2×#538—21no—
25C2×#534—21no—
26C2×#529C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#518—21no—
31C22×C4×D4—21no—
32C22×C4×D4C2211yescharacteristic
33#2973—24no—
34#2973C2218yescomplemented
35C2×#435—22no—
36C2×#435—22no—
37C2×#432C2212yescomplemented
38C2×#407C2212yescomplemented
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41#2349—24no—
42#2349C2218yescomplemented
43C2×#389—21no—
44C2×#385—21no—
45C2×#385—21no—
46C2×#382C2211yescharacteristic, complemented
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic, complemented
49C2×C4×C4⋊C4C2211yescharacteristic, complemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic, complemented
52#1520C2218yescomplemented
53#1519C2218yescomplemented
54#1513C22116yescomplemented
55#1512C22116yescomplemented
56#1509C22116yescomplemented
57#1504C22116yescomplemented
58C2×#328C2212yescomplemented
59C2×#328C2212yescomplemented
60C2×#328C2218yescomplemented
61C2×#328C2212yescomplemented
62C2×#328C2212yescomplemented
63C2×#327C2212yes—
64C2×#327C2212yes—
65C2×#327C2212yes—
66C2×#327C2212yes—
67C2×#327C2218yescomplemented
68C22×#41C2×C412yescomplemented
69C23×Q8C2×C411yescharacteristic, complemented
70C23×D4—21no—
71C23×D4C2×C411yescharacteristic, complemented
72C23×D4D411yescharacteristic
73C24×C4—21no—
74C24×C4—21no—
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C22×M16—22no—
78C23×C8—21no—
79C23×C8—21no—
80#553—216no—
81#553—28no—
82#553—216no—
83#553C2×C4116yescomplemented
84#552—28no—
85#552C2×C4116yescomplemented
86#551—216no—
87#551—216no—
88#548—28no—
89#548C2×C4116yescomplemented
90#546—28no—
91#546C2×C4116yescomplemented
92#539—28no—
93#539—28no—
94#538—28no—
95#538—28no—
96#534—28no—
97#534—28no—
98#529—24no—
99#529—24no—
100#529C2×C418yescomplemented
101#529C2318yes—
102C2×#126—22no—
103C2×#126—22no—
104C2×#126—22no—
105C2×#125—22no—
106C2×#125C2×C412yescomplemented
107C2×#124—22no—
108C2×#124C2×C412yescomplemented
109#525—24no—
110#525—24no—
111#525C2×C418yescomplemented
112#525C2318yes—
113C2×#123—22no—
114C2×#123—22no—
115C2×#123—22no—
116C2×#123—22no—
117C2×#123—22no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8C2×C412yescomplemented
124C2×C22⋊Q8C2×C412yescomplemented
125C2×C22⋊Q8C2×C414yescomplemented
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2314yes—
128C2×#121—22no—
129C2×#121—22no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121—22no—
135C2×#121C2×C412yescomplemented
136C2×#121C2×C412yescomplemented
137C2×#121C2×C414yescomplemented
138C2×#121C2312yes—
139C2×#121C2314yes—
140C2×#120—22no—
141C2×#120—22no—
142#518—28no—
143#518—28no—
144C2×C4×Q8C2×C412yescomplemented
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—28no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—48no—
152C2×C4×D4C2×C412yes—
153C2×C4×D4C2×C412yes—
154C2×C4×D4C2×C414yes—
155C2×C4×D4C2×C412yescomplemented
156C2×C4×D4D412yes—
157C2×C4×D4D412yes—
158C2×C4×D4D414yes—
159C2×C4×D4D414yes—
160C2×C4×D4C2314yes—
161C2×#117—22no—
162C2×#117—22no—
163C2×#117C2×C412yescomplemented
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4C2×C411yescharacteristic, complemented
170C22×C4⋊C4C2×C411yescharacteristic, complemented
171C22×C4⋊C4D411yescharacteristic
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—22no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4D411yescharacteristic
178C22×C22⋊C4D411yescharacteristic
179C22×C42—21no—
180C22×C42C2311yescharacteristic
181#435—216no—
182#435—216no—
183#432—24no—
184#432C2318yescomplemented
185C2×C4⋊C8—22no—
186#407—24no—
187#407C2318yescomplemented
188C2×C22⋊C8—21no—
189C2×C22⋊C8—21no—
190C2×C22⋊C8—22no—
191C2×C22⋊C8—22no—
192C2×C22⋊C8—22no—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2314yes—
196C2×C22⋊C8C2314yes—
197C2×#97—22no—
198#389—28no—
199#385—28no—
200#385—28no—
201#382—22no—
202#382C2314yescomplemented
203#380—22no—
204#380—22no—
205#380C2314yes—
206#380C2314yescomplemented
207C4×C4⋊C4—22no—
208C4×C4⋊C4C2314yescomplemented
209C2×#95—22no—
210C2×#95—22no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95C2314yes—
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2314yescomplemented
220#328C2318yescomplemented
221#328C2318yescomplemented
222#328C2318yescomplemented
223#328C2318yescomplemented
224#327C2318yes—
225#327C2318yes—
226#327C2318yes—
227#327C2318yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C25C2×D411yescharacteristic
231C2×#41—24no—
232C2×#41—84no—
233C2×#41C22×C418yescomplemented
234C22×Q8—21no—
235C22×Q8—22no—
236C22×Q8—82no—
237C22×Q8C22×C412yes—
238C22×Q8C22×C414yescomplemented
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4C22⋊C412yes—
253C22×D4C22⋊C412yes—
254C22×D4C22⋊C414yes—
255C22×D4C22×C412yes—
256C22×D4C22×C414yescomplemented
257C22×D4C2×D414yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—82no—
274C23×C4—82no—
275C23×C4—82no—
276C23×C4—82no—
277C23×C4C22×C411yescharacteristic
278C23×C4C22×C411yescharacteristic
279C23×C4C22×C412yes—
280C23×C4C22×C412yes—
281C23×C4C22×C412yes—
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C2×M16—28no—
297C2×M16—84no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—24no—
301C22×C8—24no—
302C22×C8—82no—
303C22×C8—82no—
304#126—216no—
305#126—216no—
306#126—28no—
307#126—28no—
308#125—216no—
309#125—24no—
310#125C22×C418yescomplemented
311#124—216no—
312#124—24no—
313#124C22×C418yescomplemented
314#123—216no—
315#123—28no—
316#123—28no—
317#123—28no—
318#123—28no—
319#123—216no—
320#123—216no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—216no—
330C22⋊Q8C22×C414yes—
331C22⋊Q8C22×C418yescomplemented
332C22⋊Q8C22×C418yescomplemented
333C22⋊Q8C2414yes—
334#121—216no—
335#121—216no—
336#121—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—22no—
341#121—22no—
342#121—24no—
343#121—24no—
344#121—216no—
345#121C22×C414yes—
346#121C22×C418yescomplemented
347#121C22×C418yescomplemented
348#121C2414yes—
349#120—28no—
350#120—28no—
351#120—216no—
352C4×Q8—24no—
353C4×Q8C22×C418yescomplemented
354C4×D4—28no—
355C4×D4—28no—
356C4×D4—28no—
357C4×D4—28no—
358C4×D4—28no—
359C4×D4—28no—
360C4×D4—216no—
361C4×D4—216no—
362C4×D4—24no—
363C4×D4—432no—
364C4×D4C22⋊C418yes—
365C4×D4C22⋊C418yes—
366C4×D4C22⋊C418yes—
367C4×D4C22⋊C418yes—
368C4×D4C22×C418yes—
369C4×D4C22×C418yes—
370C4×D4C22×C418yescomplemented
371C4×D4C2×D418yes—
372C4×D4C2×D418yes—
373#117—24no—
374#117—216no—
375#117—28no—
376#117—28no—
377#117C22×C418yescomplemented
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—82no—
397C2×C4⋊C4—82no—
398C2×C4⋊C4C22⋊C412yes—
399C2×C4⋊C4C22⋊C412yes—
400C2×C4⋊C4C22⋊C414yes—
401C2×C4⋊C4C22×C412yes—
402C2×C4⋊C4C22×C412yes—
403C2×C4⋊C4C22×C414yescomplemented
404C2×C4⋊C4C22×C414yescomplemented
405C2×C4⋊C4C2×D414yes—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—216no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4C22⋊C412yes—
426C2×C22⋊C4C22⋊C412yes—
427C2×C22⋊C4C22⋊C414yes—
428C2×C22⋊C4C22⋊C412yes—
429C2×C22⋊C4C22⋊C412yes—
430C2×C22⋊C4C22⋊C414yes—
431C2×C22⋊C4C2×D414yes—
432C2×C22⋊C4C2×D414yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—44no—
437C2×C42C22×C412yes—
438C2×C42C22×C412yes—
439C2×C42C2×D412yes—
440C2×C42C2×D412yes—
441C2×C42C2×D412yes—
442C2×C42C2412yes—
443C4⋊C8—28no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446C22⋊C8—24no—
447C22⋊C8—24no—
448C22⋊C8—28no—
449C22⋊C8C2414yes—
450C22⋊C8C2414yes—
451#97—28no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—21no—
459#95C2412yes—
460#95C2412yes—
461#95C2412yes—
462#95C2412yes—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—24no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—44no—
472C24—82no—
473C24—82no—
474C24C2×C22⋊C412yes—
475C24C2×C22⋊C411yescharacteristic
476C24C2×C22⋊C411yescharacteristic
477C24C2×C22⋊C412yes—
478C24C2×C22⋊C412yes—
479C24AGL(1,ℤ/8)14yes—
480C24#13714yes—
481C24C22×D411yescharacteristic
482C24C22×D412yes—
483C24C22×D412yes—
484#41—88no—
485#41—88no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—44no—
489C2×Q8—82no—
490C2×Q8—84no—
491C2×Q8—84no—
492C2×Q8C23×C414yes—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—24no—
499C2×D4—28no—
500C2×D4—24no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—416no—
512C2×D4—82no—
513C2×D4—84no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4C2×C22⋊C418yes—
518C2×D4C2×C22⋊C418yes—
519C2×D4C23×C414yes—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—44no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—48no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—48no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—816no—
576C22×C4—816no—
577C22×C4C2×C22⋊C412yes—
578C22×C4C2×C22⋊C412yes—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C411yescharacteristic
582C22×C4C2×C22⋊C411yescharacteristic
583C22×C4C2×C22⋊C412yes—
584C22×C4C2×C22⋊C412yes—
585C22×C4C2×C22⋊C412yes—
586C22×C4C2×C22⋊C412yes—
587C22×C4C2×C22⋊C412yes—
588C22×C4C2×C22⋊C412yes—
589C22×C4C2×C22⋊C412yes—
590C22×C4C2×C22⋊C414yes—
591C22×C4C2×C22⋊C414yes—
592C22×C4C23×C411yescharacteristic
593C22×C4C23×C411yescharacteristic
594C22×C4C23×C412yes—
595C22×C4C23×C412yes—
596C22×C4C23×C414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C2511yescharacteristic
608M16—88no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—44no—
612C2×C8—44no—
613C2×C8—84no—
614C2×C8—84no—
615C4⋊C4—24no—
616C4⋊C4—28no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—24no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C4⋊C4C2×C22⋊C418yes—
631C4⋊C4C2×C22⋊C418yes—
632C4⋊C4C23×C414yes—
633C4⋊C4C23×C414yes—
634C22⋊C4—28no—
635C22⋊C4—24no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—24no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4C2×C22⋊C418yes—
649C22⋊C4C2×C22⋊C418yes—
650C22⋊C4C2×C22⋊C418yes—
651C22⋊C4C2×C22⋊C418yes—
652C42—28no—
653C42—28no—
654C42—48no—
655C42C2×C22⋊C414yes—
656C42C2×C22⋊C414yes—
657C42C23×C414yes—
658C42C22×D414yes—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—48no—
679C23—42no—
680C23—42no—
681C23—48no—
682C23—48no—
683C23—48no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—48no—
688C23—84no—
689C23—84no—
690C23—168no—
691C23#41714yes—
692C23#41714yes—
693C23#41718yes—
694C23C22×C22⋊C414yes—
695C23C22×C22⋊C412yes—
696C23C22×C22⋊C411yescharacteristic
697C23C22×C22⋊C412yes—
698C23C22×C22⋊C411yescharacteristic
699C23C2×AGL(1,ℤ/8)12yes—
700C23C2×AGL(1,ℤ/8)14yes—
701C23C2×#13712yes—
702C23C2×#13714yes—
703C23C23×D411yescharacteristic
704Q8—44no—
705Q8—44no—
706Q8—84no—
707D4—216no—
708D4—216no—
709D4—44no—
710D4—44no—
711D4—48no—
712D4—416no—
713D4—44no—
714D4—44no—
715D4—84no—
716D4—88no—
717D4—88no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—48no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—816no—
775C2×C4—816no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4C22×C22⋊C414yes—
780C2×C4C22×C22⋊C414yes—
781C2×C4C22×C22⋊C411yescharacteristic
782C2×C4C22×C22⋊C411yescharacteristic
783C2×C4C22×C22⋊C414yes—
784C2×C4C22×C22⋊C412yes—
785C2×C4C22×C22⋊C412yes—
786C2×C4C24×C411yescharacteristic
787C2×C4C23×D411yescharacteristic
788C8—44no—
789C8—44no—
790C22—21no—
791C22—21no—
792C22—22no—
793C22—22no—
794C22—21no—
795C22—21no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—24no—
800C22—28no—
801C22—28no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—44no—
806C22—44no—
807C22—48no—
808C22—44no—
809C22—48no—
810C22—44no—
811C22—48no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—88no—
816C22—168no—
817C22#288312yes—
818C22C2×#41712yes—
819C22C2×#41714yes—
820C22C2×#41714yes—
821C22C2×#41712yes—
822C22#290112yes—
823C22C23×C22⋊C411yescharacteristic
824C22C22×AGL(1,ℤ/8)11yescharacteristic
825C22C22×#13711yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—24no—
831C4—22no—
832C4—22no—
833C4—24no—
834C4—24no—
835C4—44no—
836C4—44no—
837C4—44no—
838C4—44no—
839C4—82no—
840C4—82no—
841C4—82no—
842C2—21no—
843C2—22no—
844C2—21no—
845C2—24no—
846C2—24no—
847C2—44no—
848C2—84no—
849C2#1762214yesdirect product factor
850C2C2×#288311yescharacteristic
851C2C22×#41711yescharacteristic
852C2C2×#290111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2973C2semidirect
3. C2×#2349C2semidirect
4. #17622C2direct (N × H)
5. C2×#1520C2semidirect
6. C2×#1519C2semidirect
7. C2×#1513C2semidirect
8. C2×#1512C2semidirect
9. C2×#1504C2semidirect
10. C2×#1509C2semidirect
11. C22×#328C2semidirect
12. C22×#327C2semidirect
15. #3505C4semidirect
18. C2×#553C4semidirect
19. C2×#552C4semidirect
21. C2×#548C4semidirect
22. C2×#546C4semidirect
34. #2973C22semidirect
37. C2×#432C22semidirect
38. C2×#407C22semidirect
42. #2349C22semidirect
46. C2×#382C22semidirect
48. C2×#380C22semidirect
49. C2×C4×C4⋊C4C22semidirect
51. C22×#95C22semidirect
52. #1520C22semidirect
53. #1519C22semidirect
54. #1513C22semidirect
55. #1512C22semidirect
56. #1509C22semidirect
57. #1504C22semidirect
58. C2×#328C22semidirect
59. C2×#328C22semidirect
60. C2×#328C22semidirect
61. C2×#328C22semidirect
62. C2×#328C22semidirect
67. C2×#327C22semidirect
68. C22×#41C2×C4semidirect
69. C23×Q8C2×C4semidirect
71. C23×D4C2×C4semidirect
83. #553C2×C4semidirect
85. #552C2×C4semidirect
89. #548C2×C4semidirect
91. #546C2×C4semidirect
100. #529C2×C4semidirect
106. C2×#125C2×C4semidirect
108. C2×#124C2×C4semidirect
111. #525C2×C4semidirect
123. C2×C22⋊Q8C2×C4semidirect
124. C2×C22⋊Q8C2×C4semidirect
125. C2×C22⋊Q8C2×C4semidirect
135. C2×#121C2×C4semidirect
136. C2×#121C2×C4semidirect
137. C2×#121C2×C4semidirect
144. C2×C4×Q8C2×C4semidirect
155. C2×C4×D4C2×C4semidirect
163. C2×#117C2×C4semidirect
169. C22×C4⋊C4C2×C4semidirect
170. C22×C4⋊C4C2×C4semidirect
184. #432C23semidirect
187. #407C23semidirect
202. #382C23semidirect
206. #380C23semidirect
208. C4×C4⋊C4C23semidirect
219. C2×#95C23semidirect
220. #328C23semidirect
221. #328C23semidirect
222. #328C23semidirect
223. #328C23semidirect
233. C2×#41C22×C4semidirect
238. C22×Q8C22×C4semidirect
256. C22×D4C22×C4semidirect
310. #125C22×C4semidirect
313. #124C22×C4semidirect
331. C22⋊Q8C22×C4semidirect
332. C22⋊Q8C22×C4semidirect
346. #121C22×C4semidirect
347. #121C22×C4semidirect
353. C4×Q8C22×C4semidirect
370. C4×D4C22×C4semidirect
377. #117C22×C4semidirect
403. C2×C4⋊C4C22×C4semidirect
404. C2×C4⋊C4C22×C4semidirect
849. C2#17622direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#29732
C2×#23492
#176222
C2×#15202
C2×#15192
C2×#15132
C2×#15122
C2×#15042
C2×#15092
C22×#3282
C22×#3272