Finite Group Databasebeta

← #6389263

Subgroups — #6389263

Order 512.

2208 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2989C211yesmaximal, characteristic, complemented
2C2×#2988C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#23209C212yesmaximal, complemented
5#23205C212yesmaximal, complemented
6#23174C212yesmaximal, complemented
7#23150C212yesmaximal, complemented
8#22797C212yesmaximal, complemented
9#22750C212yesmaximal, complemented
10#22749C212yesmaximal, complemented
11#22648C212yesmaximal, complemented
12#22172C214yesmaximal, complemented
13#21847C211yesmaximal, characteristic, complemented
14#21847C211yesmaximal, characteristic, complemented
15#21489C214yesmaximal, complemented
16#20808C211yesmaximal, characteristic, complemented
17C2×#1767C211yesmaximal, characteristic, complemented
18C2×#532C411yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C2×C4×#41C2211yescharacteristic
21#2989—28no—
22#2988—28no—
23C2×#446C2212yes—
24C2×C8×Q8C2212yes—
25C2×#436C2212yes—
26C2×#435C2214yes—
27C2×#435C2214yes—
28C2×C8×D4C2212yes—
29C2×C8×D4C2214yes—
30C2×#432C2212yes—
31C2×#431C2212yes—
32C2×#431C2211yescharacteristic
33C2×#431C2211yescharacteristic
34C2×#423C2212yes—
35C22×C4⋊C8C2211yescharacteristic
36C22×C4⋊C8C2212yes—
37C22×C4⋊C8C2211yescharacteristic
38C22×#97C2212yes—
39C4×C4⋊Q8C411yescharacteristic
40C4×C4⋊Q8C2211yescharacteristic
41C4×#127C411yescharacteristic
42C4×#127C2211yescharacteristic
43C4×#124C411yescharacteristic
44C4×#124C411yescharacteristic
45C4×#124C2211yescharacteristic
46C4×#124C2211yescharacteristic
47C4×#121C412yes—
48C4×#121C412yes—
49C4×#121C2212yes—
50C4×#121C2212yes—
51#2297C411yescharacteristic
52#2297C411yescharacteristic
53#2293C412yes—
54#2293C412yes—
55#2285C411yescharacteristic
56C42×D4C2212yes—
57C42×D4C2212yes—
58C2×C43C2211yescharacteristic
59#1984C2212yes—
60#1984C2212yes—
61#1955C2214yes—
62#1954C2212yes—
63#1954C2212yes—
64#1940C2214yes—
65#1924C2214yes—
66#1924C2214yes—
67#1924C2214yes—
68#1923C2214yes—
69#1917C2214yes—
70#1916C2214yes—
71#1870C2214yes—
72#1869C2214yes—
73#1869C2214yes—
74#1869C2214yes—
75#1851C2214yes—
76#1850C2214yes—
77#1842C2211yescharacteristic
78#1842C2211yescharacteristic
79#1831C2211yescharacteristic
80#1831C2211yescharacteristic
81#1797C2212yes—
82#1797C2212yes—
83#1797C2212yes—
84#1797C2212yes—
85#1797C2212yes—
86#1797C2212yes—
87#1771C2214yes—
88#1767C2212yes—
89#1767C2212yes—
90#1767C2212yes—
91#1767C2212yes—
92C4×C4⋊C8C2212yes—
93C4×C4⋊C8C2212yes—
94#1753C2214yes—
95#1752C2214yes—
96C2×#336C2212yes—
97C22×#41C2×C411yescharacteristic
98C22×#41C2×C411yescharacteristic
99C22×M16C2314yes—
100C23×C8C2312yes—
101C23×C8C2314yes—
102C23×C8C2312yes—
103#532—28no—
104C2×C4⋊Q8C2×C411yescharacteristic
105C2×#127C2×C411yescharacteristic
106C2×#124C2×C411yescharacteristic
107C2×#124C2×C411yescharacteristic
108C2×#121C2×C412yes—
109C2×#121C2×C412yes—
110C4×#41—24no—
111C4×#41—24no—
112C4×#41—24no—
113C4×#41—24no—
114C2×C4×Q8C2×C411yescharacteristic
115C2×C4×Q8C2×C411yescharacteristic
116C2×C4×Q8C2311yescharacteristic
117C2×C4×Q8C2311yescharacteristic
118C2×C4×D4C2×C411yescharacteristic
119C2×C4×D4C2×C411yescharacteristic
120C2×C4×D4C2×C412yes—
121C2×C4×D4C2×C412yes—
122C2×C4×D4C2×C412yes—
123C2×C4×D4C2×C412yes—
124C2×C4×D4C2×C412yes—
125C2×C4×D4C2×C412yes—
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2311yescharacteristic
128C2×C4×D4C2312yes—
129C2×C4×D4C2312yes—
130C2×C4×D4C2312yes—
131C2×C4×D4C2312yes—
132C2×#117C2×C411yescharacteristic
133C2×#117C2×C411yescharacteristic
134C2×#117C2×C412yes—
135C2×#117C2×C412yes—
136C22×C42C2×C411yescharacteristic
137C22×C42C2×C411yescharacteristic
138C22×C42C2×C411yescharacteristic
139C22×C42C2×C411yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2312yes—
142C22×C42C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145#446—28no—
146C8×Q8—28no—
147#436—28no—
148#435—216no—
149#435—48no—
150C8×D4—216no—
151C8×D4—28no—
152#432—28no—
153#431—24no—
154#431—24no—
155#431—28no—
156#423—28no—
157C2×C4⋊C8—24no—
158C2×C4⋊C8—28no—
159C2×C4⋊C8D418yescomplemented
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2314yes—
168C2×C4⋊C8C2314yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2314yes—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×#97—44no—
183C2×#97C2314yes—
184C2×#97C2314yes—
185C2×#97C2314yes—
186C2×C4×C8C2314yes—
187C2×C4×C8C2312yes—
188C2×C4×C8C2312yes—
189#391C2×C411yescharacteristic
190#391C2×C411yescharacteristic
191#391C2×C411yescharacteristic
192#391C2×C411yescharacteristic
193#390C2×C412yes—
194#390C2×C412yes—
195#390C2×C411yescharacteristic
196#390C2×C411yescharacteristic
197#390C2×C412yes—
198#390C2×C412yes—
199#390C2×C411yescharacteristic
200#390C2×C411yescharacteristic
201#389C2×C412yes—
202#389C2×C412yes—
203#389C2×C412yes—
204#389C2×C412yes—
205#388C2×C412yes—
206#388C2×C412yes—
207#388C2×C412yes—
208#388C2×C412yes—
209#388C2×C412yes—
210#388C2×C412yes—
211#388C2×C412yes—
212#388C2×C412yes—
213#386C2×C412yes—
214#386C2×C412yes—
215#386C2×C412yes—
216#386C2×C412yes—
217#384C2×C411yescharacteristic
218#384C2×C411yescharacteristic
219#382C2×C411yescharacteristic
220#382C2×C411yescharacteristic
221#380C2×C412yes—
222#380C2×C412yes—
223C4×C4⋊C4C2×C412yes—
224C4×C4⋊C4C2×C412yes—
225C4×C4⋊C4C2×C412yes—
226C4×C4⋊C4C2×C412yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C22⋊C4C2×C412yes—
230C4×C22⋊C4C2×C412yes—
231C4×C22⋊C4C2×C412yes—
232C4×C22⋊C4C2×C412yes—
233C4×C22⋊C4C2×C412yes—
234C4×C22⋊C4C2×C412yes—
235C4×C22⋊C4C2×C412yes—
236C4×C22⋊C4C2×C412yes—
237C4×C22⋊C4C2312yes—
238C4×C22⋊C4C2312yes—
239C4×C22⋊C4C2312yes—
240C4×C22⋊C4C2312yes—
241C43C2×C411yescharacteristic
242C43C2×C411yescharacteristic
243C43C2×C411yescharacteristic
244C43C2×C411yescharacteristic
245C43C2311yescharacteristic
246C43C2311yescharacteristic
247C43C2311yescharacteristic
248C43C2311yescharacteristic
249#336C2312yes—
250#336C2312yes—
251#336C2312yes—
252#336C2312yes—
253#336C2314yes—
254#336C2314yes—
255#336C2314yes—
256#336C2314yes—
257#336C2314yes—
258#336C2314yes—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—24no—
262C2×#41—24no—
263C2×#41—24no—
264C2×#41M1618yescomplemented
265C22×Q8C22×C411yescharacteristic
266C22×Q8C22×C411yescharacteristic
267C22×D4C22×C412yes—
268C22×D4C22×C411yescharacteristic
269C22×D4C22×C412yes—
270C22×D4C22×C412yes—
271C22×D4C22×C412yes—
272C22×D4C22×C411yescharacteristic
273C23×C4C22×C412yes—
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C411yescharacteristic
277C23×C4C22×C411yescharacteristic
278C23×C4C22×C412yes—
279C23×C4C22×C412yes—
280C23×C4C22×C412yes—
281C23×C4C22×C411yescharacteristic
282C23×C4C22×C411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×M16—28no—
287C2×M16—44no—
288C2×M16—44no—
289C22×C8—24no—
290C22×C8—28no—
291C22×C8—42no—
292C22×C8—42no—
293C22×C8—42no—
294C22×C8—42no—
295C22×C8—44no—
296C22×C8—44no—
297C22×C8C2×D418yes—
298C22×C8C2412yes—
299C22×C8C2414yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2414yes—
304C4⋊Q8—24no—
305#127—24no—
306#124—24no—
307#124—24no—
308#121—28no—
309#121—28no—
310C4×Q8—24no—
311C4×Q8—24no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×D4—28no—
317C4×D4—28no—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—42no—
335C4×D4—42no—
336#117—24no—
337#117—24no—
338#117—28no—
339#117—28no—
340C2×C4⋊C4C22×C411yescharacteristic
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C22×C411yescharacteristic
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C4⋊C4C22×C412yes—
347C2×C4⋊C4C22×C412yes—
348C2×C4⋊C4C22×C412yes—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C22×C412yes—
351C2×C4⋊C4C22×C412yes—
352C2×C4⋊C4C22×C412yes—
353C2×C4⋊C4C22×C412yes—
354C2×C22⋊C4C22×C412yes—
355C2×C22⋊C4C22×C412yes—
356C2×C22⋊C4C22×C412yes—
357C2×C22⋊C4C22×C412yes—
358C2×C22⋊C4C22×C412yes—
359C2×C22⋊C4C22×C412yes—
360C2×C22⋊C4C22×C412yes—
361C2×C22⋊C4C22×C412yes—
362C2×C22⋊C4C22×C412yes—
363C2×C22⋊C4C22×C412yes—
364C2×C22⋊C4C22×C412yes—
365C2×C22⋊C4C22×C412yes—
366C2×C22⋊C4C22×C412yes—
367C2×C22⋊C4C22×C412yes—
368C2×C22⋊C4C22×C412yes—
369C2×C22⋊C4C22×C412yes—
370C2×C22⋊C4C22×C412yes—
371C2×C22⋊C4C22×C412yes—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—41no—
383C2×C42—41no—
384C2×C42C22×C412yes—
385C2×C42C22×C412yes—
386C2×C42C22×C411yescharacteristic
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C22×C412yes—
391C2×C42C22×C412yes—
392C2×C42C22×C411yescharacteristic
393C2×C42C22×C411yescharacteristic
394C2×C42C22×C411yescharacteristic
395C2×C42C22×C411yescharacteristic
396C2×C42C22×C411yescharacteristic
397C2×C42C22×C411yescharacteristic
398C2×C42C22×C411yescharacteristic
399C2×C42C22×C411yescharacteristic
400C2×C42C22×C411yescharacteristic
401C2×C42C22×C411yescharacteristic
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412C2×C42C2411yescharacteristic
413C2×C42C2412yes—
414C2×C42C2412yes—
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C4⋊C8—28no—
421C4⋊C8—28no—
422C4⋊C8—22no—
423C4⋊C8—22no—
424C4⋊C8—22no—
425C4⋊C8—22no—
426C4⋊C8—24no—
427C4⋊C8—24no—
428C4⋊C8—24no—
429C4⋊C8—24no—
430C4⋊C8—42no—
431C4⋊C8—42no—
432C4⋊C8C2×D418yes—
433C4⋊C8C2×D418yes—
434C22⋊C8—24no—
435C22⋊C8—24no—
436C22⋊C8—28no—
437C22⋊C8—28no—
438C22⋊C8—44no—
439C22⋊C8—44no—
440C22⋊C8—44no—
441C22⋊C8—44no—
442#97—28no—
443#97—28no—
444#97—44no—
445C4×C8—28no—
446C4×C8—24no—
447C4×C8—24no—
448#95C22×C412yes—
449#95C22×C412yes—
450#95C22×C412yes—
451#95C22×C412yes—
452#95C22×C412yes—
453#95C22×C412yes—
454#95C22×C412yes—
455#95C22×C412yes—
456#95C22×C412yes—
457#95C22×C412yes—
458#95C22×C412yes—
459#95C22×C412yes—
460C24C23×C412yes—
461C24C23×C412yes—
462C24C23×C411yescharacteristic
463#41—232no—
464#41—416no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8C2×M1614yes—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4C2×M1618yes—
488C2×D4C2×M1614yes—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C4×D414yes—
531C22×C4C4×D414yes—
532C22×C4C2×M1618yes—
533C22×C4C2×M1614yes—
534C22×C4#13114yes—
535C22×C4C23×C411yescharacteristic
536C22×C4C23×C411yescharacteristic
537C22×C4C23×C411yescharacteristic
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C412yes—
540C22×C4C23×C412yes—
541C22×C4C23×C412yes—
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C411yescharacteristic
547C22×C4C23×C411yescharacteristic
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C412yes—
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C22×D412yes—
555C22×C4C2×#4112yes—
556C22×C4C2511yescharacteristic
557M16—88no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—24no—
565C2×C8—24no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—24no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—48no—
576C2×C8—48no—
577C2×C8—88no—
578C2×C8C22×D418yes—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C42—24no—
612C42—24no—
613C42—24no—
614C42—24no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42C4×D414yes—
646C42C4×D414yes—
647C42C22×D412yes—
648C42C22×D412yes—
649C42C2×#4112yes—
650C42C2×#4112yes—
651C42H(5,𝔽2)12yes—
652C422−1+412yes—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23C2×C4×D412yes—
671C23C22×M1614yes—
672C23C22×M1612yes—
673C23C2×#13112yes—
674C23C24×C411yescharacteristic
675Q8—28no—
676Q8—44no—
677D4—216no—
678D4—28no—
679D4—48no—
680D4—48no—
681D4—48no—
682D4—44no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—216no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#435116yescomplemented
748C2×C4C2×C4×D412yes—
749C2×C4C2×C4×D412yes—
750C2×C4C2×C4×D412yes—
751C2×C4C2×C4×D412yes—
752C2×C4C2×C4×D412yes—
753C2×C4#52012yes—
754C2×C4#52012yes—
755C2×C4C22×M1614yes—
756C2×C4C22×M1612yes—
757C2×C4C22×M1612yes—
758C2×C4C2×#13112yes—
759C2×C4C2×#13112yes—
760C2×C4#56812yes—
761C2×C4#56812yes—
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×2−1+411yescharacteristic
766C2×C4#58511yescharacteristic
767C2×C4#58511yescharacteristic
768C8—28no—
769C8—42no—
770C8—42no—
771C8—42no—
772C8—42no—
773C8—44no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22C2×#43514yes—
795C22C22×C4×D411yescharacteristic
796C22C2×#52011yescharacteristic
797C22#342811yescharacteristic
798C22C23×M1611yescharacteristic
799C22C22×#13111yescharacteristic
800C22C2×#56811yescharacteristic
801C22C2×#56811yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—24no—
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4C2×#43514yes—
820C4C2×#43514yes—
821C4#349611yescharacteristic
822C4#349711yescharacteristic
823C4#350611yescharacteristic
824C4#350711yescharacteristic
825C2—24no—
826C2—44no—
827C2—82no—
828C2#3420611yescharacteristic
829C2C22×#43511yescharacteristic
830C2#6014411yescharacteristic
831C2#6026311yescharacteristic
832C2#6026811yescharacteristic
833C2#6028311yescharacteristic
834C2#6029411yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#532C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2989C2semidirect
2. C2×#2988C2semidirect
4. #23209C2semidirect
5. #23205C2semidirect
6. #23174C2semidirect
7. #23150C2semidirect
8. #22797C2semidirect
9. #22750C2semidirect
10. #22749C2semidirect
11. #22648C2semidirect
12. #22172C2semidirect
13. #21847C2semidirect
14. #21847C2semidirect
15. #21489C2semidirect
16. #20808C2semidirect
17. C2×#1767C2semidirect
159. C2×C4⋊C8D4semidirect
264. C2×#41M16semidirect
747. C2×C4#435semidirect

Maximal subgroups

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

subgroupindex
C2×#29892
C2×#29882
C4×#5322
#232092
#232052
#231742
#231502
#227972
#227502
#227492
#226482
#221722
#218472
#214892
#208082
C2×#17672