Finite Group Databasebeta

← #6409010

Subgroups — #6409010

Order 512.

1984 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#123C211yesmaximal, characteristic
2#23322C214yesmaximal, complemented
3#22908C214yesmaximal, complemented
4#22627C212yesmaximal, complemented
5#22554C212yesmaximal, complemented
6#22554C212yesmaximal, complemented
7D4×C22⋊C8C212yesmaximal
8#22367C214yesmaximal, complemented
9#22065C214yesmaximal, complemented
10#21955C211yesmaximal, characteristic, complemented
11#21930C211yesmaximal, characteristic, complemented
12#21912C211yesmaximal, characteristic, complemented
13#21906C211yesmaximal, characteristic, complemented
14#20715C211yesmaximal, characteristic, complemented
15C2×#1797C211yesmaximal, characteristic, complemented
16C22×#123C411yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×C8×D4C2214yes—
20C2×#432C2212yes—
21C2×#432C2212yescomplemented
22C22×C4⋊C8C2212yescomplemented
23C22×C22⋊C8C2212yes—
24C22×C22⋊C8C2212yes—
25C4×#123C412yes—
26C4×#123C412yes—
27C4×#123C412yes—
28C4×#123C412yes—
29C4×#123C2212yes—
30C4×#123C2212yes—
31C4×#123C2212yes—
32C4×#123C2212yes—
33C2×#388C411yescharacteristic
34C2×#388C411yescharacteristic
35C2×#387C411yescharacteristic
36C2×#387C411yescharacteristic
37C2×#386C411yescharacteristic
38C2×#385C411yescharacteristic
39C2×#381C411yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45#1954C2214yes—
46#1940C2214yescomplemented
47#1940C2214yescomplemented
48#1940C2214yescomplemented
49#1924C2214yescomplemented
50#1924C2214yescomplemented
51#1924C2214yescomplemented
52#1924C2214yescomplemented
53#1924C2214yescomplemented
54#1924C2214yescomplemented
55#1917C2214yescomplemented
56#1916C2214yescomplemented
57#1916C2214yescomplemented
58#1916C2214yescomplemented
59#1869C2214yes—
60#1869C2214yes—
61#1850C2214yescomplemented
62#1850C2214yescomplemented
63#1850C2214yescomplemented
64#1850C2214yescomplemented
65#1817C2212yes—
66#1817C2212yescomplemented
67#1797C2212yes—
68#1797C2212yes—
69#1797C2212yes—
70#1797C2211yescharacteristic
71#1797C2211yescharacteristic
72#1797C2211yescharacteristic
73#1797C2211yescharacteristic
74#1797C2212yescomplemented
75#1797C2212yescomplemented
76#1797C2212yescomplemented
77#1779C2212yes—
78#1779C2212yes—
79#1771C2214yescomplemented
80#1752C2214yescomplemented
81#1752C2214yescomplemented
82#1749C2212yes—
83#1749C2212yes—
84#1749C2212yescomplemented
85C4×C22⋊C8C2212yes—
86C2×#336C2212yescomplemented
87C23×D4C2×C411yescharacteristic
88C24×C4C2×C411yescharacteristic
89C24×C4C2×C411yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C23×C8C2314yes—
93C23×C8C2314yes—
94C2×#123—28no—
95C2×#123C2×C412yes—
96C2×#123C2×C412yes—
97C2×#123C2×C412yes—
98C2×#123C2×C412yes—
99C2×C4×D4—44no—
100C2×C4×D4C2×C412yes—
101C2×C4×D4C2×C412yes—
102C2×C4×D4C2312yes—
103C2×C4×D4C2312yes—
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C411yescharacteristic
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C42—44no—
118C22×C42C2×C411yescharacteristic
119C22×C42C2×C411yescharacteristic
120C22×C42C2×C411yescharacteristic
121C22×C42C2×C411yescharacteristic
122C22×C42C2×C411yescharacteristic
123C22×C42C2×C411yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C8×D4—48no—
134#432—44no—
135#432—44no—
136C2×C4⋊C8—44no—
137C2×C4⋊C8C2312yes—
138C2×C4⋊C8C2312yes—
139C2×C4⋊C8C2314yes—
140C2×C4⋊C8C2312yes—
141C2×C4⋊C8C2312yes—
142C2×C4⋊C8C2314yes—
143C2×C4⋊C8C2314yes—
144C2×C4⋊C8C2314yes—
145C2×C22⋊C8—44no—
146C2×C22⋊C8—44no—
147C2×C22⋊C8C2312yes—
148C2×C22⋊C8C2312yes—
149C2×C22⋊C8C2312yes—
150C2×C22⋊C8C2312yes—
151C2×C22⋊C8C2314yes—
152C2×C22⋊C8C2314yes—
153C2×C22⋊C8C2314yes—
154C2×C22⋊C8C2314yes—
155C2×C22⋊C8C2314yes—
156C2×C22⋊C8C2314yes—
157C2×#97C2314yes—
158C2×#97C2314yes—
159C2×#97C2314yes—
160C2×C4×C8C2314yes—
161#388C2×C412yes—
162#388C2×C412yes—
163#388C2×C412yes—
164#388C2×C412yes—
165#388C2×C412yes—
166#388C2×C412yes—
167#388C2×C412yes—
168#388C2×C412yes—
169#387C2×C412yes—
170#387C2×C412yes—
171#387C2×C412yes—
172#387C2×C412yes—
173#387C2×C412yes—
174#387C2×C412yes—
175#387C2×C412yes—
176#387C2×C412yes—
177#386C2×C412yes—
178#386C2×C412yes—
179#386C2×C412yes—
180#386C2×C412yes—
181#385C2×C412yes—
182#385C2×C412yes—
183#385C2×C412yes—
184#385C2×C412yes—
185#381C2×C412yes—
186#381C2×C412yes—
187#381C2×C412yes—
188#381C2×C412yes—
189C4×C4⋊C4C2×C412yes—
190C4×C4⋊C4C2×C412yes—
191C4×C4⋊C4C2×C412yes—
192C4×C4⋊C4C2×C412yes—
193C4×C4⋊C4C2312yes—
194C4×C4⋊C4C2312yes—
195C4×C4⋊C4C2312yes—
196C4×C4⋊C4C2312yes—
197C4×C22⋊C4C2×C412yes—
198C4×C22⋊C4C2×C412yes—
199C4×C22⋊C4C2×C412yes—
200C4×C22⋊C4C2×C412yes—
201C4×C22⋊C4C2×C412yes—
202C4×C22⋊C4C2×C412yes—
203C4×C22⋊C4C2312yes—
204C4×C22⋊C4C2312yes—
205C4×C22⋊C4C2312yes—
206C4×C22⋊C4C2312yes—
207C4×C22⋊C4C2312yes—
208C4×C22⋊C4C2312yes—
209C2×#95C2×C411yescharacteristic
210C2×#95C2×C411yescharacteristic
211C2×#95C2×C411yescharacteristic
212C2×#95C2×C411yescharacteristic
213C2×#95C2×C411yescharacteristic
214C2×#95C2×C411yescharacteristic
215C2×#95C2×C411yescharacteristic
216C2×#95C2×C411yescharacteristic
217C2×#95C2×C411yescharacteristic
218C2×#95C2×C411yescharacteristic
219#336C2312yes—
220#336C2314yes—
221#336C2312yes—
222#336C2312yes—
223#336C2312yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227#336C2314yes—
228#336C2314yes—
229#336C2314yes—
230#336C2314yes—
231C25C22×C411yescharacteristic
232C25C22×C411yescharacteristic
233C22×D4—42no—
234C22×D4—42no—
235C22×D4M1618yes—
236C22×D4C22×C412yes—
237C22×D4C22×C412yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C22×C411yescharacteristic
255C23×C4C22×C411yescharacteristic
256C23×C4C22×C411yescharacteristic
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C22×C411yescharacteristic
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C412yes—
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C22×C8—28no—
280C22×C8—44no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8C2414yes—
286C22×C8C2414yes—
287C22×C8C2414yes—
288C22×C8C2414yes—
289#123—28no—
290#123—28no—
291#123—28no—
292#123—28no—
293C4×D4—28no—
294C4×D4—44no—
295C4×D4—44no—
296C4×D4—44no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4C22×C412yes—
303C2×C4⋊C4C22×C412yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C4⋊C4C22×C412yes—
311C2×C4⋊C4C22×C412yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C22×C412yes—
321C2×C22⋊C4C22×C412yes—
322C2×C22⋊C4C22×C412yes—
323C2×C22⋊C4C22×C412yes—
324C2×C22⋊C4C22×C412yes—
325C2×C22⋊C4C22×C412yes—
326C2×C22⋊C4C22×C412yes—
327C2×C22⋊C4C22×C412yes—
328C2×C22⋊C4C22×C412yes—
329C2×C22⋊C4C22×C412yes—
330C2×C22⋊C4C22×C412yes—
331C2×C22⋊C4C22×C412yes—
332C2×C22⋊C4C22×C412yes—
333C2×C22⋊C4C22×C412yes—
334C2×C22⋊C4C22×C412yes—
335C2×C22⋊C4C22×C412yes—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42—42no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42C22×C412yes—
353C2×C42C22×C411yescharacteristic
354C2×C42C22×C411yescharacteristic
355C2×C42C22×C411yescharacteristic
356C2×C42C22×C411yescharacteristic
357C2×C42C22×C412yes—
358C2×C42C22×C412yes—
359C2×C42C22×C411yescharacteristic
360C2×C42C22×C411yescharacteristic
361C2×C42C22×C411yescharacteristic
362C2×C42C22×C411yescharacteristic
363C2×C42C22×C411yescharacteristic
364C2×C42C22×C411yescharacteristic
365C2×C42C22×C411yescharacteristic
366C2×C42C22×C411yescharacteristic
367C2×C42C2412yes—
368C2×C42C2412yes—
369C2×C42C2412yes—
370C2×C42C2411yescharacteristic
371C2×C42C2411yescharacteristic
372C2×C42C2411yescharacteristic
373C2×C42C2411yescharacteristic
374C4⋊C8—42no—
375C4⋊C8—44no—
376C4⋊C8—42no—
377C4⋊C8—44no—
378C4⋊C8—44no—
379C4⋊C8—42no—
380C4⋊C8—42no—
381C4⋊C8—44no—
382C22⋊C8—24no—
383C22⋊C8—24no—
384C22⋊C8—24no—
385C22⋊C8—28no—
386C22⋊C8—24no—
387C22⋊C8—44no—
388C22⋊C8—44no—
389C22⋊C8—44no—
390C22⋊C8—44no—
391C22⋊C8—44no—
392#97—44no—
393#97—44no—
394#97—44no—
395C4×C8—44no—
396#95C22×C412yes—
397#95C22×C412yes—
398#95C22×C412yes—
399#95C22×C412yes—
400#95C22×C412yes—
401#95C22×C412yes—
402#95C22×C412yes—
403#95C22×C412yes—
404#95C22×C412yes—
405#95C22×C412yes—
406#95C22×C412yes—
407#95C22×C412yes—
408#95C22×C412yes—
409#95C22×C412yes—
410#95C22×C412yes—
411#95C22×C412yes—
412#95C22×C412yes—
413#95C22×C412yes—
414#95C22×C412yes—
415#95C22×C412yes—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24C2×M1614yes—
429C24C2×M1614yes—
430C24C23×C412yes—
431C24C23×C411yescharacteristic
432C24C23×C411yescharacteristic
433C24C23×C411yescharacteristic
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—416no—
439C2×D4C2×M1618yes—
440C2×D4C2×M1618yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—41no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—84no—
526C22×C4—84no—
527C22×C4C2×M1614yes—
528C22×C4#13114yes—
529C22×C4C23×C412yes—
530C22×C4C23×C412yes—
531C22×C4C23×C412yes—
532C22×C4C23×C411yescharacteristic
533C22×C4C23×C411yescharacteristic
534C22×C4C23×C411yescharacteristic
535C22×C4C23×C411yescharacteristic
536C22×C4C23×C411yescharacteristic
537C22×C4C23×C411yescharacteristic
538C22×C4C23×C412yes—
539C22×C4C23×C412yes—
540C22×C4C23×C412yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C411yescharacteristic
547C22×C4H(5,𝔽2)14yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C42−1+412yes—
550C22×C4C2511yescharacteristic
551C2×C8—24no—
552C2×C8—24no—
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—88no—
564C2×C8—88no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—24no—
596C42—24no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—24no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—42no—
613C42—42no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—21no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—28no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—82no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23#51812yes—
649C23#52012yes—
650C23C22×M1614yes—
651C23C22×M1612yes—
652C23C22×M1612yes—
653C23C22×M1612yes—
654C23C2×#13112yes—
655C23#56812yes—
656C23C24×C411yescharacteristic
657D4—216no—
658D4—48no—
659C2×C4—28no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—84no—
734C2×C4—82no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4#51812yes—
739C2×C4#52012yes—
740C2×C4C22×M1614yes—
741C2×C4C2×#13112yes—
742C2×C4C2×#13112yes—
743C2×C4#56812yes—
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×H(5,𝔽2)12yes—
746C2×C4C2×2−1+411yescharacteristic
747C2×C4#58512yes—
748C8—44no—
749C8—44no—
750C8—44no—
751C8—44no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—24no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—24no—
770C22—416no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—88no—
780C22#297314yes—
781C22#299014yes—
782C22C2×#51811yescharacteristic
783C22C2×#52011yescharacteristic
784C22#342811yescharacteristic
785C22C23×M1611yescharacteristic
786C22C22×#13111yescharacteristic
787C22C2×#56811yescharacteristic
788C22C2×#56811yescharacteristic
789C4—24no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4#353412yes—
808C4#353512yes—
809C2—24no—
810C2—24no—
811C2—42no—
812C2—44no—
813C2#3437611yescharacteristic
814C2C2×#297311yescharacteristic
815C2#6023311yescharacteristic
816C2C2×#299011yescharacteristic
817C2#6026411yescharacteristic
818C2#6028211yescharacteristic
819C2#6029011yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC23×D4C2×C4
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
2. #23322C2semidirect
3. #22908C2semidirect
4. #22627C2semidirect
5. #22554C2semidirect
6. #22554C2semidirect
8. #22367C2semidirect
9. #22065C2semidirect
10. #21955C2semidirect
11. #21930C2semidirect
12. #21912C2semidirect
13. #21906C2semidirect
14. #20715C2semidirect
15. C2×#1797C2semidirect
21. C2×#432C22semidirect
22. C22×C4⋊C8C22semidirect
46. #1940C22semidirect
47. #1940C22semidirect
48. #1940C22semidirect
49. #1924C22semidirect
50. #1924C22semidirect
51. #1924C22semidirect
52. #1924C22semidirect
53. #1924C22semidirect
54. #1924C22semidirect
55. #1917C22semidirect
56. #1916C22semidirect
57. #1916C22semidirect
58. #1916C22semidirect
61. #1850C22semidirect
62. #1850C22semidirect
63. #1850C22semidirect
64. #1850C22semidirect
66. #1817C22semidirect
74. #1797C22semidirect
75. #1797C22semidirect
76. #1797C22semidirect
79. #1771C22semidirect
80. #1752C22semidirect
81. #1752C22semidirect
84. #1749C22semidirect
86. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1232
#233222
#229082
#226272
#225542
D4×C22⋊C82
#223672
#220652
#219552
#219302
#219122
#219062
#207152
C2×#17972