Finite Group Databasebeta

← #6389841

Subgroups — #6389841

Order 512.

2682 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2974C211yesmaximal, characteristic, complemented
2C2×#2973C211yesmaximal, characteristic, complemented
3C2×#2397C211yesmaximal, characteristic
4#23178C214yesmaximal, complemented
5#23177C214yesmaximal, complemented
6#22401C212yesmaximal, complemented
7#22399C212yesmaximal, complemented
8#22399C212yesmaximal, complemented
9D4×C22⋊C8C212yesmaximal, complemented
10#22267C214yesmaximal, complemented
11#21788C211yesmaximal, characteristic, complemented
12#21786C211yesmaximal, characteristic, complemented
13#21685C214yesmaximal, complemented
14#20814C211yesmaximal, characteristic, complemented
15#20469C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2212yes—
19C22×C4×D4C2212yes—
20#2974—28no—
21#2973—28no—
22C2×#436C2212yescomplemented
23C2×#436C2214yescomplemented
24C2×#435C2214yescomplemented
25C2×#435C2214yescomplemented
26C2×#435C2214yescomplemented
27C2×#435C2214yescomplemented
28C2×#435C2214yescomplemented
29C2×C8×D4C2212yescomplemented
30C2×C8×D4C2214yescomplemented
31C2×#432C2211yescharacteristic
32C2×#432C2211yescharacteristic
33C2×#431C2211yescharacteristic
34C2×#431C2211yescharacteristic
35C2×#407C2212yes—
36C2×#407C2212yes—
37C22×C22⋊C8C2212yes—
38C22×C22⋊C8C2212yes—
39#2397C412yes—
40#2397C412yes—
41#2397C412yes—
42#2397C412yes—
43#2397C2212yes—
44#2397C2212yes—
45#2397C2212yes—
46#2397C2212yes—
47C2×#399C412yes—
48C2×#399C411yescharacteristic
49C2×#399C411yescharacteristic
50C2×#392C412yes—
51C2×#392C411yescharacteristic
52C2×#392C411yescharacteristic
53C2×#376C2211yescharacteristic
54#1955C2212yescomplemented
55#1955C2212yescomplemented
56#1955C2214yescomplemented
57#1955C2214yescomplemented
58#1954C2214yescomplemented
59#1954C2214yescomplemented
60#1954C2214yescomplemented
61#1954C2214yescomplemented
62#1954C2214yescomplemented
63#1870C2214yescomplemented
64#1870C2214yescomplemented
65#1870C2214yescomplemented
66#1870C2214yescomplemented
67#1869C2214yescomplemented
68#1869C2214yescomplemented
69#1869C2214yescomplemented
70#1869C2214yescomplemented
71#1843C2212yescomplemented
72#1832C2212yescomplemented
73#1797C2212yes—
74#1797C2212yes—
75#1779C2211yescharacteristic
76#1779C2211yescharacteristic
77#1779C2211yescharacteristic
78#1779C2211yescharacteristic
79#1779C2212yes—
80#1779C2212yes—
81#1768C2214yescomplemented
82#1768C2214yescomplemented
83#1749C2212yes—
84C4×C22⋊C8C2212yes—
85#1746C2212yescomplemented
86#1726C2212yescomplemented
87C23×D4C2×C411yescharacteristic
88C23×D4C2×C412yes—
89C23×D4C2×C411yescharacteristic
90C23×D4C2×C412yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C22×M16C2314yes—
95C22×M16C2314yes—
96C23×C8C2314yes—
97C23×C8C2314yes—
98C2×C4×D4—24no—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—48no—
103C2×C4×D4—48no—
104C2×C4×D4C2×C411yescharacteristic
105C2×C4×D4C2×C412yes—
106C2×C4×D4C2×C412yes—
107C2×C4×D4C2×C412yes—
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4C2×C412yes—
110C2×C4×D4C2×C412yes—
111C2×C4×D4C2×C412yes—
112C2×C4×D4C2×C412yes—
113C2×C4×D4C2×C412yes—
114C2×C4×D4C2×C412yes—
115C2×C4×D4C2×C412yes—
116C2×C4×D4C2×C412yes—
117C2×C4×D4C2311yescharacteristic
118C2×C4×D4C2312yes—
119C2×C4×D4C2312yes—
120C2×C4×D4C2312yes—
121C2×C4×D4C2312yes—
122C2×C4×D4C2312yes—
123C2×C4×D4C2312yes—
124C2×C4×D4C2311yescharacteristic
125C2×C4×D4C2312yes—
126C2×C4×D4C2312yes—
127C2×C4×D4C2312yes—
128C2×C4×D4C2312yes—
129C2×C4×D4C2312yes—
130C22×C4⋊C4C2×C411yescharacteristic
131C22×C4⋊C4C2×C411yescharacteristic
132C22×C4⋊C4C2×C412yes—
133C22×C4⋊C4C2×C412yes—
134C22×C22⋊C4C2×C412yes—
135C22×C22⋊C4C2×C411yescharacteristic
136C22×C22⋊C4C2×C411yescharacteristic
137C22×C22⋊C4C2×C412yes—
138C22×C22⋊C4C2×C412yes—
139C22×C22⋊C4C2×C412yes—
140C22×C22⋊C4C2×C412yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143#436—28no—
144#436—48no—
145#435—216no—
146#435—216no—
147#435—216no—
148#435—48no—
149#435—48no—
150C8×D4—28no—
151C8×D4—48no—
152#432—24no—
153#432D418yescomplemented
154#431—24no—
155#431—24no—
156C2×C4⋊C8C2314yes—
157C2×C4⋊C8C2314yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162#407—28no—
163#407—28no—
164C2×C22⋊C8—28no—
165C2×C22⋊C8—28no—
166C2×C22⋊C8C2311yescharacteristic
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2311yescharacteristic
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C2×C22⋊C8C2311yescharacteristic
174C2×C22⋊C8C2311yescharacteristic
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2314yes—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2312yes—
184C2×#97C2312yes—
185C2×#97C2314yes—
186C2×#97C2312yes—
187C2×C4×C8C2312yes—
188C2×C4×C8C2312yes—
189C2×C4×C8C2314yes—
190#399C2×C412yes—
191#399C2×C412yes—
192#399C2×C412yes—
193#399C2×C412yes—
194#399C2×C412yes—
195#399C2×C412yes—
196#399C2×C412yes—
197#399C2×C412yes—
198#399C2×C412yes—
199#399C2×C412yes—
200#399C2×C412yes—
201#399C2×C412yes—
202#399C2×C412yes—
203#399C2×C412yes—
204#399C2×C412yes—
205#399C2×C412yes—
206#392C2×C412yes—
207#392C2×C412yes—
208#392C2×C412yes—
209#392C2×C412yes—
210#392C2×C412yes—
211#392C2×C412yes—
212#392C2×C412yes—
213#392C2×C412yes—
214#392C2×C412yes—
215#392C2×C412yes—
216#392C2×C412yes—
217#392C2×C412yes—
218#392C2×C412yes—
219#392C2×C412yes—
220#392C2×C412yes—
221#392C2×C412yes—
222#376C2×C411yescharacteristic
223#376C2×C412yes—
224#376C2×C411yescharacteristic
225#376C2311yescharacteristic
226#376C2311yescharacteristic
227#376C2312yes—
228C2×#95C2×C412yes—
229C2×#95C2×C411yescharacteristic
230C2×#95C2×C411yescharacteristic
231#336C2314yes—
232#336C2314yes—
233#336C2314yes—
234#336C2314yes—
235C25C22×C412yes—
236C25C22×C411yescharacteristic
237C25C22×C411yescharacteristic
238C22×D4—24no—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C22×C411yescharacteristic
250C22×D4C22×C412yes—
251C22×D4C22×C412yes—
252C22×D4C22×C412yes—
253C22×D4C22×C412yes—
254C22×D4C22×C412yes—
255C22×D4C22×C412yes—
256C22×D4C22×C412yes—
257C22×D4C22×C412yes—
258C22×D4C22×C412yes—
259C22×D4C22×C411yescharacteristic
260C22×D4C22×C412yes—
261C22×D4C22×C412yes—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C22×C412yes—
273C23×C4C22×C412yes—
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C412yes—
277C23×C4C22×C411yescharacteristic
278C23×C4C22×C412yes—
279C23×C4C22×C412yes—
280C23×C4C22×C412yes—
281C23×C4C22×C412yes—
282C23×C4C22×C411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C2×M16—28no—
289C2×M16—28no—
290C2×M16—44no—
291C2×M16—44no—
292C2×M16—44no—
293C2×M16—44no—
294C22×C8—28no—
295C22×C8—28no—
296C22×C8—44no—
297C22×C8—44no—
298C22×C8—44no—
299C22×C8—44no—
300C22×C8C2412yes—
301C22×C8C2414yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2414yes—
306C4×D4—24no—
307C4×D4—28no—
308C4×D4—28no—
309C4×D4—28no—
310C4×D4—24no—
311C4×D4—22no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—28no—
322C4×D4—28no—
323C4×D4—28no—
324C4×D4—28no—
325C4×D4—44no—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—44no—
329C4×D4—44no—
330C4×D4—44no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C22×C412yes—
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⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
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×C22⋊C4C22×C412yes—
373C2×C22⋊C4C22×C412yes—
374C2×C22⋊C4C22×C412yes—
375C2×C22⋊C4C22×C412yes—
376C2×C22⋊C4C22×C412yes—
377C2×C22⋊C4C22×C412yes—
378C2×C22⋊C4C22×C412yes—
379C2×C22⋊C4C22×C412yes—
380C2×C22⋊C4C22×C412yes—
381C2×C22⋊C4C22×C412yes—
382C2×C22⋊C4C22×C412yes—
383C2×C22⋊C4C22×C412yes—
384C2×C22⋊C4C22×C412yes—
385C2×C42—28no—
386C2×C42C22×C412yes—
387C2×C42C22×C412yes—
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C2×D414yes—
391C2×C42#4114yes—
392C2×C42C2412yes—
393C2×C42C2411yescharacteristic
394C2×C42C2411yescharacteristic
395C2×C42C2412yes—
396C4⋊C8—24no—
397C4⋊C8—24no—
398C4⋊C8—24no—
399C4⋊C8—28no—
400C4⋊C8—28no—
401C4⋊C8C2×D418yescomplemented
402C22⋊C8—22no—
403C22⋊C8—24no—
404C22⋊C8—22no—
405C22⋊C8—22no—
406C22⋊C8—22no—
407C22⋊C8—28no—
408C22⋊C8—28no—
409C22⋊C8—28no—
410C22⋊C8—28no—
411C22⋊C8—44no—
412C22⋊C8—44no—
413C22⋊C8—44no—
414C22⋊C8—44no—
415C22⋊C8—44no—
416C22⋊C8—44no—
417C22⋊C8—44no—
418C22⋊C8—44no—
419C22⋊C8C2×D418yes—
420#97—24no—
421#97—28no—
422#97C2×D418yescomplemented
423C4×C8—24no—
424C4×C8—24no—
425C4×C8—28no—
426#95C22×C411yescharacteristic
427#95C22×C412yes—
428#95C22×C411yescharacteristic
429#95C22×C412yes—
430#95C22×C412yes—
431#95C22×C412yes—
432#95C22×C412yes—
433#95C22×C412yes—
434#95C22×C411yescharacteristic
435#95C22×C411yescharacteristic
436C24—22no—
437C24—22no—
438C24—24no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—22no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24#13114yes—
453C24C23×C412yes—
454C24C23×C412yes—
455C24C23×C412yes—
456C24C23×C412yes—
457C24C23×C411yescharacteristic
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—416no—
496C2×D4—416no—
497C2×D4—432no—
498C2×D4—432no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
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—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
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—84no—
545C22×C4—88no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4—88no—
549C22×C4—84no—
550C22×C4C4×D414yes—
551C22×C4C4×D414yes—
552C22×C4C23×C412yes—
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C412yes—
556C22×C4C23×C412yes—
557C22×C4C23×C412yes—
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C23×C412yes—
564C22×C4C23×C412yes—
565C22×C4C22×D412yes—
566C22×C4C2×#4112yes—
567C22×C4C2511yescharacteristic
568M16—88no—
569M16—88no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—24no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—88no—
584C2×C8—88no—
585C2×C8C22×D418yes—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
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—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C42—24no—
624C42—24no—
625C42—24no—
626C42C4×D414yes—
627C42C4×D414yes—
628C42C22×D412yes—
629C42C22×D412yes—
630C42C2×#4112yes—
631C42C2×#4112yes—
632C42H(5,𝔽2)18yes—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—48no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—44no—
668C23—48no—
669C23—82no—
670C23—84no—
671C23—82no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—82no—
677C23—82no—
678C23C2×C4×D412yes—
679C23C2×#13114yes—
680C23C2×#13112yes—
681C23#56814yes—
682C23#56812yes—
683C23C24×C411yescharacteristic
684D4—216no—
685D4—28no—
686D4—48no—
687D4—48no—
688D4—48no—
689D4—48no—
690D4—48no—
691D4—48no—
692D4—44no—
693D4—48no—
694D4—48no—
695D4—48no—
696D4—48no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—44no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—82no—
745C2×C4—84no—
746C2×C4—82no—
747C2×C4C2×C4×D412yes—
748C2×C4C2×C4×D412yes—
749C2×C4C2×C4×D412yes—
750C2×C4C2×C4×D412yes—
751C2×C4C2×C4×D412yes—
752C2×C4#51814yes—
753C2×C4#51814yes—
754C2×C4C23×D411yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C2×H(5,𝔽2)14yes—
757C8—28no—
758C8—42no—
759C8—44no—
760C8—42no—
761C8—42no—
762C8—42no—
763C22—24no—
764C22—24no—
765C22—22no—
766C22—22no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—88no—
796C22—816no—
797C22—88no—
798C22#293314yes—
799C22C22×C4×D411yescharacteristic
800C22C2×#51812yes—
801C22C22×#13111yescharacteristic
802C22C2×#56812yes—
803C22C2×#56811yescharacteristic
804C4—24no—
805C4—24no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4#349812yes—
818C4#350812yes—
819C2—24no—
820C2—44no—
821C2—44no—
822C2—82no—
823C2—82no—
824C2#3421011yescharacteristic
825C2C2×#293311yescharacteristic
826C2#6014111yescharacteristic
827C2#6023312yes—
828C2#6023412yes—
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#2397C2
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×#2974C2semidirect
2. C2×#2973C2semidirect
4. #23178C2semidirect
5. #23177C2semidirect
6. #22401C2semidirect
7. #22399C2semidirect
8. #22399C2semidirect
9. D4×C22⋊C8C2semidirect
10. #22267C2semidirect
11. #21788C2semidirect
12. #21786C2semidirect
13. #21685C2semidirect
14. #20814C2semidirect
15. #20469C2semidirect
22. C2×#436C22semidirect
23. C2×#436C22semidirect
24. C2×#435C22semidirect
25. C2×#435C22semidirect
26. C2×#435C22semidirect
27. C2×#435C22semidirect
28. C2×#435C22semidirect
29. C2×C8×D4C22semidirect
30. C2×C8×D4C22semidirect
54. #1955C22semidirect
55. #1955C22semidirect
56. #1955C22semidirect
57. #1955C22semidirect
58. #1954C22semidirect
59. #1954C22semidirect
60. #1954C22semidirect
61. #1954C22semidirect
62. #1954C22semidirect
63. #1870C22semidirect
64. #1870C22semidirect
65. #1870C22semidirect
66. #1870C22semidirect
67. #1869C22semidirect
68. #1869C22semidirect
69. #1869C22semidirect
70. #1869C22semidirect
71. #1843C22semidirect
72. #1832C22semidirect
81. #1768C22semidirect
82. #1768C22semidirect
85. #1746C22semidirect
86. #1726C22semidirect
153. #432D4semidirect
401. C4⋊C8C2×D4semidirect
422. #97C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#29742
C2×#29732
C2×#23972
#231782
#231772
#224012
#223992
D4×C22⋊C82
#222672
#217882
#217862
#216852
#208142
#204692