Finite Group Databasebeta

← #6393562

Subgroups — #6393562

Order 512.

3451 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic
2C2×#2979C211yesmaximal, characteristic, complemented
3C2×#2935C211yesmaximal, characteristic, complemented
4#22474C211yesmaximal, characteristic, complemented
5#22474C211yesmaximal, characteristic, complemented
6#22473C211yesmaximal, characteristic, complemented
7#22472C212yesmaximal, complemented
8#22470C212yesmaximal, complemented
9#22469C211yesmaximal, characteristic, complemented
10#22402C211yesmaximal, characteristic, complemented
11#22402C211yesmaximal, characteristic, complemented
12#22401C211yesmaximal, characteristic, complemented
13#22400C212yesmaximal, complemented
14#22398C212yesmaximal, complemented
15D4×C22⋊C8C211yesmaximal, characteristic, complemented
16#21848C211yesmaximal, characteristic, complemented
17#21847C211yesmaximal, characteristic, complemented
18#21745C212yesmaximal, complemented
19#21744C212yesmaximal, complemented
20#21378C211yesmaximal, characteristic, complemented
21#21374C211yesmaximal, characteristic, complemented
22#20900C212yesmaximal, complemented
23#20899C212yesmaximal, complemented
24C22×#131C2212yescomplemented
25#3460—28no—
26#3460—28no—
27C2×#544C411yescharacteristic
28C2×#542C411yescharacteristic
29C2×#542C412yes—
30C2×#542C411yescharacteristic
31C2×#540C411yescharacteristic
32C2×#540C412yes—
33C2×#540C411yescharacteristic
34C2×#538C412yes—
35C2×#538C412yes—
36C2×#537C411yescharacteristic
37C2×#535C411yescharacteristic
38C2×#535C411yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#532C2212yes—
41C2×#532C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×#529C2212yes—
44C2×#529C2211yescharacteristic
45C2×#525C2212yes—
46C2×#525C2212yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50#2979—28no—
51#2935—28no—
52C2×#436C2211yescharacteristic
53C2×#436C2211yescharacteristic
54C2×#436C2212yescomplemented
55C2×#436C2211yescharacteristic, complemented
56C2×#436C2211yescharacteristic, complemented
57C2×#435C2212yescomplemented
58C2×#435C2212yescomplemented
59C2×C8×D4C2211yescharacteristic
60C2×C8×D4C2211yescharacteristic
61C2×C8×D4C2212yescomplemented
62C2×C8×D4C2211yescharacteristic, complemented
63C2×C8×D4C2211yescharacteristic, complemented
64C2×#431C2211yescharacteristic, complemented
65C2×#431C2211yescharacteristic, complemented
66C22×C4⋊C8C2211yescharacteristic, complemented
67C2×#408C2212yescomplemented
68C2×#408C2212yescomplemented
69C2×#408C2212yescomplemented
70C2×#408C2212yescomplemented
71C2×#408C2212yescomplemented
72C2×#407C2212yes—
73C22×C22⋊C8C2212yes—
74C2×C4×M16C2211yescharacteristic, complemented
75#1985C2211yescharacteristic, complemented
76#1985C2211yescharacteristic, complemented
77#1984C2212yescomplemented
78#1984C2211yescharacteristic, complemented
79#1984C2211yescharacteristic, complemented
80#1984C2211yescharacteristic, complemented
81#1984C2211yescharacteristic, complemented
82#1955C2211yescharacteristic
83#1955C2211yescharacteristic
84#1954C2212yes—
85#1954C2211yescharacteristic
86#1954C2211yescharacteristic
87#1954C2211yescharacteristic
88#1954C2211yescharacteristic
89#1870C2211yescharacteristic
90#1870C2211yescharacteristic
91#1870C2212yes—
92#1870C2212yes—
93#1870C2212yes—
94#1870C2212yes—
95#1870C2211yescharacteristic, complemented
96#1870C2211yescharacteristic, complemented
97#1870C2212yescomplemented
98#1870C2212yescomplemented
99#1870C2212yescomplemented
100#1870C2212yescomplemented
101#1870C2212yescomplemented
102#1870C2212yescomplemented
103#1869C2212yes—
104#1869C2212yes—
105#1869C2212yes—
106#1869C2212yes—
107#1869C2212yes—
108#1869C2212yescomplemented
109#1869C2212yescomplemented
110#1869C2212yescomplemented
111#1869C2212yescomplemented
112#1869C2212yescomplemented
113#1869C2212yescomplemented
114#1869C2212yescomplemented
115#1818C2212yescomplemented
116#1818C2212yescomplemented
117#1817C2212yescomplemented
118#1817C2212yescomplemented
119#1798C2212yescomplemented
120#1798C2212yescomplemented
121#1797C2211yescharacteristic
122#1797C2211yescharacteristic
123#1797C2211yescharacteristic, complemented
124#1797C2211yescharacteristic, complemented
125#1780C2212yescomplemented
126#1780C2212yescomplemented
127#1779C2212yes—
128#1779C2212yes—
129#1750C2212yescomplemented
130#1750C2212yescomplemented
131C4×C22⋊C8C2211yescharacteristic
132C4×C22⋊C8C2211yescharacteristic
133C4×C22⋊C8C2211yescharacteristic, complemented
134C4×C22⋊C8C2211yescharacteristic, complemented
135#1729C2212yescomplemented
136#1729C2212yescomplemented
137#1728C2212yescomplemented
138C2×#336C2212yescomplemented
139C22×#41C2×C411yescharacteristic
140C22×#41C2×C411yescharacteristic
141C22×#41C2312yes—
142C22×#41C2312yes—
143C23×D4C2×C411yescharacteristic
144C24×C4C2312yes—
145C2×#131—28no—
146C2×#131—44no—
147C2×#131—44no—
148C22×M16C2311yescharacteristic
149C22×M16C2312yes—
150C22×M16C2312yes—
151C22×M16C2311yescharacteristic
152C22×M16C2312yes—
153C22×M16C2312yes—
154C23×C8C2312yes—
155C23×C8C2312yes—
156C23×C8C2312yes—
157C23×C8C2312yes—
158C23×C8C2312yes—
159#544—28no—
160#542—28no—
161#542—216no—
162#542—28no—
163#540—28no—
164#540—28no—
165#540—216no—
166#538—216no—
167#538—216no—
168#537—28no—
169#535—28no—
170#535—28no—
171#532—28no—
172#532—28no—
173#532—24no—
174#532—24no—
175#532D418yes—
176#532D418yes—
177C2×C4⋊Q8C2×C412yes—
178C2×C4⋊Q8C2×C411yescharacteristic
179C2×C4⋊Q8C2×C411yescharacteristic
180C2×#127C2×C411yescharacteristic
181C2×#127C2×C412yes—
182C2×#127C2×C411yescharacteristic
183#529—28no—
184#529—28no—
185#529—24no—
186#529—24no—
187#529—24no—
188#529—24no—
189C2×#126C2×C412yes—
190C2×#126C2×C412yes—
191C2×#126C2×C412yes—
192C2×#126C2×C412yes—
193C2×#125C2×C412yes—
194C2×#125C2×C411yescharacteristic
195C2×#125C2×C411yescharacteristic
196C2×#124C2×C411yescharacteristic
197C2×#124C2×C412yes—
198C2×#124C2×C411yescharacteristic
199C2×#124C2×C412yes—
200C2×#124C2×C412yes—
201C2×#124C2×C412yes—
202C2×#124C2×C412yes—
203#525—28no—
204#525—28no—
205#525—28no—
206#525—28no—
207C2×#123C2×C412yes—
208C2×#123C2×C412yes—
209C2×#123C2×C412yes—
210C2×#123C2×C412yes—
211C2×#123C2×C412yes—
212C2×#123C2×C412yes—
213C2×#123C2×C412yes—
214C2×#123C2×C412yes—
215C2×C22⋊Q8C2×C412yes—
216C2×C22⋊Q8C2×C412yes—
217C2×C22⋊Q8C2×C412yes—
218C2×C22⋊Q8C2×C412yes—
219C2×C22⋊Q8C2×C411yescharacteristic
220C2×C22⋊Q8C2×C411yescharacteristic
221C2×C22⋊Q8C2×C412yes—
222C2×#121C2×C412yes—
223C2×#121C2×C412yes—
224C2×#121C2×C412yes—
225C2×#121C2×C412yes—
226C2×#121C2×C411yescharacteristic
227C2×#121C2×C412yes—
228C2×#121C2×C411yescharacteristic
229C2×#121C2×C412yes—
230C2×#121C2×C411yescharacteristic
231C2×#121C2×C411yescharacteristic
232C2×#121C2×C412yes—
233C2×#121C2×C412yes—
234C2×#121C2×C412yes—
235C2×#121C2×C412yes—
236C2×#121C2×C411yescharacteristic
237C2×#121C2×C411yescharacteristic
238C2×#121C2×C412yes—
239C2×#120C2×C412yes—
240C2×#120C2×C412yes—
241C2×#120C2×C412yes—
242C2×#120C2×C412yes—
243C4×#41—24no—
244C4×#41—24no—
245C4×#41—24no—
246C4×#41—24no—
247C2×C4×Q8C2×C411yescharacteristic
248C2×C4×Q8C2×C411yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—24no—
252C2×C4×D4—24no—
253C2×C4×D4C2×C411yescharacteristic
254C2×C4×D4C2×C411yescharacteristic
255C2×C4×D4C2×C412yes—
256C2×C4×D4C2×C411yescharacteristic
257C2×C4×D4C2×C412yes—
258C2×C4×D4C2×C411yescharacteristic
259C2×C4×D4C2×C411yescharacteristic
260C2×C4×D4C2×C411yescharacteristic
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2312yes—
273C2×#117C2×C411yescharacteristic
274C2×#117C2×C411yescharacteristic
275C2×#117C2×C411yescharacteristic
276C2×#117C2×C412yes—
277C2×#117C2×C411yescharacteristic
278C2×#117C2312yes—
279C2×#117C2312yes—
280C22×C4⋊C4C2×C411yescharacteristic
281C22×C22⋊C4C2×C412yes—
282C22×C42C2311yescharacteristic
283C22×C42C2311yescharacteristic
284C22×C42C2312yes—
285C22×C42C2311yescharacteristic
286#436—24no—
287#436—24no—
288#436—24no—
289#436—24no—
290#436—28no—
291#435—28no—
292#435—28no—
293C8×D4—24no—
294C8×D4—24no—
295C8×D4—24no—
296C8×D4—24no—
297C8×D4—28no—
298#431—24no—
299#431—24no—
300C2×C4⋊C8—24no—
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2312yes—
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308#408—28no—
309#408—28no—
310#408—28no—
311#408—44no—
312#408—44no—
313#407—44no—
314C2×C22⋊C8—44no—
315C2×C22⋊C8C2312yes—
316C2×C22⋊C8C2312yes—
317C2×C22⋊C8C2312yes—
318C2×C22⋊C8C2312yes—
319C2×C22⋊C8C2312yes—
320C2×C22⋊C8C2312yes—
321C2×C22⋊C8C2312yes—
322C2×C22⋊C8C2312yes—
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2312yes—
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2312yes—
327C2×C22⋊C8C2312yes—
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2312yes—
333C2×C22⋊C8C2312yes—
334C2×C22⋊C8C2312yes—
335C2×C22⋊C8C2312yes—
336C2×C22⋊C8C2312yes—
337C2×C22⋊C8C2312yes—
338C2×C22⋊C8C2312yes—
339C2×C22⋊C8C2312yes—
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2312yes—
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2312yes—
345C2×C22⋊C8C2311yescharacteristic
346C4×M16—24no—
347C2×#97C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2312yes—
354#336C2312yes—
355#336C2312yes—
356#336C2312yes—
357#336C2312yes—
358#336C2312yes—
359#336C2312yes—
360#336C2312yes—
361#336C2312yes—
362#336C2311yescharacteristic
363#336C2311yescharacteristic
364#336C2312yes—
365#336C2312yes—
366#336C2311yescharacteristic
367#336C2311yescharacteristic
368#336C2311yescharacteristic
369#336C2312yes—
370#336C2311yescharacteristic
371#336C2312yes—
372#336C2311yescharacteristic
373#336C2311yescharacteristic
374C25C22×C412yes—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—24no—
378C2×#41—24no—
379C2×#41—24no—
380C2×#41—24no—
381C2×#41—42no—
382C2×#41—42no—
383C2×#41—42no—
384C2×#41—42no—
385C2×#41—42no—
386C2×#41—42no—
387C2×#41—42no—
388C2×#41—42no—
389C2×#41—42no—
390C2×#41—42no—
391C2×#41C2×D418yes—
392C2×#41C2×D418yes—
393C22×Q8C22×C411yescharacteristic
394C22×Q8C22×C411yescharacteristic
395C22×Q8C22×C412yes—
396C22×Q8C22×C412yes—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—42no—
400C22×D4C22×C411yescharacteristic
401C22×D4C22×C411yescharacteristic
402C22×D4C22×C412yes—
403C22×D4C22×C411yescharacteristic
404C22×D4C22×C412yes—
405C22×D4C22×C411yescharacteristic
406C22×D4C22×C411yescharacteristic
407C22×D4C22×C411yescharacteristic
408C22×D4C22×C412yes—
409C22×D4C22×C412yes—
410C22×D4C22×C412yes—
411C22×D4C22×C412yes—
412C22×D4C22×C412yes—
413C22×D4C22×C412yes—
414C22×D4C22×C412yes—
415C22×D4C22×C412yes—
416C22×D4C22×C412yes—
417C22×D4C22×C412yes—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4C22×C411yescharacteristic
425C23×C4C22×C412yes—
426C23×C4C22×C411yescharacteristic
427C23×C4C22×C411yescharacteristic
428C23×C4C22×C411yescharacteristic
429C23×C4C22×C412yes—
430C23×C4C22×C412yes—
431C23×C4C22×C411yescharacteristic
432C23×C4C22×C412yes—
433C23×C4C22×C412yes—
434C23×C4C22×C411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441#131—432no—
442C2×M16—22no—
443C2×M16—24no—
444C2×M16—24no—
445C2×M16—22no—
446C2×M16—24no—
447C2×M16—24no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—24no—
451C2×M16—24no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—42no—
455C2×M16—42no—
456C2×M16—42no—
457C2×M16—42no—
458C2×M16—42no—
459C2×M16—42no—
460C22×C8—24no—
461C22×C8—24no—
462C22×C8—24no—
463C22×C8—24no—
464C22×C8—24no—
465C22×C8—24no—
466C22×C8—24no—
467C22×C8—42no—
468C22×C8—42no—
469C22×C8—42no—
470C22×C8—42no—
471C22×C8—42no—
472C22×C8—42no—
473C22×C8—42no—
474C22×C8—42no—
475C22×C8C2412yes—
476C22×C8C2411yescharacteristic
477C22×C8C2412yes—
478C22×C8C2411yescharacteristic
479C22×C8C2412yes—
480C22×C8C2411yescharacteristic
481C22×C8C2412yes—
482C22×C8C2411yescharacteristic
483C22×C8C2411yescharacteristic
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C4⋊Q8—28no—
488C4⋊Q8—24no—
489C4⋊Q8C22⋊C418yes—
490#127—28no—
491#127—24no—
492#127C22⋊C418yes—
493#126—28no—
494#126—28no—
495#126—28no—
496#126—28no—
497#125—28no—
498#125—24no—
499#125—24no—
500#124—28no—
501#124—24no—
502#124—28no—
503#124—28no—
504#124—28no—
505#124—24no—
506#124C22⋊C4116yes—
507#123—28no—
508#123—28no—
509#123—28no—
510#123—28no—
511#123—28no—
512#123—28no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516C22⋊Q8—28no—
517C22⋊Q8—24no—
518C22⋊Q8—28no—
519C22⋊Q8—24no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522#121—28no—
523#121—28no—
524#121—28no—
525#121—24no—
526#121—28no—
527#121—28no—
528#121—24no—
529#121—28no—
530#121—28no—
531#121—28no—
532#121—24no—
533#121—24no—
534#121—28no—
535#121—28no—
536#121C22⋊C418yes—
537#121C22⋊C418yes—
538#121C22⋊C4116yes—
539#120—28no—
540#120—28no—
541#120—28no—
542#120—28no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×D4—24no—
550C4×D4—24no—
551C4×D4—24no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—24no—
555C4×D4—22no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—24no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4C2×D414yes—
576C4×D4C2×D414yes—
577C4×D4C2×D414yes—
578C4×D4C2×D414yes—
579C4×D4C2×D418yes—
580C4×D4C2×D418yes—
581#117—24no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—28no—
586#117—24no—
587#117—24no—
588#117—24no—
589#117—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4C22×C411yescharacteristic
592C2×C4⋊C4C22×C412yes—
593C2×C4⋊C4C22×C411yescharacteristic
594C2×C4⋊C4C22×C411yescharacteristic
595C2×C4⋊C4C22×C411yescharacteristic
596C2×C4⋊C4C22×C411yescharacteristic
597C2×C4⋊C4C22×C412yes—
598C2×C4⋊C4C22×C411yescharacteristic
599C2×C4⋊C4C22×C411yescharacteristic
600C2×C4⋊C4C22×C412yes—
601C2×C4⋊C4C22×C411yescharacteristic
602C2×C4⋊C4C22×C412yes—
603C2×C4⋊C4C22×C412yes—
604C2×C4⋊C4C22×C412yes—
605C2×C4⋊C4C22×C412yes—
606C2×C4⋊C4C22×C412yes—
607C2×C4⋊C4C22×C412yes—
608C2×C4⋊C4C22×C412yes—
609C2×C4⋊C4C22×C411yescharacteristic
610C2×C4⋊C4C22×C411yescharacteristic
611C2×C4⋊C4C22×C412yes—
612C2×C22⋊C4—28no—
613C2×C22⋊C4C22×C412yes—
614C2×C22⋊C4C22×C412yes—
615C2×C22⋊C4C22×C412yes—
616C2×C22⋊C4C22×C411yescharacteristic
617C2×C22⋊C4C22×C412yes—
618C2×C22⋊C4C22×C411yescharacteristic
619C2×C22⋊C4C22×C411yescharacteristic
620C2×C22⋊C4C22×C412yes—
621C2×C22⋊C4C22×C411yescharacteristic
622C2×C22⋊C4C22×C411yescharacteristic
623C2×C22⋊C4C22×C411yescharacteristic
624C2×C22⋊C4C22×C412yes—
625C2×C22⋊C4C22×C412yes—
626C2×C22⋊C4C22×C412yes—
627C2×C22⋊C4C22×C412yes—
628C2×C22⋊C4C22×C412yes—
629C2×C22⋊C4C22×C412yes—
630C2×C22⋊C4C22×C412yes—
631C2×C22⋊C4C22×C412yes—
632C2×C22⋊C4C22×C412yes—
633C2×C22⋊C4C22×C412yes—
634C2×C22⋊C4C22×C412yes—
635C2×C22⋊C4C22×C412yes—
636C2×C22⋊C4C22×C412yes—
637C2×C22⋊C4C22×C412yes—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42C22×C411yescharacteristic
645C2×C42C22×C411yescharacteristic
646C2×C42C22×C411yescharacteristic
647C2×C42C22×C412yes—
648C2×C42C22×C412yes—
649C2×C42C22×C411yescharacteristic
650C2×C42C22×C411yescharacteristic
651C2×C42C22×C411yescharacteristic
652C2×C42C2×D414yes—
653C2×C42C2×D414yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C4⋊C8—22no—
660C4⋊C8—24no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—22no—
666C22⋊C8—24no—
667C22⋊C8—22no—
668C22⋊C8—22no—
669C22⋊C8—24no—
670C22⋊C8—24no—
671C22⋊C8—24no—
672C22⋊C8—24no—
673C22⋊C8—24no—
674C22⋊C8—24no—
675C22⋊C8—24no—
676C22⋊C8—24no—
677C22⋊C8—22no—
678C22⋊C8—24no—
679C22⋊C8—22no—
680C22⋊C8—24no—
681C22⋊C8—22no—
682C22⋊C8—22no—
683C22⋊C8—42no—
684C22⋊C8—42no—
685C22⋊C8—41no—
686C22⋊C8—42no—
687C22⋊C8—41no—
688C22⋊C8—41no—
689C22⋊C8—42no—
690C22⋊C8—41no—
691C22⋊C8—42no—
692C22⋊C8—42no—
693C22⋊C8—42no—
694C22⋊C8—42no—
695C22⋊C8—42no—
696C22⋊C8—42no—
697#97—22no—
698#97—22no—
699C4×C8—22no—
700C4×C8—22no—
701C4×C8—22no—
702C4×C8—22no—
703C4×C8—24no—
704C24—24no—
705C24—24no—
706C24—42no—
707C24—42no—
708C24—42no—
709C24—42no—
710C24—42no—
711C24C23×C412yes—
712C24C23×C411yescharacteristic
713C24C23×C412yes—
714C24C23×C411yescharacteristic
715C24C23×C412yes—
716C24C23×C411yescharacteristic
717#41—48no—
718#41—48no—
719#41—48no—
720#41—48no—
721#41—416no—
722#41—416no—
723#41—84no—
724#41—84no—
725#41—84no—
726#41—84no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—24no—
730C2×Q8—22no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—42no—
734C2×Q8—42no—
735C2×Q8—41no—
736C2×Q8—42no—
737C2×Q8—42no—
738C2×Q8C2×C22⋊C418yes—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—24no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—24no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—416no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—41no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4C2×C22⋊C414yes—
789C2×D4C2×C22⋊C414yes—
790C2×D4C2×C22⋊C418yes—
791C2×D4C2×C22⋊C418yes—
792C2×D4C2×C22⋊C418yes—
793C2×D4C2×C22⋊C418yes—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—22no—
814C22×C4—24no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4C2×C22⋊C414yes—
859C22×C4C2×C22⋊C414yes—
860C22×C4#13114yescomplemented
861C22×C4C23×C411yescharacteristic
862C22×C4C23×C411yescharacteristic
863C22×C4C23×C411yescharacteristic
864C22×C4C23×C411yescharacteristic
865C22×C4C23×C412yes—
866C22×C4C23×C411yescharacteristic
867C22×C4C23×C412yes—
868C22×C4C23×C412yes—
869C22×C4C23×C411yescharacteristic
870C22×C4C23×C412yes—
871C22×C4C23×C411yescharacteristic
872C22×C4C23×C411yescharacteristic
873C22×C4C23×C411yescharacteristic
874C22×C4C23×C412yes—
875C22×C4C23×C411yescharacteristic
876C22×C4C23×C411yescharacteristic
877C22×C4C22×D412yes—
878C22×C4C22×D414yes—
879C22×C4C22×D414yes—
880C22×C4C22×D414yes—
881C22×C4C22×D414yes—
882C22×C4C22×D412yes—
883C22×C4C2511yescharacteristic
884M16—28no—
885M16—48no—
886M16—48no—
887M16—44no—
888M16—84no—
889M16—84no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—22no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—22no—
902C2×C8—22no—
903C2×C8—22no—
904C2×C8—21no—
905C2×C8—22no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—22no—
909C2×C8—21no—
910C2×C8—22no—
911C2×C8—22no—
912C2×C8—22no—
913C2×C8—22no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—22no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—22no—
923C2×C8—21no—
924C2×C8—48no—
925C2×C8—48no—
926C2×C8—48no—
927C2×C8—84no—
928C2×C8—84no—
929C2×C8H(5,𝔽2)12yes—
930C2×C8H(5,𝔽2)12yes—
931C4⋊C4—24no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—24no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4C2×C22⋊C414yes—
950C4⋊C4C2×C22⋊C414yes—
951C4⋊C4C2×C22⋊C418yes—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—24no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4C2×C22⋊C418yes—
974C22⋊C4C2×C22⋊C418yes—
975C22⋊C4C2×C22⋊C418yes—
976C22⋊C4C2×C22⋊C418yes—
977C42—22no—
978C42—22no—
979C42—24no—
980C42—22no—
981C42—24no—
982C42—22no—
983C42—21no—
984C42—21no—
985C42—22no—
986C42—21no—
987C42—22no—
988C42—21no—
989C42C2×C22⋊C414yes—
990C42C2×C22⋊C414yes—
991C42C22×D412yes—
992C42C22×D412yes—
993C42C22×D412yes—
994C42C22×D412yes—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—22no—
1000C23—21no—
1001C23—21no—
1002C23—22no—
1003C23—22no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—21no—
1009C23—22no—
1010C23—22no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—22no—
1015C23—21no—
1016C23—21no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—21no—
1021C23—22no—
1022C23—22no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—22no—
1027C23—21no—
1028C23—22no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—48no—
1034C23—48no—
1035C23—84no—
1036C23—84no—
1037C23—84no—
1038C23—84no—
1039C23—84no—
1040C23C22×C22⋊C414yes—
1041C23C22×C22⋊C412yes—
1042C23C22×C22⋊C414yes—
1043C23C2×#13112yes—
1044C23C24×C411yescharacteristic
1045Q8—48no—
1046Q8—44no—
1047Q8—44no—
1048Q8—84no—
1049D4—28no—
1050D4—28no—
1051D4—48no—
1052D4—48no—
1053D4—48no—
1054D4—48no—
1055D4—48no—
1056D4—44no—
1057D4—44no—
1058D4—44no—
1059D4—48no—
1060D4—44no—
1061D4—84no—
1062D4—84no—
1063D4—84no—
1064D4—84no—
1065D4—84no—
1066D4—84no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—28no—
1082C2×C4—28no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—44no—
1120C2×C4—48no—
1121C2×C4—44no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—82no—
1135C2×C4—82no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4C22×C22⋊C412yes—
1141C2×C4C22×C22⋊C414yes—
1142C2×C4C22×C22⋊C412yes—
1143C2×C4C22×C22⋊C412yes—
1144C2×C4C22×C22⋊C412yes—
1145C2×C4C22×C22⋊C414yes—
1146C2×C4C22×C22⋊C412yes—
1147C2×C4C2×#13112yes—
1148C2×C4C2×#13112yes—
1149C2×C4#56812yes—
1150C2×C4C23×D411yescharacteristic
1151C2×C4C23×D411yescharacteristic
1152C2×C4C2×H(5,𝔽2)11yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C8—22no—
1157C8—22no—
1158C8—42no—
1159C8—42no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—42no—
1164C8—41no—
1165C8—41no—
1166C8—42no—
1167C8—41no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—24no—
1172C22—24no—
1173C22—22no—
1174C22—24no—
1175C22—24no—
1176C22—22no—
1177C22—24no—
1178C22—22no—
1179C22—24no—
1180C22—41no—
1181C22—42no—
1182C22—42no—
1183C22—41no—
1184C22—42no—
1185C22—42no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—42no—
1190C22—42no—
1191C22—41no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—41no—
1199C22—42no—
1200C22—41no—
1201C22—42no—
1202C22—41no—
1203C22—42no—
1204C22—41no—
1205C22—42no—
1206C22—41no—
1207C22—42no—
1208C22—42no—
1209C22—41no—
1210C22—816no—
1211C22C23×C22⋊C411yescharacteristic
1212C22C4×H(5,𝔽2)11yescharacteristic
1213C22C4×H(5,𝔽2)11yescharacteristic
1214C22C22×#13111yescharacteristic
1215C22C2×#56811yescharacteristic
1216C22#357311yescharacteristic
1217C22#357311yescharacteristic
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—24no—
1223C4—22no—
1224C4—24no—
1225C4—41no—
1226C4—42no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4#288014yes—
1234C4#348411yescharacteristic
1235C4#348511yescharacteristic
1236C4#349611yescharacteristic
1237C4#349611yescharacteristic
1238C2—42no—
1239C2—44no—
1240C2—44no—
1241C2—42no—
1242C2—81no—
1243C2—82no—
1244C2#3425611yescharacteristic
1245C2C2×#288011yescharacteristic
1246C2#6006511yescharacteristic
1247C2#6031211yescharacteristic
1248C2#6031911yescharacteristic
1249C2#6032111yescharacteristic
1250C2#6032611yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#3460C2
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. C2×#2979C2semidirect
3. C2×#2935C2semidirect
4. #22474C2semidirect
5. #22474C2semidirect
6. #22473C2semidirect
7. #22472C2semidirect
8. #22470C2semidirect
9. #22469C2semidirect
10. #22402C2semidirect
11. #22402C2semidirect
12. #22401C2semidirect
13. #22400C2semidirect
14. #22398C2semidirect
15. D4×C22⋊C8C2semidirect
16. #21848C2semidirect
17. #21847C2semidirect
18. #21745C2semidirect
19. #21744C2semidirect
20. #21378C2semidirect
21. #21374C2semidirect
22. #20900C2semidirect
23. #20899C2semidirect
24. C22×#131C22semidirect
54. C2×#436C22semidirect
55. C2×#436C22semidirect
56. C2×#436C22semidirect
57. C2×#435C22semidirect
58. C2×#435C22semidirect
61. C2×C8×D4C22semidirect
62. C2×C8×D4C22semidirect
63. C2×C8×D4C22semidirect
64. C2×#431C22semidirect
65. C2×#431C22semidirect
66. C22×C4⋊C8C22semidirect
67. C2×#408C22semidirect
68. C2×#408C22semidirect
69. C2×#408C22semidirect
70. C2×#408C22semidirect
71. C2×#408C22semidirect
74. C2×C4×M16C22semidirect
75. #1985C22semidirect
76. #1985C22semidirect
77. #1984C22semidirect
78. #1984C22semidirect
79. #1984C22semidirect
80. #1984C22semidirect
81. #1984C22semidirect
95. #1870C22semidirect
96. #1870C22semidirect
97. #1870C22semidirect
98. #1870C22semidirect
99. #1870C22semidirect
100. #1870C22semidirect
101. #1870C22semidirect
102. #1870C22semidirect
108. #1869C22semidirect
109. #1869C22semidirect
110. #1869C22semidirect
111. #1869C22semidirect
112. #1869C22semidirect
113. #1869C22semidirect
114. #1869C22semidirect
115. #1818C22semidirect
116. #1818C22semidirect
117. #1817C22semidirect
118. #1817C22semidirect
119. #1798C22semidirect
120. #1798C22semidirect
123. #1797C22semidirect
124. #1797C22semidirect
125. #1780C22semidirect
126. #1780C22semidirect
129. #1750C22semidirect
130. #1750C22semidirect
133. C4×C22⋊C8C22semidirect
134. C4×C22⋊C8C22semidirect
135. #1729C22semidirect
136. #1729C22semidirect
137. #1728C22semidirect
138. C2×#336C22semidirect
860. C22×C4#131semidirect

Maximal subgroups

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

subgroupindex
C2×#34602
C2×#29792
C2×#29352
#224742
#224732
#224722
#224702
#224692
#224022
#224012
#224002
#223982
D4×C22⋊C82
#218482
#218472
#217452
#217442
#213782
#213742
#209002
#208992