Finite Group Databasebeta

← #6603208

Subgroups — #6603208

Order 512.

1507 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36394C211yesmaximal, characteristic, complemented
2C4×#556C211yesmaximal, characteristic, complemented
3#33085C211yesmaximal, characteristic, complemented
4#33085C211yesmaximal, characteristic, complemented
5#33070C211yesmaximal, characteristic, complemented
6#29502C211yesmaximal, characteristic, complemented
7#29496C211yesmaximal, characteristic, complemented
8#29373C211yesmaximal, characteristic
9#29372C211yesmaximal, characteristic
10#29196C211yesmaximal, characteristic, complemented
11#28159C211yesmaximal, characteristic, complemented
12#27387C211yesmaximal, characteristic, complemented
13#27366C211yesmaximal, characteristic, complemented
14#27219C211yesmaximal, characteristic, complemented
15#27198C211yesmaximal, characteristic, complemented
16#26781C211yesmaximal, characteristic, complemented
17#26764C211yesmaximal, characteristic, complemented
18#26613C211yesmaximal, characteristic
19#26596C211yesmaximal, characteristic
20#25069C211yesmaximal, characteristic, complemented
21#25005C211yesmaximal, characteristic, complemented
22#24201C211yesmaximal, characteristic, complemented
23#24197C211yesmaximal, characteristic
24#23110C211yesmaximal, characteristic, complemented
25#23012C211yesmaximal, characteristic, complemented
26#22830C211yesmaximal, characteristic, complemented
27#22820C211yesmaximal, characteristic, complemented
28#22780C211yesmaximal, characteristic
29#21507C211yesmaximal, characteristic
30#21124C211yesmaximal, characteristic, complemented
31#21120C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#462C2211yescharacteristic
34C2×#463C2211yescharacteristic
35C2×#461C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40#2864C2211yescharacteristic
41#2863C2211yescharacteristic
42#2863C2211yescharacteristic
43#2599—21no—
44#2599—21no—
45#2581C2211yescharacteristic
46#2580C2211yescharacteristic
47#2577—21no—
48#2577—21no—
49#2575—21no—
50#2575—21no—
51#2508C2211yescharacteristic
52#2508C2211yescharacteristic
53#2447C2211yescharacteristic
54#2447C2211yescharacteristic
55#2373—21no—
56#2373—21no—
57#2367C2211yescharacteristic
58#2367C2211yescharacteristic
59#2365C2211yescharacteristic
60#2362—21no—
61#2356C2211yescharacteristic
62#2356C2211yescharacteristic
63#2356C2211yescharacteristic
64#2355C2211yescharacteristic
65#2354C2211yescharacteristic
66#2349C2211yescharacteristic
67#2347—21no—
68#2343—21no—
69#2343—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×#126—21no—
72C4×#126—21no—
73C4×#124C2211yescharacteristic
74C4×#124C2211yescharacteristic
75C4×#124C2211yescharacteristic
76C4×C22⋊Q8—21no—
77#2293C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×Q8C2211yescharacteristic
80C42×Q8C2211yescharacteristic
81C42×Q8C2211yescharacteristic
82C42×D4C2211yescharacteristic
83C4×#117—21no—
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2074C2211yescharacteristic
91#2074C2211yescharacteristic
92#2074C2211yescharacteristic
93#2074C2211yescharacteristic
94#2068C2211yescharacteristic
95#2068C2211yescharacteristic
96#2066C2211yescharacteristic
97#2066C2211yescharacteristic
98#2042C2211yescharacteristic
99#2042C2211yescharacteristic
100#2042C2211yescharacteristic
101#2042C2211yescharacteristic
102#2015C2211yescharacteristic
103#2015C2211yescharacteristic
104#2015C2211yescharacteristic
105#2015C2211yescharacteristic
106#2012C2211yescharacteristic
107#2012C2211yescharacteristic
108#1985C2211yescharacteristic
109#1985C2211yescharacteristic
110#1983C2211yescharacteristic
111#1973C2211yescharacteristic
112#1971C2211yescharacteristic
113#1969C2211yescharacteristic
114#1968C2211yescharacteristic
115#1960C2211yescharacteristic
116#1960C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1949C2211yescharacteristic
120#1936C2211yescharacteristic
121#1935C2211yescharacteristic
122#1934C2211yescharacteristic
123#1933C2211yescharacteristic
124#1928C2211yescharacteristic
125#1928C2211yescharacteristic
126#1928C2211yescharacteristic
127#1927C2211yescharacteristic
128#1927C2211yescharacteristic
129#1927C2211yescharacteristic
130#1927C2211yescharacteristic
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1920C2211yescharacteristic
139#1920C2211yescharacteristic
140#1920C2211yescharacteristic
141#1919C2211yescharacteristic
142#1919C2211yescharacteristic
143#1919C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1917C2211yescharacteristic
147#1917C2211yescharacteristic
148#1916C2211yescharacteristic
149#1916C2211yescharacteristic
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1847C2211yescharacteristic
181#1839C2211yescharacteristic
182#1839C2211yescharacteristic
183#1836C2211yescharacteristic
184#1831C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic
189#1802C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#107C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1767C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1745C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#556—24no—
210#556—24no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C4×Q8D411yescharacteristic
219C2×C4×Q8D411yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117—21no—
237C2×#117—21no—
238C22×C42—21no—
239#463—24no—
240#462—24no—
241#461—24no—
242#442—24no—
243#440—24no—
244#440—24no—
245C4×SD16—24no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—21no—
296#400—21no—
297#399—21no—
298#398—21no—
299#398—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#395—21no—
305#393—21no—
306#391—21no—
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#389—21no—
322#389—21no—
323#389—21no—
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#384C2311yescharacteristic
383#383—21no—
384#383—21no—
385#383—21no—
386#383—21no—
387#383—21no—
388#382—21no—
389#382—21no—
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#381—21no—
396#381—21no—
397#380—21no—
398#380—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4D411yescharacteristic
411C4×C4⋊C4D411yescharacteristic
412C4×C4⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440#376—21no—
441#376—21no—
442#376—21no—
443C2×#95—21no—
444C43—21no—
445C43—21no—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16—41no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8#4114yes—
527#126—28no—
528#126—28no—
529#124—22no—
530#124—22no—
531#124—22no—
532#124—22no—
533#124—22no—
534#124—41no—
535C22⋊Q8—28no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—42no—
547C4×Q8—42no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4#4114yes—
566#117—28no—
567#117—44no—
568#117—44no—
569#117—44no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—44no—
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2×D411yescharacteristic
661C2×C42C2×D411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—22no—
671#107—41no—
672#107—41no—
673#107—41no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102#4114yes—
711#97—22no—
712#97—22no—
713#97—22no—
714#97—41no—
715C4×C8—22no—
716C4×C8—41no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24—21no—
771C24—21no—
772C2×Q8—22no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8C2×#4112yes—
792C2×Q8C2×#4112yes—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4C2×#4112yes—
804C2×D4C2×#4112yes—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—24no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C2511yescharacteristic
852Q16—82no—
853Q16—82no—
854SD16—44no—
855SD16—44no—
856SD16—44no—
857D8—44no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8C2×#4112yes—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4C2×#4112yes—
933C4⋊C4C2×#4112yes—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—41no—
975C42—41no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—41no—
981C42—41no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—81no—
995C42—81no—
996C42C2×#4112yes—
997C42C2×#4112yes—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23C23×D411yescharacteristic
1013Q8—22no—
1014Q8—22no—
1015Q8—22no—
1016Q8—22no—
1017Q8—44no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026D4—22no—
1027D4—22no—
1028D4—22no—
1029D4—22no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—48no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—162no—
1120C2×C4#52512yes—
1121C2×C4#52512yes—
1122C2×C4#57512yes—
1123C2×C4#57512yes—
1124C2×C4C22×#4111yescharacteristic
1125C2×C4C22×#4111yescharacteristic
1126C2×C4C22×#4111yescharacteristic
1127C2×C4#58511yescharacteristic
1128C2×C4#58511yescharacteristic
1129C2×C4#58511yescharacteristic
1130C8—22no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22C2×#52511yescharacteristic
1153C22D4×#4111yescharacteristic
1154C22#348711yescharacteristic
1155C22C2×#57511yescharacteristic
1156C22C2×#57511yescharacteristic
1157C22#358411yescharacteristic
1158C22#358611yescharacteristic
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—42no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4#347511yescharacteristic
1188C4#347511yescharacteristic
1189C4#351211yescharacteristic
1190C4#352111yescharacteristic
1191C2—82no—
1192C2—82no—
1193C2#3622811yescharacteristic
1194C2#6055911yescharacteristic
1195C2#6059511yescharacteristic
1196C2#6144211yescharacteristic
1197C2#6145511yescharacteristic
1198C2#6189411yescharacteristic
1199C2#6190211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36394C2semidirect
2. C4×#556C2semidirect
3. #33085C2semidirect
4. #33085C2semidirect
5. #33070C2semidirect
6. #29502C2semidirect
7. #29496C2semidirect
10. #29196C2semidirect
11. #28159C2semidirect
12. #27387C2semidirect
13. #27366C2semidirect
14. #27219C2semidirect
15. #27198C2semidirect
16. #26781C2semidirect
17. #26764C2semidirect
20. #25069C2semidirect
21. #25005C2semidirect
22. #24201C2semidirect
24. #23110C2semidirect
25. #23012C2semidirect
26. #22830C2semidirect
27. #22820C2semidirect
30. #21124C2semidirect
31. #21120C2semidirect

Maximal subgroups

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

subgroupindex
#363942
C4×#5562
#330852
#330702
#295022
#294962
#293732
#293722
#291962
#281592
#273872
#273662
#272192
#271982
#267812
#267642
#266132
#265962
#250692
#250052
#242012
#241972
#231102
#230122
#228302
#228202
#227802
#215072
#211242
#211202