Finite Group Databasebeta

← #6547345

Subgroups — #6547345

Order 512.

1430 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38972C211yesmaximal, characteristic, complemented
2#34481C211yesmaximal, characteristic, complemented
3#30142C211yesmaximal, characteristic
4#30141C211yesmaximal, characteristic
5#30000C211yesmaximal, characteristic, complemented
6#29550C211yesmaximal, characteristic, complemented
7#29549C211yesmaximal, characteristic, complemented
8#29459C211yesmaximal, characteristic, complemented
9#29443C211yesmaximal, characteristic, complemented
10#29196C211yesmaximal, characteristic, complemented
11#28254C211yesmaximal, characteristic, complemented
12#27314C211yesmaximal, characteristic, complemented
13#27295C211yesmaximal, characteristic, complemented
14#26777C211yesmaximal, characteristic, complemented
15#26760C211yesmaximal, characteristic, complemented
16#26611C211yesmaximal, characteristic
17#26594C211yesmaximal, characteristic
18#26185C211yesmaximal, characteristic, complemented
19#26169C211yesmaximal, characteristic, complemented
20#25068C211yesmaximal, characteristic, complemented
21#25004C211yesmaximal, characteristic, complemented
22#24201C211yesmaximal, characteristic, complemented
23#24197C211yesmaximal, characteristic
24#23695C211yesmaximal, characteristic, complemented
25#23694C211yesmaximal, characteristic, complemented
26#23686C211yesmaximal, characteristic
27#23112C211yesmaximal, characteristic, complemented
28#23014C211yesmaximal, characteristic, complemented
29#22824C211yesmaximal, characteristic, complemented
30#22774C211yesmaximal, characteristic
31#22677C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#462C2211yescharacteristic
36C2×#461C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#441C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2864C2211yescharacteristic
44#2775—21no—
45#2775—21no—
46#2773—21no—
47#2773—21no—
48#2644C2211yescharacteristic
49#2644C2211yescharacteristic
50#2581C2211yescharacteristic
51#2580C2211yescharacteristic
52#2517—21no—
53#2517—21no—
54#2515—21no—
55#2515—21no—
56#2508C2211yescharacteristic
57#2508C2211yescharacteristic
58#2448C2211yescharacteristic
59#2448C2211yescharacteristic
60#2383—21no—
61#2383—21no—
62#2367C2211yescharacteristic
63#2367C2211yescharacteristic
64#2365C2211yescharacteristic
65#2360—21no—
66#2357C2211yescharacteristic
67#2351C2211yescharacteristic
68Q8×C4⋊C4C2211yescharacteristic
69Q8×C4⋊C4C2211yescharacteristic
70Q8×C4⋊C4C2211yescharacteristic
71D4×C4⋊C4C2211yescharacteristic
72#2347—21no—
73#2334—21no—
74#2334—21no—
75#2326C2211yescharacteristic
76#2326C2211yescharacteristic
77#2323—21no—
78#2320C2211yescharacteristic
79#2320C2211yescharacteristic
80#2320C2211yescharacteristic
81#2320C2211yescharacteristic
82#2317—21no—
83C4×C4⋊Q8C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2295C2211yescharacteristic
86#2293C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic
100#2072C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2056C2211yescharacteristic
112#2056C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#1985C2211yescharacteristic
128#1985C2211yescharacteristic
129#1973C2211yescharacteristic
130#1968C2211yescharacteristic
131#1960C2211yescharacteristic
132#1960C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1943C2211yescharacteristic
136#1942C2211yescharacteristic
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1933C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1862C2211yescharacteristic
181#1847C2211yescharacteristic
182#1842C2211yescharacteristic
183#1836C2211yescharacteristic
184#1832C2211yescharacteristic
185#1832C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1767C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#102C2211yescharacteristic
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×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C22×C4⋊C4—21no—
236#464—42no—
237#464—42no—
238#462—24no—
239#461—24no—
240#442—24no—
241#441—42no—
242#440—24no—
243#440—42no—
244C4×Q16—42no—
245C4×SD16—42no—
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×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#393—21no—
318#391D411yescharacteristic
319#391D411yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389D411yescharacteristic
347#389D411yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#387D411yescharacteristic
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384—21no—
413#384—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#383—21no—
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382—21no—
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#380—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453#376C2311yescharacteristic
454#376C2311yescharacteristic
455C43C2311yescharacteristic
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8C2×D411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—41no—
505C2×Q16—41no—
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×SD16—41no—
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8#4114yes—
528#126—28no—
529#126—28no—
530#124—22no—
531#124—22no—
532#124—22no—
533#124—22no—
534#124—22no—
535#124—41no—
536C22⋊Q8—28no—
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—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—82no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4#4114yes—
566#117—28no—
567#117—82no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
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⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—82no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
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—41no—
671#107—41no—
672#107—41no—
673#107—41no—
674#106—22no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#97—22no—
716#97—22no—
717#97—41no—
718#97—41no—
719C4×C8—41no—
720C4×C8—41no—
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#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C24—21no—
776C2×Q8—22no—
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—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—41no—
793C2×Q8—41no—
794C2×Q8C2×#4112yes—
795C2×Q8C2×#4112yes—
796C2×Q8H(5,𝔽2)12yes—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4C2×#4112yes—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—24no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
850Q16—44no—
851Q16—44no—
852SD16—28no—
853SD16—82no—
854SD16—82no—
855D8—44no—
856C2×C8—21no—
857C2×C8—21no—
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×C82−1+412yes—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
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—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4C2×#4112yes—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C42—24no—
967C42—24no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42C2×#4112yes—
997C42C2×#4112yes—
998C23—22no—
999C23—41no—
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—22no—
1018Q8—22no—
1019Q8—44no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026D4—22no—
1027D4—22no—
1028D4—41no—
1029D4—41no—
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—21no—
1055C2×C4—21no—
1056C2×C4—21no—
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—22no—
1066C2×C4—22no—
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—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—48no—
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—41no—
1116C2×C4—41no—
1117C2×C4—162no—
1118C2×C4—162no—
1119C2×C4—162no—
1120C2×C4#52512yes—
1121C2×C4#52512yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C22×#4111yescharacteristic
1124C2×C4C2×H(5,𝔽2)11yescharacteristic
1125C2×C4C2×2−1+411yescharacteristic
1126C2×C4#58511yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—22no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22C2×#52511yescharacteristic
1151C22#348811yescharacteristic
1152C22#349711yescharacteristic
1153C22#358411yescharacteristic
1154C22#358511yescharacteristic
1155C22#358611yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—41no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4#349211yescharacteristic
1186C4#349311yescharacteristic
1187C4#351311yescharacteristic
1188C4#351511yescharacteristic
1189C2—82no—
1190C2—161no—
1191C2#3577211yescharacteristic
1192C2#6056511yescharacteristic
1193C2#6059511yescharacteristic
1194C2#6202611yescharacteristic
1195C2#6208211yescharacteristic
1196C2#6238911yescharacteristic
1197C2#6240911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38972C2semidirect
2. #34481C2semidirect
5. #30000C2semidirect
6. #29550C2semidirect
7. #29549C2semidirect
8. #29459C2semidirect
9. #29443C2semidirect
10. #29196C2semidirect
11. #28254C2semidirect
12. #27314C2semidirect
13. #27295C2semidirect
14. #26777C2semidirect
15. #26760C2semidirect
18. #26185C2semidirect
19. #26169C2semidirect
20. #25068C2semidirect
21. #25004C2semidirect
22. #24201C2semidirect
24. #23695C2semidirect
25. #23694C2semidirect
27. #23112C2semidirect
28. #23014C2semidirect
29. #22824C2semidirect
31. #22677C2semidirect

Maximal subgroups

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

subgroupindex
#389722
#344812
#301422
#301412
#300002
#295502
#295492
#294592
#294432
#291962
#282542
#273142
#272952
#267772
#267602
#266112
#265942
#261852
#261692
#250682
#250042
#242012
#241972
#236952
#236942
#236862
#231122
#230142
#228242
#227742
#226772