Finite Group Databasebeta

← #6486341

Subgroups — #6486341

Order 512.

1424 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37359C211yesmaximal, characteristic, complemented
2#34331C211yesmaximal, characteristic
3#33092C211yesmaximal, characteristic, complemented
4#33085C211yesmaximal, characteristic, complemented
5#33076C211yesmaximal, characteristic, complemented
6#33067C211yesmaximal, characteristic, complemented
7#30144C211yesmaximal, characteristic, complemented
8#30128C211yesmaximal, characteristic
9#30088C211yesmaximal, characteristic, complemented
10#30076C211yesmaximal, characteristic
11#27506C211yesmaximal, characteristic, complemented
12#27488C211yesmaximal, characteristic, complemented
13#27381C211yesmaximal, characteristic, complemented
14#27362C211yesmaximal, characteristic, complemented
15#27088C211yesmaximal, characteristic, complemented
16#27063C211yesmaximal, characteristic
17#26769C211yesmaximal, characteristic
18#26763C211yesmaximal, characteristic, complemented
19#26534C211yesmaximal, characteristic, complemented
20#26278C211yesmaximal, characteristic, complemented
21#26099C211yesmaximal, characteristic, complemented
22#25659C211yesmaximal, characteristic
23#25336C211yesmaximal, characteristic, complemented
24#25070C211yesmaximal, characteristic, complemented
25#24680C211yesmaximal, characteristic, complemented
26#24194C211yesmaximal, characteristic
27#22233C211yesmaximal, characteristic, complemented
28#22159C211yesmaximal, characteristic, complemented
29#22026C211yesmaximal, characteristic, complemented
30#21623C211yesmaximal, characteristic, complemented
31#21133C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×C4×SD16C2211yescharacteristic
37#2863C2211yescharacteristic
38#2859C2211yescharacteristic
39#2789—21no—
40#2776—21no—
41#2769—21no—
42#2766—21no—
43#2758—21no—
44#2719—21no—
45#2713—21no—
46#2713—21no—
47#2647C2211yescharacteristic
48#2645C2211yescharacteristic
49#2581C2211yescharacteristic
50#2570C2211yescharacteristic
51#2567C2211yescharacteristic
52#2546C2211yescharacteristic
53#2514C2211yescharacteristic
54#2511C2211yescharacteristic
55#2507C2211yescharacteristic
56#2506C2211yescharacteristic
57#2367—21no—
58#2367C2211yescharacteristic
59#2367C2211yescharacteristic
60#2366C2211yescharacteristic
61#2359—21no—
62#2359—21no—
63#2355C2211yescharacteristic
64#2354C2211yescharacteristic
65#2354C2211yescharacteristic
66Q8×C4⋊C4C2211yescharacteristic
67#2349—21no—
68#2335—21no—
69#2335—21no—
70#2331C2211yescharacteristic
71#2326C2211yescharacteristic
72#2326C2211yescharacteristic
73#2320C2211yescharacteristic
74C4×#127C2211yescharacteristic
75C4×#124—21no—
76#2295C2211yescharacteristic
77#2293—21no—
78#2275C2211yescharacteristic
79#2275C2211yescharacteristic
80C42×Q8C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2097C2211yescharacteristic
84#2096C2211yescharacteristic
85#2095C2211yescharacteristic
86#2094C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2084C2211yescharacteristic
90#2084C2211yescharacteristic
91#2084C2211yescharacteristic
92#2083C2211yescharacteristic
93#2072C2211yescharacteristic
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic
100#2065C2211yescharacteristic
101#2056C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2015C2211yescharacteristic
112#2014C2211yescharacteristic
113#1990C2211yescharacteristic
114#1988C2211yescharacteristic
115#1985C2211yescharacteristic
116#1984C2211yescharacteristic
117#1983C2211yescharacteristic
118#1971C2211yescharacteristic
119#1968C2211yescharacteristic
120#1958C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1948C2211yescharacteristic
124#1948C2211yescharacteristic
125#1948C2211yescharacteristic
126#1948C2211yescharacteristic
127#1940C2211yescharacteristic
128#1939C2211yescharacteristic
129#1936C2211yescharacteristic
130#1933C2211yescharacteristic
131#1928C2211yescharacteristic
132#1928C2211yescharacteristic
133#1927C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1927C2211yescharacteristic
138#1927C2211yescharacteristic
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1920C2211yescharacteristic
142#1919C2211yescharacteristic
143#1919C2211yescharacteristic
144#1919C2211yescharacteristic
145#1919C2211yescharacteristic
146#1919C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1847C2211yescharacteristic
184#1840C2211yescharacteristic
185#1839C2211yescharacteristic
186#1832C2211yescharacteristic
187#1831C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1768C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#559—24no—
207#559—24no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×#124—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236#489—24no—
237#476—24no—
238#464—24no—
239C4×SD16—24no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#401—21no—
290#401—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391D411yescharacteristic
317#391D411yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390—21no—
328#390—21no—
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389D411yescharacteristic
342#389D411yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387D411yescharacteristic
386#387D411yescharacteristic
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#383—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#380—21no—
412#380—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
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—
438#376C2311yescharacteristic
439#376C2311yescharacteristic
440C2×#95—21no—
441C2×#95—21no—
442C43—21no—
443C43C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
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#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
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
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C2411yescharacteristic
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C2×Q16—22no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—82no—
518#127—22no—
519#127—22no—
520#125—82no—
521#125—82no—
522#124—28no—
523#124—22no—
524#124—22no—
525#124—22no—
526#124#4114yes—
527#123—28no—
528#123—28no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—82no—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—82no—
553C4×D4—82no—
554C4×D4—82no—
555C4×D4#4114yes—
556#117—82no—
557#117—82no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
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×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—41no—
652#107—41no—
653#107—41no—
654#106—22no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664C4⋊C8—22no—
665C4⋊C8—22no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#97—22no—
697#97—41no—
698C4×C8—22no—
699C4×C8—41no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
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#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C24—21no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—41no—
772C2×Q8—42no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8C2×#4112yes—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4C2×#4112yes—
793C2×D4C2×#4112yes—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C2511yescharacteristic
841Q16—82no—
842SD16—44no—
843SD16—82no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
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—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
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—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
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⋊C4C2×#4112yes—
929C4⋊C42−1+412yes—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C42—24no—
949C42—22no—
950C42—22no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—41no—
964C42—41no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42C2×#4112yes—
979C42C2×#4112yes—
980C23—22no—
981C23—22no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C23×D411yescharacteristic
995Q8—22no—
996Q8—22no—
997Q8—44no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—162no—
1005D4—22no—
1006D4—22no—
1007D4—22no—
1008D4—22no—
1009D4—48no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—84no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
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—22no—
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—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
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—84no—
1096C2×C4—84no—
1097C2×C4—162no—
1098C2×C4—162no—
1099C2×C4—162no—
1100C2×C4—162no—
1101C2×C4#52512yes—
1102C2×C4#52512yes—
1103C2×C4#57712yes—
1104C2×C4#57712yes—
1105C2×C4C22×#4111yescharacteristic
1106C2×C4C22×#4111yescharacteristic
1107C2×C4C2×2−1+411yescharacteristic
1108C2×C4#58511yescharacteristic
1109C2×C4#58511yescharacteristic
1110C2×C4#58511yescharacteristic
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22C2×#52511yescharacteristic
1134C22#348711yescharacteristic
1135C22#348911yescharacteristic
1136C22C2×#57711yescharacteristic
1137C22C2×#57711yescharacteristic
1138C22#358511yescharacteristic
1139C22#358611yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—42no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4#345511yescharacteristic
1169C4#346111yescharacteristic
1170C4#351511yescharacteristic
1171C4#352111yescharacteristic
1172C2—82no—
1173C2—82no—
1174C2#3520511yescharacteristic
1175C2#6058811yescharacteristic
1176C2#6059111yescharacteristic
1177C2#6191611yescharacteristic
1178C2#6192111yescharacteristic
1179C2#6220511yescharacteristic
1180C2#6223611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
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. #37359C2semidirect
3. #33092C2semidirect
4. #33085C2semidirect
5. #33076C2semidirect
6. #33067C2semidirect
7. #30144C2semidirect
9. #30088C2semidirect
11. #27506C2semidirect
12. #27488C2semidirect
13. #27381C2semidirect
14. #27362C2semidirect
15. #27088C2semidirect
18. #26763C2semidirect
19. #26534C2semidirect
20. #26278C2semidirect
21. #26099C2semidirect
23. #25336C2semidirect
24. #25070C2semidirect
25. #24680C2semidirect
27. #22233C2semidirect
28. #22159C2semidirect
29. #22026C2semidirect
30. #21623C2semidirect
31. #21133C2semidirect

Maximal subgroups

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

subgroupindex
#373592
#343312
#330922
#330852
#330762
#330672
#301442
#301282
#300882
#300762
#275062
#274882
#273812
#273622
#270882
#270632
#267692
#267632
#265342
#262782
#260992
#256592
#253362
#250702
#246802
#241942
#222332
#221592
#220262
#216232
#211332