Finite Group Databasebeta

← #7181339

Subgroups — #7181339

Order 512.

1217 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C211yesmaximal, characteristic
2#39999C211yesmaximal, characteristic, complemented
3#32527C211yesmaximal, characteristic
4#32526C211yesmaximal, characteristic, complemented
5#32479C211yesmaximal, characteristic, complemented
6#32472C211yesmaximal, characteristic
7#32434C211yesmaximal, characteristic, complemented
8#32433C211yesmaximal, characteristic
9#32356C211yesmaximal, characteristic
10#32343C211yesmaximal, characteristic, complemented
11#29316C211yesmaximal, characteristic, complemented
12#29194C211yesmaximal, characteristic
13#28031C211yesmaximal, characteristic
14#28030C211yesmaximal, characteristic, complemented
15#28012C211yesmaximal, characteristic, complemented
16#28010C211yesmaximal, characteristic
17#27501C211yesmaximal, characteristic, complemented
18#27498C211yesmaximal, characteristic
19#27369C211yesmaximal, characteristic
20#27368C211yesmaximal, characteristic, complemented
21#26325C211yesmaximal, characteristic
22#26324C211yesmaximal, characteristic
23#25297C211yesmaximal, characteristic
24#25297C211yesmaximal, characteristic
25#25067C211yesmaximal, characteristic, complemented
26#25000C211yesmaximal, characteristic, complemented
27#23779C211yesmaximal, characteristic, complemented
28#23149C211yesmaximal, characteristic, complemented
29#22739C211yesmaximal, characteristic, complemented
30#22725C211yesmaximal, characteristic, complemented
31#22150C211yesmaximal, characteristic
32C2×#464C2211yescharacteristic
33C2×C8×Q8C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35#2864C2211yescharacteristic
36#2794—21no—
37#2793—21no—
38#2789—21no—
39#2758—21no—
40#2716—21no—
41#2713—21no—
42#2655—21no—
43#2594—21no—
44#2592C2211yescharacteristic
45#2592C2211yescharacteristic
46#2581C2211yescharacteristic
47#2581C2211yescharacteristic
48#2573—21no—
49#2566C2211yescharacteristic
50#2565C2211yescharacteristic
51#2533—21no—
52#2528—21no—
53#2527—21no—
54#2525—21no—
55#2523—21no—
56#2514C2211yescharacteristic
57#2514C2211yescharacteristic
58#2514C2211yescharacteristic
59#2513C2211yescharacteristic
60#2512C2211yescharacteristic
61#2511C2211yescharacteristic
62#2511C2211yescharacteristic
63#2511C2211yescharacteristic
64#2509C2211yescharacteristic
65#2508C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506C2211yescharacteristic
68#2373—21no—
69#2357C2211yescharacteristic
70#2356C2211yescharacteristic
71#2355C2211yescharacteristic
72#2355C2211yescharacteristic
73#2355C2211yescharacteristic
74#2355C2211yescharacteristic
75#2336—21no—
76C4×C4⋊Q8C2211yescharacteristic
77C4×#125C2211yescharacteristic
78C4×#124C2211yescharacteristic
79#2295C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2099C2211yescharacteristic
83#2097C2211yescharacteristic
84#2097C2211yescharacteristic
85#2096C2211yescharacteristic
86#2095C2211yescharacteristic
87#2095C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2074C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2056C2211yescharacteristic
116#2056C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2026C2211yescharacteristic
120#1984C2211yescharacteristic
121#1984C2211yescharacteristic
122#1983C2211yescharacteristic
123#1969C2211yescharacteristic
124#1969C2211yescharacteristic
125#1969C2211yescharacteristic
126#1968C2211yescharacteristic
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic
129#1958C2211yescharacteristic
130#1958C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1947C2211yescharacteristic
143#1947C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1939C2211yescharacteristic
149#1939C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1921C2211yescharacteristic
169#1921C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1878C2211yescharacteristic
177#1877C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1846C2211yescharacteristic
185#1846C2211yescharacteristic
186#1844C2211yescharacteristic
187#1835C2211yescharacteristic
188#1835C2211yescharacteristic
189#1834C2211yescharacteristic
190#1805C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C4×#106C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C2×C4⋊Q8D411yescharacteristic
206C2×#126—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215#464—24no—
216C8×Q8—24no—
217C8×Q8—24no—
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#401—21no—
273#401—21no—
274#401—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#395—21no—
305#395—21no—
306#393—21no—
307#393—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391D411yescharacteristic
313#391D411yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#389—21no—
331#389—21no—
332#389D411yescharacteristic
333#389D411yescharacteristic
334#389D411yescharacteristic
335#389D411yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—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#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#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#385—21no—
397#385—21no—
398#384D411yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#383—21no—
406#383—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442#376—21no—
443#376—21no—
444C43C2311yescharacteristic
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#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
481C22×Q8C2×D411yescharacteristic
482C22×Q8C2×D411yescharacteristic
483C22×Q8C2411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C2×Q16—22no—
488C2×Q16—41no—
489C2×Q16—41no—
490C2×SD16—22no—
491C2×SD16—41no—
492C2×SD16—41no—
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C4⋊Q8—24no—
502#126—44no—
503#125—41no—
504#125—41no—
505#125—44no—
506#124—22no—
507#124—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4C2×D411yescharacteristic
543C2×C4⋊C4C2×D411yescharacteristic
544C2×C4⋊C4C2×D411yescharacteristic
545C2×C4⋊C4C2×D411yescharacteristic
546C2×C4⋊C4C2×D411yescharacteristic
547C2×C4⋊C4C2×D411yescharacteristic
548C2×C4⋊C4C2×D411yescharacteristic
549C2×C4⋊C4C2×D411yescharacteristic
550C2×C4⋊C4C2×D411yescharacteristic
551C2×C4⋊C4C2×D411yescharacteristic
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42—21no—
585C2×C42—21no—
586C2×C42—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42C2×D411yescharacteristic
596C2×C42C2×D411yescharacteristic
597C2×C42C2×D411yescharacteristic
598C2×C42C2×D411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606#107—41no—
607#107—41no—
608#107—41no—
609#107—41no—
610#107—41no—
611#107—41no—
612#107—41no—
613#107—41no—
614#107—41no—
615#106—22no—
616#106—41no—
617#106—41no—
618#106—41no—
619#106—41no—
620#106—41no—
621#106—41no—
622#106—41no—
623#106—41no—
624C4⋊C8—22no—
625C4⋊C8—22no—
626C4⋊C8—22no—
627C4⋊C8—22no—
628C4⋊C8—22no—
629C4⋊C8—22no—
630C4⋊C8—41no—
631C4⋊C8#4114yes—
632#103—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103—41no—
639#103—41no—
640#103—41no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#102—22no—
646#102—22no—
647#102—41no—
648#102—41no—
649#102—41no—
650#102—41no—
651#102—41no—
652C4×C8—22no—
653C4×C8—22no—
654C4×C8—22no—
655C4×C8—22no—
656C4×C8—22no—
657C4×C8—22no—
658C4×C8—41no—
659C4×C8—41no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
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#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C24—21no—
730C2×Q8—22no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—41no—
747C2×Q8—41no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C2511yescharacteristic
787Q16—82no—
788SD16—82no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8C2×#4112yes—
811C2×C8C2×#4112yes—
812C2×C82−1+412yes—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4#13514yes—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—81no—
884C22⋊C4—81no—
885C22⋊C4—81no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—41no—
904C42—41no—
905C42—41no—
906C42—42no—
907C42—42no—
908C42—42no—
909C42—42no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42C2×#4112yes—
920C422−1+412yes—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23C23×D411yescharacteristic
929Q8—44no—
930Q8—44no—
931Q8—41no—
932Q8—41no—
933Q8—41no—
934Q8—41no—
935Q8—41no—
936Q8—41no—
937Q8—41no—
938Q8—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—162no—
1026C2×C4#54712yes—
1027C2×C4#54712yes—
1028C2×C4C2×#13512yes—
1029C2×C4C2×#13512yes—
1030C2×C4C2×#13512yes—
1031C2×C4C22×#4111yescharacteristic
1032C2×C4C2×2−1+411yescharacteristic
1033C2×C4C2×2−1+411yescharacteristic
1034C2×C4#58511yescharacteristic
1035C2×C4#58511yescharacteristic
1036C2×C4#58511yescharacteristic
1037C8—22no—
1038C8—22no—
1039C8—22no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8—41no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22C2×#54711yescharacteristic
1053C22#348711yescharacteristic
1054C22#349711yescharacteristic
1055C22C22×#13511yescharacteristic
1056C22#358411yescharacteristic
1057C22#358411yescharacteristic
1058C22#358611yescharacteristic
1059C4—22no—
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4#351611yescharacteristic
1089C4#352111yescharacteristic
1090C4#355511yescharacteristic
1091C4#355711yescharacteristic
1092C2—161no—
1093C2#4524211yescharacteristic
1094C2#6123411yescharacteristic
1095C2#6128011yescharacteristic
1096C2#6188711yescharacteristic
1097C2#6193011yescharacteristic
1098C2#6235811yescharacteristic
1099C2#6241211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39999C2semidirect
4. #32526C2semidirect
5. #32479C2semidirect
7. #32434C2semidirect
10. #32343C2semidirect
11. #29316C2semidirect
14. #28030C2semidirect
15. #28012C2semidirect
17. #27501C2semidirect
20. #27368C2semidirect
25. #25067C2semidirect
26. #25000C2semidirect
27. #23779C2semidirect
28. #23149C2semidirect
29. #22739C2semidirect
30. #22725C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#399992
#325272
#325262
#324792
#324722
#324342
#324332
#323562
#323432
#293162
#291942
#280312
#280302
#280122
#280102
#275012
#274982
#273692
#273682
#263252
#263242
#252972
#250672
#250002
#237792
#231492
#227392
#227252
#221502