Finite Group Databasebeta

← #6575015

Subgroups — #6575015

Order 512.

2113 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3266C211yesmaximal, characteristic
2C2×#2949C211yesmaximal, characteristic, complemented
3#35791C211yesmaximal, characteristic
4#35723C211yesmaximal, characteristic, complemented
5#33139C211yesmaximal, characteristic, complemented
6#33019C211yesmaximal, characteristic, complemented
7#33018C211yesmaximal, characteristic, complemented
8#27936C211yesmaximal, characteristic, complemented
9#27664C211yesmaximal, characteristic, complemented
10#26256C211yesmaximal, characteristic, complemented
11#26256C211yesmaximal, characteristic, complemented
12#26186C211yesmaximal, characteristic, complemented
13#26182C211yesmaximal, characteristic, complemented
14#26181C211yesmaximal, characteristic, complemented
15#26177C211yesmaximal, characteristic, complemented
16#25037C211yesmaximal, characteristic, complemented
17#25036C211yesmaximal, characteristic, complemented
18#24923C211yesmaximal, characteristic, complemented
19#24919C211yesmaximal, characteristic, complemented
20#24914C211yesmaximal, characteristic, complemented
21#24910C211yesmaximal, characteristic, complemented
22#24540C211yesmaximal, characteristic, complemented
23#24538C211yesmaximal, characteristic, complemented
24#24053C211yesmaximal, characteristic, complemented
25#24050C211yesmaximal, characteristic
26#22678C211yesmaximal, characteristic, complemented
27#22677C211yesmaximal, characteristic, complemented
28#22444C211yesmaximal, characteristic, complemented
29#22444C211yesmaximal, characteristic, complemented
30#22437C211yesmaximal, characteristic, complemented
31#21569C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#518C2211yescharacteristic
38#3266—28no—
39C2×#497C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#468C2211yescharacteristic
43C2×#467C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#461C2211yescharacteristic
46C2×#452C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#448C2211yescharacteristic
49C2×#450C2211yescharacteristic
50#2949—28no—
51C2×#440C2211yescharacteristic
52C2×#440C2211yescharacteristic
53C2×#440C2211yescharacteristic
54C2×#440C2211yescharacteristic
55C2×#440C2211yescharacteristic
56C2×#440C2211yescharacteristic
57C2×#440C2211yescharacteristic
58C2×C4×SD16C2211yescharacteristic
59C2×C4×SD16C2211yescharacteristic
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×#435C2211yescharacteristic
63C2×#427C2211yescharacteristic
64C2×#419C2211yescharacteristic
65C2×#418C2211yescharacteristic
66C2×#405C2211yescharacteristic
67#2625—21no—
68#2625C2211yescharacteristic
69#2625C2211yescharacteristic
70#2622—21no—
71#2499—21no—
72#2499C2211yescharacteristic
73#2499C2211yescharacteristic
74#2485—21no—
75#2485C2211yescharacteristic
76#2485C2211yescharacteristic
77#2483—21no—
78#2447C2211yescharacteristic
79#2447C2211yescharacteristic
80#2446—21no—
81#2446—21no—
82#2446C2211yescharacteristic, complemented
83#2446C2211yescharacteristic, complemented
84#2444—21no—
85#2443—21no—
86#2423—21no—
87#2423C2211yescharacteristic, complemented
88#2422C2211yescharacteristic
89#2421—21no—
90#2421C2211yescharacteristic, complemented
91#2420C2211yescharacteristic
92#2419—21no—
93#2419—21no—
94#2412—21no—
95#2395—21no—
96#2395C2211yescharacteristic
97C2×#397—21no—
98#2351C2211yescharacteristic, complemented
99Q8×C4⋊C4C2211yescharacteristic, complemented
100#2349C2211yescharacteristic
101D4×C4⋊C4C2211yescharacteristic
102Q8×C22⋊C4C2211yescharacteristic
103Q8×C22⋊C4C2211yescharacteristic, complemented
104Q8×C22⋊C4C2211yescharacteristic, complemented
105#2339C2211yescharacteristic
106#2339C2211yescharacteristic
107D4×C22⋊C4C2211yescharacteristic
108#2097C2211yescharacteristic, complemented
109#2097C2211yescharacteristic, complemented
110#2095C2211yescharacteristic, complemented
111#2095C2211yescharacteristic, complemented
112#2087C2211yescharacteristic, complemented
113#2086C2211yescharacteristic, complemented
114#2076C2211yescharacteristic, complemented
115#2075C2211yescharacteristic, complemented
116#2074C2211yescharacteristic, complemented
117#2073C2211yescharacteristic
118#2072C2211yescharacteristic, complemented
119#2071C2211yescharacteristic
120#2056C2211yescharacteristic, complemented
121#2056C2211yescharacteristic, complemented
122#2055C2211yescharacteristic
123#2055C2211yescharacteristic
124#2043C2211yescharacteristic, complemented
125#2043C2211yescharacteristic, complemented
126#2042C2211yescharacteristic
127#2042C2211yescharacteristic
128#2036C2211yescharacteristic, complemented
129#2035C2211yescharacteristic, complemented
130#2034C2211yescharacteristic
131#2033C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1971C2211yescharacteristic, complemented
135#1971C2211yescharacteristic, complemented
136#1969C2211yescharacteristic, complemented
137#1969C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1942C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1924C2211yescharacteristic, complemented
147#1924C2211yescharacteristic, complemented
148#1917C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1878C2211yescharacteristic, complemented
155#1878C2211yescharacteristic, complemented
156#1878C2211yescharacteristic, complemented
157#1878C2211yescharacteristic, complemented
158#1878C2211yescharacteristic, complemented
159#1878C2211yescharacteristic, complemented
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1870C2211yescharacteristic
169#1865C2211yescharacteristic, complemented
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1851C2211yescharacteristic
182#1847C2211yescharacteristic, complemented
183#1847C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic
186#1818C2211yescharacteristic
187#1809C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1808C2211yescharacteristic
190#1805C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic, complemented
198#1787C2211yescharacteristic, complemented
199#1786C2211yescharacteristic
200#1771C2211yescharacteristic, complemented
201#1771C2211yescharacteristic, complemented
202#1753C2211yescharacteristic, complemented
203#1753C2211yescharacteristic, complemented
204#1752C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C23×D4C2311yescharacteristic
209C2×#137—24no—
210C2×#137—24no—
211C2×#137—24no—
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16—24no—
216C22×SD16—24no—
217C22×SD16D418yes—
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×M16C2311yescharacteristic
225C22×M16C2311yescharacteristic
226C23×C8C2311yescharacteristic
227D4×Q8—24no—
228D4×Q8—42no—
229#546—24no—
230#546—42no—
231C2×C4⋊Q8—21no—
232C2×C4⋊Q8C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244#519—24no—
245#519—42no—
246#518—24no—
247#518—42no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117—21no—
269C2×#117—21no—
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C22×C4⋊C4—21no—
274C22×C22⋊C4—21no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—21no—
277C22×C22⋊C4—21no—
278#497—24no—
279#485—42no—
280#485—42no—
281#468—24no—
282#467—24no—
283#464—24no—
284#461—24no—
285#452—24no—
286#451—24no—
287#450—24no—
288#448—24no—
289#440—24no—
290#440—24no—
291#440—24no—
292#440—24no—
293#440—24no—
294#440—24no—
295#440—24no—
296C4×SD16—24no—
297C4×SD16—24no—
298C4×SD16—24no—
299C4×SD16—24no—
300#435—24no—
301#427—24no—
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316#419—24no—
317#418—24no—
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353#405—24no—
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361#400—21no—
362#400—21no—
363#400—21no—
364#400—21no—
365#400—21no—
366#400D411yescharacteristic
367#399—21no—
368#399D411yescharacteristic
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398D411yescharacteristic
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#397—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#397—21no—
389#397—21no—
390#397—21no—
391#397—21no—
392#397D411yescharacteristic
393#397D411yescharacteristic
394#397D411yescharacteristic
395#394—21no—
396#394—21no—
397#394—21no—
398#394—21no—
399#394D411yescharacteristic
400#394D411yescharacteristic
401#391—21no—
402#391—21no—
403#391—21no—
404#391—21no—
405#391—21no—
406#391—21no—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#384—21no—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#382—21no—
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#381—21no—
468#381—21no—
469#381—21no—
470#381—21no—
471#381—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482#380C2311yescharacteristic
483#379—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4—21no—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493C4×C22⋊C4C2311yescharacteristic
494C2×#95—21no—
495C2×#95—21no—
496C2×#95—21no—
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C25—21no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—41no—
537C22×Q8—41no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×Q8—41no—
541C22×Q8C2×D414yes—
542C22×Q8C2411yescharacteristic
543C22×Q8C2411yescharacteristic
544C22×Q8C2411yescharacteristic
545C22×Q8C2411yescharacteristic
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—22no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4C2×D414yes—
555C22×D4C2×D411yescharacteristic
556C22×D4C2411yescharacteristic
557C22×D4C2411yescharacteristic
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—21no—
561C23×C4—21no—
562C23×C4—21no—
563C23×C4—21no—
564C23×C4—21no—
565C23×C4—21no—
566C23×C4—21no—
567C23×C4—21no—
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570#137—416no—
571C2×Q16—22no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—41no—
579C2×Q16—41no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—232no—
585C2×SD16—22no—
586C2×SD16—22no—
587C2×SD16—22no—
588C2×SD16—22no—
589C2×SD16—22no—
590C2×SD16—22no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16C2×D414yes—
594C2×SD16C2×D414yes—
595C2×SD16C2×D414yes—
596C2×SD16C2×D414yes—
597C2×SD16#4114yes—
598C2×SD16#4114yes—
599C2×M16—22no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—22no—
603C2×M16—41no—
604C2×M16—41no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8C2×D414yes—
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C4⋊Q8—22no—
617C4⋊Q8—41no—
618C4⋊Q8—44no—
619#124—22no—
620#124—41no—
621#123—44no—
622#123—82no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—44no—
629C22⋊Q8—44no—
630C22⋊Q8—41no—
631#121—22no—
632#121—44no—
633#121—41no—
634#120—44no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—44no—
650C4×Q8—44no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—44no—
668C4×D4—44no—
669C4×D4—44no—
670#117—22no—
671#117—22no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—44no—
677#117—44no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—82no—
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4—44no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—82no—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773#107—22no—
774#107—22no—
775#107—22no—
776#107—22no—
777#107—22no—
778#107—41no—
779#107—41no—
780#106—22no—
781#106—22no—
782#106—41no—
783#106—41no—
784C4⋊C8—22no—
785C4⋊C8—41no—
786C4⋊C8—41no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#103—41no—
805#103—41no—
806#103—41no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—41no—
816#102—41no—
817C22⋊C8—22no—
818C22⋊C8—22no—
819C22⋊C8—22no—
820C22⋊C8—41no—
821C22⋊C8—41no—
822#97—22no—
823#97—22no—
824#97—22no—
825#97—22no—
826#97—22no—
827C4×C8—22no—
828C4×C8—22no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95—21no—
866#95—21no—
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871#95C2×D411yescharacteristic
872#95C2×D411yescharacteristic
873#95C2×D411yescharacteristic
874#95C2×D411yescharacteristic
875#95C2×D411yescharacteristic
876#95C2×D411yescharacteristic
877C24—21no—
878C24—21no—
879C24—24no—
880C24—42no—
881C24—42no—
882C24—81no—
883C24—81no—
884C24—81no—
885C24—81no—
886C24C22×D411yescharacteristic
887C24C22×D411yescharacteristic
888#41—44no—
889#41—82no—
890#41—82no—
891#41—82no—
892C2×Q8—24no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—28no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×Q8—44no—
922C2×Q8—44no—
923C2×Q8—82no—
924C2×Q8—82no—
925C2×Q8—82no—
926C2×Q8C22×D412yes—
927C2×Q8C22×D412yes—
928C2×Q8C2×#4112yes—
929C2×Q8C2×#4112yes—
930C2×D4—28no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4C22×D412yes—
955C2×D4C22×D412yes—
956C2×D4C2×#4112yes—
957C2×D4C2×#4112yes—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—24no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4—81no—
1006C22×C4—81no—
1007C22×C4—81no—
1008C22×C4—81no—
1009C22×C4—81no—
1010C22×C4—81no—
1011C22×C4—81no—
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D411yescharacteristic
1024C22×C4C22×D412yes—
1025C22×C4H(5,𝔽2)12yes—
1026C22×C4C2511yescharacteristic
1027Q16—44no—
1028Q16—44no—
1029Q16—82no—
1030SD16—28no—
1031SD16—28no—
1032SD16—28no—
1033SD16—44no—
1034SD16—82no—
1035SD16#123116yescomplemented
1036M16—44no—
1037M16—44no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—28no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8C22×D412yes—
1060C2×C8C22×D412yes—
1061C2×C8C2×#4112yes—
1062C2×C8C2×#4112yes—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—21no—
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—81no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4—81no—
1111C4⋊C4—81no—
1112C4⋊C4—81no—
1113C4⋊C4—81no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—22no—
1183C23—21no—
1184C23—21no—
1185C23—48no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—84no—
1197C23—84no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23—162no—
1202C23D4212yes—
1203C23C23×D411yescharacteristic
1204Q8—22no—
1205Q8—22no—
1206Q8—22no—
1207Q8—22no—
1208Q8—22no—
1209Q8—48no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—84no—
1221Q8C2×#12314yes—
1222D4—22no—
1223D4—22no—
1224D4—22no—
1225D4—22no—
1226D4—22no—
1227D4—48no—
1228D4—44no—
1229D4—41no—
1230D4—41no—
1231D4—84no—
1232D4—162no—
1233D4C2×#12314yes—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—48no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—84no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4D4212yes—
1330C2×C4C23×D411yescharacteristic
1331C2×C4C22×#4111yescharacteristic
1332C2×C4C22×#4111yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4#58511yescharacteristic
1335C2×C4#58511yescharacteristic
1336C8—22no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8C2×#12314yes—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—24no—
1348C22—42no—
1349C22—41no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—42no—
1363C22—41no—
1364C22—42no—
1365C22—41no—
1366C22—41no—
1367C22—42no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—168no—
1373C22C2×D4211yescharacteristic
1374C22D4×#4111yescharacteristic
1375C22D4×#4111yescharacteristic
1376C22#358511yescharacteristic
1377C22#358611yescharacteristic
1378C22#358611yescharacteristic
1379C22#358611yescharacteristic
1380C4—22no—
1381C4—24no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—42no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4C22×#12311yescharacteristic
1407C4#348511yescharacteristic
1408C4#351311yescharacteristic
1409C4#351311yescharacteristic
1410C2—42no—
1411C2—44no—
1412C2—81no—
1413C2—82no—
1414C2D4×#12311yescharacteristic
1415C2#6106011yescharacteristic
1416C2#6108011yescharacteristic
1417C2#6150311yescharacteristic
1418C2#6151311yescharacteristic
1419C2#6151411yescharacteristic
1420C2#6151411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2949C2semidirect
4. #35723C2semidirect
5. #33139C2semidirect
6. #33019C2semidirect
7. #33018C2semidirect
8. #27936C2semidirect
9. #27664C2semidirect
10. #26256C2semidirect
11. #26256C2semidirect
12. #26186C2semidirect
13. #26182C2semidirect
14. #26181C2semidirect
15. #26177C2semidirect
16. #25037C2semidirect
17. #25036C2semidirect
18. #24923C2semidirect
19. #24919C2semidirect
20. #24914C2semidirect
21. #24910C2semidirect
22. #24540C2semidirect
23. #24538C2semidirect
24. #24053C2semidirect
26. #22678C2semidirect
27. #22677C2semidirect
28. #22444C2semidirect
29. #22444C2semidirect
30. #22437C2semidirect
31. #21569C2semidirect
82. #2446C22semidirect
83. #2446C22semidirect
87. #2423C22semidirect
90. #2421C22semidirect
98. #2351C22semidirect
99. Q8×C4⋊C4C22semidirect
103. Q8×C22⋊C4C22semidirect
104. Q8×C22⋊C4C22semidirect
108. #2097C22semidirect
109. #2097C22semidirect
110. #2095C22semidirect
111. #2095C22semidirect
112. #2087C22semidirect
113. #2086C22semidirect
114. #2076C22semidirect
115. #2075C22semidirect
116. #2074C22semidirect
118. #2072C22semidirect
120. #2056C22semidirect
121. #2056C22semidirect
124. #2043C22semidirect
125. #2043C22semidirect
128. #2036C22semidirect
129. #2035C22semidirect
134. #1971C22semidirect
135. #1971C22semidirect
136. #1969C22semidirect
137. #1969C22semidirect
138. #1943C22semidirect
139. #1943C22semidirect
140. #1942C22semidirect
141. #1942C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1924C22semidirect
147. #1924C22semidirect
148. #1917C22semidirect
149. #1917C22semidirect
154. #1878C22semidirect
155. #1878C22semidirect
156. #1878C22semidirect
157. #1878C22semidirect
158. #1878C22semidirect
159. #1878C22semidirect
169. #1865C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
182. #1847C22semidirect
183. #1847C22semidirect
187. #1809C22semidirect
188. #1809C22semidirect
190. #1805C22semidirect
192. #1803C22semidirect
197. #1787C22semidirect
198. #1787C22semidirect
200. #1771C22semidirect
201. #1771C22semidirect
202. #1753C22semidirect
203. #1753C22semidirect
1035. SD16#123semidirect

Maximal subgroups

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

subgroupindex
C2×#32662
C2×#29492
#357912
#357232
#331392
#330192
#330182
#279362
#276642
#262562
#261862
#261822
#261812
#261772
#250372
#250362
#249232
#249192
#249142
#249102
#245402
#245382
#240532
#240502
#226782
#226772
#224442
#224372
#215692