Finite Group Databasebeta

← #7022280

Subgroups — #7022280

Order 512.

1809 conjugacy classes of subgroups.

The subgroup lattice has 1453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45097C211yesmaximal, characteristic, complemented
2#44960C211yesmaximal, characteristic, complemented
3#32674C211yesmaximal, characteristic, complemented
4#32624C211yesmaximal, characteristic, complemented
5#32183C211yesmaximal, characteristic, complemented
6#32172C211yesmaximal, characteristic, complemented
7#31901C211yesmaximal, characteristic, complemented
8#31224C211yesmaximal, characteristic, complemented
9#30755C211yesmaximal, characteristic, complemented
10#30748C211yesmaximal, characteristic, complemented
11#28368C211yesmaximal, characteristic, complemented
12#28133C211yesmaximal, characteristic, complemented
13#27214C211yesmaximal, characteristic, complemented
14#27065C211yesmaximal, characteristic, complemented
15#26602C211yesmaximal, characteristic, complemented
16#26596C211yesmaximal, characteristic, complemented
17#25793C211yesmaximal, characteristic, complemented
18#25642C211yesmaximal, characteristic, complemented
19#25373C211yesmaximal, characteristic, complemented
20#24645C211yesmaximal, characteristic, complemented
21#24531C211yesmaximal, characteristic, complemented
22#24477C211yesmaximal, characteristic, complemented
23#24364C211yesmaximal, characteristic, complemented
24#24363C211yesmaximal, characteristic, complemented
25#24218C211yesmaximal, characteristic, complemented
26#24194C211yesmaximal, characteristic, complemented
27#23426C211yesmaximal, characteristic, complemented
28#22582C211yesmaximal, characteristic, complemented
29#22443C211yesmaximal, characteristic, complemented
30#22294C211yesmaximal, characteristic, complemented
31#22201C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#559C2211yescharacteristic
35C2×#535C2211yescharacteristic
36C2×#496C2211yescharacteristic
37C2×#495C2211yescharacteristic
38C2×#483C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#464C2211yescharacteristic, complemented
41C2×#462C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic, complemented
44C2×#459C2211yescharacteristic
45C2×#459C2211yescharacteristic, complemented
46C2×#452C2211yescharacteristic
47C2×#449C2211yescharacteristic
48C2×#447C2211yescharacteristic
49C2×#440C2211yescharacteristic
50C2×C4×SD16C2211yescharacteristic
51C2×#417C2211yescharacteristic
52C22×#102C2211yescharacteristic
53#2752—21no—
54#2749—21no—
55#2741—21no—
56#2717—21no—
57#2701—21no—
58#2697—21no—
59#2686—21no—
60#2684—21no—
61#2610—21no—
62#2592C2211yescharacteristic
63#2581C2211yescharacteristic, complemented
64#2578—21no—
65#2548C2211yescharacteristic, complemented
66#2547C2211yescharacteristic
67#2545C2211yescharacteristic
68#2544C2211yescharacteristic
69#2534—21no—
70#2531—21no—
71#2513C2211yescharacteristic, complemented
72#2513C2211yescharacteristic, complemented
73#2504C2211yescharacteristic
74#2471—21no—
75#2448C2211yescharacteristic, complemented
76#2447C2211yescharacteristic
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic, complemented
79#2444—21no—
80#2435C2211yescharacteristic
81#2432C2211yescharacteristic
82#2431C2211yescharacteristic
83#2425—21no—
84#2418—21no—
85#2396C2211yescharacteristic
86#2367C2211yescharacteristic, complemented
87#2366C2211yescharacteristic
88#2356C2211yescharacteristic, complemented
89#2344C2211yescharacteristic
90#2341C2211yescharacteristic
91#2339C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93#2324C2211yescharacteristic
94#2323C2211yescharacteristic
95#2311C2211yescharacteristic
96#2097C2211yescharacteristic, complemented
97#2092C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2056C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2041C2211yescharacteristic
116#2015C2211yescharacteristic
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic, complemented
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic, complemented
123#2013C2211yescharacteristic, complemented
124#2013C2211yescharacteristic, complemented
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic, complemented
131#2012C2211yescharacteristic, complemented
132#2011C2211yescharacteristic
133#2011C2211yescharacteristic
134#2011C2211yescharacteristic
135#2011C2211yescharacteristic
136#1985C2211yescharacteristic, complemented
137#1984C2211yescharacteristic, complemented
138#1983C2211yescharacteristic
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic
141#1982C2211yescharacteristic
142#1973C2211yescharacteristic
143#1972C2211yescharacteristic
144#1972C2211yescharacteristic, complemented
145#1970C2211yescharacteristic
146#1970C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1960C2211yescharacteristic, complemented
149#1958C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1893C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1877C2211yescharacteristic, complemented
183#1877C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic, complemented
186#1864C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1824C2211yescharacteristic
191#1809C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C2×#135—42no—
210C2×#135—42no—
211C2×#135—42no—
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×D8C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C23×C8C2311yescharacteristic
229#559—42no—
230#559—42no—
231#535—42no—
232#535—42no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#124—21no—
238C2×#124—21no—
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#123—21no—
246C2×#123—21no—
247C2×#123—21no—
248C2×#123—21no—
249C2×C22⋊Q8C2311yescharacteristic
250C2×#121—21no—
251C2×#121—21no—
252C2×#121C2311yescharacteristic
253C2×#120—21no—
254C2×#120—21no—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×#117—21no—
267C2×#117C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C22⋊C4—21no—
270#496—42no—
271#495—42no—
272#483—42no—
273#468—24no—
274#464—42no—
275#463—42no—
276#463—42no—
277#462—42no—
278#459—42no—
279#459—42no—
280#452—42no—
281#449—42no—
282#447—42no—
283#440—42no—
284C4×SD16—42no—
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#417—24no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#102—42no—
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#400D411yescharacteristic
340#399—21no—
341#399D411yescharacteristic
342#398D411yescharacteristic
343#398D411yescharacteristic
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#396—21no—
357#396—21no—
358#396D411yescharacteristic
359#396D411yescharacteristic
360#395—21no—
361#395D411yescharacteristic
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#393—21no—
375#393D411yescharacteristic
376#392—21no—
377#392—21no—
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#383—21no—
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#381—21no—
457#381—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380—21no—
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#379—21no—
466#379—21no—
467#379—21no—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479#376—21no—
480C2×#95—21no—
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4C2411yescharacteristic
552AGL(1,ℤ/8)—416no—
553#135—416no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—41no—
588C2×D8—41no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8—41no—
595C2×D8—41no—
596C2×D8—41no—
597C2×D8—41no—
598C2×D8—41no—
599C2×M16—41no—
600C2×M16—41no—
601C2×M16#4114yes—
602C22×C8—22no—
603C22×C8—41no—
604C22×C8—41no—
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C4⋊Q8—41no—
614C4⋊Q8—41no—
615#127—22no—
616#127—22no—
617#127—22no—
618#127—41no—
619#127—41no—
620#127—41no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—22no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#124—41no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—44no—
634#124—82no—
635#123—44no—
636#123—44no—
637#123—82no—
638#123—82no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641#121—22no—
642#121—22no—
643#121—44no—
644#121—44no—
645#120—44no—
646#120—44no—
647C4×Q8—22no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665C4×D4—44no—
666C4×D4—82no—
667#117—41no—
668#117—41no—
669#117—82no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
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—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—82no—
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×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#107—22no—
770#107—41no—
771#106—41no—
772#106—41no—
773#106—41no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778C4⋊C8—41no—
779C4⋊C8—41no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102—41no—
813#102—41no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816#97—41no—
817#97—41no—
818C4×C8—41no—
819C4×C8—41no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
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#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—42no—
864C24—42no—
865C24—81no—
866C24—81no—
867C24—81no—
868C24—81no—
869C24—81no—
870C24C22×D411yescharacteristic
871#41—44no—
872#41—44no—
873#41—44no—
874#41—44no—
875#41—82no—
876#41—82no—
877#41—82no—
878#41—82no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—41no—
897C2×Q8—41no—
898C2×Q8—41no—
899C2×Q8H(5,𝔽2)12yes—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—82no—
943C2×D4—82no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4—81no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4—81no—
958C2×D4—81no—
959C2×D4—81no—
960C2×D4—81no—
961C2×D4—81no—
962C2×D4H(5,𝔽2)12yes—
963C2×D4H(5,𝔽2)12yes—
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—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C2×#4112yes—
1017C22×C4H(5,𝔽2)12yes—
1018C22×C4C2511yescharacteristic
1019Q16—44no—
1020Q16—82no—
1021SD16—28no—
1022SD16—44no—
1023SD16—44no—
1024SD16—44no—
1025SD16—82no—
1026SD16—82no—
1027SD16—82no—
1028D8—44no—
1029D8—44no—
1030D8—44no—
1031D8—82no—
1032D8—82no—
1033D8—82no—
1034M16—44no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
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—44no—
1058C2×C8C2×#4112yes—
1059C2×C8C2×#4112yes—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
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—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C22⋊C4—81no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—21no—
1161C42—21no—
1162C42—21no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—81no—
1167C42—81no—
1168C42—81no—
1169C42—81no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—22no—
1177C23—22no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—84no—
1212C23—84no—
1213C23—162no—
1214C23—162no—
1215C23—162no—
1216C23—162no—
1217C23—162no—
1218C23#55012yes—
1219C23C23×D411yescharacteristic
1220Q8—22no—
1221Q8—22no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8—41no—
1229Q8—41no—
1230Q8—41no—
1231Q8—41no—
1232Q8—82no—
1233D4—22no—
1234D4—22no—
1235D4—22no—
1236D4—22no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—41no—
1249D4—41no—
1250D4—41no—
1251D4—41no—
1252D4—41no—
1253D4—84no—
1254D4—84no—
1255D4—84no—
1256D4—84no—
1257D4—84no—
1258D4—162no—
1259D4—162no—
1260D4—162no—
1261D4—162no—
1262D4—162no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
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—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—84no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—162no—
1342C2×C4—162no—
1343C2×C4—162no—
1344C2×C4—162no—
1345C2×C4—162no—
1346C2×C4#55012yes—
1347C2×C4C22×#4111yescharacteristic
1348C2×C4C2×H(5,𝔽2)11yescharacteristic
1349C2×C4C2×H(5,𝔽2)11yescharacteristic
1350C2×C4C2×H(5,𝔽2)11yescharacteristic
1351C2×C4C2×H(5,𝔽2)11yescharacteristic
1352C2×C4#58511yescharacteristic
1353C8—22no—
1354C8—22no—
1355C8—41no—
1356C8—41no—
1357C8—41no—
1358C8—41no—
1359C8—41no—
1360C8—41no—
1361C22—22no—
1362C22—22no—
1363C22—22no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—81no—
1401C22—81no—
1402C22—81no—
1403C22—168no—
1404C22C2×#55011yescharacteristic
1405C22#348411yescharacteristic
1406C22#348811yescharacteristic
1407C22#358411yescharacteristic
1408C22#358411yescharacteristic
1409C22#358511yescharacteristic
1410C22#358511yescharacteristic
1411C4—22no—
1412C4—42no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—41no—
1424C4—41no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4—81no—
1433C4—81no—
1434C4—81no—
1435C4#349011yescharacteristic
1436C4#349411yescharacteristic
1437C4#353211yescharacteristic
1438C4#353411yescharacteristic
1439C2—42no—
1440C2—82no—
1441C2—82no—
1442C2—161no—
1443C2—161no—
1444C2—161no—
1445C2#4309911yescharacteristic
1446C2#6142411yescharacteristic
1447C2#6142411yescharacteristic
1448C2#6161411yescharacteristic
1449C2#6167811yescharacteristic
1450C2#6206111yescharacteristic
1451C2#6209311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45097C2semidirect
2. #44960C2semidirect
3. #32674C2semidirect
4. #32624C2semidirect
5. #32183C2semidirect
6. #32172C2semidirect
7. #31901C2semidirect
8. #31224C2semidirect
9. #30755C2semidirect
10. #30748C2semidirect
11. #28368C2semidirect
12. #28133C2semidirect
13. #27214C2semidirect
14. #27065C2semidirect
15. #26602C2semidirect
16. #26596C2semidirect
17. #25793C2semidirect
18. #25642C2semidirect
19. #25373C2semidirect
20. #24645C2semidirect
21. #24531C2semidirect
22. #24477C2semidirect
23. #24364C2semidirect
24. #24363C2semidirect
25. #24218C2semidirect
26. #24194C2semidirect
27. #23426C2semidirect
28. #22582C2semidirect
29. #22443C2semidirect
30. #22294C2semidirect
31. #22201C2semidirect
40. C2×#464C22semidirect
41. C2×#462C22semidirect
43. C2×#463C22semidirect
45. C2×#459C22semidirect
63. #2581C22semidirect
65. #2548C22semidirect
71. #2513C22semidirect
72. #2513C22semidirect
75. #2448C22semidirect
78. #2445C22semidirect
86. #2367C22semidirect
88. #2356C22semidirect
96. #2097C22semidirect
97. #2092C22semidirect
100. #2066C22semidirect
103. #2065C22semidirect
104. #2056C22semidirect
105. #2056C22semidirect
106. #2055C22semidirect
107. #2055C22semidirect
108. #2055C22semidirect
111. #2054C22semidirect
119. #2015C22semidirect
122. #2014C22semidirect
123. #2013C22semidirect
124. #2013C22semidirect
130. #2012C22semidirect
131. #2012C22semidirect
136. #1985C22semidirect
137. #1984C22semidirect
144. #1972C22semidirect
147. #1968C22semidirect
148. #1960C22semidirect
149. #1958C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
152. #1935C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
160. #1926C22semidirect
161. #1925C22semidirect
162. #1921C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
172. #1880C22semidirect
173. #1880C22semidirect
174. #1880C22semidirect
179. #1879C22semidirect
180. #1878C22semidirect
181. #1878C22semidirect
182. #1877C22semidirect
183. #1877C22semidirect
184. #1865C22semidirect
185. #1864C22semidirect
186. #1864C22semidirect
187. #1862C22semidirect
198. #1762C22semidirect
199. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#450972
#449602
#326742
#326242
#321832
#321722
#319012
#312242
#307552
#307482
#283682
#281332
#272142
#270652
#266022
#265962
#257932
#256422
#253732
#246452
#245312
#244772
#243642
#243632
#242182
#241942
#234262
#225822
#224432
#222942
#222012