Finite Group Databasebeta

← #7517150

Subgroups — #7517150

Order 512.

1917 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3346C211yesmaximal, characteristic, complemented
2C2×#3097C211yesmaximal, characteristic, complemented
3#45114C211yesmaximal, characteristic, complemented
4#35689C211yesmaximal, characteristic
5#31200C211yesmaximal, characteristic, complemented
6#31101C211yesmaximal, characteristic, complemented
7#30790C211yesmaximal, characteristic, complemented
8#30564C211yesmaximal, characteristic, complemented
9#27939C211yesmaximal, characteristic, complemented
10#26803C211yesmaximal, characteristic, complemented
11#26570C211yesmaximal, characteristic, complemented
12#26352C211yesmaximal, characteristic, complemented
13#26132C211yesmaximal, characteristic, complemented
14#26127C211yesmaximal, characteristic, complemented
15#26069C211yesmaximal, characteristic, complemented
16#25981C211yesmaximal, characteristic, complemented
17#25532C211yesmaximal, characteristic, complemented
18#25244C211yesmaximal, characteristic, complemented
19#25217C211yesmaximal, characteristic, complemented
20#25122C211yesmaximal, characteristic, complemented
21#25024C211yesmaximal, characteristic, complemented
22#24867C211yesmaximal, characteristic, complemented
23#24595C211yesmaximal, characteristic, complemented
24#24562C211yesmaximal, characteristic, complemented
25#24396C211yesmaximal, characteristic, complemented
26#24098C211yesmaximal, characteristic, complemented
27#22939C211yesmaximal, characteristic, complemented
28#22855C211yesmaximal, characteristic, complemented
29#22851C211yesmaximal, characteristic, complemented
30#22661C211yesmaximal, characteristic, complemented
31#20847C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#536C2211yescharacteristic
35C2×#520C2211yescharacteristic
36#3346—28no—
37C2×#501C2211yescharacteristic
38#3097—28no—
39C2×#484C2211yescharacteristic
40C2×#484C2211yescharacteristic
41C2×#484C2211yescharacteristic
42C2×#481C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#485C2211yescharacteristic
46C2×#485C2211yescharacteristic
47C2×#483C2211yescharacteristic
48C2×#483C2211yescharacteristic
49C2×#480C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#468C2211yescharacteristic
53C2×#465C2211yescharacteristic
54C2×#465C2211yescharacteristic
55C2×#448C2211yescharacteristic
56C2×#440C2211yescharacteristic
57C2×#435C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C2×#427C2211yescharacteristic
62C22×#107C2211yescharacteristic
63C22×#107C2211yescharacteristic
64C2×#419C2211yescharacteristic
65C22×#103C2211yescharacteristic
66C2×#408C2211yescharacteristic
67C2×#408C2211yescharacteristic
68#2713—21no—
69#2700—21no—
70#2696—21no—
71#2687—21no—
72#2636—21no—
73#2615C2211yescharacteristic
74#2604—21no—
75#2580—21no—
76#2558—21no—
77#2536C2211yescharacteristic
78#2503C2211yescharacteristic
79#2501C2211yescharacteristic
80#2492—21no—
81#2492C2211yescharacteristic
82#2487C2211yescharacteristic
83#2459—21no—
84#2457—21no—
85#2456—21no—
86#2456—21no—
87#2455—21no—
88#2455—21no—
89#2441C2211yescharacteristic
90#2441C2211yescharacteristic
91#2439C2211yescharacteristic
92#2421C2211yescharacteristic
93#2417C2211yescharacteristic
94#2415C2211yescharacteristic
95#2414C2211yescharacteristic
96#2414C2211yescharacteristic
97#2409C2211yescharacteristic
98#2397—21no—
99#2388C2211yescharacteristic
100#2362C2211yescharacteristic
101#2361C2211yescharacteristic
102#2361C2211yescharacteristic
103#2352C2211yescharacteristic
104D4×C4⋊C4C2211yescharacteristic
105D4×C4⋊C4C2211yescharacteristic
106#2346C2211yescharacteristic
107Q8×C22⋊C4C2211yescharacteristic
108#2311C2211yescharacteristic
109#2095C2211yescharacteristic
110#2095C2211yescharacteristic
111#2092C2211yescharacteristic
112#2092C2211yescharacteristic
113#2088C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2083C2211yescharacteristic
117#2077C2211yescharacteristic
118#2076C2211yescharacteristic
119#2075C2211yescharacteristic
120#2072C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2059C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2055C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2035C2211yescharacteristic
134#2034C2211yescharacteristic
135#2033C2211yescharacteristic
136#2033C2211yescharacteristic
137#2026C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1955C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1947C2211yescharacteristic
147#1944C2211yescharacteristic
148#1943C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1921C2211yescharacteristic
158#1919C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1877C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1872C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1847C2211yescharacteristic
192#1847C2211yescharacteristic
193#1824C2211yescharacteristic
194#1809C2211yescharacteristic
195#1808C2211yescharacteristic
196#1807C2211yescharacteristic
197#1803C2211yescharacteristic
198#1787C2211yescharacteristic
199#1776C2211yescharacteristic
200#1763C2211yescharacteristic
201#1752C2211yescharacteristic
202#1752C2211yescharacteristic
203#1736C2211yescharacteristic
204#1735C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#554—24no—
215#554—42no—
216#553—24no—
217#553—42no—
218#536—24no—
219#536—42no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244#520—24no—
245#520—42no—
246C2×C4×Q8—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273#501—24no—
274#485—24no—
275#485—24no—
276#485—24no—
277#485D418yescomplemented
278#484—24no—
279#484—24no—
280#484—24no—
281#483—24no—
282#483—24no—
283#481—24no—
284#480—24no—
285#479—24no—
286#474—24no—
287#468—24no—
288#465—24no—
289#465—42no—
290#448—24no—
291#440—24no—
292#435—24no—
293#435—24no—
294#428—24no—
295#428—24no—
296#427—24no—
297C2×#107—24no—
298C2×#107—42no—
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#107C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×#106C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324#419—24no—
325C2×#103—24no—
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×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346#408—24no—
347#408—24no—
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×C22⋊C8C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×#97C2311yescharacteristic
361C2×#97C2311yescharacteristic
362#400—21no—
363#400—21no—
364#400—21no—
365#400—21no—
366#400—21no—
367#399—21no—
368#399—21no—
369#399—21no—
370#399—21no—
371#399—21no—
372#398—21no—
373#398—21no—
374#397—21no—
375#397—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#395—21no—
381#395D411yescharacteristic
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394D411yescharacteristic
387#394D411yescharacteristic
388#394D411yescharacteristic
389#393—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#393D411yescharacteristic
394#392—21no—
395#392—21no—
396#392—21no—
397#392—21no—
398#392—21no—
399#392D411yescharacteristic
400#392D411yescharacteristic
401#392D411yescharacteristic
402#391—21no—
403#391—21no—
404#391—21no—
405#391—21no—
406#391—21no—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#390—21no—
412#390—21no—
413#390—21no—
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—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#386—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#382—21no—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—21no—
469#381—21no—
470#380—21no—
471#380—21no—
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482C4×C4⋊C4—21no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
488C4×C22⋊C4C2311yescharacteristic
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491#376—21no—
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
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#340C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8C2×D411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C2×D411yescharacteristic
540C22×D4C2×D411yescharacteristic
541C22×D4C2×D411yescharacteristic
542C22×D4C2×D411yescharacteristic
543C22×D4C2×D411yescharacteristic
544C22×D4C2×D411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—41no—
569C2×M16—41no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C4⋊Q8—22no—
588C4⋊Q8—41no—
589C4⋊Q8—44no—
590#126—44no—
591#125—22no—
592#125—41no—
593#125—44no—
594#124—44no—
595#123—44no—
596#123—44no—
597#123—44no—
598#123—82no—
599#123—82no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8C2×D414yes—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—44no—
620#121—41no—
621#121—41no—
622#121—41no—
623C4×Q8—22no—
624C4×Q8—41no—
625C4×Q8—44no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—44no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—44no—
638C4×D4—44no—
639C4×D4—44no—
640C4×D4—44no—
641C4×D4—82no—
642C4×D4—82no—
643C4×D4—82no—
644C4×D4—82no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—22no—
649#117—41no—
650#117—41no—
651#117—41no—
652#117—41no—
653#117—41no—
654#117C2×D414yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
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⋊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—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—41no—
774#107—41no—
775#107—41no—
776#107—41no—
777#107—41no—
778#107C2×D414yes—
779#106—22no—
780#106—22no—
781#106—22no—
782#106—22no—
783#106—22no—
784#106—41no—
785#106—41no—
786#106C2×D414yes—
787C4⋊C8—22no—
788C4⋊C8—22no—
789C4⋊C8—41no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103C2×D414yes—
803#103C2×D414yes—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—41no—
808#102—41no—
809#102—41no—
810C22⋊C8—22no—
811C22⋊C8—22no—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—41no—
819C22⋊C8C2×D414yes—
820C22⋊C8#4114yes—
821#97—22no—
822#97—22no—
823#97—41no—
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#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861C24—21no—
862C24C22×D411yescharacteristic
863C24C22×D411yescharacteristic
864C24C22×D411yescharacteristic
865C24C22×D411yescharacteristic
866#41—44no—
867#41—44no—
868#41—44no—
869#41—44no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—41no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—42no—
889C2×Q8—81no—
890C2×Q8—81no—
891C2×Q8—81no—
892C2×Q8—82no—
893C2×Q8—82no—
894C2×Q8C22×D412yes—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—41no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—41no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D412yes—
1000C22×C4C22×D411yescharacteristic
1001C22×C4C2×#4112yes—
1002C22×C4H(5,𝔽2)12yes—
1003C22×C42−1+412yes—
1004C22×C4C2511yescharacteristic
1005SD16—44no—
1006SD16—82no—
1007M16—44no—
1008M16—44no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—44no—
1030C2×C8—44no—
1031C2×C8—44no—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C2×#4112yes—
1035C2×C8C2×#4112yes—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4C22×D412yes—
1090C4⋊C4C22×D412yes—
1091C4⋊C4C22×D412yes—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
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—42no—
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—
1134C42—24no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23D4212yes—
1183C23#54712yes—
1184C23#57812yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—44no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—84no—
1196Q8—162no—
1197D4—44no—
1198D4—44no—
1199D4—44no—
1200D4—44no—
1201D4—44no—
1202D4—44no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—162no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
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—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
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—84no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4D4212yes—
1309C2×C4#54712yes—
1310C2×C4C23×D411yescharacteristic
1311C2×C4C22×#4111yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×2−1+411yescharacteristic
1314C2×C4#58511yescharacteristic
1315C2×C4#58511yescharacteristic
1316C8—22no—
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22C2×D4211yescharacteristic
1360C22C2×#54711yescharacteristic
1361C22#348511yescharacteristic
1362C22C2×#57811yescharacteristic
1363C22#358511yescharacteristic
1364C22#358511yescharacteristic
1365C22#358611yescharacteristic
1366C4—22no—
1367C4—22no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—42no—
1379C4—42no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4D4×#4111yescharacteristic
1392C4#348911yescharacteristic
1393C4#351311yescharacteristic
1394C4#353511yescharacteristic
1395C2—42no—
1396C2—42no—
1397C2—42no—
1398C2—81no—
1399C2—161no—
1400C2#5899511yescharacteristic
1401C2#6107611yescharacteristic
1402C2#6108211yescharacteristic
1403C2#6127311yescharacteristic
1404C2#6129111yescharacteristic
1405C2#6174711yescharacteristic
1406C2#6179611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35689C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3346C2semidirect
2. C2×#3097C2semidirect
3. #45114C2semidirect
5. #31200C2semidirect
6. #31101C2semidirect
7. #30790C2semidirect
8. #30564C2semidirect
9. #27939C2semidirect
10. #26803C2semidirect
11. #26570C2semidirect
12. #26352C2semidirect
13. #26132C2semidirect
14. #26127C2semidirect
15. #26069C2semidirect
16. #25981C2semidirect
17. #25532C2semidirect
18. #25244C2semidirect
19. #25217C2semidirect
20. #25122C2semidirect
21. #25024C2semidirect
22. #24867C2semidirect
23. #24595C2semidirect
24. #24562C2semidirect
25. #24396C2semidirect
26. #24098C2semidirect
27. #22939C2semidirect
28. #22855C2semidirect
29. #22851C2semidirect
30. #22661C2semidirect
31. #20847C2semidirect
277. #485D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33462
C2×#30972
#451142
#356892
#312002
#311012
#307902
#305642
#279392
#268032
#265702
#263522
#261322
#261272
#260692
#259812
#255322
#252442
#252172
#251222
#250242
#248672
#245952
#245622
#243962
#240982
#229392
#228552
#228512
#226612
#208472