Finite Group Databasebeta

← #7515703

Subgroups — #7515703

Order 512.

1969 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3346C211yesmaximal, characteristic, complemented
2C2×#3103C211yesmaximal, characteristic, complemented
3#59110C211yesmaximal, characteristic
4#36547C211yesmaximal, characteristic, complemented
5#31166C211yesmaximal, characteristic, complemented
6#31141C211yesmaximal, characteristic, complemented
7#30969C211yesmaximal, characteristic, complemented
8#30860C211yesmaximal, characteristic, complemented
9#28348C211yesmaximal, characteristic, complemented
10#26967C211yesmaximal, characteristic, complemented
11#26947C211yesmaximal, characteristic, complemented
12#26903C211yesmaximal, characteristic, complemented
13#26627C211yesmaximal, characteristic, complemented
14#26605C211yesmaximal, characteristic, complemented
15#26550C211yesmaximal, characteristic, complemented
16#26487C211yesmaximal, characteristic, complemented
17#26473C211yesmaximal, characteristic, complemented
18#26372C211yesmaximal, characteristic, complemented
19#26356C211yesmaximal, characteristic, complemented
20#25543C211yesmaximal, characteristic, complemented
21#25495C211yesmaximal, characteristic, complemented
22#25130C211yesmaximal, characteristic, complemented
23#25078C211yesmaximal, characteristic, complemented
24#24602C211yesmaximal, characteristic, complemented
25#24583C211yesmaximal, characteristic, complemented
26#23964C211yesmaximal, characteristic, complemented
27#23035C211yesmaximal, characteristic, complemented
28#23012C211yesmaximal, characteristic, complemented
29#22936C211yesmaximal, characteristic, complemented
30#22902C211yesmaximal, characteristic, complemented
31C2×#1863C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#3346—28no—
37C2×#501C2211yescharacteristic
38#3103—28no—
39C2×#484C2211yescharacteristic
40C2×#481C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#480C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#475C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#474C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#468C2211yescharacteristic
50C2×#465C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#460C2211yescharacteristic
53C2×#460C2211yescharacteristic
54C2×#461C2211yescharacteristic
55C2×#448C2211yescharacteristic
56C2×#448C2211yescharacteristic
57C2×#440C2211yescharacteristic
58C2×C4×SD16C2211yescharacteristic
59C2×C4×SD16C2211yescharacteristic
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×#435C2211yescharacteristic
63C2×#431C2211yescharacteristic
64C2×#428C2211yescharacteristic
65C22×#107C2211yescharacteristic
66C22×#103C2211yescharacteristic
67C22×#103C2211yescharacteristic
68#2855—21no—
69#2855C2211yescharacteristic
70#2715—21no—
71#2710—21no—
72#2583—21no—
73#2579—21no—
74#2550C2211yescharacteristic
75#2504C2211yescharacteristic
76#2466—21no—
77#2465—21no—
78#2465—21no—
79#2462—21no—
80#2462—21no—
81#2454C2211yescharacteristic
82#2451C2211yescharacteristic
83#2451C2211yescharacteristic
84#2445C2211yescharacteristic
85#2443—21no—
86#2439C2211yescharacteristic
87#2434C2211yescharacteristic
88#2430—21no—
89#2429C2211yescharacteristic
90#2429C2211yescharacteristic
91#2428C2211yescharacteristic
92#2425—21no—
93#2420C2211yescharacteristic
94#2416—21no—
95#2416C2211yescharacteristic
96#2409C2211yescharacteristic
97#2365C2211yescharacteristic
98#2365C2211yescharacteristic
99#2363C2211yescharacteristic
100#2361C2211yescharacteristic
101#2360C2211yescharacteristic
102#2360C2211yescharacteristic
103#2349C2211yescharacteristic
104#2345C2211yescharacteristic
105#2339—21no—
106C4×#123—21no—
107C4×#123C2211yescharacteristic
108C2×#389C2211yescharacteristic
109#2097C2211yescharacteristic
110#2097C2211yescharacteristic
111#2087C2211yescharacteristic
112#2087C2211yescharacteristic
113#2085C2211yescharacteristic
114#2085C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic
120#2066C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2055C2211yescharacteristic
124#2055C2211yescharacteristic
125#2043C2211yescharacteristic
126#2041C2211yescharacteristic
127#2036C2211yescharacteristic
128#2035C2211yescharacteristic
129#2026C2211yescharacteristic
130#2026C2211yescharacteristic
131#2024C2211yescharacteristic
132#2023C2211yescharacteristic
133#2014C2211yescharacteristic
134#2013C2211yescharacteristic
135#2013C2211yescharacteristic
136#2013C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#1981C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic
145#1960C2211yescharacteristic
146#1960C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1944C2211yescharacteristic
150#1942C2211yescharacteristic
151#1942C2211yescharacteristic
152#1940C2211yescharacteristic
153#1936C2211yescharacteristic
154#1935C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1927C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1894C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1880C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1872C2211yescharacteristic
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1863C2211yescharacteristic
192#1862C2211yescharacteristic
193#1853C2211yescharacteristic
194#1852C2211yescharacteristic
195#1851C2211yescharacteristic
196#1850C2211yescharacteristic
197#1824C2211yescharacteristic
198#1776C2211yescharacteristic
199#1771C2211yescharacteristic
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1752C2211yescharacteristic
203C2×#340C2211yescharacteristic
204C2×#336C2211yescharacteristic
205C22×#41—21no—
206C23×Q8C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#554—24no—
217#554—42no—
218#553—24no—
219#553—42no—
220#532—24no—
221#532—42no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#126—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123D411yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121—21no—
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—24no—
251C2×C4×Q8—42no—
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×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4—21no—
268C22×C4⋊C4—21no—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C42—21no—
274C22×C42C2311yescharacteristic
275#501—24no—
276#485—24no—
277#484—24no—
278#481—24no—
279#481D418yescomplemented
280#480—24no—
281#479—24no—
282#475—24no—
283#475—24no—
284#474—24no—
285#468—24no—
286#468—24no—
287#465—24no—
288#465—42no—
289#461—24no—
290#460—24no—
291#460—24no—
292#448—24no—
293#448—24no—
294#440—24no—
295C4×SD16—24no—
296C4×SD16—24no—
297C4×SD16—24no—
298C4×SD16—24no—
299#435—24no—
300#431—24no—
301#428—24no—
302C2×#107—24no—
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×#103—24no—
323C2×#103—42no—
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×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362#399—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#393—21no—
388#393—21no—
389#392—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#390—21no—
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388D411yescharacteristic
429#388D411yescharacteristic
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—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#387D411yescharacteristic
444#387D411yescharacteristic
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#386D411yescharacteristic
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#385—21no—
464#385—21no—
465#385D411yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—21no—
469#381—21no—
470#381D411yescharacteristic
471#380—21no—
472#380—21no—
473#380—21no—
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4C2311yescharacteristic
488C4×C22⋊C4C2311yescharacteristic
489C4×C22⋊C4C2311yescharacteristic
490C2×#95—21no—
491C2×#95—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#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—44no—
519C2×#41—44no—
520C2×#41—82no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—22no—
525C22×Q8—22no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C2×D411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
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×C4C2×D411yescharacteristic
552C23×C4C2×D411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598#127—22no—
599#127—41no—
600#126—44no—
601#125—22no—
602#125—41no—
603#125—44no—
604#124—44no—
605#123—24no—
606#123—44no—
607#123—82no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—44no—
614C22⋊Q8—44no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—41no—
624#121—41no—
625#121—44no—
626#121—44no—
627#121—82no—
628#121—82no—
629#121C2×D414yes—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—44no—
641C4×Q8—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—44no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—44no—
654C4×D4—44no—
655C4×D4—82no—
656#117—22no—
657#117—41no—
658C2×C4⋊C4—21no—
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—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—44no—
697C2×C4⋊C4—82no—
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D414yes—
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
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×C42—22no—
747C2×C42—22no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—44no—
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
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—41no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—41no—
777#106C2×D414yes—
778#106C2×D414yes—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—41no—
784#103—22no—
785#103—22no—
786#103—22no—
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—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103#4114yescomplemented
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102C2×D414yes—
811#102C2×D414yes—
812C22⋊C8—22no—
813C22⋊C8—22no—
814C22⋊C8—41no—
815C22⋊C8—41no—
816C22⋊C8C2×D414yes—
817#97—22no—
818#97—41no—
819#97—41no—
820C4×C8—22no—
821C4×C8—22no—
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#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863C24—21no—
864C24—21no—
865C24C22×D411yescharacteristic
866C24C22×D411yescharacteristic
867#41—816no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—28no—
871C2×Q8—21no—
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—21no—
884C2×Q8—21no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—81no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×Q8C2×#4112yes—
898C2×Q82−1+412yes—
899C2×D4—22no—
900C2×D4—24no—
901C2×D4—22no—
902C2×D4—22no—
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—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4C22×D412yes—
932C22×C4—22no—
933C22×C4—22no—
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—22no—
945C22×C4—24no—
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—41no—
961C22×C4—41no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
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#13714yes—
989C22×C4C22×D411yescharacteristic
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×C4C22×D411yescharacteristic
1002C22×C4H(5,𝔽2)12yes—
1003C22×C4C2511yescharacteristic
1004SD16—44no—
1005SD16—44no—
1006SD16—44no—
1007SD16—44no—
1008SD16—44no—
1009SD16—82no—
1010M16—44no—
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—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—44no—
1033C2×C8—82no—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C2×#4112yes—
1037C4⋊C4—24no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
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—41no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
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—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4C22×D412yes—
1092C4⋊C4C22×D412yes—
1093C4⋊C4C22×D412yes—
1094C4⋊C4C2×#4112yes—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—24no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
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—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C42—22no—
1127C42—22no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23D4212yes—
1173C23C2×#13712yes—
1174C23#57712yes—
1175C23C23×D411yescharacteristic
1176Q8—22no—
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—48no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—84no—
1190Q8—162no—
1191D4—22no—
1192D4—22no—
1193D4—44no—
1194D4—48no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—162no—
1205D4—162no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—28no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
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—22no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
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—48no—
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—84no—
1292C2×C4—84no—
1293C2×C4—82no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4D4212yes—
1301C2×C4C2×#13712yes—
1302C2×C4C2×#13712yes—
1303C2×C4C23×D411yescharacteristic
1304C2×C4C22×#4111yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×2−1+411yescharacteristic
1307C2×C4#58511yescharacteristic
1308C2×C4#58511yescharacteristic
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—42no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22#326614yes—
1345C22C2×D4211yescharacteristic
1346C22D4×#4111yescharacteristic
1347C22#348911yescharacteristic
1348C22C22×#13711yescharacteristic
1349C22C2×#57711yescharacteristic
1350C22#358411yescharacteristic
1351C22#358511yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4—41no—
1360C4—42no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—42no—
1369C4—41no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4D4×#4111yescharacteristic
1379C4#348911yescharacteristic
1380C4#349211yescharacteristic
1381C4#353311yescharacteristic
1382C2—24no—
1383C2—81no—
1384C2—82no—
1385C2—161no—
1386C2#5899311yescharacteristic
1387C2C2×#326611yescharacteristic
1388C2#6107411yescharacteristic
1389C2#6144011yescharacteristic
1390C2#6152111yescharacteristic
1391C2#6211411yescharacteristic
1392C2#6221311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59110C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ 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×#3103C2semidirect
4. #36547C2semidirect
5. #31166C2semidirect
6. #31141C2semidirect
7. #30969C2semidirect
8. #30860C2semidirect
9. #28348C2semidirect
10. #26967C2semidirect
11. #26947C2semidirect
12. #26903C2semidirect
13. #26627C2semidirect
14. #26605C2semidirect
15. #26550C2semidirect
16. #26487C2semidirect
17. #26473C2semidirect
18. #26372C2semidirect
19. #26356C2semidirect
20. #25543C2semidirect
21. #25495C2semidirect
22. #25130C2semidirect
23. #25078C2semidirect
24. #24602C2semidirect
25. #24583C2semidirect
26. #23964C2semidirect
27. #23035C2semidirect
28. #23012C2semidirect
29. #22936C2semidirect
30. #22902C2semidirect
31. C2×#1863C2semidirect
279. #481D4semidirect
801. #103#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33462
C2×#31032
#591102
#365472
#311662
#311412
#309692
#308602
#283482
#269672
#269472
#269032
#266272
#266052
#265502
#264872
#264732
#263722
#263562
#255432
#254952
#251302
#250782
#246022
#245832
#239642
#230352
#230122
#229362
#229022
C2×#18632