Finite Group Databasebeta

← #7525675

Subgroups — #7525675

Order 512.

1765 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59208C211yesmaximal, characteristic
2#36482C211yesmaximal, characteristic, complemented
3#31943C211yesmaximal, characteristic, complemented
4#31911C211yesmaximal, characteristic, complemented
5#31639C211yesmaximal, characteristic, complemented
6#31553C211yesmaximal, characteristic, complemented
7#28982C211yesmaximal, characteristic, complemented
8#28879C211yesmaximal, characteristic, complemented
9#28094C211yesmaximal, characteristic
10#27860C211yesmaximal, characteristic, complemented
11#27699C211yesmaximal, characteristic, complemented
12#27564C211yesmaximal, characteristic, complemented
13#27559C211yesmaximal, characteristic, complemented
14#27225C211yesmaximal, characteristic, complemented
15#27201C211yesmaximal, characteristic, complemented
16#26659C211yesmaximal, characteristic, complemented
17#25965C211yesmaximal, characteristic, complemented
18#24937C211yesmaximal, characteristic, complemented
19#24894C211yesmaximal, characteristic, complemented
20#24819C211yesmaximal, characteristic, complemented
21#24533C211yesmaximal, characteristic, complemented
22#24527C211yesmaximal, characteristic, complemented
23#24501C211yesmaximal, characteristic, complemented
24#23855C211yesmaximal, characteristic
25#22900C211yesmaximal, characteristic, complemented
26#22875C211yesmaximal, characteristic, complemented
27#22773C211yesmaximal, characteristic, complemented
28C22⋊C4×SD16C211yesmaximal, characteristic, complemented
29D4×#103C211yesmaximal, characteristic, complemented
30C2×#1880C211yesmaximal, characteristic, complemented
31#20735C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#448C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×#431C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic, complemented
45C22×#102C2211yescharacteristic
46#2855—21no—
47#2855C2211yescharacteristic
48#2757—21no—
49#2749—21no—
50#2603—21no—
51#2566C2211yescharacteristic
52#2534—21no—
53#2526—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2504C2211yescharacteristic
57#2503—21no—
58#2503C2211yescharacteristic
59#2490C2211yescharacteristic
60#2486—21no—
61#2486C2211yescharacteristic
62#2483—21no—
63#2480—21no—
64#2446—21no—
65#2446—21no—
66#2446C2211yescharacteristic, complemented
67#2446C2211yescharacteristic, complemented
68#2442C2211yescharacteristic
69#2421—21no—
70#2421—21no—
71#2421C2211yescharacteristic, complemented
72#2421C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2408C2211yescharacteristic
75#2361C2211yescharacteristic
76#2358—21no—
77#2357C2211yescharacteristic
78#2351C2211yescharacteristic, complemented
79#2351C2211yescharacteristic, complemented
80D4×C4⋊C4C2211yescharacteristic
81Q8×C22⋊C4C2211yescharacteristic
82Q8×C22⋊C4C2211yescharacteristic, complemented
83Q8×C22⋊C4C2211yescharacteristic, complemented
84D4×C22⋊C4C2211yescharacteristic
85C4×#123—21no—
86C4×#123C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2283C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2026C2211yescharacteristic, complemented
116#2026C2211yescharacteristic, complemented
117#2013C2211yescharacteristic
118#2013C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#1991C2211yescharacteristic, complemented
122#1981C2211yescharacteristic, complemented
123#1968C2211yescharacteristic
124#1968C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1956C2211yescharacteristic, complemented
128#1939C2211yescharacteristic, complemented
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1933C2211yescharacteristic, complemented
134#1933C2211yescharacteristic, complemented
135#1928C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1923C2211yescharacteristic, complemented
138#1923C2211yescharacteristic, complemented
139#1919C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1919C2211yescharacteristic, complemented
142#1918C2211yescharacteristic, complemented
143#1916C2211yescharacteristic, complemented
144#1916C2211yescharacteristic, complemented
145#1893C2211yescharacteristic
146#1893C2211yescharacteristic
147#1892C2211yescharacteristic
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic, complemented
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic, complemented
168#1869C2211yescharacteristic
169#1865C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic, complemented
173#1850C2211yescharacteristic
174#1850C2211yescharacteristic, complemented
175#1835C2211yescharacteristic, complemented
176#1824C2211yescharacteristic, complemented
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic
179#1808C2211yescharacteristic
180#1807C2211yescharacteristic
181#1805C2211yescharacteristic, complemented
182#1805C2211yescharacteristic, complemented
183#1805C2211yescharacteristic, complemented
184#1805C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—24no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218D4×Q8—24no—
219D4×Q8—42no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#125C2311yescharacteristic
224C2×#123—21no—
225C2×#123D411yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8—24no—
236C2×C4×Q8—42no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42—21no—
258C22×C42C2311yescharacteristic
259#479—42no—
260#450—42no—
261#448—24no—
262#448—42no—
263C4×SD16—24no—
264C4×SD16—42no—
265C8×D4—42no—
266#431—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103—42no—
279C2×#103—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102—42no—
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#392—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388D411yescharacteristic
391#388D411yescharacteristic
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385D411yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#382—21no—
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#381—21no—
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#381D411yescharacteristic
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8#4114yes—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—416no—
555C2×SD16#4114yes—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575C4⋊Q8—44no—
576#126—82no—
577#125—41no—
578#125—41no—
579#123—24no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—41no—
587#121—22no—
588#121—41no—
589#121—41no—
590#121—41no—
591#120—44no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—44no—
607C4×Q8—44no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—44no—
615C4×D4—82no—
616C4×D4—82no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—44no—
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—44no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—41no—
724#107—41no—
725#106—22no—
726#106—41no—
727#106—41no—
728#106—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C4×C8—22no—
768C4×C8—41no—
769C4×C8—41no—
770C4×C8—41no—
771C4×C8—41no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C2×Q8—24no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—28no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—44no—
852C2×Q8—44no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—82no—
856C2×Q8—82no—
857C2×Q8—82no—
858C2×Q8C2×#4112yes—
859C2×Q8C2×#4112yes—
860C2×Q8C2×#4112yes—
861C2×Q8H(5,𝔽2)12yes—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4#13514yes—
889C2×D4C2×#4112yes—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—41no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2×#4112yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956SD16—28no—
957SD16—44no—
958SD16—44no—
959SD16—44no—
960SD16—82no—
961SD16—82no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—44no—
986C2×C8—82no—
987C2×C8—82no—
988C2×C8C2×#4112yes—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—41no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C42—22no—
1077C42—22no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—22no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23#54612yes—
1130C23C2×#13512yes—
1131C23C2×#13512yes—
1132C23#57712yes—
1133C23C23×D411yescharacteristic
1134Q8—22no—
1135Q8—22no—
1136Q8—22no—
1137Q8—22no—
1138Q8—22no—
1139Q8—48no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—84no—
1147Q8#55114yes—
1148D4—28no—
1149D4—22no—
1150D4—22no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—84no—
1158D4—84no—
1159D4—162no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—44no—
1202C2×C4—48no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—44no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4#54612yes—
1253C2×C4C2×#13512yes—
1254C2×C4#57712yes—
1255C2×C4C22×#4111yescharacteristic
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4#58511yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22#330114yes—
1298C22C2×#54611yescharacteristic
1299C22D4×#4111yescharacteristic
1300C22#348811yescharacteristic
1301C22C22×#13511yescharacteristic
1302C22C2×#57711yescharacteristic
1303C22C2×#57711yescharacteristic
1304C22#358611yescharacteristic
1305C4—22no—
1306C4—22no—
1307C4—24no—
1308C4—22no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4C2×#55111yescharacteristic
1332C4#349111yescharacteristic
1333C4#351311yescharacteristic
1334C4#353411yescharacteristic
1335C2—24no—
1336C2—42no—
1337C2—82no—
1338C2—161no—
1339C2#5901111yescharacteristic
1340C2C2×#330111yescharacteristic
1341C2#6118511yescharacteristic
1342C2#6143211yescharacteristic
1343C2#6152011yescharacteristic
1344C2#6195611yescharacteristic
1345C2#6205511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
2. #36482C2semidirect
3. #31943C2semidirect
4. #31911C2semidirect
5. #31639C2semidirect
6. #31553C2semidirect
7. #28982C2semidirect
8. #28879C2semidirect
10. #27860C2semidirect
11. #27699C2semidirect
12. #27564C2semidirect
13. #27559C2semidirect
14. #27225C2semidirect
15. #27201C2semidirect
16. #26659C2semidirect
17. #25965C2semidirect
18. #24937C2semidirect
19. #24894C2semidirect
20. #24819C2semidirect
21. #24533C2semidirect
22. #24527C2semidirect
23. #24501C2semidirect
25. #22900C2semidirect
26. #22875C2semidirect
27. #22773C2semidirect
28. C22⋊C4×SD16C2semidirect
29. D4×#103C2semidirect
30. C2×#1880C2semidirect
31. #20735C2semidirect
35. C2×#479C22semidirect
44. C22×#103C22semidirect
66. #2446C22semidirect
67. #2446C22semidirect
71. #2421C22semidirect
72. #2421C22semidirect
78. #2351C22semidirect
79. #2351C22semidirect
82. Q8×C22⋊C4C22semidirect
83. Q8×C22⋊C4C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2074C22semidirect
100. #2074C22semidirect
103. #2068C22semidirect
106. #2066C22semidirect
115. #2026C22semidirect
116. #2026C22semidirect
121. #1991C22semidirect
122. #1981C22semidirect
127. #1956C22semidirect
128. #1939C22semidirect
133. #1933C22semidirect
134. #1933C22semidirect
135. #1928C22semidirect
136. #1927C22semidirect
137. #1923C22semidirect
138. #1923C22semidirect
139. #1919C22semidirect
140. #1919C22semidirect
141. #1919C22semidirect
142. #1918C22semidirect
143. #1916C22semidirect
144. #1916C22semidirect
149. #1892C22semidirect
167. #1872C22semidirect
169. #1865C22semidirect
170. #1863C22semidirect
172. #1853C22semidirect
174. #1850C22semidirect
175. #1835C22semidirect
176. #1824C22semidirect
181. #1805C22semidirect
182. #1805C22semidirect
183. #1805C22semidirect
184. #1805C22semidirect
185. #1805C22semidirect
188. #1803C22semidirect
191. #1787C22semidirect
193. C8×C4⋊C4C22semidirect
194. C4×#103C22semidirect
195. C4×#103C22semidirect
196. C4×#103C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
200. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592082
#364822
#319432
#319112
#316392
#315532
#289822
#288792
#280942
#278602
#276992
#275642
#275592
#272252
#272012
#266592
#259652
#249372
#248942
#248192
#245332
#245272
#245012
#238552
#229002
#228752
#227732
C22⋊C4×SD162
D4×#1032
C2×#18802
#207352